Lecture 1 | Modern Physics: Special Relativity (Stanford)



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Lecture 1 of Leonard Susskind’s Modern Physics course concentrating on Special Relativity. Recorded April 14, 2008 at Stanford University.

This Stanford Continuing Studies course is the third of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on classical mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

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this program is brought to you by Stanford University please visit us at stanford.edu this quarter we're going to learn about field theory classical field theory fields such as the electromagnetic field gravitational field other fields in nature which I won't name right now propagate which means they change according to rules which give them a wave-like character moving through space and one of the fundamental principles of field theory in fact more broadly nature in general is the principle of relativity the principle the special printless the the principle of special relativity in this particular case the principle of special relativity well let's just call it the principle of relativity goes way back there was not an invention of Einstein's I'm not absolutely sure when it was first announced or articulated in the form which I'll spell it out I don't know whether it was Galileo or Newton or those who came after them but those early pioneers certainly had the right idea it begins with the idea of an inertial reference frame now inertia reference frame this is something a bit tautological about an inertial reference frame Newton's equations F equals MA are satisfied in an inertial reference frame what is an inertial reference frame it's a frame of reference in which Newton's equations are satisfied I'm not going to explain any further what an inertial reference frame is except to say that the idea of an inertial reference frame is by no means unique a reference frame first of all was a reference frame in tale of a reference frame first of all entails a set of coordinate axes in ordinary space X Y & Z and you know how to think about those but it also entails the idea that the coordinate system may be moving or not moving relative to whom relative to whomever we sitting here or you sitting here in this classroom here define a frame of reference we can pick the vertical direction to be the z axis the horizontal direction along my arms here to be the x axis X plus that way X my X is minus in that direction and which one have I left out I've left out the y axis which points toward you from me so there are some coordinate axes for space XY and Z and I didn't this in addition to specify a frame of reference one also imagines that this entire coordinate system is moving in some way relative to you sitting there presumably with a uniform velocity in a definite direction if your frame of reference is an inertial frame of reference in other words if when you throw balls around or juggle or do whatever is supposed to do in an inertial frame of reference if you find yourself in an inertial frame of reference then every other frame of reference that's moving with uniform velocity relative to you now remember what uniform velocity means it doesn't just mean with uniform speed it means with uniform speed in an unchanging direction such a frame of reference is also inertial if it's accelerated or if it starts standing still and then suddenly picks up some speed then it's not an inertial frame of reference all inertial frames of reference according to Newton and also I think also Galileo Galileo was often credited with the idea but I never read enough of Galileo to know whether he actually had it or not neither did I read enough of Newtons they both wrote in languages that I don't understand what was I saying oh yes right according to both Newton and anybody else who thought about it very hard the laws of physics are the same in all inertial reference frames laws of physics meaning F equals MA the forces between objects all the things that we would normally call laws of nature or laws of physics don't distinguish between one frame of reference of and another if you want a kind of pictorial example that I like to use a lot when I'm explaining this to the children or to grownups I like to think about the laws of juggling there are very definite procedures that you train your body to do uh in order to be able to juggle balls correctly now you can imagine yourself being in a railroad car moving with perfectly uniform velocity down the x axis and trying to juggle do you have to compensate for the fact that the train is moving and for particular when you throw a ball up into the air that you have to reach over to the right to compensate for the fact that the train is moving to the left my left your right the answer is no you don't the laws of juggling are the same in every reference frame and every inertial reference frame whatever you do in one reference frame you do exactly the same thing and you'll succeed or fail depending on whether you're a good juggler or not but it will not depend on whether you're moving with uniform velocity so the laws of juggling are the same in every inertial reference frame the laws of mechanics are the same in every inertial reference frame the laws Newtonian laws of gravity are the same in every inertial frame according to Newton what about the laws of electrical phenomena well there there was a clash the clash had to do with Maxwell's equations Maxwell's equations were the field equations the field theory that governed the electromagnetic field and the way that it propagated and sent waves electromagnetic waves that we ordinarily call light or radio waves or so forth and the fundamental dilemma as you all know I'm sure you all know the fundamental dilemma was both according to well here was the dilemma Maxwell's equations said light moves with a certain velocity if you take the various constants that appear in Maxwell's equations and put them together in the right way you get the velocity of waves moving down an axis and that velocity comes out to be a certain number out of Maxwell's equations you have two choices one is to believe that Maxwell's equations are true laws of nature as good as any other laws of nature in which case the principle of relativity says they should be the same in every reference frame but if it follows from Maxwell's equations that the speed of light is three times ten to the eighth meters per second which is about what it is if it follows from Maxwell's equations that light moves that fast and if Maxwell's equations are laws of physics fundamental laws of physics and if the laws of physics are the same in every reference frame then the speed of light must be the same in every reference frame but that was very hard to swallow because if a light beam is going down that axis and you chase it and run along with it that lets say three-quarters of the speed of light then you want to see that light ray moving much more slowly than three times ten to the eighth meters per second relative to you on the other hand the light ray going in the other direction since you're sort of running into it you should see going even faster so all these possibilities could not simultaneously be correct that the laws of nature are the same in every reference frame and that Maxwell's equations are laws of physics in the same sense that Newton's laws of physics namely the same in every reference frame something had to give well the point was of course that they were good laws of nature and that they were the same in every reference frame the thing that had to give is our concepts of velocity space and time and how we measure velocity especially velocities were up which are up near the speed of light now I'm not going to spend the full amount of time that I did previously on the special theory of relativity that can be found on lectures from how long ago and there on the Internet I believe relativity and electromagnetism I think that was maybe about three quarters ago I've lost track yeah they're up there they're on the net and they're the lectures on relativity special relativity and electromagnetic theory we're just going to cut through it real fast we're going to cut through the basic ideas of relativity a little more mathematically than I would do if I were teaching it for the first time I teach it the first time I tend to teach it the way Einstein first conceived of it how do you measure distances how do you measure velocities how do how does the propagation of light influence these things instead I'm going to take a more mathematical view of it and think about the properties of various kinds of coordinate transformations coordinates now consists not only of XY and Z but also time T so imagine every event in the world is characterized by just like every particle would be characterized by a position x y&z every event taking place in space-time is characterized by four coordinates X Y Z and T let's suppress for the moment y&z let's just forget I forget them for the moment and concentrate on X and T that would be appropriate if we were mainly interested in motion along one axis let's focus on that motion along the x axis let's suppose there is no motion along y&z then we can forget y&z for the moment momentarily we'll come back to them and think of motion along X and T and the various reference frames that might be moving along the x axis alright here's here's time vertically is space horizontally physicists always draw space horizontally and time vertically I found out that mathematicians are at least certain computer scientists always draw time going horizontally I didn't know that and I got into an enormous argument with a quantum computer scientist which was ultimately resolved by the fact that he had time going horizontally and I had it going vertically these are traditions I guess traditions grow up around subjects but time is north and X is east I guess or at least time is upward yeah yeah yeah that's what that that that's the point that is the point yes they're thinking of time is the independent variable and everybody knows that it's a law of nature that the independent variable should be horizontal ok all right now let's in let's imagine a moving observer moving down the x axis with a velocity V let's take his origin of spatial coordinates his origin of spatial coordinates at time T equals zero is just the same let's assume that my I'll be the moving observer I move down the x-axis I am my own origin there's nobody who was your origin that seat is vacant over there so that absent a human over there is the center of the x-coordinates in your frame I'm the X prime coordinates and of course I being very egocentric will take my x-acto is origin to be where I am there I do I move down the x-axis we pass each other our origins pass each other at t equals 0 so that means at T equals 0 your axis and my axes are the same or your origin in my origin is the same but then as I move down the x axis my core my coordinate center moves to the right most of the right that's supposed to be a straight line that's as good as I can do under the circumstances that's a straight line and it's moving with velocity V which means it's X prime equals SR it means x equals VT but it's also that's the way you describe it in terms of your coordinates my centre you described by saying x equals VT how do I describe it I just say X prime my coordinate X prime is 0 X prime equals 0 is the same as x equals VT all right what's the relationship between X Prime and X and T well it's easy to work out if you believe this picture the X prime coordinate is the distance from my origin the x coordinate is the distance from your origin so one of these is X the other is X prime the upper one here is X prime the low and here is X and the relationship between them is that they differ by an amount VT in particular X is equal to X prime minus VT or X prime is equal to X plus VT will have it wrong yes I do X prime is X minus BT and X is X prime plus VT yeah I think I have that's correct now all right what about time itself well according to Newton and according to Galileo and according to everybody who came afterward up until Einstein time is just time is just time is just time there was no notion that time might be different in different reference frames Newton had the idea of a universal time sort of God's time God upon his cloud ticking off with his with his super accurate watch and that time was universal for everybody no matter how they were moving and so everybody would agree on what on the time of any given event in this map of space and time here and so the other equation that went with this is that T prime is equal to T let's forget the top equation here let's just forget it one might say that this was the Newtonian or the Galilean transformation properties between X and T your coordinates and the coordinates that I ascribe to a point in space-time now let's examine a light ray moving down the plus x axis if it starts at the origin here then it moves along a trajectory which is x equals CT C being the speed of light now shortly I'm going to set C equal to 1 we're going to work in units in which C is equal to 1 but not quite yet incidentally once you understand a bit of relativity working in coordinates in which C is not equal to 1 is about as stupid as using different units for x and y are if we used yards for x and feet for y then we will have all kinds of funny factors in our equations which would be conversion factors from X which is measured in feet to Y which is measured in our yards the cycle has its uses log scale has its uses no long skilling long scale well let common interest yep I'm not sure we good but okay I'm just saying it is quite often in practical circumstances that one uses different scales yeah you sometimes you might there might be a good reason I mean um it wouldn't be totally unreasonable for a sailor to use different units for horizontal direction and vertical direction hmm I mean he's used to moving around horizontally he might use what miles miles versus fathoms or something nautical miles versus paddles yeah Persian is relative but um when you talk about a frame of reference you need to specify a period of time because obviously goes that 15 billion years there is no yeah we're ignoring now the fact that the universe began at some time and we're imagining now as Newton did and as the early Einstein did that the universe has just been here forever and ever and ever unchanging totally static and space and time have properties which don't change with time now of course that's incorrect in the real world and at some point we will take up the subject of cosmology and find that's not right but as long as we're interested in time intervals which are not I suspect this is what you're getting at as long as we're interested in time intervals which are not too long in particular time intervals over which the universe doesn't expand very much and so forth we can mainly say the properties of space don't change over a period of time and so everything just stays the same as always was is that what you're asking it seems that that this assumption if it is made it needs to what you're describing so well so the question is without imagining to some point as it doesn't lead it doesn't lead to what I'm describing where is this this room for different formulas here this is a formula which is based on an assumption the assumption being that time is universal that's what Einstein found was wrong basically what he found is that when you're in a moving frame of reference to different the observers will not agree about what time a particular event takes place this is the culprit here this one and some modifications to this one but in any case to see what's wrong let's go to Maxwell's equations Maxwell's equations say that light always moves with this velocity C being some numbers in meters per second okay 3 times 10 to the 8th meters per second we will later as I said say C equals 1 let's imagine a light beam moving down the x axis let's describe how X prime sees it in other words you see the light move this way to the right how do I see the light well let's see what I see let's just work it out X prime will be X which is CT for that light ray minus VT which is the same as C minus VT all this says is that I see the light moving with a diminished velocity a velocity C minus V why is that because I'm moving along with the light so naturally I see it move slowly the slow compared to what you see it what about the light going in the other direction supposing it was a light beam going in the other direction then how would you describe it you would describe it as x equals minus CT and if I do exactly the same thing I will find that X prime is equal to X that's minus CT – VT which is the same as minus C plus V times T so what this says is that I will see the light moving also in the negative direction that's the minus sign but I'll see it moving with an enhanced velocity C plus V if this were the right story and if these were the right transformation laws for space and time then it could not be the case that Maxwell's equations are laws of physics or laws of nature in the sense that they were true in every reference frame they would have to be corrected in moving frames just like the juggler who had to reach to the right who didn't actually but who thought he had to reach to the right to collect the ball when train is moving the physicist interested in light beams would have to correct things for the motion of his reference frame now it's an experimental fact that this is not the case that you don't have to correct for motion was the famous Michelson Morley experiment Einstein he just rejected he just felt this can't be right Maxwell's equations were much too beautiful to be relegated to the approximate or to the contingent on which reference frame and so he said about to find a framework in which the speed of light would be the same in every reference frame and he basically focused on these equations and after various very very beautiful Gedanken experiments thought experiments about light and about measuring and so forth he came to a set of formulas called the Lorentz transformations I'm going to explain them the Lorentz transformations in a more mathematical way not fancy mathematics but just get we want to get right to the heart of it and not spend the three weeks doing it the best way is to a mathematical problem but before I do let me set up a different mathematical problem which is for most of you you've seen me do this before but nonetheless let's go through it again the problem of rotation of coordinates we're going to do this quickly let's just take spatial coordinates now for the moment two dimensional spatial coordinates let's forget X and T and just concentrate on X&Y two coordinates in space instead of events in space-time concentrate on a point in space a point in space has coordinates and we can determine those coordinates the x and y coordinates just by dropping perpendicular to the x axis in the y axis and we would describe this point as the point at position let's just call it X Y now there's nothing sacred about horizontal and vertical so somebody else may come along some crazy mathematician a really nutty one who wants to use coordinates which are at an angle relative to the vertical maybe a couple of beers and you don't know the difference between vertical and worth worth worth we should give this direction a name oblique yeah all right the oblique observer the blue observer can blue be seen everybody can see blue okay good ah the blue observer also characterizes points by coordinates which he calls X Prime and Y Prime the X Prime and the Y prime coordinates are found by dropping perpendicular to the X Prime and the Y prime axis so here's X prime is y prime and given a point X Y there's a role it must be a role if you know the value of x and y you should be able to deduce the value of X I'm in y-prime if you know the angle between the two coordinates between the x coordinate and the X prime coordinate and the formulas simple we've used it least in these classes many times I'll just remind you what it is that's X prime is equal to x times cosine of the angle between the two frames between the two coordinate systems minus y times sine of the angle and Y prime is equal to minus plus I think X sine of theta plus y cosine theta I just want to remind you about a little bit of trigonometry all of trigonometry is encoded in two very simple formulas I've used them this signs on these signs of are on the right let's Ella and X prime is bigger than X for small theta since ours here are all so it's Auto Expo Rhine is bigger than it is is it yeah let's see if you rotate it to the next so that y is y prime is zero it's further out X prime rook will have it backward yeah what's your gift I'm not gonna fit nobody so let's say just make sure the links take survive is the little perpendicular there no my life primary so that's y prime y prime is this is why I'm here right right that's why I'm in X prime is bigger than X so there has to be a plus sign on the second you know its prime is bigger than X let's see um yeah X prime is bigger than X yeah X prime is bigger than X looks like that's probably right probably sign but then this one must be man negative yeah okay there's an easy way to correct for it another way to correct for it just call this angle minus theta that would also do the trick because cosine of minus theta is the same as cosine of theta and sine changes sign when you change theta 2 minus theta so if instead of calling this angle theta I called it minus theta then my previous formulas would be right it's true true but the it's an excuse all right what do we know about sine and cosine it's important to understand sine and cosine everything you ever learned about trigonometry can be codified in two very simple formulas if you know about complex numbers the two very simple formulas are that cosine of theta is e to the I theta plus e to the minus I theta over 2 and sine of theta is e to the I theta minus e to the minus I theta over 2i those two formulas contain everything about trigonometry you don't have to know any other formulas other than these for example I will assign you the homework problem of using these two formulas to find cosine of the sum of two angles but the way you would do it is just write the sum of two angles in here and then reexpress the Exponential's in terms of cosine and sine that's easy to do e to the I theta is equal to cosine of theta plus I sine theta and e to the minus I theta is cosine of theta minus I sine theta so work through these formulas get familiar with them they're extremely useful formulas once you know them you will never have to remember any trigonometric formulas again the other thing to know is that e to the I theta times e to the minus I theta is 1 all right e to the anything times e to the minus the same thing is one those things characterize all trigonometric formulas in particular as was explained to me by Michael a number of times if we multiply e to the I theta times e to the minus I theta we will get one on this side but on this side we will get cosine squared of theta plus sine squared of theta naught minus sine squared but plus sine squared cosine squared and then ice minus I squared sine squared that gives us cosine squared plus sine squared cosine squared theta plus sine squared theta so that's equivalent to the fact that e to the I theta times e to the minus I theta is 1 all right now the most important fact that again follows from the simple trigonometry is that when you make the change of coordinates from XY to X prime Y prime something is left unchanged namely the distance from the origin to the point XY that's something which is you know you count the number of the molecules along the blackboard from here to here and that doesn't change when I change coordinates so the distance from the origin to the point XY has to be the same independent of which coordinate axes we use well let's take the square of that distance the square of that distance we know what it is let's call it s squared I'm not sure why I use s but s for distance s s for distance s for space I think it must be for space that I'm using it for the spaces for the spatial distance from the origin to the point XY we know what that is it's Pythagoras theorem x squared plus y squared but as I said there's nothing special about the XY axes we also ought to be able to calculate it as X prime squared plus y prime squared well it's not too hard to work out that X prime squared plus y prime squared is x squared plus y squared it's easy to use do X prime squared plus y prime squared will have x squared cosine squared theta it will also have x squared sine squared theta when you add them you'll get x squared plus y squared you know you know the rigmarole so it follows from cosine squared plus sine squared equals 1 that X prime squared plus y prime squared equals also equal is equal to x squared plus y squared work that out make sure that you have this on the control that you understand why from the trigonometry not from the the basic physics of it or the basic geometry of it is clear make sure that you understand that you can see that from the trigonometry okay one last thing about sines and cosines if I plot on the blackboard for every angle if I plot sine or cosine along the horizontal axis supposing I plot cosine of theta along the horizontal axis and sine of theta along the vertical axis then if I plot all possible angles they will correspond to a bunch of points that lie on a unit circle Y on a unit circle because sine squared plus cosine squared equals 1 so one might call the properties of sine and cosine the properties of circular functions circular in that they're convenient for rotating they're convenient for describing unit circles points on unit circles are described in terms of coordinates which are cosines and sines of angles and so forth it's natural to call them circular functions these are these are not the functions that come in to the transformation the new transformation properties first of all these are wrong and I don't want to use X what's X ya ya now just wrong Newton had it wrong Newton or Galileo however it was postulated who postulated it Einstein modified it now we're going to have to make sure that Einstein's modification doesn't change things in situations where Newton knew where Newton's equations were good approximations the situations where I'm Stan's modifications are important is when we're talking about frames of reference moving very rapidly up near the speed of light before the 20th century nobody or nothing had ever moved faster than a hundred miles an hour probably well of course some things did light did but for all practical purposes light didn't travel at all it's just when you turned on the switch the light just went on so light didn't travel nothing and anybody's experienced direct experience traveled faster than 100 or 200 miles an hour and well I should say nothing travels faster than 100 miles an hour and then live to tell about it so all of experience was about very slow velocities on the scale of the speed of light on the scale of such velocities newton's formulas must be correct they work they're they're very useful they work Nutan got away with it so there must be good approximations it better be that whatever einstein did to the equations in particular to these two equations here had been a reduced to newton's equations in the appropriate limit okay let's come back now to light light according to the Newton formulas doesn't always move with the speed of light but let's let's try to figure out what it would mean of a better formula of a replacement for this but light always moves with the speed of light first of all let's set the speed of light equal to one that's a choice of units in particular it's a choice of the relation between space units and time units if we work in our light years for spent for a distance and years for time then light moves one light year per year the speed of light is one if we use seconds and light seconds it's also one whatever whatever scale we use for space if we use for time the time that it takes light to go that distance one unit of space if we use that for time units then the speed of light is equal to one now from the ordinary point of view of very slowly moving things those are odd units but if we were electrons with neutrinos and whizzing around like photons they would be the natural units for us speed of light equals one so let's set the speed of light equal to one as I said it's just the choice of units and then a light ray moving to the right just moves along a trajectory x equals T C is just equal to one a light ray moving to the left is x equals minus T how can we take both of these equations and put them together sorry x equals minus T can I write a single equation which if it's satisfied is a light ray either moving to the left or to the right yes here's an equation x squared equals T squared it has two solutions x equals T and X equals minus T the two square roots or x squared equals T squared is equivalent to either x equals T or x equals minus T in other words this equation here has the necessary and sufficient condition for describing the motion of a light ray either to the right or to the left supposing we found a replacement for this equation which had the following interesting property that whenever let's let's write it this way X square minus T squared equals 0 this is even better for our purposes x squared minus T squared equals 0 that's the necessary and sufficient condition to describe the motion of a light ray supposing we found a new set of rules a new set of transformation properties which which um had the property that if x squared minus T squared is equal to 0 then we will find that X prime squared minus T prime squared is equal to 0 in other words supposing this implied this and vice-versa then it would follow that what the unprimed observer you and your seats see is a light ray the primed observer me moving along also see as a light ray both of us agreeing that light rays move with unit velocity now this doesn't work for Newton's formula here it just doesn't work if X is equal to T it does not follow that X prime is equal to the T prime in fact it says something quite different okay so the form of these equations must be wrong let's look for some better equations now at this point let's in fact let's even be a little bit more ambitious it turns out being a little bit more ambitious actually simplifies things let's not only say that when X square minus T squared is equal to zero then X prime squared minus T prime squared is equal to zero let's say something even bolder let's say the relation between XT and X prime T prime is such that x squared minus T squared is equal to X prime squared minus T prime squared in other words pick any X and any T and calculate X square minus T squared then take the same point except reckoned in the primed coordinates in other words we take a certain event a light bulb goes off someplace you say that corresponds to X and T I say it corresponds to X Prime and T Prime but let's require just to try it out see if we can do it let's look for transformations so that X square minus T squared will always be equal to X prime squared minus T's prime squared that would be enough to ensure that everybody will agree about the speed of light why if x squared minus T squared equals X prime minus T prime squared for all X and T and so forth then when X square minus T squared equals zero X prime minus T prime squared will be zero and then if this is a light ray so is this a light ready everybody get the logic ok good so let's assume now that let's ask can we find transformations which have this particular property now it's not so different from looking for transformations which preserve x squared plus y squared equals x prime squared plus y prime squared it's just a little minus sign other than a minus sign here X square minus T squared look of these two is very similar and the mathematics is quite similar here are the transformations which preserve x squared plus y squared what are the transformations which preserve x squared minus T squared well they are the Lorentz transformations they are the fundamental transformations of the special theory of relativity they're not this but they're closely related or perhaps one should say closely analogous to these equations here but we have to substitute for circular trigonometry hyperbolic trigonometry so let's go back and remember a little bit about hyperbolic functions instead of circular functions well I didn't want to erase that all right these are the basic rules governing circular functions cosine theta this sine theta is equal to this and the e to the I theta in terms of cosine and sine all right let's see if we have a yeah we do have a blank blackboard here let me write whoops what did I do here I erased something I didn't mean to erase incidentally does everybody see how I got this side from the side you just add and subtract the equations appropriately and you isolate it to the I theta e to the minus R theta that's elementary exercise alright hyperbolic functions what are hyperbolic functions alright those are functions of the form hyperbolic cosine cosh hyperbolic cosine first of all the angle theta is replaced by a variable called Omega which I will call Omega Omega is called a hyperbolic angle it doesn't go from zero to two pi and then wind around on a circle it goes from minus infinity to infinity goes from minus infinity to infinity so it's a variable that just extends over the entire real axis but it's defined in a manner fairly similar to cosine and sine cosh Omega is by definition you're not allowed to ask why this is definition e to the Omega plus e to the minus Omega over 2 all we do is substitute for theta or for Omega theta I theta substitute Omega and that gives you hyperbolic functions likewise or similarly there's the hyperbolic sine and that's given by e to the Omega minus e to the minus Omega over 2 essentially you throw away all eyes out of that formula out of the top formulas just throw away all Sun all eyes the equations on the right-hand side become e to the Omega equals hyperbolic cosh Omega plus sin Chi Omega and e to the minus Omega equals cosh so mega- cinch Omega I think that's right is it right gosh – cinch it is yeah it is right okay now what about the analog of cosine squared plus sine squared equals one that simply came by multiplying this one by this one so let's do the same operation multiplying e to the Omega by each by e to the minus Omega gives one and now that gives cosh squared minus cinch squared you see we're getting a minus what we want we want that minus the minus is important we want the well somewhere is under here was a formula with a minus sign yeah we want to get that – into play here that's cos Omega squared knockouts Prakash squared Omega minus sin squared Omega so it's very similar everything you want to know about hyperbolic trigonometry and the theory of these functions is called hyperbolic trigonometry everything you ever want to know is codified in these simple formulas these in these and they're more or less definitions but there are the useful definitions now yeah go ahead yeah not only is it worth mentioning I was just about to mention it so I squared minus y squared is what hyperbola yeah right exactly so if I were to play the same game that I did here namely plot on the horizontal and vertical axis the values not of cosine of theta and sine of theta but cosine cosine cosh of that of Omega and since Omega what's in other words on the x-axis now we're going to plot cos Omega and on the y-axis cinch Omega then this is a hyperbola not a circle but a hyperbola and it's a hyperbola with asymptotes that are at 45 degrees you can see let me show you why why the asymptotes are at 45 degrees when Omega is very large when Omega is very large then e to the minus Omega is very small right when Omega is very large e to the minus Omega is very small and that means both cosh and cinch are both essentially equal to e to the plus Omega in other words when Omega gets very big cosh and cinch become equal to each other and that's this line here cash equals cinch along this line here so when Omega gets very large the curve asymptotes to to a curve which is a 45 degrees it's not hard to see that in the other direction when Omega is very negative that that it asymptotes to the other asymptotic line here so that's why it's called hyperbolic geometry it the hyperbolic angle the hyperbolic angles the caches the cinches play the same role relative to hyperbolas as sines and cosines do two circles any questions No so cosh Omega equals zero how would you plot that hi purple okay show me hmm Oh cos squared minus sin squared equals zero no that's no no cos squared minus sin squared equals one in the same sense that sine squared plus cosine square it never equals zero I think what I think you want to ask a different question I think oh well since Omega equals zero is the horizontal axis the costume a equals zero is the vertical eyebrows right okay well this is the x-intercept yeah it's it's the vertex I just think here's one point on a minute oh man the x-intercept there is one yeah because Kostroma cost of zero is one to see that just plug one r 0 in here 1 plus 1 divided by 2 is 1 at least it was yesterday yeah stores okay so now we we're sort of starting to cook a little bit we're starting to see something that has that nice minus sign in it but what's it got to do with X and T and X Prime and T prime we're now set up to make let's call it a guess but it's a guess which is based on the extreme similarity between hyperbolas and circles cautions and cosines and so forth he is the guess I'm going to make and then we'll check it we'll see if it does the thing we wanted to do my formula instead of being this has gotten with and we're now going to have instead of x and y we're going to have x and t time and x later on we'll put back y&z we're going to have to put back y&z but they're very easy okay so let's start with X prime X prime is the coordinate given to a point of space-time by the moving observer namely me and I'm going to guess that it's some combination of X and T not too different but not the same as where is it X prime equals X minus VT I'm going to try cosh Omega X let's write X cos Omega minus T sin Omega sort of in parallel with this I could put a plus sign here but you can go back and forth between the plus and the minus by changing the sign of Omega just as you did here so this let's do it this way X cos Omega minus T sin Omega and T prime going to look similar but without the extra minus sign here this you know the relation between sines cosines and cautious and cinches is one of just leaving out an eye you go from sines and cosines the clashes and cinches by leaving out the I well if you track it through carefully you'll find that this minus sign was really an I squared it's not going to matter much I will just tell you it was really came from some I squared and if you leave out I I squared just becomes one squared is no minus sign so here's the guess for the formula connecting X prime T Prime with X and T it equals let's say X since Omega – no – plus T cos Omega in this case there are two minus signs in this case there was only one minus sign okay but but let's check what do we want to check we want to check that X prime squared minus T prime squared is equal to x squared minus T squared your ask you're probably asking yourself what is this Omega what does it have to do with moving reference frames I'll tell you right now what Omega is it's a stand-in for the velocity between the frames we're going to find the relationship between Omega and the relative velocity of the reference frames in a moment there has to be a parameter in the lower end these are the lines in these are the Lorentz transformations connecting two frames of reference in the Lorentz transformations as a parameter it's the velocity the relative velocity that parameter has been replaced by Omega it's a kind of angle relating the two frames a hyperbolic angle but we'll we'll come back to that for the moment let's prove that with this transformation law here that X prime squared minus T prime squared is equal to zero ah is equal to X square minus T squared I'm getting to that point in the evening where I'm going to make mistakes all right this is easy you just work it out you use all you have to use is that cosine squared minus sine squared is 1 you can work that out by yourself but we can just see little pieces of it here X prime squared will have x squared cos squared Omega t prime squared will have x squared sin squared Omega if I take the difference between them I'll get a term with an x squared times cos squared minus sin squared but cos squared minus sin squared is one fine so we'll find the term with an x squared when we square take the square of the difference between the squares of this and this and likewise will also find the T squared the cross term when you square X Prime you'll have XT cost cinch when you square T Prime you'll have XT costs inch when you subtract them it'll cancel and it's easy to check that's our basically one liner to show that with this transformation here x prime squared minus T's prime squared is x squared minus T squared which is exactly what we're looking for let me remind you why are we looking for it if we find the transformation for which the left-hand side and the right-hand side are equal then if x squared equals T squared in other words if the right-hand side is 0 the left-hand side will also be 0 but x squared but x equals T that's the same as something moving with the speed of light in the X frame of reference if this being 0 is equivalent to the left hand side being 0 it says that in both frames of reference the light rays move with the same velocity so that's the basic that's the basic tool that we're using here X prime squared minus T prime squared is equal to x squared minus T squared all right that does follow by a couple of lines using cos squared minus N squared equals 1 but what I want to do let's take another couple of minutes now let's take a break for five minutes and then come back and connect these variables Omega with the velocity of the moving frame of reference somebody asked me a question about the ether and what it was that people were thinking somehow Einstein never got trapped into this mode of thinking um well what were they thinking about when they were thinking about the ether what exactly was the michelson-morley experiment well I'll just spend the minute or two mentioning it certainly Maxwell understood that his equations were not consistent with with Newtonian relativity he understood that but his image of what was going on is that the propagation of light was very similar to the propagation of sound in a material or water waves propagating on water and of course it is true that if you move relative to the atmosphere or move relative to the substance that sound is propagating in you'll see sound move with different velocities depending on your motion if you're at rest in a gas of material isn't there's a natural sense in which is a particular rest frame the rest frame is the frame in which on the average the molecules have zero velocity if you're in that reference frame then first of all light has the same velocity that way as that way number one and it has a velocity that's determined by the properties of the fluid that the sound is moving in okay Maxwell more or less thought that light was the same kind of thing that there was a material and the material had a rest frame and that particular rest frame was the frame in which light would move with the same velocity to the left as to the right and he thought that he was working out the mechanics or the behavior of this particular material and that we were pretty much at rest relative to this material and that's why we saw light moving the same way to the left of the right one would have to say then that Maxwell did not believe that his equations were a universal set of laws of physics but that they would change when you moved from frame to frame just happened by some luck we happen to be more or less at rest relative to the ether to this strange material um of course you could do an experiment with sound if you're moving through the sound you can check that the velocity in different directions is different you do let's not worry exactly how you do that that's what the Michelson Morley experiment was Michelson and Morley I suppose said look the earth is going around in an orbit maybe at one season of the year we just happen to be at rest relative to the ether by accident and some other season six months later we're going to be moving in the opposite direction and we won't well we won't be at rest only at one point in the orbit could we be at rest relative the–this or at any other point in the orbit we wouldn't be so if we measure in November that light moves the same than all possible directions then in what's what's the opposite of November May then in May we should find that light is moving with great with the different velocities in different directions and he tried it and a very fancy and sophisticated way of measuring the relative velocity in different directions but he found that there was no discrepancy that the light traveled the same velocity in every direction at every time of year there were all sorts of ways to try to rescue the ether but none of them worked none of them work and the result was one had to somehow get into the heart of space and time and velocity and mid distance and all those things in a much deeper way in a way that didn't involve the idea of a material at rest in some frame of reference that that propagated the light okay oh where are we I forgotten where we were when we stopped somebody remind me whoo-hah Omega yeah what is Omega forgotten Omega Oh how Omega is really metal speed of light but to the velocity of the moving reference frame here we have two reference frames X T and X Prime and T prime what's the relationship between them well the whole goal here was to understand the relationship between frames of reference moving with relative velocity between them Omega is not exactly the relative velocity but it is closely related to it okay let's say let's see if we can work out the relationship we know enough to do it let's see if we can work out the relationship between Omega and the velocity of the moving frame all right again let's go back to this picture there's a frame of reference moving let's redraw it here's my origin moving along okay what does it mean to say that from your perspective my frame of reference so my origin is moving with velocity V well by definition this is not a law now this is a definition and says that this line here has the equation x equals VT that's the definition of this V here my origin moves relative to your origin it moves with a uniform constant velocity that's an assumption that we're talking about two inertial frames of reference and you in your frame of reference will write x equals VT that's the definition of V if you like what will I call it I will call it X prime equals zero all along there I will say X prime is equal to zero it's my origin of coordinates okay now let's come to this transformation law here and see if we can spot how to identify V well X prime equals zero that's this trajectory moving at an angle with a velocity V X prime equals zero is the same as saying X cos Omega equals T sin Omega X prime equals zero set this side equal to zero and that says that X cos Omega equals T sin Omega all right so whatever the connection between velocity and Omega is it must be such that when X prime is equal to zero X cos Omega equals T sin Omega well let's look at that equation it also says that X is equal to sin CH Omega over cos Omega times T well that's interesting because it's also supposed to be equivalent to x equals VT now I know exactly how to identify what the velocity is as a function of Omega the velocity of the moving transformation the moving coordinate system must just be sin Chi Omega over cos Omega that's the only way these two equations can be the same x equals VT x equals sin Chi Omega over cos Omega times T so now we know it we know what the relationship between velocity and Omega is write it down the velocity of the moving frame now this is not the velocity of light it's just the velocity of the moving frame must just be cinch Omega over cos omega well actually i want to invert this relationship i want to find sin and cos omega in terms of the velocity i want to rewrite these Lorentz transformations where are they i want to rewrite these Lorentz transformations in terms of the velocity that's the familiar form in which you learn about it in in elementary relativity books X prime is equal to something with velocities in it to exhibit that all we have to do is to find Cinch and cosh Omega in terms of the velocity that's not very hard let's let's work it out the first step is to square it and to write V squared is equal to cinch Omega squared over cosh Omega squared that was easy next I'm going to get rid of since Omega squared and substitute where is it I lost it one is equal to cos Omega squared minus cinch Omega squared alright so wherever I see cinch Omega squared I can substitute from here namely cosh squared Omega minus one is equal to sine squared Omega so here we are this is just equal to hash of Omega squared minus one divided by cost of Omega squared or let's multiply by what I want to do is solve for cost Omega in terms of velocity I want to get rid of all these cautions and cinches of Omega and rewrite it in terms of velocity so first x cost Omega squared we have cosh squared Omega times V squared equals cosh squared Omega minus one or it looks to me like this is cosh squared Omega times one minus V squared equals one what I've done is transpose yeah cos squared times V squared minus cos squared itself that gives you cos squared 1 minus V squared equals 1 change the sign can everybody see that the second line follows from the first I'll give you a second yeah yeah yeah it's clear ok finally we get that cos Omega is equal to 1 divided by 1 minus V squared but now I have to take the square root cos Omega / one minus V squared and then take the square root and that gives you cos Omega now we've all seen these square roots of 1 minus V squared in relativity formulas here's where it begins the kayne we begin to see it materializing what about sin Chi Omega let's also write down sin Chi Omega well from here we see that sin Chi Omega is just equal to V times cos Omega this is easy since Omega equals V times cos Omega sorrow sin Chi Omega is V divided by square root of 1 minus V squared let's go back to these Lorentz transformations over here and write them getting rid of the trigonometric functions the hyperbolic trigonometric functions and substituting good old familiar velocities let's get rid of this and substitute the good old ordinary velocities ok so we have here X prime equals x times cos Omega and that's divided by square root of 1 minus V squared then this minus T times sin Omega which is V over the square root of 1 minus V squared or if I put the two of them together and combine them over the same denominator it's just X minus VT divided by square root of 1 minus V squared I think most of you have probably seen that before maybe slightly different let's let's clean it up a little bit X prime equals X minus VT divided by the square root of 1 minus V squared what about T prime T Prime is equal to t minus V X over square root of 1 minus V squared T prime is equal to T times cos cost is just 1 over square root and then x times sin CH that gives us the extra V in other words the formulas are more or less symmetrical and those are all good old Lorentz transformations now what's missing is the speed of light let's put back the speed of light the put back the speed of light is an exercise in dimensional analysis there's only one possible way the speed of light can fit into these equations they have to be modified so that they're dimensionally correct first of all one is dimensionless has no dimensions it's just one velocity is not dimensionless unless of course we use dimensionless notation for it but if velocity is measured in meters per second then it's not dimensionless how do we make V squared dimensionless we divide it by the square of the speed of light in other words this V squared which is here which has been defined in units in which the speed of light is 1 has to be replaced by V squared over C squared likewise over here V squared over C squared now velocity times time does have notice first of all the left hand side has units of length the right hand side this is dimensionless X has units of length but so does velocity times time so this is okay this is dimensionally consistent as it is but over here it's not the left hand side has dimensions of time that's all right 1 minus V squared over C square that's dimensionless this has units of time but what about velocity times X velocity times X does not have units of time in order the given units of time you have to divide it by C square okay let's check that velocity is length all the time times length divided by C squared that's length square R which gets correct but it's correct all right this is probably familiar to most of you who've seen relativity once or twice before these are the equations relating to different moving coordinate systems moving relative to the x axis but you see the deep mathematics or the mathematical structure of it in many ways is best reflected by this kind of hyperbolic geometry here and you know most physicists by now never write down the Lorentz transformations in this form much more likely to write them in this form easier to manipulate easier to use trigonometry or or hyperbolic trigonometry it's a little exercise it's a nice little exercise to use this the hyperbolic trigonometry to compute their to compute the compounding of two Lorentz transformations if frame two is moving relative to frame one with velocity V and frame three Israel moving relative to two with velocity V Prime how is three moving relative to one the answer is very simple in terms of hyperbolic angles you add the hyperbolic angles not the velocities but the hyperbolic angles the hyperbolic angle of three moving relative to one is the hyperbolic angle of three moving relative to two plus two moving relative to one and then you use a bit of trigonometry or hyperbolic trigonometry to figure out how you do the inches and kosh's of the sum of 2 hyperbolic angles very straightforward and I'll leave it as an exercise to see if you can work that out much easier than anything else ok so there there we have the Lorentz transformations yeah oh oh absolutely yes that's that's that's a good point yeah when we that's right if we have frame 1 let's call this x1 and y1 x2 and y2 and finally x3 and y3 well then the angle of – let's call F of 3 relative to 1 let's call it theta 1 3 is just equal to theta 1 2 plus theta 2 3 the angle connecting frame one with frame 3 is just the sum of the angle theta 1 2 plus theta 2 3 so in that respect the Lorentz transformations are much simpler in terms of the Omegas it's the Omegas which combined together to add when you add velocities now how different is omega from the velocity let's work in units in which the speed of light is equal to 1 where is our formula for velocity all right let's take this formula over here what a cinch Omega 4 small Omega let's put the C squared there a let's not put the C square there or not put the C square there since Omega is essentially Omega when Omega is small just like sine is omega where is theta when theta is small the cinch function the cost function looks like like this the cinch function looks like this but it but it crosses the axis with a slope of 1 for small Omega cinch Omega is proportional to Omega for small velocity one minus V squared is very close to 1 if the velocity is a hundredth of the speed of light then this to within one ten-thousandth is just 1 if we're talking about velocities a millionth of the speed of light then this is very close to 1 and so since Omega and velocity are very close to each other it's what's going on here Thanks okay so for small velocities Omega and velocity are the same the actual correct statement is that V over C is like Omega the dimensionless velocity over the speed of light is like Omega for small Omega and small velocity so for small velocity adding velocities and adding omegas are the same things but when the velocities get large the right way to combine them to find relationships between different frames is by adding Omega and not adding velocities when you add Omega like compounding velocities as you've got it there I guess you won't go greater than 45 degrees that guess because that would be faster than light no but Omega no more you see this bit the speed of light is V equals one that corresponds to Omega equals infinity yeah yeah so Omega Omega runs over the whole range from minus infinity to infinity but when it does V goes from minus the speed of light to the speed of light so you can add any omegas and still add any omegas Omega that's right there's no there's no speed limit on Omega is this like we just go on that diagram it looks like it's greater than 45 degrees if here where where I make a and I guess they use the definition of state along the hyperbola yeah that's right sorry where are we right there today I guess that's theta though isn't it this is Theta that's a good oh god yeah right right yeah Omega is the distance along hyperbola that's right distances that's right Omega is a kind of distance along the hyperbola all right now let's let's talk about that a little bit all right now that we've established the basic mathematics structure of the transformations I think we should go back and talk about some simple relativity phenomena and derive them oh one thing which is important which I yeah well let's see we're here are my Lorentz transformations over here I said we should we ought to at the end make sure that our transformations are not too dissimilar from Newton's in particular when the velocities are small they should reduce to Newton that's all we really know that's or at least that's all that Newton really had a right to assume that when the velocities are smaller than something or other that his equations should be good approximations isn't adding velocity good enough isn't velocities adding good enough in fact you're right in fact you're right but let's just look at the transformations themselves all right as long as the velocity is a small percentage of the speed of light an ordinary velocities are what a hundred miles an hour versus 186,000 miles an hour what is that it's small right and it's doubly small when you square it so for typical ordinary velocities even the velocities of the earth around the Sun and so forth fairly large velocities what 60 kilometers per second or something like that 60 kilometers per second is pretty fast that's the that's the orbital earth around the Sun it's pretty fast but it's nowhere near 300,000 kilometers per No yeah looks here on a thousand meters per second we're I'm sorry three times ten to the eighth no three times three hundred thousand kilometers per second right 60 kilometers per second three hundred thousand kilometers per second small fraction and then square it so for ordinary motions this is so close to one that the deviation from one is negligible so let's start with the top equation for the top equation this is negligible and it's just x prime equals X minus VT the bottom equation here you have a C squared in the denominator whenever you have a C squared in the denominator that's a very very large thing in the denominator this is negligible compared to T so here the speed of light is also in the denominator just forget this and it's just T but it's just T prime equals T it's just D prime equals T so in fact Newton's formulas are essentially correct for slow velocities no no significant departure from Newton until the velocities get up to be some some appreciable fraction of the speed of light okay let's talk about proper time proper time and then let's do a couple of relativity examples yeah question the bottom equation when X is very large yes that's right when X is exceedingly large you get a correction but that correction that X has to be very large look let's let's discuss before we do anything else let's let's let's talk about that a little bit X minus VT one minus V squared over C squared yeah let's alright in my drawings I'm going to sitt C equal to one but in the equations you can leave the C there okay this equation we understand apart from this one minus V squared over C squared in the denominator it's just this x equals V T or X minus V X minus X minus VT that's Newton let's look at this one over here okay let's look at the surface T prime equals zero T prime equals zero is the set of points that I in my moving reference frame call T call time equals zero it's what I call the set of points which are all simultaneous with the origin T prime equals zero is just everyplace in space-time which has exactly the same time according to my frame of reference and I will therefore call all those points synchronous at the same time what do you say about them if T prime is equal to zero that says that T is equal to V over C squared X now let's set C equal to one for the purpose of drawing just for the purpose of drawing I don't want this huge number C squared to distort my drawings too much it says the T equals V X what does the surface T equals V X look like it looks like this T equals V X which is also X is equal to 1 over V T so it's just a uniform line like that all of these points are at different times from your reckoning this ones later this ones later this ones later and so forth according to my reckoning all these points are at the same time so we disagree about what's simultaneous this was this was the hang-up incidentally this was the basic hang-up that took so long to overcome that took Einstein to overcome it the idea that simultaneity was the same in every reference frame nobody in fact it was so obvious that nobody even thought to ask a question is simultaneous does it mean the same thing in every reference frame no it doesn't in more in your reference frame the horizontal points are all simultaneous with respect to each other in my reference frame what I call horizontal what I call simultaneous you do not okay so simultaneity had to go let me point out one more thing about these equations I'm not going to solve them for you but I will tell you the solution anyway how do you solve for X and T in terms of X Prime and T Prime well think about it in the case of angles supposing I have a relationship like X prime is equal to X cosine theta what is it plus plus y sine theta and y prime is equal to X minus X sine theta plus or Y cosine theta and supposing I want to solve for x and y in terms of X Prime and Y Prime you know what the solution is just change theta 2 minus theta and write that X is equal to X prime cosine of minus theta but what's cosine of minus theta right cosine theta plus y sine of minus theta what's sine of minus theta minus sine theta times y and likewise for y prime Y prime is equal to minus x times sine of minus theta so that becomes plus X sine theta plus y cosine of minus theta which is cosine theta you don't have to go through the business of solving the equations you know that if one set of axes is related to the other by rotation by angle theta the second one is related to the first one or vice versa the first one is related to the second one by the negative of the angle if to go from one frame to another you rotate by angle theta and to go from the second frame back to the first you rotate by angle minus theta so you just write down exactly the same equations interchange Prime and unprimed and substitute for theta minus theta same thing for the Lorentz transformations exactly the same thing if you want to solve these for X and T write down the same equations replace primed by unprimed and change the sign of omegas to minus the sines of omegas change sinus rgn of all the sign all the cinches okay in other words just send Omega 2 minus Omega and that will solve the equations in the other direction yeah yes it's also the same as changing V 2 minus V yes the way to see that is to go right what was it what do we have cosh Omega yep yeah that's right via sign yes that was correct yeah you just well you change Omega 2 minus Omega it has the action of changing V 2 minus V you can just check that from the equations good alright let's let's talk about proper time a little bit proper time if you're doing ordinary geometry you can measure the length along a curve for example and the way you do it is you take a tape measure and you you know sort of take off you take off equal intervals equal equal little separations you can think of these separations as differential distances DS squared small little differential distances and that differential distance is d x squared plus dy squared with the x squared and the y squared are just the differential increments in x and y DX and dy this is d s alright so that's the way and you add them up you add them up that's the way you compute distances along curves it's quite obvious that if you take two points the distance between those two points depends on what curve not the same for every curve so I'll measure the longer curve you have to know not only the two points but you have to know the curve in order to say what the distance between those points are of course the distance between its longer straight line that's that's well-defined but the distance along a curve depends on the curve in any case D s squared equals the x squared plus dy squared is the basic defining notion of distance between two neighboring points if you know the distance between any two neighboring points in a geometry you basically know that geometry almost essentially completely so given this formula for the distance between two points you can compute if you like the distance along a curve because you've got to take the square root of this and then add them up don't anhedonia the squares add the differential distances all right the important thing is here that square root of DX squared plus dy squared which is the distance between neighboring points doesn't depend on your choice of axes I could choose X Y axes I could choose X prime y prime axes if I take a little differential displacement the X and the y or I just take two points two neighboring points don't even give them labels and measure the distance between them the distance between them should not depend on conventions such as which axes are used and so when I make rotational transformations the X square plus dy squared doesn't change the X and the y may change but the x squared plus dy squared does not change the same thing is true in relativity or the analogous thing we don't measure distances along the paths of particles let's say now that this curve here is the path of a particle moving through space-time there's a particle moving through space-time and we want some notion of the distance along it the notion of distance along it another example would just be a particle standing still as a particle standing still particle standing still is still in some sense moving in time I wouldn't want to say that the distance between these two points and space-time is zero they're not the same point I wouldn't like to say it's zero I would like to say there's some kind of notion of distance between them but it's quite clear that that distance is not measured with a tape measure this point and this point are the same point of space boom here at this point of space and that at a later time boom again at the same point of space two events at the same point of space how do I characterize and some nice way the distance between those two events that occurred in the same place you don't do it with a tape measure all right what do you do with a clock a clock you take a clock and you start it at this point tic tic tic tic tic tic tic a stopwatch you press it at this point tic tic tic tic tic it picks off intervals and then you stop it at that point and you see how much time has evolved that's a notion of distance along a particle trajectory it's not the distance the particle moves in space it's a kind of distance that it's moved through space-time and it's not zero even if the particle is moving standing perfectly still in fact what it is is it's the time along the trajectory what about a moving particle well you can imagine that a moving particle carries a clock with it of course not all particles carry clocks but we can imagine they carry clocks with them as they move and we can start the clock over here and then the clock over here what is the time read off by this moving clock the time read off by a moving clock is much like the distance along a curve measured by a tape measure in particular it should not depend on the choice of coordinates why not this is a question that has nothing to do with coordinates I have a clock made in the standard clock Factory the standard clock Factory and I don't know we're in Switzerland someplace makes a certain kind of clock that clock gets carried along with a particle and we ask how much time evolves or how much time elapses or how much the clock changes between here and here that should not depend on a choice of coordinates it shouldn't depend on a choice of coordinates because it's a physical question that only involves looking at the hands of the clock in fact we can ask it for little intervals along along the trajectory we could ask how much time elapses according to the clock between here and here well the answer again should not depend on what coordinates you use which Lorentz frame you use and there's only one invariant quantity that you can make out of the D X's and DTS describing this point describing these two points there's a little interval DT and there's a little interval DX now we're in space and time not ordinary not ordinary space and the quantity which is invariant there's really only one invariant quantity that you can make out of it it is DT squared minus DX squared it's the same quantity x squared minus T squared for a whole you know for a whole interval the T squared minus DX squared that's the quantity which is invariant it's minus D it's the negative of what I wrote over here x squared minus T squared okay this quantity is equal to the X prime squared minus DT power sorry DT prime squared minus the X prime squared the same algebra goes into this as goes into showing that X prime squared minus T prime squared equals x squared minus T squared incidentally this is the same as saying T prime squared minus X prime squared equals T squared minus x squared doesn't matter which way you write it all right so that suggests that suggests that the time read off the invariant time read off along a trajectory between two points separated by DX and DT is just the square root of DT squared minus DX squared why the square-root incidentally okay you're going to integrate in detail I can integrate DT yeah well alright why not just DT square minus the x squared for the time between here and here is it here's an answer supposing we go to you two intervals exactly the same as the first one we go an interval over here DX and DT and then we go another DX in DT what happens when we double the interval to DT squared minus DX squared it gets multiplied by four because everything is squared well I wouldn't expect a clock when it goes along you know when it goes along a trajectory for twice the the interval here to measure four times the the time I expected to measure twice the time so for that reason the square root is the appropriate thing here okay that's called D tau squared the tau squared the proper time along the trajectory of an object you're right that's just the towel or D tau squared being the x squared minus DT squared the Tau is called the proper time let's go I think we'll let's see the towel is called the proper time and it is the time read by a clock moving along a trajectory it's not just DT that's the important thing it's not just DT the T squared minus the x squared let's do one last thing let's just do the twin paradox in this language I think I think I've had it I'm going to finish you can do the twin paradox in this language all you have to do is to compute the proper time along two trajectories one that goes out with a uniform velocity turns around and comes back with the same uniform velocity versa a trajectory which just goes from one point to the st. the another point along a straight line and it's no more weird it's no weirder really from this perspective than saying the distance from one point to another along two different curves do not have to agree the proper time along two different curves in general will not agree what is a little bit weird is that because of this minus sign the proper time this way is less than the proper time this way that's the consequence of this minus sign here moving with some DX decreases the proper time all right we'll do a little bit more next time but then I want to get to the principles of field theory and and connect some of this with field equations for interesting wave fields the preceding program is copyrighted by Stanford University please visit us at stanford.edu

9 Rules of Personal Space



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We discuss the rules of personal space. GMM #512!
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today we speak of the unspoken rules of personal space let's talk about that a good mythical morning we have an imaginary bubble around us and that imaginary bubble is called personal space or imaginary bubble I like personal space we've got anthropologists Edward T hall now he defines he's here back at yeah we've got him here with us no I don't even know if he's alive back in 1966 brother DUP he defined personal space as the region surrounding a person which they regard as psychologically theirs yeah now people's opinions about personal space vary widely I mean culturally it varies yeah and then from person to person it varies yeah and it is largely unspoken so I thought today it would be fun to have a conversation about the unspoken rules of personal space so by speaking about them they're no longer unspoken I hope I'm not breaking anything yeah I thought about um so what I want to do is I want to propose rules of personal space for particular places and scenarios okay will you find yourself and hey this is just one guy's opinion I'm gonna run it by you maybe demonstrate some of these things you let me know what you think and let's see if we can arrive collectively at what are feasible rules we sit kind of of personal space is it kind of close yeah maybe closer than people realize yet the camera makes us seem farther but we're this almost this is two inches well people don't know that that's two inches plus the camera changes it since they don't sit on a GMM desk I'm going to make it more relatable and take it to an airplane so you sit down an airplane basically I think most people would agree you're pretty much in somebody's personal space just by virtue of your your ticket assignment right unless let's assume that we're strangers on a plane I got a couple of rules for us well first of all we should be a little bit closer because I mean yeah you're right up on the right the plane and let's say you're on the armrest first of all my rule is you can talk to the person but you should only glance at them you should never turn and face them yeah that's when maintain icon where you from I don't even know because you're staring right through my soul and it's making me uncomfortable okay you know where you hedid oh I know where I'm headed now cuz I'm not looking at you but I'm giving you a little glance wait where you headed I'm just yeah other side of the world man you gonna get some of those peanuts you're gonna get some of those pretzels I got both long as far as I'm gonna pick one I know I'm gonna get both overtime okay so that's it only glance no face-to-face I agree with that I don't think anyone's doctor I have one woman one time she had a worst breath and I was hoping she would start eating something because when you eat stuff sometimes it covers it up it pushes I didn't send it smell like rotten peanuts after she got through the peanuts what she was she looking at you want to talk where are you from where you heard it yeah don't square out to people and then the armrest there's never a scenario when you can share the armrest okay you might want to attempt that but it no halfsies it's not gonna work it first come first serve and then whenever they remove that thing like remove it you got to be totally ready to take over I'm one time there I'm locked in I don't go to the bathroom some time for that armrest – movies my first rule is don't sit down right next to a stranger unless you have to I mean don't we all agree with this but you were telling me last week that this happened to you I went to a movie by myself I'm not proud of it but I did in a whole family a family of eight came in and they've kid that all around you sit right next to me okay what's up kid well he's a kid but hey kid you in a row there was hardly anybody in the theater I'm gonna add this rule okay check this out at it you must leave an even number of blank spaces in between you and the closest stranger you should never leave one space because that's inconsiderate to how things work typically with movies people come in pair nobody goes to movie by themselves um so you got to leave an even number of spaces and then if you're forced to sit beside somebody because of it's just crowded all the rules of the airplane apply and you shouldn't talk during a movie anyway yeah oh yeah yeah armrests and everything okay you ready to go to an elevator how do you choose who gets to put the drink in the armrest though first come first serve now elevator you're pretty much forced to be in people's spaces and there's a genuine there's a general assumption that okay when you go in and then what you turn and everybody faces the door and looks at the number above the door and everybody's quiet okay I'll propose a rule that you can have a conversation with somebody and even face them a little bit if you can touch one side of the elevator with a part of your body any part and they're touching the other side of the elevator like with their hand or something that lets you know I'm far enough away from them that I can turn and look at them a little bit like I'm hold on to the side they don't have to be touching the side of the elevator but if they are right where you from this side of the elevator I kind of is it over there I live in here did you fart I'm not no dude it wasn't me and there's only one other person here I didn't but D smell it it was a guy before us it was me oh where you from decided the elevator okay and then there's kind of a psycho zone and all so my general rule which I think applies in an elevator is if you can smell somebody you're too close to talk to them well what it smells strong though some people hold it permeate the hole they ate garlic or something don't talk to him okay if you can smell somebody don't talk you're too close to talk to it okay agree or disagree agree I don't like smelling people in general let's go to the DMV line let's just say this is any line okay okay my rule that I propose in terms of personal space is you can't put too much personal space in between you because you'll get skipped in line okay the proper amount of space to put in between you and the person in front of you is slightly only slightly above the average human being body depth that way no one's going to skip you but if you go any closer than that you're gonna get mule-kicked about someone and who's angry about being in the DMV line the widest part of a person in that dimension is their buttocks did so you got to get well at least on me it depends on who it is you've got to go from the furthest most point to the bacchus most point of the average human okay all right and I'm just going by feel on that seriously edges but don't feel people okay I want to be clear I'm not saying feel somebody yeah it's because I use the words in some countries you're basically like chest to back extremely crowded subway which is basically like a concert mosh pit here's my rule for this if you are touching more than two places with an individual that you do not know like others shoulder touch there's a knee touch and there's like a risk touch because like we're slammed together in a subway it's kind of weird we wouldn't say like this probably in a crowded subway you might I feel like at this point the rule is you have to talk to hey man but you should do it with an apologetic looking I'm sorry where you from hey YUM I shall live in the subway which makes this even more appropriate I'm gonna move over here so you just have to embrace the awkwardness that's my rule for that you have to talk to the person okay I don't like talking it's strange if you're touching that much you have taught too and now I'm going to shift to people that you know okay so what we're going to do is we're going to move back and put your cheer in here all right let's say we're coworkers all right we're in the break room hey George the proper distance to stand from a co-worker is determined by out stretching your arm and barely touching your finger tip which is usually your middle finger because it's long as to their nose hey then then bring it down you see that news brain then bring it down do that mentally and then you see the new supervisor Sally yeah she's you you mean pantsuit oh-ho I call head stripe answer yeah just checking you don't want to be any closer to someone having that type of conversation unless it's Sally and if hahahahahaha your boss if Sally is your boss you got to touch their nose Holly Levin touching didn't shimmy back a little bit shimmy that that's it oh all right so now for friends say men friends are a little bit closer okay I say the rule for this to determine your optimal personal space is reach out like you're gonna grab their ears and now at this point here anything can you hear anything yeah okay yeah that you want to be able to talk to you friend this is all happen your mind by the way you see Sally today well I don't work with you I'm your friend yeah yeah alright you talk about her tonight yeah our friend so the hands come down that's mental and but you would imagine grabbing them opening that's how you know you're the proper distance from a from a friend like like that right that that actually you don't do that you just you imagine but if we're both interested in Sally right hey Sally and then I'm like I've never met a don't listen to him Sally never met a Sally ever what about a Tammy yeah lots of Tammy's okay all right so then move in a little bit more now we're on our first date we are we're waiting at Applebee's are you salad we're waiting at Applebee's to get our table you do the elbow reach we're in you touch right there that's how close you need to be on a first date you gonna get some riblets or what or basket a basket of Riblet yeah a basket I like you let's have a second day and again my hand should never be there don't ever want Sally to know that like you don't like me she's turned right all right and now finally say you been married a year now you PDA you can do whatever you want if you want to hang out with your wife or your whatever that's fine but when you're just hanging out having a normal conversation you know you're at the proper distance when you just give a little this and then the knee hits what the knee hills there's I go one at a time Sally I'm so glad I got it right you know you're at the right spot so the knees hit let me go to oh oh no I thought it let you go down one person is that okay right see you this is comfortable if we've been married to you yeah yeah right you say okay well it's like a mechanics in it there's a lot of mechanics and there's so much more we could talk about but I'll leave it to you guys in the comments thanks for liking this video whoa you know what time it is it's not well I know what time it is time spin the wheel make sure you head on over to our Facebook page we are doing our back-to-school contest over there you submit photos we have an assignment every single day this week and you can win amazing merchandise from rhettandlink video also click through to good mythical more where I tell you how to deal with the close talker two blades of grass here the lawnmower start hey Harry hey Bill just chilling out being grass yeah yeah how she's aged what do you hear that just that low Rumble yah yah yah yah aah familiar sound from mythology I think it's mythology well a mythological no mower sound is my tummy I'm hungry grass gets hungry you know how the grass stomach's how loud they can get you're right we eat sunlight and water let's just chop open up here comes the sunlight okay here's the deal that actually induced a burp are you okay with that oh and you're about to make it

BIOL G-11 U-1 || The Scientific Method



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The scientific method is a series of steps followed by scientific investigators to answer specific questions about the natural world. It involves making observations, formulating a hypothesis, and conducting scientific experiments. Scientific inquiry starts with an observation followed by the formulation of a question about what has been observed. The steps of the scientific method are as follows:

Observation
Question
Hypothesis
Experiment
Results
Conclusion
Observation
The first step of the scientific method involves making an observation about something that interests you. This is very important if you are doing a science project because you want your project to be focused on something that will hold your attention. Your observation can be on anything from plant movement to animal behavior, as long as it is something you really want to know more about.​ This is where you come up with the idea for your science project.

Question
Once you’ve made your observation, you must formulate a question about what you have observed. Your question should tell what it is that you are trying to discover or accomplish in your experiment. When stating your question you should be as specific as possible.​ For example, if you are doing a project on plants, you may want to know how plants interact with microbes. Your question may be: Do plant spices inhibit bacterial growth?

Hypothesis
The hypothesis is a key component of the scientific process. A hypothesis is an idea that is suggested as an explanation for a natural event, a particular experience, or a specific condition that can be tested through definable experimentation. It states the purpose of your experiment, the variables used, and the predicted outcome of your experiment. It is important to note that a hypothesis must be testable. That means that you should be able to test your hypothesis through experimentation.​ Your hypothesis must either be supported or falsified by your experiment. An example of a good hypothesis is: If there is a relation between listening to music and heart rate, then listening to music will cause a person’s resting heart rate to either increase or decrease.

Experiment
Once you’ve developed a hypothesis, you must design and conduct an experiment that will test it. You should develop a procedure that states very clearly how you plan to conduct your experiment. It is important that you include and identify a controlled variable or dependent variable in your procedure. Controls allow us to test a single variable in an experiment because they are unchanged. We can then make observations and comparisons between our controls and our independent variables (things that change in the experiment) to develop an accurate conclusion.​

Results
The results are where you report what happened in the experiment. That includes detailing all observations and data made during your experiment. Most people find it easier to visualize the data by charting or graphing the information.​

Conclusion
The final step of the scientific method is developing a conclusion. This is where all of the results from the experiment are analyzed and a determination is reached about the hypothesis. Did the experiment support or reject your hypothesis? If your hypothesis was supported, great. If not, repeat the experiment or think of ways to improve your procedure.

hello teacher hello students welcome to today's lesson on scientific methods so far in our unit on the science of biology we have been discussing the meaning of science we have concluded that it is an ongoing effort to find new information and principles which can increase human knowledge and understanding we have talked about research and investigations into natural occurrences and ideas today we will be learning about scientific methods we will demonstrate how scientific methods are used to make significant observations and discoveries as well we will learn how these methods are used to solve problems and prove ideas this is going to be a very interesting lesson let us get started scientific method is the process by which scientists approach their work they do so in a logical and sensible manner scientific method is a way of observing and explaining events while trying to establish if the explanations are true or false for years people explained what they saw without testing their ideas to determine if they were correct for instance people used to believe in spontaneous generation this idea suggests that non living objects could give rise to living objects as an example before refrigeration existed butchers would hang animal carcasses from the ceiling in their shops because the meat was not refrigerated the shop was always full of flies people believed that over time the meat would spontaneously turn into flies now that rationale and scientific methods are used to explain occurrences like this we know that meat does not spontaneously turn into flies why do you think it is important to determine whether something is true or false using scientific methods right your ideas on a piece of paper students let's get ready begin [Applause] you time's up let's get back to our lesson welcome back students I am sure everyone had some interesting ideas it is important to use scientific methods to determine whether something is true or false because it makes the explanation valid and accurate if people explained natural occurrences and ideas without using scientific methods that supply evidence for their statements a lot of misleading and unreliable information would be spread it is challenging to explain or further understand something if assumptions are made by using scientific method the true information is revealed and it becomes possible to fully understand an idea or occurrence a number of stages are involved in the scientific method direct your attention to the diagram on the screen this shows us the scientific method let us go through each step and discuss it in greater detail the first step is to ask a question when biologists see something happen and they do not understand why or how it happens naturally they want to find out more the next step would be research biologists try to find as much information as possible about their question perhaps someone else has already looked into this question and has discovered an answer it would be important to know information like this before continuing on with the scientific method next a hypothesis is constructed a hypothesis is an educated guess a biologist thinks the explanation of an observation will be a hypothesis has to be stated in such a way that it can be tested in an experiment based on a hypothesis a prediction is made a prediction is an educated guess as to how the biologist thinks the experiment will turn out the following step is to design and carry out an experiment to test the hypothesis then the results of the experiment are analyzed and conclusions are drawn based on the data attained the next step is to accept or reject the hypothesis during this step the biologist refers back to the original hypothesis to determine whether or not it matches the information attained by the experiment the final step is to report the results in this step the biologists can decide whether or not to share the results with other biologists someone else might decide to take the work further or investigate another aspect of the same experiment while others may want to disprove the results this is the final step of the scientific method let us refer back to the example of rotting meat that we talked about earlier in this lesson by using the same scientific method we just learned biologist Francesco Redi disproved the idea that rotting meat spontaneously turned into flies the experiment ready conducted was considered the first true experiment in 1668 ready carried out an experiment using jars that contained meat some jars were left open and exposed to air while others were sealed ready hypothesized that only flies could produce more flies he predicted that flies would be found in the open jars and not in the closed jars his results his predictions and when he shared his results other biologists obtained similar results from their own tests Reddy was able to conclude that flies cannot be produced from rotting meat he also went on to say that it was improbable that any form of spontaneous generation could occur students we have time for one more activity let us review some of the terms we learned today please write the definitions for the following terms students let's get ready begin you time's up let's get back to our lesson hello again everyone I am sure this was a simple activity for you let us review the answers together scientific method is defined as the process by which scientists approach their work hypothesis is defined as an educated guess about how an observation can be explained it must be stated in a way that it can be tested by an experiment prediction is an educated guess as to how the biologist thinks the experiment will turn out spontaneous generation is defined as the belief that living things can appear from nonliving objects were you able to define every term if so great work this brings us to the end of our lesson today we learned about the scientific method we discussed the steps in the scientific method and looked at the work of biologist Francesco Redi who conducted the first scientific experiment until next time thank you teacher Thank You students Oh

Lecture 1 | The Theoretical Minimum



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(January 9, 2012) Leonard Susskind provides an introduction to quantum mechanics.

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The Rules of Snooker – EXPLAINED!



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Ninh explains the Rules of Snooker – a popular cue sports table game from England.
This is a beginner’s explanation of Snooker Rules.
Watch this short video tutorial guide on how to play Snooker under World Snooker Rules.
Learn about potting, snookered, fouls, free balls, maximum break 147 and more!

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Images: Google, Ronnie O’Sullivan
Music: ‘Drag Racer’ by The Doug Wood Band
Narrated, Directed and Produced by Ninh Ly

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and explains the rules of snooker the object of the game is for you to win more frames than your opponents snooker is a game that's usually played between two people and to win a frame you must score more points than your opponents to score you must use a wooden cue to hit a white ball known as a cue ball into a coloured ball and for that ball to go into any of the pockets on the table this is known as potting the ball the table is roughly 12 feet by 6 feet and the amounts have points vary depending on the color of the ball being plotted the 15 red balls on the table are worth 1 point each the yellow ball is worth 2 points the green ball 3 points the brown ball 4 points the blue ball 5 points the pink ball 6 points and the black ball is worth a maximum of 7 points in snooker the rules stipulate that you must hit a red ball on the table if you mash the pot a red ball you are then given a free choice to pot a different coloured ball to add more points to your total score if you successfully potted a color ball after a red you score the relevant number of points and the coloured ball is put back onto the table the entire process begins again and you'll be allowed to try and get another red ball into one of the pockets if at any time you fail to pass a relevant ball it is the end of your turn and your opponent will be given the chance to aim for a red ball so that they can score themselves once all the red balls have been potted you must aim for the rest of the colored balls in ascending order the highest score after the black ball has been potted wins games you usually played to the best of eleven 15 or 17 frames and winning more frames than your opponent wins you the game now that sounds a bit too simple there's more isn't there you guessed it there's a lot of things you cannot do in snooker you cannot touch any of the balls with anything except your cue you cannot pop the cue ball accidentally or otherwise you can't hit an incorrect coloured ball out of turn you cannot hit any of the balls off the table you cannot hit the cue ball twice in one stroke and you cannot move it touching ball these infractions result in a foul and your opponent will be awarded four points and the next shot files can also be awarded five six or seven points for fouls involving the blue pink or black balls respectively snooker is a very strategic game and that's basically the rules in a nutshell but there's a few other things you'll need to understand before playing or watching a game for example cannon a cannon is where a player hits the cue ball to contact more than one ball this is usually a strategic play to leave the cue ball in a favorable position for the next shot touching ball if the cue ball is touching another ball the referee will call touching ball you must play your next shot without moving this bulb otherwise a foul will be called against you snookered you can strategically hit the cue ball to make it difficult for your opponent to hit the next required ball when a ball is blocking a shot to the next required fall this is known as being snookered and makes the next shot very difficult for your opponent foul animus if a player fouls and fails to hit the required coloured ball the opponent will be awarded four points or more and has free choice to play the next shot where the ball lies or have the balls reset to the previous positions and make the offending player try the shots again free ball if a player fouls unleash the cue ball in a snooker position he is eligible to declare a free ball he can pause any colored ball and will always score one point for it however he will retain the next shot so this is usually a strategic play to stay on the table conceding if a player does not think that he has a realistic chance to win the frame or realizes that there isn't enough points on the table to get a win the player can't concede defeat and a new frame will start conceding is usually done verbally or by not returning to the table when it's your shot maximum break the maximum you can score in one trip to the table is 147 points this involves spotting a red then passing a black repeating this process 15 times and then proceedings pop the colors in order without fouling if you manage to do this this is known as a maximum break or a 147 and is the equivalence of a perfect game in ten pin bowling or pitching a perfect game in baseball it's not impossible just rare snooker is a popular game worldwide and once you played or watched a few games the rules will become clear if you found this video it's all helpful please like share and subscribe it takes me ages to make one of these things and good karma is very much appreciated be sure to follow me on Twitter also but in the meantime enjoy snooker

Jim Crow and America's Racism Explained



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warning if you do not know the significance of the 14th amendment watch at your own risk a 14th amendment video is linked in the description for your learning convenience hey guys welcome to hippies history we're gonna take a quick look at the term Jim Crow its meaning its influence its impact on the United States of America because you need to know whether you're a kid in school whether you're a lifelong learner or whether you're cray-cray and the Internet understanding Jim Crow should be a requirement of citizenship so let's talk a little bit about the origin of the word Jim Crow before we go into kind of the concept of de jure and de facto segregation jump Jim Crow was an old song and dance routine that originated in 1828 which was written by a white comedian by the name of TD daddy Rice who would perform in blackface basically to make fun of slaves feel about turnabout and do you though every time I feel about a jump Jim poo the term Jim itself is short for Jimmy like I'm going to Jimmy a lock and that was a crowbar so a crowbar in the 1800's was sometimes called a gym or a jimmy and then of course crow itself was used as a term for blacks as early as the 1700s in terms of jump Jim Crow farmers used to feed their crows corn soaked whiskey then the crows would get drunk and kind of dance around not being able to fly as the farmers you know kind of beat the crows to death so there's multiple meanings behind the term Jim Crow they all refer in a negative connotation to slaves and to freedmen to blacks and now we're going to turn that term Jim Crow into a system of racial oppression so Jim Crow laws and that would be segregation de jure meaning that by jurisdiction local and state ordinance and we're also going to talk about federal ordinances which mandate by law segregation now early on right after the Civil War that's where we're going to start in 1865 we still had those southern governments that wouldn't be controlled by kind of Confederate forces so those southern white democratic dominated legislatures would pass something called Black Codes right after the Civil War that severely limited the rights of these new freedmen and most of these Black Codes were based on vagrancy laws where if you were black you had to prove that you had a job and that job was recognized by whites and if you couldn't do that you would be forced into labor you could be put in prison and then kind of you know leased out to people in order to do job so many historians have called Black Codes slavery by another name but that's going to change during Reconstruction because starting in 1867 the republican-dominated Congress is going to basically mandate through the enforcement of the 13th and 14th and 15th amendment the military occupation of the south this is the period of history from basically 1867 to 1877 about a decade called reconstruction and during Reconstruction the Black Codes were eliminated and for the most part african-americans were allowed to vote and you did have African Americans that were elected to high office you had governor's there was a african-american senator there were african-american state legislators so it was kind of working but of course it's all being held together by military occupation and then there was an incident in Louisiana in 1873 called the Colfax Massacre and this is really kind of the southern democratic forces trying to coalesce around groups in order to take back what they see as their rightful place as leaders of these southern governments and in Louisiana at the Colfax Massacre in 1873 there was a group called the white League in this white League unlike the Klan which was kind of a terrorist under the ground organization the white leagues and the redshire it's groups throughout the south we're open about their you know opposition to african-american rights and they're wanting of power so it Colfax this white League basically attacked a courthouse that was being held by Republican forces and we basically have a mini civil war at Colfax we ended up having about 150 African Americans that were murdered maybe more we're not really sure about mass graves and people that were thrown into the river and such but that culminated in a federal trial with the conviction of some of those people who did that based on the 1870 enforcement act saying that you know Congress is going to have the ability to prosecute people that are violating the rights of freedmen in 1876 the Supreme Court comes out with a decision called United States versus Cruz shank where they basically kind of take the teeth out of the enforcement act by saying that because this white League was not a government group of a private organization the Enforcement Act didn't hold that private groups could discriminate you how to get them a different way you probably had to use state and local courts which we're going to work back then so that's kind of a breakdown of federal control over you know the southern governments and the the rise of what's going to become Jim Crow and then really it all falls apart in the election of 1876 you can watch there's a video on the compromise of 1877 you can click down in the description below to watch that but basically there is a deal in the presidential election where the Southern Democrats kind of give their votes to the Republicans in Rutherford beat Hayes them you'll Tilden the Democrat lost even though he was from New York that's another story but the the sticking point the compromise sellout is going to be the end of military occupation in the south by reconstruction forces that they're going to be able to own their governments again and this is really the beginning of the birth of Jim Crow and segregation de jure down south so let's take a look at some of the specifics of what Jim Crow laws we're talking about and how they're going to affect freedmen african-americans in the south as they seek to claim the mantle of the American dream now Congress wasn't done in the 1870s they passed something called the Civil Rights Act of 1875 which was basically kind of a reclaimed to the 14th amendment in terms of public accommodations that there would be no segregation in places of public accommodations like restaurants and hotels and trains and all of that kind of jazz but that's going to be torn apart in 1896 with Plessy versus Ferguson now Plessy versus Ferguson isn't based on schools even though Brown versus Board of Ed is going to overturn it it's really based on the concept of segregation by legislation and in Louisiana it was always illegal for blacks and whites to ride out the same car but the separate car Act of Louisiana kind of added coloreds to the mix they had a classification for mixed races and if you were one-eighth of African ancestry you were considered colored and you couldn't ride on the train so this was an organized effort by the black and colored community to fight this new law and Homer Plessy who was 1/8 black he was very of light complexion kind of walked onto the train one day and he had to announce to the steward of the train his racial heritage because nobody could tell just by looking at him then he proceeded to sit down and get arrested and him the spirit of Rosa Parks which launched the court case Plessy vs. Ferguson where the court is going to end up saying separate is equal that segregation laws are constitutional because they are still given african-americans I'm a seat at the table it's just a separate table and it's an equal table and of course we all know that not to be true so Jim Crow itself in terms of segregation de jure is going to be the laws that are passed which are going to segregate African Americans from whites so following Plessy versus Ferguson the South kind of has legislative and judicial authority to segregate and they're going to do that rapidly by passing laws Jim Crow laws which are going to segregate not only the public schools but libraries and hospitals and transportation and all of that jazz the other big huge segregation de jure peace is going to be voting restrictions and you would only have to look at Louisiana to see the effect that Jim Crow is going to have on voting rights we we talked about this before Louisiana had african-american representation they were being elected to high office you know all the way up through the 1870s by 1900 there's only a couple hundred african-americans that are registered to vote only 0.5 of the african-american population had registered to vote that could vote and in fact in North Carolina it was zero no african-americans registered to vote how did they do this they did this by passing a series of poll taxes meaning that you had to pay to vote and that got a huge majority of the african-american population from being able to vote because they simply couldn't afford it and then they had literacy and comprehension tests where you had to put you know pen to paper and prove that you were smart enough to vote now you might ask well there were certainly a lot of poor whites that couldn't read and write so how they get away with it they had something called grandfather clauses where if you could prove your ancestry and your grandfather voted that you were allowed to vote and of course African Americans don't have that luxury because of slavery so that's how they did it and now that is a humongous humongous thing because that means that if African Americans can't vote their interests are not going to be served they're not going to be in any type of powerful situation where their voice is going to be heard their interests are going to be served so they are literally going to get swept under the rug and of course we could also talk about the effect in terms of cultural social psychological effect on African Americans I don't even want to talk about all of the lost opportunity all of the poet's we didn't get to read all of the scientific inventions that didn't get invented all of the books that were written all of the songs that were never heard because of course Jim Crow is putting a kibosh on that because it's literally putting a plug in the in the hose of opportunity I don't know that analogy works but I think that you get what I mean now it's not just state and local that's the majority of it and we're not even talking about segregation de-facto just segregation by custom and of course in the south this means you know calling everybody sir you know crossing the road if a white person is coming at you there were even customs where if you pulled up to a stop sign you had to let the white guy go even if he got to the stop sign after you lie kid you not and this is of course not just regulated to the southern hemisphere of the United States we have segregation de facto in the north we have banking policies and housing policies and all kinds of different private customs which are going to put African Americans in a different category in the north as well but of course it's more widespread in the south we also have federal Jim Crow federal you know segregation and we're going to put the blame squarely on maybe one of the most racist presidents a Democrat by the name of Woodrow Wilson even though Woodrow Wilson was the head of Princeton in New Jersey and people tend to think of Memphis as a progressive he may have been a progressive in some respects but he was born down in Virginia you know before the Civil War so he's the first southerner to be elected to the presidency of the United States since the Civil War and one of his first things that he's going to do he's going to segregate the federal workplace he's going to segregate the army in fact if you were applying for a position in the Wilson administration you had to send a photo just to make sure you were the right you know skin color so Wilson and the Democrats are just as guilty as the Democrats in the south on a state and local level of kind of making this happen so we've talked a little bit about you know Jim Crow and in terms of segregation de jure and a little bit of segregation de facto there's lots more that we could talk about and of course the enforcement of at least segregation de facto and I guess segregation de jure is happening through the use of terrorist organizations like the KKK which are widespread throughout the early 20th century what you're going to use intimidation humiliation and violence to make sure that african-americans are put in their place that they're not fighting back but why don't we start talking about kind of the slow road to the end of this you know century Jim Crow system of racial so we're gonna get to the good stuff in a moment we'll talk a little bit about kind of the civil rights movement as most people understand it in terms of Martin Luther King and Montgomery and Selma and all of the laws that are passed but one of the earlier origins of the fight against Jim Crow and segregation occurs on the federal level and there was an incident in 1946 called the blinding of Isaac Woodward jr. where a member of the armed services an african-american Isaac Woodward who had just been honorably discharged literally a few hours later had an incident with the Sheriff Department where he was beaten to a bloody pulp where he was basically blinded and that caught the attention of the nation and there were popular songs written about it Woody Guthrie one of my favorite musical peeps wrote a song called the blinding of Isaac Woodward this caught the attention of the Truman administration who forcefully went after the guys who did this one of the sheriff's in the Sheriff's Department the local police they were then tried in a federal court in South Carolina where it happened and of course you know what happened they were all found not guilty by an all-white jury this probably changed harry truman's approach immediately after that he starts giving speeches to the n-double-a-cp he puts civil rights on the radar and he issues two executive orders 98 80 and 98 81 and using his power of the presidency he wipes away Wilson's action desegregating the army and desegregating the federal workplace that's really the first big movement we have in terms of knocking down Jim Crow and of course that's at the federal level the southern states are going to be much slower to respond so we're going to have to have darn it all a civil rights movement based on the concept of non-violence and of course most people associate this with Martin Luther King the the Baptist preacher from Alabama who's going to be the spiritual leader of the civil rights movement and of course that's going to really begin in Montgomery Alabama in 1955 in 1956 where Martin Luther King using what he's learned from kind of the teachings of Jesus and Mohandas Gandhi of non-violence to do the bus boycott which is successful it was successful they desegregated the buses they showed african-americans and progressive whites that they could use their power of citizens to boycott and to engage in civil disobedience in order to change the law so that's eventually going to lead of course we all know about the I have a dream speech in Washington in 1963 there's lots I'm skipping guys by the way but that's going to result in the 1964 Civil Rights Act the 1965 Voting Rights Act court cases like the 1967 loving versus Virginia Court case which is going to legalize interracial marriage throughout the south and we're going to slowly start chipping away at Jim Crow through federal action and through Supreme Court decisions not to mention the biggest one that I skipped which is the reversal of Plessy versus Ferguson in the 1954 court case Brown versus Board of Education where the court is going to rule down that separate is inherently unequal which is going to begin the process of desegregating schools throughout the south not private institutions that's going to have to happen through federal legislation kind of a repeat of the Civil Rights Act of 1875 in the Civil Rights Act of 1964 which is going to use the interstate commerce clause to kind of broaden the scope of ending segregation so it's including public accommodations hotels restaurants and such like that that's going to be challenged in the heart of Atlanta Motel versus United States where the court is going to upheld the Civil Rights Act of 1964 really striking down segregation in the southern hemisphere of the United States and of course that's going to be followed up in 1965 when King and the civil rights forces focus on voting rights they get the 1965 Voting Rights Act which is going to basically put voting registration and elections under an umbrella of federal oversight to make sure that these places that are discriminating aren't doing that as much and African Americans are going to be able to vote again and start to participate in the American democracy in 1968 we get the Federal Housing Act which is of course addressing the housing discriminatory practices that are occurring out throughout the United States and that's pretty much the end of big federal legislation to attack the heart of Jim Crow so there you go guys that was quick and simple we're giving you really the direct nation of Jim Crow there's so much more to learn and to understand which I highly encourage you to do hopefully you wrapped your brain enough to understand the significance of Jim Crow and the impact it had on the United States for generations to come so there you go guys getting up for the learning we hope that your brain is a little bit bigger than when you started before we certainly hope that you understand the scope and impact of the system of racism known as Jim Crow on the history and the development of the United States of America so I'm going to say because I always say it remember it because it's true where your attention goes your energy flows we'll see you guys next time as you press

Philosophy Lectures 01.01: Laws of Nature



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All of these lectures take place on the Atheos discord server. Atheos is a discord primarily for discussions on philosophy of religion as well as formal debates on atheism and theism. We also welcome discussion on other fields in philosophy as well as math and science.

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all right he's here so I think that's usually double in size really quickly yeah thanks I guess I'll start now so actually tiny if you have anything else you need to let me know but with that said I was gonna do a short lecture on laws of nature which might not seem like a very interesting topic but as it turns out there's a lot of discussion on it in metaphysics and philosophy of science and as it and I was mentioning before a lot of the debate on it actually ends up relating to a lot of other fields that you probably wouldn't expect like freewill the conceptions of incompatible is incompatible as free wills and different kinds of compatibles free laws like david lewis's they're very much related to how we view laws of nature and similarly to determinism and for people here who are interested in philosophy of religion there are entire books related to God and sort of laws of nature and in fact there's a there's a famous one I was mentioning before by Foster which I'll talk about later there's also a famous paper by um Nancy Cartwright where she basically argues that if we're if we take a specific view on the laws of nature that means God has to exist there's no either love the laws of nature's don't exist or God doesn't exist or presumably if we take the laws of nature's as being some certain way it would be a contradiction to say that God doesn't exist which is it which is kind of a controversial claim but there's a whole dearth of arguments with respect to the laws of nature that end up relating to a bunch of other fields so I think there's probably some utility even if you're not super interested in metaphysics or you know philosophy of science there's some utility to learn about the topic in terms of just other fields and also because it's nice to you know be knowledgeable about other things that you might not you know be super interested in so I do want to make a few notes before I start so firstly I will be going in some detail on specific views and arguments and if I ever found any point you know you get lost or you have a question just let me know and either in chat I'll be looking at chat and or even if you want I guess you could unmute and just ask it and then toward the end I also have just a period where you can ask questions another thing that I will mention is that toward the end I can provide like really famous papers or articles or books even on this topic and I will say that when you when you go through the literature people use like a bunch of different terms or the same thing and that can be really confusing so sometimes you'll hear people talk about systems view human sirenians Ramsey Lewis regularity theory and a lot of those times a lot of those things are either very related or basically the same thing and so it can get really confusing with someone saying oh yeah I prescribed to Ramsey's view or Lewis's view and though they're basically very similar and similarly you know people will say oh you know this is Armstrong view or drets Keys view the universals approach the anti human approach and they're all really the same thing so just for for ease I'm going to be using a kind of a singular set so I don't start you know just throwing around different words and assuming you know what they mean now I'm gonna be I'm gonna try to be very careful and sort of defining the words I use and assuming you know you don't need any background knowledge on modality or no logical necessity or anything like that I think that's all in terms of just kind of booking keeping stuff in terms of you know actually learning the laws of nature I want to kind of construe the debate in in terms of two questions and they're absolutely related but these are the two main questions that philosophers care about when it comes to laws of nature the first one is for the lack of a better phrase what is the nature of laws of nature we often you know in science class you probably heard about laws of nature you probably have a kind of prima facie conception of what they are these sort of universal kind of rules that govern the world some of you may not agree some of you some of you might take a different approach oh they're just descriptions they're nothing more there's no some grand you know rule that governs the world but the question that I'm sort of bringing up and that people have debated since I mean for a very long time actually is what exactly is it that we're referring to when we talk about laws of nature what are they if anything and some people will say they're these sorts of real kind of governing things that actually control the world some will say they're nothing like that they're just mere our best descriptions of the world and some will actually go full-blown anti-realist and say the concept of laws are eaten are not even coherent and I'll go through all the different kind of views on this and then the second question is there's a whole literature on this as well is what are the kind of sufficient and necessary conditions for me to be able to say that something is law so I might have two propositions and I want to be able to say this one is a law of nature and this one is it and at first glance that may seem really easy but actually as it turns out is actually very complicated there's a lot of little tricks and issues we have to sort of untangle before we can even get there so in terms of this lecture I want to kind of touch on both and give you guys kind of the overarching views of the you know famous philosophers who've tackled this problem and there's actually a lot of really famous philosophers who have actually you know discussed this problem the classic one is David Lewis who's everywhere anyone who works in analytical philosophy knows and maybe worships David Lewis he's an enormous figure Armstrong is another one who has a kind of differing view and he's he was also a huge and analytical philosophy on people like to Lee and wretzky and all these people have kind of huge contributions and if you if you know philosophy of science you probably know van Franzen who's famous for his kind of anti-realist views about philosophy science and he also has a lot of contributions to this so the goal here I think is to kind of sketch out the different views and then give kind of the arguments people make against each one and then I guess on your own you can kind of figure out which one you think is is the most compelling so I think I'll start with the first question which is what exactly what the hell are we actually talking about when we talk about laws of nature and I referenced before that in everyday use many people have this conception that these laws of nature's are like the kind of fundamental rules that the world follows and that they have real sort of causal power so that when I jump up and I'm pushed down by gravity there's a real force a law that forces me not to be able to you know go up high up and keep floating up into the you know space or whatever and so this view is generally speaking considered a kind of universals approach and someone like Armstrong holds something like this and they're all they're also oftentimes called nonhumans so I'm gonna step back and you know I don't want to throw a bunch of like language and lingo and start with first of all what humans supervenience is and human supervenience is obviously named after David Hume but it's not something David Hume specifically created it's actually a creation of David Lewis and the idea of it comes from there's a very very famous collection of papers by David Lewis it's in this is the second volume of that collection and he defines it and he says that it's he names it in honor of David Hume and he says that and actually I think let me see I have the paper right here so I'll just I'll use his words so I don't want to you know misinterpret or give you guys the wrong idea since you know it's his own words so he says humans supervenience is named in honor of the great earth sometimes you'll see great instead of greater but that's the actual cause greater denier of necessary connections she David Hume that'll explain what he means by this in a second he says it is the doctrine that all there is to the world is a vast mistake of local matters matters of particular fact just one little thing and then another and then I'll skip a little bit and then he says and that is all there is no difference without difference in the arrangement of qualities all else supervenes on that so I'll explain what this means David Lewis thinks that the only things that exist on the fundamental levels are particular states of affairs matters of fact there's no when we think about the world we almost all intuitively think that there's this world and then there's these sort of natural sort of necessary and kind of universal relations between parts of the world so like when we go back to laws nature we think that there's something that governs sort of the what happens in the world but David Luce rejects this completely he says the only things that happen are in particular specific parts of space and time there's only particular matters and states of affairs so there's no universal or necessary relations among them so the way he puts it is instead of looking at the world as a one kind of kind of thing united by these sort of laws and stuff all the things the only things that exists are little space-time points and what happens there that's it and in and as it turns out if you take this view of human supervenience this rules out a lot of things first of all it clearly requires us to be physicalists we canwe it clearly requires we can't have things like you know souls or certain kinds of dualism are completely ruled out and similarly it's very strongly against necessary facts that kind of override all everything so he's clearly very against this and as you can probably guess this goes wildly against what we think of laws of nature because like I said before many people take laws of nature as being these kind of overriding governing rules and David Lewis clearly rejects this so the question then and I should actually mention that the reason he calls it he calls the his view humane suitings is an honor David Hume and he mentions that he's the one of the great deniers of necessary connections what he means as David Hume is really famous among other things in saying that he was very skeptical of any talk about necessity so a lot of philosophers will discuss necessity and it give me different things but one simple way of looking at it is something is necessary if it must obtain then in every possible world it must be the case and David Hume is really skeptical of this kind of RAD he's skeptical of our ability to see what is necessary so for example very often someone will say the law of identity is necessary and I say why and they say because it's inclusive inconceivable that there's a world where the law of identity isn't the case and David Humes whole point is I do I don't agree I can imagine literally nothing I can imagine that nothing exists and that nothing is necessary so why should we care why should we think anything's necessary at all and that's what he's referencing and David Lewis clearly agrees he's very skeptical of these kinds of necessary truths that kind of permeate everything in space and time and he thinks that everything gyah that happens is just on a particular specific spatial temporal point that's it as he says is just a mosaic of local matters of particular fact just one little thing and then another and that's it so this is a pretty stark and kind of I don't know I don't know if I'd say controversial but it's it's kind of a big claim and it goes against many of our intuitions so the question then for Lewis is what do we make of laws of nature clearly they're not these sorts of grand statements that govern the world they must be something else and that's where his view of laws nature comes in and this is one of the there's two big main famous views on the laws nature and David Lewis's is one and he's in the human camp and he says this he basically treats the laws of nature as being a kind of best deductive says the axioms of our best deductive system so I'll explain what that means basically this idea actually as most people will say that Ramsey in early or the late 1920s came up with this idea and he was basically saying that when we define law hood all we mean is that if we knew everything and we wanted to systemize our knowledge as a deductive system then the general axioms in that system would be the fundamental laws of nature so what he means by that is let's say we have a book that God gives us with every fact of the world now obviously this book is going to be enormous and it's basically impossible for us to go through and read and understand everything so God clearly clever and so what he says is look I don't have to list out every single thing what I'll do is I'll just create a deductive system and I'll list axioms and whatever you know you can deduce by yourself and that's exactly what Ramsey and David Lewis treat the laws of nature as they say there there's these sort of regularities we see in nature and what we want is to create a system and the best system and I'll explain what they mean by best system is the system that is both it that sort of optimizes simplicity and strength of our formal system and the axioms of that system are just what the laws of nature are so just a quick and I did this yesterday as well so I briefly explained what strength and simplicity here means so when we talk about you know you need to even though any sort of logic or math for this but you see this a lot in math where we'll talk about formal systems so we have these axioms we have these rules of deduction and we can create new we can prove new propositions and there's these two competing notions of strength and simplicity so formal system is strong if it can prove a lot of things and a formal system is simple if it doesn't have many axioms and these are as I said sort of counteract so if I have just one axiom there's probably not much I can prove on the other hand if I take every proposition as an axiom I can prove literally everything right that's an extremely strong system but there are a ton of axiom so it's not simple so David Lewis says look we have all these sort of facts about the world what we're gonna do is we're gonna try to create a deductive system that sort of optimizes simplicity and strength and then the axioms of that deductive system are simply what we call the laws of nature now this seems at least at first glance to be a nice kind of little answer to this because now we have kind of a it's not a constructive proof like if I gave you two propositions without knowing the our best deductive system you couldn't tell me which immediately was along which wasn't although we can maybe use other notions but it does sort of answer some of our concerns about laws of nature it does give us an answer of what they are there they're basically the actions or a detect system and it also gives us other accounts in terms of say counterfactuals and the like now the problem with this view that many people have is that it seems that it almost makes lots of nature's mind dependent it B is basically saying that there's these sorts of regularity to see nature we create a system and ax injures learn at laws of nature and people might say well how are we supposed to decide which deductive system we like the most maybe this one is a little simpler and this one's a little stronger how do we decide and there's you know there's a there's a few answers David Lewis gives but he hasn't really taken as a serious threat but I think the more problematic portion is not necessarily the vagueness of you know simplicity and strength there's mathematical terms of beings for that it's rather that their mind dependent because many people don't think the laws of nature mind dependent for example if I destroyed every you know living sentient being many of us here presumably would think that the laws of nature would still exist they wouldn't just disappear and so this approach might be very kind of difficult to accept if you want to have this kind of grand mid a physical role for the laws of nature now to sort of contrast this I'm gonna go over sort of the the view that I mentioned before by Armstrong which is kind of how many of us naturally think of the laws of nature so he rejects this humane approach and he takes an anti humane approach he thinks that the laws of nature are real metaphysical rules that really govern the world and he says that and now I'll talk about this later when I when I talk about the second question he says that what makes something a law is something called a necess it a tional a ssin and it's it's actually kind of big what exactly that is if you will dissipate what it is but the intuitive notion is that something is a law of nature if it is necessarily the case and not necessarily in the sense of every possible world but in the sense kind of a weaker necessity now I'll give you an example so it's more clear what I mean let's say I say there's you know three people in this room right now that's true and it's true everywhere in the universe that there's three people in this room right now but no one in their right mind would say that's a law of nature right and you might ask why is that not a law of nature whereas something like nothing can move past the speed of light is the law of nature what's the difference and most people say well one is just an accident you know it just happened to be the case that there's three people in the room right now but it could be the case that there's four people in the room and whereas it seems to us that the law the sort of moving past the speed of light is much more kind of necessary it seems to me much more fundamental and not just a mere accident and so that's where Armstrong's view comes in he says that laws of nature are simply things that hold this sort of necessary relation and I I do want to make it clear that he's not necessarily saying that the laws of nature themselves are actually necessary in every possible world there are views like this and I will talk about them but specifically this sort of the view him and read see and truly they all hold the basically the same view none of them necessarily believe that they still think that there's some contingency involved is just that within our world if something must necessary medicines to take another that's a law of nature so for example if it turns out all X's must be wise and that's necessary in our world then presumably he would argue that that's a law of nature now one argument that David Lewis makes against Armstrong is saying that when he talks about this neces necessary sort of relation he's really vague he kind of talks about types and tokens he kind of mentions other things but he's never super exact about what exactly it is because if he's too exact sometimes it almost seems like he's going into a full-blown nest arianism which I'll explain what that is and sometimes when he's saying kind of being a little too vague as well it comes off as being just very trivial like he's saying nothing that's actually interesting at all and sometimes it's what he's saying is basically what David Lewis is saying so the a classic argument against his view specifically is that he's very big and keeps shifting back and forth about exactly what this relation is but in terms of sort of the classic arguments against these two positions there's a few really influential ones so I'm going to go back to David Lewis's view which is basically this kind of systems approach where basically you know we take a system best axioms those are laws of nature there's something dead and a good way to kind of contrast these two views it seems like an example and this is a very fancy famous example in the literature this comes up all the time suppose we have two worlds and in both worlds there is they're there in terms of non law matters they're the same so both worlds are just let's say one particle traveling at some constant speed that's that's all there is to it now if I take David Lewis is humane approach or human approach excuse me the laws of nature in both of those worlds are the same because presumably they end up with the same best deductive system and they both end up with the same axes because the non law matters of fact are the same but that doesn't necessarily need to be the case with Armstrong you for example while they may look the same they might actually have different laws of nature for example one may have just kind of Newtonian style law of nature where without anything stopping it this lone particle will you know travel this rate at this you know speed and that's it but in the other world it might be some completely different law of nature and so the laws of nature are different whereas in David Lewis's approach they must be the same and that's what sometimes you will call a supervenience kind of argument so moving kind of along the same path there's a very famous argument against david lewis's approach that um I think Uli is probably most famous for although there's a few other people Peter Menzies makes this argument and so the argument basically goes that imagine there's two worlds similar to what I just said before and let's just say that in both worlds there's these particles will call them exes and there are these fields let's call them wise and as it turns out in both worlds it never it's never the case that X is inter wise the the X particles never enter the Y fields but suppose that as it turns out one of the worlds has the law that when in X particle in terms of Y field it has an up charge and or up spin rather and then in the other one it has a down spin now that never happens right so they're they're indistinguishable in terms of the non law states of affairs but if a word to be the case that an X entered a Y in one of them it would have one spin in the other and it would have a different one the argument is that if sort of David Lewis's approach is true then these must have the same laws of nature because we're just looking at what actually happens but clearly they don't have the same laws of nature so there's clearly some sort of contradiction and so taking this human approach is false we're fundamentally missing something important about laws of nature now there's there's a lot of famous kind of responses to this argument one by a philosopher named Bibi she argues that basically this is just a kind of false dilemma and that you're just assuming that the laws of nature you're basically convincing people by using our you regular intuition about laws of nature and then tricking people into saying oh it must be the case because we are also kind of up used to our views of laws of nature being these kind of governing entities and that in reality there's actually no problem here because if the laws of nature are really just our best axioms for our best detector systems then those two things could in those two different laws nature's wouldn't be laws of nature's at all so it's a false dilemma and then of course there's the whole fight about that but that's that's one classic kind of back and forth that's going that's sort of happened with Dave and Lewis's view in terms of Armstrong view the kind of more natural view that I think many people into we hold there I've already brought up one kind of famous kind of argument that is too vague and that didn't speak ashed out more but there's also something I want to talk about in terms of kind of an argument almost from like queerness and if you if you've know anything about say Error theory you've probably heard arguments for queerness and the idea is that if we really do think that the laws of nature have these sort of special properties that govern the world they're extraordinarily strange what are they even right they're clearly not like entities we're used to like atoms and chairs and so on so what actually are they what's happening and this is actually a serious problem because we might also further ask in a virtue of what do these laws of nature obtain and this is this is a problem because if they all the laws of nature really have these sort of special power and influence why are they there what what in virtue of what do they obtain now the classic answer that many people have given is God and I mentioned this in the start where certain people will argue the only good explanation for why there are these laws of nature's must be some even further kind of explanation in terms of God there's there's you know the entire books written on this I don't want to get too deep into this now some people don't obviously don't want to accept this and so they say look we might be able to kind of appeal to some ultra necessary facts of in God but why don't we just say that the laws of nature themselves are necessary in that and I mean here necessary in a strong sense where every possible world has the same set of laws and you'll sometimes hear this as being called lonnis karien ism and this is kind of a strange view because this also goes wildly against our intuitions when we talk about just you know regular you know laws of nature it doesn't seem insane for me to say oh what if you know the speed of light was different or that something could you know maybe go past this veto a little bit there doesn't seem to be any prima facie sort of insanity for me to say that but of course people who are along as Koreans will say oh no no what you're doing here is you're just saying that some sort of conceivability implies possibility but I reject that you know just because you can conceive that the laws of nature are different doesn't mean that they could be different that's just a mistake and many people sort of reject this kind of intuition but the problem here is that many long assess Aryans also want to be able to keep sort of counterfactuals and ability to discuss counterfactuals in their kind of arsenal so it makes no sense for if you know you came up to me and you said you know why do you think the laws of nature are necessary I think they could be different I said oh no no no you're just using conceivability to entail possibility that's nonsense and you said okay okay and then in the same breath I started doing the same thing with without with with things that are not laws of nature so I say oh you know you know if this had happened then it possibly this could have happened and you say wait why do you think that and I say well I mean that's that's obvious right like this chair could have been two feet instead of three feet away from you listen what's the problem and you say well you're doing the same thing you're just using conceivability as possibility why can you do it for regular things but I can do it for the laws of nature and that's a serious problem and that's that's there's a lot of discussion on why we can say this about laws of nature but not other things and if it does turn out we're wrong then this man collapsed into full-blown kind of necessary anism where everything every proposition is necessary that is you know the chair next to me is let's say two feet away if it were three feet away that would that's just completely impossible there's no possible world where the chair next to me could have been one foot further away than it is now and the vast vast majority of philosophers despite what seemingly is popular in discord but among actual philosophers nest arianism is extraordinarily unpopular and many who are worried that if we're to sort of gun ho with longest Arianism it might collapse into full-blown necessary anism so that's what another argument people have made in terms of why we have to be careful about this sort of necessary relation in and there are actually other views that people have sort of put forward as well there's a famous guy named bird who who has something called the dispositional ISM about laws of nature and he technically Falls so like like I said before there's there's generally two classes of people there's to meet a humanist and then there's people who reject humanism and the general distinction is basically about what exactly laws of nature are right so if I'm like I find someone like David lowest receiving David Lewis then I don't think the laws of nature hold this real source special role I think they're just descriptions that that's all they are whereas if I reject that I think they have a real sort of important role and under sort of this non humanist view we have people like Armstrong and truly but there's another person that I just mentioned Byrd who argues for something called dispositional ISM which I don't want to get too much into this is a very weird idea it's basically he rejects this sort of inference we all make that basically objects have these properties and that laws sort of affect these properties basically he thinks that if flaws are powers then powers are basically thrust upon properties by you know laws of nature and then in different worlds where those laws do not hold those same properties will not have the powers they have in this world and so the disposition list here regards properties as having sort of no nomic and causal powers essentially so which is really strange most people don't think that the property of some object actually has you know causal power but they do and so this this kind of ties into the to the position to get too deep into that because I feel like it's very very strange and most people just think they either get completely lost will be bored but I will say that it does it does basically collapse also into a very kind of necessary view of a lot of things and but although Byrd argues that it's not an issue at all he doesn't care but many people are very averse to accept that for that reason so in the beginning I kind of mention that there were two questions and sort of I kind of each gave a quick survey of the two big sort of positions on the laws of nature Armstrongs versus Louis's although to be fair there's it's not even fair really to say it's armstrong's because like I said Julian threats both came up with it basically at the same time so sometimes the literature you'll see it it's like the truly dress Armstrong view or maybe just the dress view or whatever but nowadays I think it's mostly just freeze called Armstrong view versus like the David Lewis or the ramsey who who's a ramsey for the record was like a mathematician who ended up dying really earth-like early like in his 20s so those are the two flicks that's that you can really think of it as a kind of debate between those two positions though there are other positions and one that I will also briefly mention is a full-blown anti-realist position someone like bossman present beliefs something like this where he thinks that even though people who hold to David Lewis's view think that laws are kind of not really these grand things they still they're still they still have used they still have utility they still are things we can talk about whereas more full-blown anti-realist think the entire notion of laws is kind of incoherent or use completely useless and that they don't exist simpliciter there there there we shouldn't even really worry about them as much as we do and that we were making a mistake when we think about science as being kind of discovering laws of nature and that there's no actual such thing at all up so now in terms of the first question we can take you know either view or another view but in terms of the second question while the well it's certainly related to the first one we we still need to flesh it out a little bit more so just just to recap the second question was the first question was what exactly is the nature of these laws that we're talking about the second one is let's say we have a theory about the nature what exactly is required for something to be long and I and some of these views already answer that so for example Lewis's view says something is a law if it's in our best adductor system it's an axiom of that system but it we we still need to kind of flesh out some more what exactly you know might happen let me start from a prima fashion notion of laws to a more kind of serious notion so let's imagine I just didn't say anything about David Lewis or arm stronger burg or any of those people and let's imagine that you just came in for the first time and I asked you what what's required for something to be a law of nature so like if I said tell me those specific things that I can use to be able to say oh this is a law of nature and this is not a lot nature now most people would probably say like something like oh that's easy something is a law of nature if it's true everywhere in the universe right and like I already said in an example that doesn't seem right because there are certain things that are true technically everywhere in the universe but they're clearly not laws of nature so for instance the figure out the example I use I think in my in this room there's three people that is true and it's true everywhere in the universe that in this room there are three people but that that's clearly not a law of nature right so we might say okay okay how do we do this instead of just everywhere in the universe let's add time so let's say if it's true everywhere and at any time in the universe then it's a lot nature and in in terms of in terms of sort of our theories of time this might work so certain theories of time it won't work but I won't get into that as a whole different topic oh just grant that it does work that this extra edition kind of fixes our problem and we have a good definition but it as it turns out this is still not sufficient and there's a very famous example that you'll often see in the literature I think I don't know who came up with it may be bird came up with it but the idea is basically let's let's imagine the two propositions so in one proposition we're wondering is it a law of nature that there's sort of I think uses like some diameter of a gold ball in the universe and as it turns out no one has ever creator of no one or no nothing sort of accident has ever happened where we end up with a large ball of gold so if that's never happened anytime any space in the universe right and the other example uses uranium and we know this can't happen because it will collapse your uranium you can't by definition of our best physical and chemical chemistry theories you can't create a ball of uranium that large but in in principle you could for gold it just never happened right it just our universe let's say from the beginning to the end of it assume there is an end or a beginning let's say no one ever it just never happened it could have happened but it just never did so technically it does fall under our criteria that it has to be true everywhere in space and time so that no one ever created or never happened that a gold ball that large ever were obtained but there still seems to be something fundamentally kind of at odds here because one clearly seems like a law of nature or at least it's more of a law of nature than the other one or the uranium ball can't happen in principle whereas the gold ball could have happened it just didn't so this is very similar to what I was talking about in terms of sort of accidental person is sort of necessary occurrences so we need to kind of further kind of add on to our definition and most people here will kind of do this with counterfactuals they'll say well right so it as it turned out there was no gold ball that size but given the same laws of nature it could have been the case that there could have been a ball of gold that large whereas in our uranium case that could never have been the case because we know from you know how how unstable certain elements are unstable and if we try doing that it would collapse it would never work right so that's the difference and so as it turns out most people kind of agree with this but as it turns out there's actually a ton of extra things that we might need so for example there's some obvious ones for example almost everyone agrees that laws major have to be true right there's no there aren't many people who think that you can have a law of nature that's false although I will say that there's a there's a famous paper by Nancy Cartwright I think I mentioned her before she always has these hot takes where she says that laws of nature are not actually factual and I'm not gonna get into what she means is it's a mess but she argues that laws of nature are just kind of representations the only appeal to something they don't actually state it as a fact or something like that and and so I guess that technically I should mention that because there are people who make that claim but for the vast majority of people they think that laws of nature are factual they're truths they're not sort of they can't be false but another thing is that they also need to be factual in the sense of not logical so if I say you know the law of identity is true most people do most people are going to be somewhat like if we're gonna take that as a law of nature generally we talk about nature we're talking about sort of spatiotemporal rail of relations and the like and another thing that you might you might wonder as well okay so we have all these kind of caveats and all these requirements for what exactly is a law of nature but are there sort of are there any other ones we need and that's kind of where the debate is because some people will say no no that's totally sufficient we don't need much more other people say no there's these examples for example sometimes people bring up proper names sometimes will people bring up sort of conditional and claims and like and so that's the entire kind of discussion on that though I think it's to be perfectly honest I think it's rather boring and so I really want to get into that too much but that's kind of just a very quick overview of the second question that is sort of what what is it what's required for something to be a law of nature and the debate is on kind of the fringe views not the obvious ones like like I said most you will agree that laws of nature had to be true where the debate is are these a little more minor nitpicks about what's required so actually I don't know how long I've been going when did I start you know in about 40 minutes yeah okay yeah that's probably 6:20 okay yeah so I don't want to go keep going too long because I think I wanted to do like 3540 minutes and then maybe let questions let people ask questions because I don't want to keep rambling on about like these really specific things but yeah if you have any questions just like unmute if you can or just like type it in yeah go for it you while no questions okay do we want to ask the questions in the though where does it matter is can you amou I don't know if you guys have the ability to meet if you can't just under your just ask it what's my position uh you know I I don't know if I have a position I think intuitively I think like many people I think and I actually should mention that I approached you to mention this most philosophers are reject you mean a humane tip can say jhemini ism so they don't accept something like David Lewis's view at least if we take philpapers seriously it's not like a huge discrepancy it's not like 90 percent rejected but the the most of them are anti Hume and so in terms of my own views I probably I don't think I'd probably lean more toward Armstrong's view than Louis's view because just this idea that all we're doing when we talk about laws of nature is a kind of like nice optimization problem it just goes way against what I think naturally many people think and of course you know Lewis would say who cares what you know people intuitively think but if I had to pick one I'd probably go against I would probably go against Lewis's view and I will say that Luce is not the only person in that camp there's other kinds of theories his theory is usually called system theory sometimes redundancy theory or never done see sorry the hell is it called regularity theory right and so there are other views that are not just David Lewis is under the sort of human camp but he's the classic one and he's probably considered the most successful at it because a lot of them end up being they're called quote unquote naive theories and they collapse into some sort of triviality so he's generally considered the best of that camp and I think even today he's he's considered like people still argue about his view versus other more modern views so I probably probably say it's fair to have him as the sort of forefront of that yeah I probably just have to say I might lean against it you have anyone has questions or if you want me to like be more specific about something let me know I was trying to avoid going too deep and using too many too much lingo but if you want I wouldn't mind you I'm sure he'd want you to explain what's wrong with Vanessa that arianism where's Hui I don't think he is he I think you guys I don't think so well I mean that's I think I can answer that but I feel like it's I think I think everyone's heard probably might take some nest arianism I think it's just the first problem with it is just that it seems extraordinarily unintuitive and and that's actually that has a that has a importance in philosophy at least nowadays like I was mentioning Lewis's view and modal realism he's famous for this many people didn't even try really arguing so super against it they just said it's it sounds ridiculous it goes wildly against what we believe therefore why should I believe it and people do the same kind of thing with nest arianism they say you know if you're really telling me that I couldn't have worn a red shirt versus a blue shirt today it's just completely impossible there's no possible world where that could have happened I'm gonna be kind of skeptical that I should take it seriously that's basically what most people do although there are technically some more formal kind of arguments against it in terms of law nesset Arianism I kind of mentioned that some people are worried first of all why we should even think this and you know some people have called the kind of an ad hoc kind reaction to being able to ground the laws of nature because like I said if we really do take the laws of nature as being these kind of real metaphysical important things asking what we're you know what are they where they come from if anything why are they there those kind of questions brings up a lot of problems whereas under David Lewis's view there's no problem whatsoever right if I just say they're they're just kind of a mind dependent kind of best explanation on best explanation rather best sort of axiomatic deduction of what we see there's there's no question of you know what what what grounds them in virtue of what do they obtain or anything like that it's just very obvious that's just what they are they're just axioms we've used to kind of describe the world best that's all there is so that's one argument against sort of the any credit kind of nest Arian view so I see billow joined that's good you just missed an entire lecture yeah if you guys have any questions let me know otherwise I don't know if I I feel like I covered what I wanted to there's probably some stuff I could talk about in terms of induction because the induction comes up quite a bit but I think maybe I'll leave that for a different different time Dirk went you wait where did you pick me I'll see it weekly lectures texts Oh oh yes sir I see that okay yeah I think I can go over that again so the argument is basically to start from the beginning as I mentioned there are the idea of Lewis's kind of systems theory is that when we have two identical worlds and I say identical here in terms of donned law things so like forget there any that forget that any laws exist just imagine there's kind of these sort of particular facts that matter if they're the same in both worlds they're identical in that sense let's say you know spatiotemporal or whatever then on david lewis's account they have to have the same laws of nature because remember all with all the laws of nature are under his view are just kind of our best deductive systems and the axioms i got repeated like a million times at this point so I'm just kind of sick of saying that but hopefully you understand what I mean by that so presumably we would have the same deductive system in both we'd have the same axioms in both and so they have the same laws of nature now the argument that I mentioned that Carol and to Lee and those people make is that suppose we have two worlds that are as David Lewis as I just mentioned the same in long law matters however in one in in in one world something that actually never ends up happening has something associated with it so like the example I used was imagine there's the X's and Y's and as it turns out in both worlds X's and Y's never interact but if they did interact then in one world x and y interaction would have sort of a as a consequence and the other one would have B as a consequence although they never do react right we have to be really careful about that as it turns out these two worlds never have an interaction between X and Y's and the argument is that according to David Lewis's view if we take his new seriously those must have the same laws of nature but we just we can imagine a case where they don't have the same laws of nature where one even though it never happens if an x and y interacted it would lead to a and the other one is late to be so they don't the same laws nature's so there's clearly something we're missing here and then the counters that the counter response I gave was that the people will say they oh you're just kind of presupposing your view of laws of nature under our view there would be no law of nature that explains it cuz it never happens so it makes no sense to say there's a law of nature that explains something that never occurs because that's not what a lot of nature even is according to David Lewis so all you're doing here is just kind of pushing your view on us and saying oh you can't explain this so you know your view is wrong but you know that's clearly a mistake and on this front I think I think both views have some point but I do kind of agree with the counter response that they are kind of presupposing their view of laws of nature and then saying oh why can't you explain this even though under de luces view it's not a law of nature at all so Quentin did without sort of going to the latter part the first part kind of makes sense what the argument exactly is okay good if you have any questions let me know about it I can also send you like the the paper I mean the bigger they put it probably better than I do beanie has a good paper on this yeah any other questions all right well okay you guys like a minute or two if not then thanks for coming and hopefully you know a little bit more about the raging debate in laws of nature

Slavery – Crash Course US History #13



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In which John Green teaches you about America’s “peculiar institution,” slavery. I wouldn’t really call it peculiar. I’d lean more toward horrifying and depressing …

Plato's dialogue, the Symposium (part 3) – Introduction to Philosophy



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We finish our 3-session examination of Plato’s Symposium by examining the last two speeches, focusing primarily on Socrates’ speech — which turns out not to be a speech at all, but dialectical questioning of Agathon, and recounting a set of dialectical conversations with the philosopher of Love, Diotima. Alcibiades’ speech praises not Love, but rather Socrates( who Alcibiades is in love with) and discusses his the difference between his inner character and external appearance.

Two key Platonic doctrines about Love are discussed in Socrates’ recounted conversations with Diotima — the ladder of Love, by which we ascend from bodies ultimately to the very source and epitome of beauty itself; and the notion of Love as a desire to bring to birth in the beautiful, and thereby participate in immortality

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we're finishing up the symposium and we've got two more speeches to go there's a little bit of you know back and forth dialogue that's kind of interesting in there at the end of the symposium this particular good well the last will hint about what's going on so we'll see if we can get to that but this is the main stuff Socrates is talking for quite a while and this is really the core symposium the thing that most people remember about the symposium 20 years later is Aristophanes speech and you know people in half and your seem to be searching for your missing you know lost self and all that sort of but Socrates speech is the one where you really get the most important material and then it looks like things have come to a close and what happens this guy Agathon shows up drunk with a little bunch of friends comes in Boston to the party and you know all sorts of interesting stuff and Sue's and then he gets a speech a typical Agathon everyone has to make exceptions for him don't we do a speech exactly on the topic that who else was and he says I'm not going to give you a really good speech I'm just kind of jumping things up because I'm drunk I'm gonna talk about Socrates instead and it is connected with love why because the Agathon what he's in love with Socrates man so much so that Socrates who's Athena old guy and the tough guy has to tell Agathon you got to get in between the two of us because Agathon you know he's always trying to get get after me so it's kind of a funny thing you know a lot of funny images of us and well we'll get to that the big stuff so Socrates won't give a regular speech and this is pretty typical Socrates one of the things that here's here's a term that we use a lot when we're talking about Socrates and I think it has a bit of a different meaning these days when something is ironic or a person is being ironic what it what does that mean – usually we don't really talk about people being ironic right yeah situations or things that people say and there's usually like some sort of bitterness to it like look at that the guy who committed all these crimes stealing cars his own car got stolen isn't that ironic that's a different sense of irony than what Plato is talking about or or or Socrates does with Socrates he'll think of irony as having like two layers there is the lower layer of you know don't really know or you don't say no really why don't you tell me all about it you seem so smart give me your opinion I'm not the entire time Socrates really has something so I mean um for example Socrates says I'm not a good speaker I'm just gonna have to like it out the way it ordinarily do yes I use a good speaker yeah he's a great speaker particularly when he can bring somebody else into the dialogue and then recite their words or perhaps make them up on the spot we don't know existed or not and give up an entire speech he's able to replicate this this sorta stuff is the stuff that Socrates is saying coherent does it hang together as as a speech that's part of speech writing right and public speaking is being able to talk without seeming like you're just rambling around did Socrates as discussion seem just rambling around no point to them or was there a point to them he does know what he's doing he kind of pretends like he doesn't irony is a pretending to be less capable and knowledgeable than you actually are so as to get people off their guard and this is actually you know a good thing to do in a lot of contexts I highly recommend it to you because people will say all sorts of things when they think that you're actually not that bright reveal things to you that they wouldn't ordinarily reveal I don't know for example we can talk about irony in terms of dress I don't dress like this in most contexts you know if I'm going out to a nice dinner party yes if I'm teaching yes but most of the time I'm more of a jeans and flannel kind of guy and I don't look like a sort of typical academic and listen to what people say and when people are left or are dumb they'll say a lot of really interesting things well they thank you guys so Socrates does that and he gets us is you know fellow interlocutors lot start quite often and then now is he doing it just to be a jerk to show how clever he is might seem that way sometimes but really he's trying to teach he's trying to bring out something from his fellow speakers and he's going to do this with the Agathon might seem like kind of bad manners it's Agathon's house right Agathon is the host of the party you just want a contest you just gave a great speech what did Socrates do immediately after that ask you a few questions and one of those questions reveal to us about ex-con in his speech yeah yeah he doesn't know anything he was praising love and he was saying love has this this quality remember love is beautiful totally beautiful love is totally good and then he just like opens up the floodgates of rhetoric yeah and like psychic she says you like gave us a bath pour it over our poured it over our heads where's the big flaw in Agathon's views about this so active is able to get about one little point you might not require because he spent so much time like going through particular examples but what is this point what he's talking let's just start with two towards love beauty they just love usually the act I'm saying mom is yeah let me say something like desiring what if it's the other way around did you ever you didn't so percent of love is not beauty love is not beauty because love let's look that's going to be the conclusion because love desires so there is a desire in there but it's flipped around now if I have desire or something why do I desire it generally yeah already have it exactly so if you decide for one who know everything you really like this truck you desire it until you actually have it then of course once you have it you desire to keep it yeah but so long as I've got this piece of Chagas you know you have to just decide you're hungrily think about all the things you could write on the board so love desires beauty so lovely is not beauty love laughs and the same thing for the good love loves the good love his love of the good and so love is not good Agathon was completely wrong he was he was saying love is like the best of these things its beauty itself its goodness itself instead of love is actually steering us towards those things now if that's the case if love is not good love must be evil done right where love is and that beauty love must be ugly and that's where Agathon more or less ly as a lock Socrates says well let me tell you this story about this lady that I needed a long time ago her name was do de ma she was a you know some sort of religious leader you know priestess prophetess here she was able to you know keep the plague from happening in Athens for for over a decade you know if he goes down like a list of her she is the philosopher of love he goes to her for love lessons that sounds you know a little bit like he's you know a young guy going to you know brothel you know learn about sexual techniques or something like that it's nothing like that this is more along the lines where we talked about with tonic love he wants to spend time with her so that he can acquire wisdom so he can acquire knowledge so he can become a better person and she knows about this for this stuff so she says well you're making a really mistaken assumption you know you have good and bad of these not good or the automatically bad or somebody is neither here you know they're not fair beautiful are they necessarily ugly what's your experience if you're not getting an A in this class are you necessarily getting enough why not yeah there's BC and D right Paris has some kind of weird thing I hate losses I think they don't have d-minuses not sure exactly why but a C would be like right in between three would be what we call mean for middle between one extreme and another extreme right some things are definitely good some things are definitely bad some things are that you know or sometimes good sometimes bad good in certain respects bad in other respects think about beauty and and ugliness have any of you liked seeing these things on websites were they they show famous actors and models with you know they're in there sort of gone through their native habitat their environment on velocity magazine pages and then they show them without the photoshopping without the makeup what else Photoshop you make people do a lot maybe out with their kids or something like that big difference right now you know some people are still pretty good-looking even after you take all the makeup off some of them are right you're like wow that's some that makeup artist deserves a million bucks a year because they turn that that person who was waiting over here and something over here wonder how they even thought to apply it to them I mean they could have applied it to anybody and probably resolved but there's quite a few people who are just sort of in-between right and then what light you're looking at them in their have the experience of being attracted to somebody and you know just physically attracted you like the way they look and then what are they they're doing some some different light you're like what's wrong with their babies I don't like their hair actually you think I like their hair I thought that was one of the best things about them but it's kinda scraggly yeah pick whatever you like that would be in between they're not you don't like stop a clock ugly but they're not beautiful either and we can talk this way about a lot of different things and do demand I actually does bring up a lot of different examples so what are some of the other things that she she brings up as these these extremes that service yeah mortal or beyond mortal where women law doesn't either once love isn't immortal because love can die but love comes back to life as human beings at Plato's got a whole different account I can say afterlife no we don't go into that human beings you know when the body dies that that body's done it doesn't come back to life you're gonna say stuff like well you know it feeds the fishes or grass grows out of it but that's not that body coming to life that's other things growing on it what else so the divinity is an important attribute is lot of lies no I mean even if we put plate on the side and you've been in love would you call your feeling of love particularly otherwise about things maybe in a lot of cases no leads that are just crazy stuff what was not entirely ignorant either the ignorance the way Plato understands this are not only lacking in knowledge but they're ok with them they're fine of them they're happy with that there's a called self satisfied with their condition the philosopher the literally wisdom lumber they want what they don't have but they can at least recognize that they don't have it this is kind of an important point that that doesn't get stretched a lot here but does get stressing on your Platonic dialogues being conscious of your own lack of wisdom your own ignorance on certain topics is already in advance beyond ignorance it's not yet – no but it's to know that there's something more for you to know and it also makes you look a little bit more humble right you're less likely to say I know all about that ignorant people quit often don't even know they're ignorant that's what ignorant they are this is Kayla that aggression but it's it's a great example for this sort of thing they did a study and then some years ago I was British people who disagree remember right yeah and they were looking at a lot of different ranges of qualities of people you know that we divide things up by what they call four tiles so like you know 75 100 percent 75 down to 50 and we can do this like test scores like all of you are probably the top quartile pretty selective school you can do this with other things too like physical attractiveness ability to get worked on you know all sorts of things what was really interesting was the fact that people in the top quartile generally know that they're at the top of their game people in the middle two quartiles generally have a fairly decent idea about where they fit in they asked people to rate themselves what do you think about people in the Bob really the results were just guessing yeah probably exactly yeah not only do they not realize they're in the bottom quartile they don't place themselves in like the next highest quartile or even the next they think that they're at the time so people who are particular stupid will often think that they're really brilliant that you know that's exactly what Socrates is talking about here ignorant people are not just like you know people who are like saying yeah I don't really know anything I have to admit it to you those are the people who are actually in the middle the people who are convinced that they actually have knowledge they're the ones who are in there so love is this in-between day and she's got this great discussion of love as being the intermediary between the gods and he's a dime own and in between sort of communicative interpretive spirit this is a you know common belief for the Greeks out there were these these in-between kind of things if you wanted to get something done you know necessarily have gone directly you don't or the gods it she's got the story as well about his birth which I'm going to skip over it's kind of a nice comic story about it essentially what we call it I mean they wouldn't call it a date rape because they're not actually like out of date together you got this guy who's passed out this woman who says I want to have a kid by him so I actually have something and had sex with him manages to get him get out in the game so to speak and brings to Bertha a child namely love who's who's the in-between because she's over here she is poverty she never has anything and her his day out is plenty so love is in between poverty and plankton there's always something in my stuff coming out he lacks resources but he can always find resources there's this whole beautiful description in there but then we start extending this to other people love is not the only philosopher Socrates says who died autumn are the lovers of wisdom if they're neither the wise are the foolish just as well love is one of them wisdom is a multiple to any love is of the beautiful love is a philosopher of over with them and those who do philosophy and philosophy can be very broad here you can think of what you're doing in your major it's doing something like philosophy you're trying to acquire knowledge you're trying to acquire wisdom that places you in this category here you can't learn until you actually realize what you you don't know now she shifts gears she's going to start talking about the mysteries of love which is unveiling through these lesser and then greater mysteries we come again to this question loved one what does the lover one we've all felt love right at least you know the form of sexual attraction or excitement about something admiration friendship the questions what are we actually driving after what is what is moving us you know Aristophanes setting was to be reunited with our right somebody liked it Eric semi kiss would say well you know it's for things to be in alignment and healthy the elements the elements of something different and she does this Socratic question with him leading him through through a dialectic she says somebody might say of the beautiful and what love is of the beautiful question is what so what a beautiful things that we feel love towards hesitate are those a sort of crime thing that we tend to feel long to it's beautiful or handsome there are traffic yeah are there other people weird you know they look at other people and I'm like person was really attractive so I'm gonna flip through a magazine traction or something like that are there other things that we we love because it's beautiful maybe we don't use the word love we use other and good because they're warm and cuddly and they are cute when they do this or that but anybody I mean there are certainly animals where we look at the Baja horse is amazing look at its grace you know there are hardened gamblers who like throwing it I'll slit your throat and throw right there life's amounts of wife savings they might do that their life savings the way out of horse race who can nevertheless at the same time appreciate the grace are running horses something that the humanity has been fascinated with for watching you know big cats at play we're hunting there's really something to that going some people like to go hunting by the way not just you know to shoot it here but to watch the deer to watch them walk there's a certain grace to that there are the natural things to you like you might you know like a particular part we're surrounded by natural beauty here and lots of valley you know there's a walk down to the boathouse look at the Hudson River and that could be an object of love for you something of beauty you know some people do go down there frequently music can strike us that way there are certain musical pieces that were not able to say exactly what it is that we love about them but we do love them right there may be certain movies certain poems certain other types of works captain but then again you might love your car because you love them the lines and the design of your car yeah so in it all sorts of things so she asked well when a person who loves the beautiful what is it that they really desire we want possession and here they come to to kind of a halt she says what do you get out of that when you possess some some article of beauty so let's take something really easy to relate to I'm willing to bet that for every one of you I asked you about your mp3 collections there's some song in your mp3 collections that you if you had to like only pick one song that you could keep an image difficult and there's two or three or ten but if there is only if there if I said you can only keep one song I'm going to delete your entire collection and you'll never be a little upload another song again which one would you pick you pick a song it's not going well I've got the storage space I'll put it on there it's one that you feel really connected to you possess that right you you probably listen to it and willing to that at least once a week yeah sometimes it moves you and sometimes it doesn't what is it that you actually are getting out of that socrates isn't able to say are we able to put our finger around there yeah feels good yeah this yeah maybe maybe it's a way of you know some people think that art is a way of dealing with the pain of life you know it brings us up okay maybe there's something to that guy named Schopenhauer yeah much much later than Plato Socrates isn't able to figure out what we actually want on having the beautiful a lot of them's we don't know I mean we're attracted to somebody we date them we get into a relationship with them why did I get into this now that we change it to dance a little bit more manageable why do people want good things as opposed to just beautiful things well what is it that they want they want possession I'll be good those who possess the good what do they actually gain up the good thing that they want what else what are they really driving it and you know we think about the beautiful that's what we want to we think the beautiful is going to make us happy a beautiful object that we yeah that's why we're often so disappointed right because we we get something and it is beautiful mineral life of to think of the beautiful course you know the source is so so wonderful but now I got to feed the thing clean the stables do all this whatever word hurt the horse is sick and it's got to go to the back man this thing is hard to ride it's try to bite may or may may or may not go well but we're actually driving after happiness this is our our fundamental goal in life and if you ask further well what does somebody want to get out of being happy that's one of those points where you can give somebody legitimately as a philosopher the blank stare and say what do you mean wait wait you know you don't want to be happy because you know even the people who just want to be miserable and bitch and whine all the time they want to be happy that's just what happiness consists in for them I think you know it's so cool right they're never happy unless they're humming happy they still want to be happy we all want happiness and it you know takes on different shapes and we imagine it in different ways but this is something that drives all of us according to Plato and according to many other philosophers so we're maybe happy by acquiring good things and how long are we going to be happy so long as we have these good things so how long do we want to keep the good things forever exactly eternal so you know this goes a long way to explaining why we are oftentimes in the midst of such funny not very happy people you know a lot of the things that we have are not designed to last we live in a throwaway society if Plato is right then having a few nice things that you can keep for a long time you know for example I have this dossier I've had this dossier juror quite awhile and my wife was the one who was instrumental in me getting it and latha she you know talked us into spending the money on it because it wasn't cheap so it's a coach one even buying in an outlet it was it was pricey this is great compared to the other Nazi aids that I've had that had fallen apart I am tough on equipment I break things I'm not careful you know it's kind of scuffed this will probably last me you know a good portion of the rest of my career and it fits nice looks nice and like the wind feels the other things that I bought the pasture I said well for half the price I could get you know this one I wasn't as happy with them it didn't make me as happy it wasn't just you know the the duration it was the quality we want things that will make us happy forever we seek eternal happiness eternal possession of the good now here there's a digression that I want to spend a little time of time on because it is important when you use these terms like love and love and poetry yeah we can talk about words in broad senses of the term and very narrow specific senses of the time so for example let's take clothing all right you wouldn't call that necessarily a shirt per se but like a blouse right or a what you're wearing yeah oh no you're wearing a dress yeah I couldn't see under the desk I mean it is a blouse a kind of shirt in a broad sense right but when you say shirt you generally mean something more like this what makes it a blouse well just the fact of a woman where is it I'm not a fashion person we also talked about you know t-shirts possibly is button-down shirts that's more specific right they all fall into the category of shirt but you might pick some were described things more more carefully now what about love and lover when we think of love we tend to think of a few things so we talked about the innocent friendship romantic love and attraction love that program and siblings share that sort of thing might extensive like love whoa country or I love this food I love this song we're the lovers when we call somebody a lover what what are we talking about yeah where did you raise me in there yeah right here person you're interested in like that you know yeah and it's usually romantic rival physical nature yeah I don't I don't call I'm not for instance a we wouldn't call me a lover of my friend over there right or we don't call me a lover of my mom it's funny too because my my adopted mom drove me nuts you know I couldn't picture anybody do something like like like that to be involved but you know some people do what else do we talk about we're so we have we have lovers in the romantic sense we call somebody a lover they give me a wine lover right chocolate lover car lover who say horse lover and all that sounds a little ambiguous kind of get worried maybe that's kind of dirty right what about poet nature into contemporary poets that come to mind who's your favorite color I'd drown oh yeah not exactly contemporary got to reach passionate that's like that almost two centuries right we don't I mean we do have poets these days right where you wanted to find poets where should you probably go yeah regardless ah yeah we do our poetry through through lyrics poetry and the rhyming sense rap and hip-hop are probably the closest to an ancient Greek poetry because the ancient Greek poetry was not only about and the ride it was about meter so if you have a rhythm where it's going and that's part of the words that's like ancient Greek Atlanta poetry like for example aristocracy had frog sang bracket kick xbox Cox Beca connects coax coax alumni first but that's from this that's ancient Greek from his has played the frogs it was in poetry and they had that rhythm to it that done the Odyssey is written in meter as a matter of fact a lot of the old biblical stuff is written in meter as well the Greek set up had even broader conception of poetry so it included what we call plays it would include what we include as music history was not poetry but in a broader sense everything that's creative is poetry everything which is bringing something from non-being a state of not existing to existing is poetry so how many are any of you athletes if you have it what about sports doing this play what's up Rick Carelli Chris rowing crew okay what else rowing crew yeah track okay where is it must be cross-country this season right okay rugby okay any other sports every time that you guys are engaged in athletic competitions you're creating something you're creating a performance rowing requires and actually I mean is that something you can even sort of do your own thing like your bro how would that work out you wouldn't live on your teammates it'd be infuriating right everyone has to work together there's something about being on a team when everything actually comes together we're like when you're running and you get that groove you know and moving ahead you know what feels like you're in slow motion you can like see the other people sort of receding into the background there's a lot very aesthetic about that when you you may not think of it this way when you mow the lawn how many of you have ever like cut grass more than once in your life now how did it feel other than being tired maybe ticked off the after you mowed the whole lawn and I went from being the shabby scraggly unkempt can't thank to being a very neatly groomed green was there any pleasure in them you created something we're all creative we're all poets we're all lovers according to the only one it's just a question of what we actually create or love and the broad sense all of us are are tied into this and all of humanity so she says going back to the good we want to have the everlasting possession of the good how do we do this well this is where the poetry and the lover stuff comes in we as she says bring to earth so you have a blogger and then you have some sort of let's call it a medium okay and the medium itself has to be in some way beautiful the lover has desire and the hand desire to create something in the medium to bring to birth in the metaphor that she has we're all pregnant we're all pregnant either in our bodies or our souls and it you know it's kind of a weird way of thinking about so it doesn't match to what we what you learn in health class but sexual reproduction the way it works I mean we know now that you actually need you know chromosomes are both parents and the egg contributes the sperm contributes something put all that side just just right and imagine this what is it that we're actually trying to do when we're creating things we're trying to bring something to birth in a beautiful medium or at least a potentially beautiful think about food and cooking for example how many of you ever worked at restaurants so you know that there's a lot of things you probably don't want to see going on behind the scenes and restaurants that drive with your experience and sometimes the uncooked food stuff someone's very attractive some of its really ugly you know but when it's cooked and it's plated and you produce something you may have taken a medium that was not by itself beautiful and you've created something beautiful food by the way is is a object of art to be consumed that way you can tell that it's really great as nothing's left unusual because music we want to have that for recording but we all want to create so the question is what kind of things do we create we're trying to create so as to have something that is going to be eternal left behind so when that she uses just man here we need to think about this in terms of women and the traction from that as well when human beings are attracted to each other and I have sex with each other what are they trying to do have a good time maybe you can express their love for each other but what they're really trying to do is make babies the reason why they're trying to make babies is to leave something behind to leave something human behind not just a lump of flesh not just any other thing but something that's light to them behind don't don't parents will often see something of themselves and their children or those who don't are sometimes disappointed they don't see something other I can't believe that you're my kid a lot of times they they they see a lot of themselves in their children and you know you watch kids over time they often turn out quite similar weirdly enough like I don't I don't physically if you looked if you put picture of my adopted dad and then me next to each other we don't actually resemble each other that much he was we had his hair was going gray when he was 18 he was very thin not particularly around the athletic well we both wore glasses what else it was a short guy about 5 foot 10 I'm since 3 when I was a teenager that my dad had died people would say you look so much like your dad you're like Holliman can that be I took out his mannerisms you know eventually you come to resemble people well that's that's great from Plato's perspective because that means that you actually get to leave a little bit of yourself behind you get to enjoy eternity that's your bit of immortality that's what the level of the body what about at the level of the the soul so she talks about other things what are what are the sort of things that people want to leave behind as what we call their people just actually have a legacy a lot of people don't start thinking about this I think until they get older I'm thinking about death thinking about the meaning of their life you know they get in their 40s or 50s suddenly they're about something different sometimes it coincides with a midlife crisis right what are the kinds of things that people want to leave behind but I mean some people are crazy they say I just want to destroy everything in sight or I'd like to kill everybody who belongs to this class she wasn't talking about that for what what makes you memorable would be like Steve Jobs yeah innovators and now it's not just enough to bring something to the world that hasn't been done before because you know the guy who had invented jello wrestling I'm sure his name is down somewhere right but we don't we don't like we don't talk about it like Steve patents right well there are a lot of people like jello rust like I think I don't really don't I'm just picking this out of random we could pick any other thing what did Steve Jobs do that was so important and he introduced something that made people's lives better if he'd introduce something that made people's lives worse he would be remembered but he would be remembered as infamous right like a lot of times people don't want to be remembered when that happens like you know who is the first person who transmitted this disease the population we usually don't notice knew that they died of it but you know they don't think they want to be known as that that the guy who is responsible for the building collapse Bangladesh last that semester he'll be remembered as a terrible guy you know and Steve Jobs was not a great guy personally apparently but he really was able to get something interesting done he would be somebody who'd fit into what do know calls those who are pregnant to the soul why well because he he actually ordered she talks about families and states he ordered a company that changed our culture you know the fact that we walk around with these things rely on them for so much what else building sometimes yeah they try to make a ton of money I mean every one of these buildings that you walk through it's got a name on it that's somebody who gave a lot of money to this College maybe to build this particular building they wanted to leave something of themselves behind or that it was to remember their husband their wife parents what else have any of you ever had a particularly not just good in the sense of any other subject but conscientious teacher who tried to cultivate you as a person and your time in middle school or high school or maybe if you're lucky you'll have some people like that here in college probably in your major major what are they after they they want the good for you but they also want to leave behind a legacy of what people oftentimes call spiritual children they want to leave behind people whose lives they improve the Ottoman and Socrates are like that Socrates is like that for a lot of younger people some people want to be remembered for great deeds you know it's like my chilis fighting other people leave behind poetic workers don't them musicians want to be behind that one song that will stand the test of time and people will be listening loving a hundred years from now 200 years from now it's kind of an interesting thing to think about how much of our music that we have we live in a golden age of music there's never been such great music produced as at this time in history in all different genres how much of that is going to stand the test of time it will be listened to avidly by people a hundred years from now just as eagerly as you listen to it today that's worth thinking about that's what musicians once they start thinking about their craft that's one of the things they aim that's part of their legacy he talks about homer and hesiod and I wouldn't want to have children like they do what did they leave behind when we're left behind The Odyssey and the Iliad two really great classic words that have stood the test of time you know you may have been like required to read them in some classroom I had this boring crap trust me when you get older and you reread the stuff you're gonna love this I understand why they they kept copying these Scrolls out by hand for centuries so that we can have this Plato himself as his leaving behind children like that so that's that's all an interesting set of reflections on what we wanted and loved the last thing she talks about she calls all this stuff up to this point lesser mysteries what is the greater mystery what is the real revelation sort of laughter then you climb up a locker moving from one thing to the next to the next to the next ultimately reaching the pinnacle Beautiful's itself which you can't see touch smell here you can only envision with your mind you can only capsicum catch a glimpse of it through through your contemplation but it's what makes everything else beautiful everybody that sort of trickles down everything below well that's the very bottom our bodies physical forms bodies are beautiful I think they are attracted not just human bodies but animal bodies too right and we see them now you even even paintings we need to go to the museum you like Bob I don't understand what this paintings about but I like the colors there's something in it that responds to me physical things we start excuse me we start off being in love with one body he says and then we should move on to another one and fall in love with that one experience love inside and then come to realize that all these beautiful bodies that we loved then they had something in common that transcends them which is you know the sort of beautiful beautiful form we have a type you know once you actually this is kind of psychedelic but looking back on it you know over 40 years of this sort of stuff once you figure out what your type is you've really saved yourself a lot of time when it comes to dating and romance and all that sort of stuff now you can go and find you know a beautiful body that has set that type hopefully that that beautiful body will be connected to something that's more important than the body is the beautiful soul if you don't like the word soul because of its fee illogical you know implications say personality you know we often joke about it we're not good-looking with their two great personality personality does matter over time more than most because personality is more permanent and we'll stick with it you know if you're overweight you can drop the weight you know if you're out of shape you can you can go to the gym and work out use makeup to cover up you know there's problems with things you can get implants good things taken out you can do all sorts of things to the body right not so easy to do the personality if you're a jerk can you get a can you get a jerk jerkiness removal we're not you know they try to do stuff like that or you know programs and southbound on but it takes a lot time we have to do a lot of painful digging and sometimes it doesn't take you know but falling in love with beautiful souls that's a higher level that's getting you closer to to what's most real what's most valuable now here's where it gets really interesting what makes Souls good he uses this term as laws and institutions the way in which you you live something that transcends you so for instance being up sports team that is an example of institution yep being on a sports team for instance rowing right you have to coordinate in ways which in other sports you don't have to so much to to a very tight to reviewed with the guys on your your squad right where do they call the crew did you learn how to do that by being a boat with wrong or did you already have that developed at that level before but you everybody you kind of learn paddle everybody or it's all in place so you're learning something valuable that is that is actually contributing something to your soul they will be able to transfer it on their areas you know you get it with a bunch of different colleagues at work you know wherever you're having to go you'll have some difficult colleagues trust me and you think well I got out of like learn how to be in sync with them and if I can do with these these guys on the rowing team I think I can transfer some of those skills that's the institution having affected your soul having made your soul better have you made your soul some respects more beautiful more what it ought to be all sorts of when when the institutions are good when the laws are good they make the soul they make the personality good these good these are not to be the law is in the sense of like the laws of the municipality they could be the way your family works they could be all sorts of things along those lines we also use the words of practices with us what would make those good so you know you move from loving people's souls to be like that person is great I like this Socrates guy I like this play-doh guy any sort thing about yeah I like what you know whatever it is that could like form them I love that even more well Sciences or wisdoms forms of knowledge the things you're studying in your majors that's would actually inform our good laws of institutions knowledge understand that becomes something that you become attractive and you know you could you could become attractive that in the way which would be very early called monogamous right you you are in love with sociology or accounting or you know pick other things like that people do fall in love with their job and when they fall in love with their job hopefully it's not just they like filling in forms and that sort of thing they actually like Indians that are the basis and eventually if you work through many of these you will catch a glimpse of this that which is beautiful in itself not beautiful because something else has made it so everything trickles down in this hierarchy from the top downward but you have to go as a human being you have to go up this ladder you can't just jump – well you know let's say you do this lecturing you're like yeah beautiful itself hell I'm gonna skip all this intermediary nonsense you should give me that dr. Sadler if Plato was right you would actually have to spend some time learning right you probably don't even spend a lot of time learning out a lot of bodies and then learning how to love Souls learning how to love laws and institutions learning how to love knowledge for its own sake and then seeing something beyond knowledge itself that is even more attractive even more desirable it's not like you can short-circuit it there's no there's no 10-point system to get you through quicker or anything like that no crash course kind of an interesting idea this is where Socrates leaves off and that's where the suppose you'd really want to end isn't it what happens instead who shows up rich you know good-looking playboy yeah Elsa babies shows up yeah and his speech is kind of ramble I'm not going to go over all the like you know who's gonna sit next to who business because we don't have time for that but this speech kind of rambles across three different things one of these is this this very confessional you know story of how I loved but didn't succeed he tries to seduce Socrates and not just seduce him like you know I want to take classes from here he wants literally to get Socrates to sleep with them because he thinks that if he can do that then he's like puffs on his nice face guy he thinks that Socrates will share his virtue and wisdom with them that's gonna be one of these older men these kind of things that were you know so common with the ancient Greeks and you know Elsa Biden is a super good-looking rich charming who can't eat yet turns out you can't get Socrates and so you get this this this long story about his painful experience of rejection yeah it starts up first I stuffed the Serpent's Elena thought for sure this is gonna work out it's almost like a you know watching one of these date movies you know first they tried to do this and the person just doesn't get right we like that you're a really great friend Alcibiades Alcibiades want something more then he wrestles with the Greeks like to resume kit so if anything's gonna work it's gonna be that Socrates doesn't do anything that what is with this guy invites him to dinner first time Socrates eats dances thanks for dinner see you later well the second time Alcibiades finds a way to keep them there overnight get Socrates you know sleeping gets under the covers with Socrates still nothing's happening finally you know maybe we get this law little little speech thing and he says do you know what I'm meditating I think that of all the lovers who have ever had I've ever had you were the only one who's worthy of me and yet you appear too modest to speak now I feel I should be a fool to refuse you this or any other favor therefore I son delay their feet all that I have all of my friends have in the hope that you will assist me in the way of virtue which I desire above all things and I should certainly have more reason to be ashamed of what Wiseman say if I were to refuse a favor to such as you none of the world where mostly fools blah-blah-blah-blah-blah and Socrates says thanks that's really nice flattered we'll talk about that some other time so now Alcibiades has been turned down yeah and she finds himself that's not the way that it's often happens in real life right when when these sort of situations occur the person who's originally trying to like it out like aren't you attracted to me they get back to their turn right friendship is great expression since we want jits if we if we wanted waiting meeting follow me and I won't run away from you run away from me and I don't follow you and that's exactly what happens and that's kind of interesting but what's more interesting is as talked about with this guy's why is this guy Socrates so attractive that's worth have any views I've seen pictures of Socrates you should go online you know google it they've got busts of them you know these sort of head snatches he's ugly he is you know ugly as sin got this squished face you know he looks like somebody hit him with a shovel maybe he was short he was fat he was balding it's sort of uh the sort of guy who would you'd expect you know to go out when he was about four years old and buy a red sports car you know because he has to compensate for all these other things so why are all these these young guys who have a lot going for them why are they all attracted to this guy Socrates well this is about the inner and the outer or what we often call the exit spirit and that's what's here these are fancy words were saying outside inside and Alcibiades says Socrates is like these satyr statues the satyrs are these half goat half half-man things that generally you know like to cause a lot of trouble in ancient Greece and you know try to sleep with the nay ads of the names you know that female sent me divine beings and they're kind of wild and really kind of ugly you know goats are not particularly good-looking things anyway not very good man so Socrates looks like one of these statues but open him up inside what's inside golden treasures what are the golden treasures and Agathon speech he talked about love and all the virtues and there's been a lot of talk about different virtues like courage temperance over the course of this dialogue Socrates according nail societies is the guy who has these how do we know that well he's got temperance which has to do with regulating your your desires and your pursuit of pleasure because he doesn't sleep with this this kid who's trying to seduce everybody else oh no the town seems to want to sleep with so imagine you know put input in our context you know whatever it whatever way your taste go some supermodel the who's rich and charming and brilliant besides they want to hang out with you because they won't sleep with you are you able to to say this we probably should think this through where you sleep with them Socrates says let's think it through he is temperate he's also just he doesn't take advantage of people what else what about courageous how do we know that Socrates is courageous what else does how somebody tell us where did he get to see Socrates yeah a couple of couple different times Socrates is able to put up in physical hardships and other people I'm really bothered as a matter of fact it ticks off the other troops that he doesn't seem affected by then on the retreat and you know if you had if you first of all ancient work there back then when they talk about the heavy armed troops these were guys who carried these big shields you probably seen them in a few movies then these long Spears and then they carried a short sword and the whole goal was to like use that shield to keep the other guy from doing what he wants to do so what you wanted to ram their spear through his belly yeah or maybe you know cut across a hat or something I'm going to get too close to use the spear you get the story out of destruction yeah very blunt start stuff I mean I would scare that the crap out of most people anyway I think it's you know it takes a lot of courage to be engaged in modern warfare but but it probably takes a bit more to get close up and personal with people than to shoot them from do other yards away a little bit easier to do that scary but not not SK so Socrates now they're on the retreat and you're them to retreat when you guys have lost and there's the enemy has them you know more of their troops coming in and there's two ways you can retreat one is using I'm getting the hell out of here and everybody takes off and if you do that they're gonna kill all because they just come in and run you down or do you can retreat in good order that's what Socrates is helping them do one with this guy who becomes another general lockets it was actually a dialogue like it's about courage socrates not only saves Alcibiades life he tells the generals I don't want the reward for valor give it to Alcibiades so clearly he has courage does Socrates have wisdom wait his words and trans people even the out of distance like these these flute signs Mircea stuff the satyr so they also buy these is it's telling us something about side but he's doing it the way to wrong people here it was kind of rambling here at there how does this end alcibiades you know some work people first in everybody starts drinking heavy lot of people pass out some people say I'm getting out of here like eczema guess drink very much who's left up again yeah what's that decided socrates son is there there's two other guys still at the table drinking still talking about them the guy who's marrying it says I was like passed out and I woke up I couldn't remember station but he understood within the main topic was it was whether the tragic the tragedy writer can be also a comedy writer and who are the tragedy and how many layers Aristophanes and Agatha so he's discussing their craft with them after this this total bust out pardon that's where it leaves off we never actually hear any any platonic discussion of that Jesus or like throwing that out there's and well at another time we'll talk about this and that's that's where it is so you've got all these different conceptions of love rolled into this one dialogue and now it's time for you to sort your thing about how to sort things out which of these you want to think about

Plato's dialogue, the Crito – Introduction to Philosophy



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In this lecture from my Fall 2011 Introduction to Philosophy class at Marist College, we discuss Plato’s Crito.

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today we're looking at the dialogue credo and this is different than the apology although it's very closely connected with right you notice there's some narrative continuity what happened in the apology then we talked about last class Socrates what happened so it's killing he doesn't get killed in that one he's on his way though isn't it yeah very very good yeah he cuz I'm trial he makes a couple speeches they're not they're not speeches that are good actually going to get him off because he kind of you know Pope said the people that are that are charging him and they sentence him to death now normally in the ancient world you would be sentence and then he'd be killed not long afterwards there's a camp for Socrates because there's a religious festival point we don't have to look at the details of that very much it had to do if you've heard of Theseus and the Minotaur it had to do with a religious festival that was set that was set around that and they sent a ship up and after the ship came back then they can execute people again so they're waiting to execute him he's sitting in a Cell he's got you know lots of free time yeah it was it wasn't too bad for him he was you know reading books and making friends with the jailers and just sort of going about his day the way normally does people come and visit him and creeper comes and credo has been coming if you if you looked at the dialog a couple times you realize credo has been coming during each day at a certain time of the day he's showing up early this day and he's showing up early because he's got a break out of jail plant so that's that's where this this takes off socrates could get away credo is rich kratos a foreigner credo has bribed the guards he's arranged for transportation he's talked things over with people he's actually got a cup here opposes a couple different places you go to Thessaly you could go here you've got friends over here because Socrates did in fact have a lot of friends so credo is putting forth the real proposal for him credo has done everything that needs to be done for this why is he doing this well you know when you read the apology did you feel Socrates deserve to die no did anyone feel he deserves done if you look at the Forum in in iler you notice that I started sort of a devil's advocate kind of thing I've started some threats why that guy Socrates deserves to die and I invite you to respond to it you know that can be class participation for those who don't like to talk in class too much or those who actually do talk in class and enjoy you know stirring things up that you can do that as well but yeah most of you don't think he deserves to die credo didn't think he deserve to die either a lot of people didn't think so they considered it to be what they talk about in this as an unjust verdict right we have that in our society you're right some people get statins to don't actually deserve to get sentenced I don't know what the actual proportions are I can tell you that when I when I worked in a prison and actually they taught philosophy and religious studies in a maximum-security prison and I got to know some of the guys here as well because I was teaching the same class as you know over and over and over again and they weren't going anywhere you know they weren't transferring to other other places other schools they were taking classes with me and one other philosophy professor and we talked about all sorts of things including their cases and most of the people in our prisons actually are guilty of something right but there are some cases if you talk to prisoners you find out that there's a lot fewer cases than they often think of as you know pure travesties of justice where a person is innocent and doesn't deserve it at all Socrates looks like he doesn't deserve to die though I mean he made a case that he was doing good things in the city did any of you find that that idea convincing that he was doing something useful those are all things that he was teaching you right do you think that that served any purpose in society to make people better or I mean it was he really corrupting people that was where they were gonna kill him because they thought he was corrupting the young there was the charges so the core question that we're gonna look at today the Socrates says ok let's think about this is credos plan should he do it we're gonna look at the arguments for that we're going to look at some of the the basic ideas underlying that before that thought I want to talk about a few interesting features of this text it is connected to the apology right the Euthyphro by the way that you're reading for next class that's also connected in time that's right before he goes in the law court so he has one big discussion then he goes in gives a speech then he loses his case goes to jail and then the day before he dies two days before he dies he talks with credo then there's another dialogue which we're not going to read called the Phaedo which is his last day the day that he dies which concludes with him dying wait do you guys see any sort of inconsistency with what went on in the apology in this dialogue Socrates is he going to leave why not yeah yeah yeah you're right about all those the Simmons is the right thing the just thing to do he doesn't want to be inconsistent with himself and it would also be breaking the laws now is this consistent with the guy who said you can put me to death if you want but I'm never gonna stop doing philosophy some people you know when they first read this they say you know the apology this guy was saying I'm gonna keep doing what I'm doing you're not gonna stop me in this one he's saying I'm gonna go along with what the state says so is there a contradiction when he knows what he's doing it's not illegal in the first place they're saying that it is okay that's a good point yeah so there isn't a contradiction no danger himself okay yeah that's something to keep in mind is the apology yeah there's there are Plato's scholars who think exactly along the lines that that you've laid out that Socrates thought he wasn't gonna get a fair trial period so he did making sort of what do they call that a bully pulpit again even if he was using it as an opportunity to to say what he wanted to say one last time and get it through maybe even stick it to them a little bit you know we we do get there's another thing that's on there we get to see Socrates put to the test it's one thing to say all sorts of things about morality and justice and you know what's right and wrong and how important it is to stand up for what's true it's a whole different thing when you put to the test isn't how many of you ever experience situations of temptation where some moral stand that you were taking you found it was difficult to maintain you had to do something that was painful well this is really painful that he's gonna die so what he's dying for it better be pretty valuable just being true to yourself in some sense I don't know if that's worth dying for being true to yourself along the lines of something that matters maybe that's that's worth dying for what's going on you brought up the laws you notice that he he actually makes the laws talk what do you think is going on with that this is something that people read the dialog event fascinated or confused or entertained by them why do you think he did that if you have any views about it if you don't maybe you do by the time we get get through this I'll just let that question kind of set another thing to think about that's going to come up this this semester over and over again is this question of what do you actually owe to your society especially if your society isn't perfect it isn't doing things the way you know what to be there's something that we call civil disobedience if you guys heard this term before I probably in high school right who do you associate it with yeah Gandhi yeah Gandhi's a great example who did Gandhi influenced that you would put it to work here in the United States yeah Luther King yeah anybody before Gandhi that you can think of in America gets tied in with this this kind of trivia but henry david thoreau somebody ever read him you had to read him in the English Lit maybe or an English American lip English and English class they all talk about this idea of civil disobedience and they end up taking a different stance than Socrates does here in the Credo Martin Luther King had had followed Socrates lines and said well the laws are the laws and I benefited by them so I really don't have any right to transparent transgress them then would he have marched what all those other peoples marched with them they took a different stand or at least what appears to be a different stand when I first look at it right I mean Martin Luther King also made a distinction between just laws and not just laws just laws you have to follow unjust laws it's actually wrong to follow and then that's a letter to letter from a Birmingham jail which you've probably have read in high school again yeah no should read it it's it's important to know to read but Martin Luther King is not basing his stuff on Socrates in the Credo basing it on other philosophical types because Socrates is taking a stance that says well you know you owe something to society you love something to the state you can you can go out there and be a gadfly but if the state decides it wants to crush the gadfly and you should go along with that so we won't look at that theme a little bit more as well let's look now at the actual text credo comes in and what does he say you know first day back and forth about you know I've been reading a Saab and the boat is coming sort of stuff but what they really get to the meat of it credo says hey I've got an escape plan for you let's do it you know here's and here's all the the ins and outs of it Socrates says let's think about this credo is is going to make some appeals he's going to bring up some some good or some values some things that are going to be lost if Socrates doesn't leave so what is what are the goods at stake here obviously its life right loses life well so what is this credo worried about yeah yeah that's that's a good concern isn't it Socrates has a responsibility to educate kids you know and this is in a Iron Age Society which did not have a social welfare system where if you know Socrates was in the free class of citizens we have property but you could very easily leave that class your kids could become slaves if you're going into debt or stuff like that if you didn't have somebody strong guiding the house bringing the kids on a ride who knows what happened for kids it's not like the state was gonna take charge or you know social services whatever they call it here in New York would come in so that's a real concern so there socrates allows himself to die he's not going to be able to do that what else what other values other concerns that come we'll call that reputation and he talks about something that he's going to have to endure when he loses his reputation to shame that's a powerful motivator isn't it nobody wants to be ashamed you can get a you can get people to put up with a lot of things that are painful or that hurt their interests if you don't chain them but if you do shame them that sometimes hurts people worse any other thing you don't think about bullying for example this is sort of a digression you have these cases where these kids are bullied especially through electronic media and then what do they do why does it become an issue they complain the school says I don't do that anymore that's not how it goes what do they do that really gets everybody's attention yeah they choose death over Shane because Shane is that strong of a social motivator even in our day and night they're not really actually like Socrates out there maybe making up a misguided decision but it's one that's understandable isn't it what else what are some other values doesn't want to look like like a bad guy who prefers money to his friends is there anything else that he thinks is going to be lost you're getting a good list here what's the first thing he says I'm gonna lose it doesn't save my reputation I'm gonna lose somebody that I can't replace a great friend friendship it's hard to be friends with a dead person you know yeah why would you lose is good reputation if you refuse to this favor credo is worried about his own reputation so I should probably this is credos loss this is also triggers loss this is what's a good question there's there is one thing that's like that again you gather you're not going to catch this the first time you can read their taxes this is why we have these things sessions while I talk about you know reading with text multiple times credo says Socrates you're taking the easy way out so it's not just credo you know to be it's also soccer cyclist you Socrates you're taking the easy way out by letting them kill you it sounds a little strange that way well what's his reasoning you're not consistently following the path that you've actually laid out the path of goodness they've got the virtue the path of courage you know you should be courageous and leave the city take a chance kind of live in Thessaly you know you should have left you shouldn't let those those those enemies of yours win if you do there's something wrong with you Socrates that's what credo is saying if you're reading between the lines actually this is kind of a digression to free though we don't know this from this dialogue we know this from another dialogue he's a really emotional guy so you can just picture credo there you know shaking and expostulating with misaki's he has two credo it has to be led away crying what Socrates actually does die there's kind of a mistaken attitude on credo sparks Socrates is quite what's the mistake that big what if you had to just identify one thing that's wrong with credo is reasoning one main thing that ties it together what if Socrates criticized says you're you're thinking of the right thing here I'll give you a hand who should create a be listening to we're thinking about how they they would see yourself well creeper doesn't mention no and then Socrates himself in this one is Kent humble he doesn't claim that he is he himself knows let me change the question who shouldn't he be listening to there's a the search phrase in there who gets it one who thinks that these things are all really the cream does but he's getting that from somebody or from some group of people decided yet we would call it society in the Credo that's called the many sort of you know mass of people that you just sort of pick and you know they're not necessarily people who thought things through as a matter of fact they're probably going along with whatever happens to be popular at the time you know think about the Whig mobs behave they you don't look at mobs from wall guidance right the mobs do things I think about the way or many people can be persuaded by easy emotional appeals and actually you know quite frankly most people don't like to think very long and hard about things these things right here are values they are good but are they the real good are they what's what's truly valuable for somebody like Socrates credo is too concerned about what the many think and there's sort of a common temptation that credo is exemplifying i know i've fallen prey to this temptation myself i suspect that many probably falling prey to it as well you know what's right and what's wrong but there's this tendency to say you know in this case the rules don't apply in this case I'm gonna look at other goods that have to be served yeah you know across the board it still applies for instance what's you know shouldn't be mean to people right but maybe there's times you shouldn't be mean to people but let's take a one that that is probably easy to relate to you shouldn't lose your temper and swear at people should we all agree that you shouldn't do that does anybody think that that's a good thing to do that you ought to be doing that then you're not living life fully if you're not doing that there are some people who think that you know you can tell because the way they live their life when they get me a dance we're a people a lot now when do we get a dance where people usually yeah exactly we if we hurt us but we think that we actually had a coming we we may get a little mad but we don't get mad like when we think that they they're doing something really wrong to us and if it's not right for us to get mad and swear at people it's not right across the board but there's this tendency to say well you know you did something to me first so I get to do this in this case and that's okay for me credo is doing something like that it's okay to break the laws if the laws don't turn out the way you wanted to if the verdict doesn't doesn't play out the way you want then you know you should you know resort to other things what does it do to a society if you if too many people start doing that let's say with the legal system too many people started saying all except the court verdict provided it goes from my way but if it doesn't I'm gonna find some way to undermine that I can get a society work like that no rules have to be honored by by at least most people or else things break down so credo is a little bit you know mistaken Socrates says we have to think about is this the right thing to do and are we going to look at what the many say no we have to look at what somebody else would say and he says we need to know whether this is the right thing to do in this situation but also in other situations right who is Socrates going to be persuaded by it's not going to be persuaded by credo or the many so I mean that he's just stubborn I take my stand here and nobody will will convince me otherwise is that a rational way to behave no so if it's not the many because they don't really know what they're talking about and they make all sorts of you know goofy decisions and I believe all sorts of things one day and that in all sorts of other things the next day who should he get his his verdict from who should he look that would be an interesting that he doesn't in this case if he were to do that then that would be sort of pushing the problem upstairs to God right that some people do do that Socrates is notable in part for not doing that and you might say that one of the ways to divide philosophy apart from another discipline called theology they don't teach theology classes here do that because it's a private school but it's not a Catholic school with theology you you look to God and then try to figure out what God is actually saying and make some sense of it we're gonna look at that a little bit with the Euthyphro next class but Socrates is doing he thinks that the answer is within us if you look close or within him within the human mind he he wants to get his information he wants to get his advice from somebody who actually does know somebody who actually is wise and notice he's not claiming himself to be wise in this his dialogue he's just claiming to have certain principles that he he thinks are right and unless somebody can prove those principles the whole he's gonna stick with them so who do we want we want the person who knows about good and evil and what should be done now what I'd like you to do just for a minute or so think to yourself about some case in your life where you relied on you had to make a decision about something right and wrong you made the wrong decision yeah the reason that you did so is because you looked at what everybody else thought about or the way everybody else felt or how people might look at you if you didn't make the decision that you did and it seemed okay at the time but then you realize later it wasn't the right thing to do maybe it had some bad consequences or maybe you felt you know remorse about it afterwards think about that for a minute yeah a lot of this stuff makes more sense when you apply it within the context of your own life all of you can relate to that right because you all had an experience like that at least one in your lifetime even it's something that's trivial as picking on some kid because all the other kids are picking on that kid we're stealing it you know stealing candy because your peer group said we're going in to steal candy today hang on what does it gets for candy in second grade I'm so nervous to do everything I was hanging out with the third graders yeah and you know to be cool and hang with the third graders you had to do the things that the third graders doing they were in shoplifting at the time shoplifting can worsen freeze a moment yeah well things have changed since the present kid I mean we live way out in the country and we had this uh.this it wasn't even ah what do we call it a convenience store right and he had like a candy aisle yeah one of the kids went to the front and got a got a bought something so he had a bag and then he walked back my house and then we were supposed to take the candy and like put it in the bag and it was a fiasco because you know what are we doing we're dropping it in there's really no way is he and like the the clerk is over there looking at and I you know are just thinking about Oh God we're gonna get caught we're gonna get caught you know my parents are gonna kill me we didn't get caught and you know the candy there's actually an expression there's there's no food so sweetest food that you've stolen it was pretty sweet but you know think about it you think about it later I was not the right thing to do did did the fact that my my older compete really everybody's doing this that make it a good thing to do no and I could think of much for myself a lot of big things a long way that I've done where rather foolishly I listen to people that I shouldn't have listened to and then you you know reap the fruits all of you can think of something like that right in your life who could you have gone to you know the Socrates doesn't tell you in this dialogue who actually does know he gives you some characteristics of the person that that would know we're going to talk about that a moment like just will actually do a little way no dialogue back and forth about that I'm gonna get that but keep this in the back of your head as we're going through the restless who would have known in the situation that you found yourself what the right thing to do was who would have given you the good advice I'm going to skip over how the many actually goes wrong what's really key here in this this discussion about whenever we find ourselves in a tough situation like Socrates is then we have to actually ask ourselves what is to be done it's that question that he asks in the text because we don't always know that's what we call practical reasoning the part of philosophy that's called ethics you guys are later on down the line I'm going to take higher-level ethics class when your juniors and seniors hopefully you're gonna learn some things about ethics before you get to be juniors and seniors so you can make some pretty technical decisions on the way right dad is all concerned with what what ought to be done what should we be doing what shouldn't we be doing in this case you know that's a particular problem should Socrates leave and break the rules of the city Socrates says that a good life is to be valued not just these things not just life by itself but a good life and there's a lot of different ways to answer the question what is the good life which is a question of ethics again ethics is not just about right and wrong what you should do and what you shouldn't do it's also about what kind of life you think is good for human beings to live and I think all of you want to be successful right you're all planning to have careers that's part of why you're in college that would be a component to the good life for you but it would that be the only thing you require for the good life to the career there are some people I talked about this earlier today in my ethics class who see the good life precisely in terms of work and just work maybe somebody you know are they are they getting the whole picture what goes wrong in those certain cases okay I mean they're if they're pursuing a real good a genuine good they do it a little bit too much there's no balance okay look that's a good place to start there's no balance so if we've got when you have a balance you have some sort of thing in the middle and then you have two sides work over here what's what's on the other side there should be there yeah mostly they all work and no play makes Jack a dull boy you're next yeah usually people who are what we call workaholics their family lives suffer they have higher rates of divorce their kids you know later on so you weren't ever there for me that's probably one of the greatest damages that takes place they also don't develop you know when we play we develop other aspects of ourselves and you know if you're workaholic you also won't be enjoying some some other Goods you won't be developing yourself all of you know people like that right they've made some sort of mistake with respect to what the good life is Socrates thinks that the good life he says is a life that's just and honorable that's what makes life good for him fundamentally so if he has to choose between being jealous and educating his kids he's going to take being just doing the right thing there are plenty of people who would be perfectly fine with doing the wrong thing so long as it helps of kids right again you probably know people who have done that my mom would actually she would she was very hard on us as kids but she had no problem about lying to people so long as that you know opened up opportunities for us I thought that was a little weird myself but you know people Socrates thinks that if it can't be a just life it's almost worse than they're not living just an honorable that's what he wants to be so that's what's motivating him the other thing is how does he finding how is he finding all these things out there reasoning and this is not something that's talked about in the dialogue that this is going to be a theme with us over the semester when we use this word reason we have a couple different meanings for this right why are you here you have a reason to be here because you're taking a class for credit so that's one sense of the term reason but you are also rational right you are a human being and because you're a human being you are a reasoning being you are a rational being that's why you know we we have classrooms and we talk about these sorts of things dogs you know get training the dogs teach each other in classrooms give each other grades tell each other how they ought to progress the other you know reading this text or something like that no we do that B reason about things we reason about things on all different levels sometimes we do it poorly and sometimes you do it well but that's part of that's what makes us distinctively human one of the definitions for human being that came up brilliant philosophy is the rational animal so Socrates thinks that this is part of what makes most human being rational following reason not just following our heart or desires but following reason what reason tells us is the right thing to do and he's going to follow it up here's where it gets really interesting a reason itself the rational life is a good thing so you can put that into the balance you know when you're doing practical reasoning a lot of what you're doing is weighing does this side way more well than I should do this action does this side way more than I should do this action for Socrates one of the things that's really heavy that's pushing down the scale is being rational being consistent sticking with what he had said before now yes sort of a standard filter' the wise man and what is the wise man why it's about here's where I want to introduce another theme that you're gonna see come up throughout the semester as well we call these moral values and they're they're you know instantiated they take certain forms we can debate about them in fact do debate about them the next dialogue that we're going to read we're gonna see not only do we debate about them we get angry at each other about them what do we get angry at each other about what do we debate about when it comes to moral things you could say abortion or euthanasia right those are topics what is the real general thing we don't ask ourselves abortion yes or no we say is abortion right or adjust just or unjust right we can also ask the whether things are good or yeah maybe Justin and good might be the same thing in some cases but maybe they're not in some cases you know all of you are healthy right I hope so being healthy is good being sick is bad it's not that you become a unjust person by being unhealthy but it's not good for you to be Socrates says that the the person we want to look to the wise person is somebody who knows about the just and the unjust the good of the bad and then uses some other terms can you remember what those terms were uses kind of formula and he says the just and the unjust the good and the bad and he changes or at least the translator changes the terms that he uses yeah well then the wise is the one who actually knows about this and the unwise is the one who has all mixed up about it or think they think that they've got the right thing but they're mixed you know they've got a walk yeah see it but we can change those two evils who want to and that's good the Greek terms are pretty malleable you can make them fit things uses another thing that we wouldn't normally think of as moral but in terms of what we call aesthetic how things appear to us uses terms like this or the Oh everything on this side is banned over the other side it's good right he wasn't being fair in the sense you know each person gets like a candy bar and you don't you know take anything more than as your do or anything like that or everyone you know follow the rules he means Fair is in beautiful another way of translating this is beautiful by the way of translating it is noble or thanks and another way that he does it in this is honor or dishonor well how do you think that that's important for somebody to know about isn't that kind of weird I mean for somebody to be a good ethics guide sure they ought to be able to tell you what's right and wrong yeah I don't know yeah I don't know it's what's good and what's bad why should they know things about you know like what's noble and what's bass you know when you don't use terms like that we talked about people's be like a decent person for you know repugnant or stand-up guy or a punk we have all sorts of terms for these sorts of things those are more in this category that in the category the just or the unjust you know it's lying behind this idea goodness is attractive and evil is in some way discordant or ugly and it might appear beautiful from this side or noble from this side but then you take a walk around it you see that it's not with any of these things you can distinguish between what's apparently that and what's really that and the person who knows who is wise would know about all these sorts of things how do you think they find out about that well for Socrates it was – reasoning not just listening to the crowd not just accepting things were you know on face value but actually thinking about them that's how he got himself in trouble going around looking for the person who could meet these criteria so when he was going around to all these politicians isn't this the sort of stuff that politicians ought to be knowledgeable about what's really just and unjust as they turned out not to be so that's why they're getting so that's that's why that's the kind of person that he's looking for that person doesn't show up on this dialog so you have to ask yourself you know here's a good place for us to actually sort of pause think back to the mistake that you made who should have listened to is there somebody who would have been knowledgeable or at least more knowledgeable than where you work at the time about what was just an unjust was good or bad what was honorable or dishonorable who could you think of probably done that expresser right flew into your life I know you know I had I had some grandparents I wouldn't go for something like that my grandpa my dad side he would have been a good guy to break long he did terrible things and didn't you know none brand about it now his wife his long-suffering wife his second walk is that right – actually she was a very good you know boys I could go to her did you have people like that in your life who do you have now again you know most likely it's not gonna be your ethics professor prettier of a philosophy professor who do you go to to find out you have to figure out what's right and wrong cuz you're not a genius that yeah my parents yeah and if your parents actually truly you know dunno Socrates would say perfect you found them somebody like this is a solid gold yeah even when you're a kid though you could have just asked yourself well is there anything you know that was wrong with your doing so you didn't though I need to ask anybody yeah I need to do is think about it yeah I mean you know Socrates seems to think that something along those lines a deep in their heart of hearts we actually you know could figure it out but it's buried under a lot of stuff there's one problem with that too there are an inflated uh something about this there are some people that we read nowadays terms sociopaths sociopaths lack a sense of that's why they're so dangerous and that's why they don't respond to treatment because they don't care they're only interested in certain Goods like power and pleasure things like that they'll do anything that it takes to get it we're gonna look at that a little bit more when we look at Republic look one that I'd like you to keep thinking about that this is this notion of who should you go to that that's you know there are certain big ideas that when the semester is over and actually when you've left Maris I would really really like you to carry with you I don't expect that you're going to remember most of what we actually cover in class because people don't that's what you have your notes for things like that there are certain issues certain basic ideas that I really like you to have as part of your toolkit in these and one of those is this notion of who should I place my trust in who should I be getting my understanding of moral values from because that's a project that you each one of you as an individual as a developing human being that as one who's actually early in your development all of you were around you know 18 19 maybe this is something that you should you know think very carefully about because you don't want to be 40 years old and realizing that you made the wrong decisions with this what else that is important about this dialogue Socrates he brings up the laws right what are the laws stadium what is Socrates saying to himself and to credo and putting in the mouth of the Athenian laws they're pretty hard on the birthday I mean he goes up the the dialog like just the law saying Socrates don't break us Socrates says screw you I'm breaking you he didn't the laws make arguments they give you reasons why he should stay around and obey what are those reasons can you remember any of them yet yeah they provided they not only educated reason they provided a very framework in which that could happen which his parents could marry and he could be legitimate that sounds like something that you know you ought to pay somebody anything else yeah yeah you know in the ancient world the laws compare themselves to mothers and fathers in the ancient world things were quite a bit different in the relationship between children and parents than the in our curve most of us parents were month had a much higher status compared to their their children and there wasn't a lot of you know democracy in the household or you know what do you think a little Johnny you know about this or that it was the parents decided because they're the ones who made you and some parents will actually say I made you and I can unmake you you know things like that the water was sort of like super parents they made the parents so you know Socrates yeah the water saying he's like a slave what else there's something that we brought up earlier they say what are you doing are you going by any act of yours to overturn us the laws in the whole state do you imagine a state can subsist and not be overthrown in which the decisions of why have no power that are set aside and overthrown by individuals if Socrates does the wrong thing in this case it is it has repercussions for the society doesn't it we just talked about this a little bit could a society last if everyone says well all looks at the laws so long as you know turns out my favor as soon as it doesn't I'm going to break can you have a society like that can even play a game like that you know let's say we're playing what do you want to play baseball football hockey anything will sit just right did you ever play chess with somebody who cheats it's very hard to cheat at chess how would you do it you'd have to break a rule enough just like well you know my pawn can actually move like a queen there's not much of a game with Jesus do that and you know you won't feel the play sooner or later you can't tell anything apart the laws also say what was our agreement with you when you entered into the courtroom what were you agreeing were you to abide by the sentence of the state if you don't like the way things go in your state Socrates then why did you stick around for 70 years if you think the laws are bad laws why didn't you go off to Sparta you keep talking and they say this dialogue you keep saying that Sparta and Crete have better laws than us because Socrates and Plato were actually sort of critics of democracy and Athens was a democracy Sparta was depending on how you want to see it and Oleg Archy or an aristocracy not everybody gets a vote not everybody has to hold office so you know if Socrates didn't like it why didn't he go somewhere else as a matter of fact he liked it so much the laws say that you never left the only time you ever left was to go on military service everybody else you know they go on vacation somewhere you didn't you went on vacation here what do they call it a staycation right that's the new term for when you take off work and you just sit around the house watch TV or play games you chips and don't go into work so what do you think the laws have a good case so they have a good case for Socrates yes there no yes why yeah it's a lot harder to integrate these days used to be a lot easier what else any of you have any of you have other reasons for finding this convincing or do you think that the laws are wrong Socrates making the wrong choice yeah what do you think all of you have an opinion I know people when they read this text they're you know sometimes they're like yeah this is great but sometimes like this is this is absolute yes I can't believe that that they don't they'd go along with this fascist stuff go to extreme positions let's put it a different way though so if Socrates let's say Socrates does owe this to the state what about you and the society that we live who do you all thanks to all of you have debts and I don't just mean you know financially you know do you guys have you guys have loans a lot of you and if loans aren't paying it then scholarships of some sort or mom and dad and if it's mom and dad come Thanksgiving if you're spouting stuff at the dinner table how American society is fascist or you know is terrible or something like that they'll they'll remind you who's paying for your education you owe them something and if you decide to not major in business as you originally planned and to major in art history it's done you may get a call from mom or dad saying I'm shelling out all this money for your education you owe me so there's there's that but who else to you old things too let's think about the fabric of society all of you are healthy all of you are relatively well-adjusted I'm assuming you know you didn't go through war or you know you weren't you know the victim of crime crime for stuff like that do you owe anybody for that yeah country yeah the country as a whole you know we just have this big 9/11 the day the 10 year anniversary and the FBI was on high alert agents were called in for the entire weekend working on double shifts and stuff like that the people on the bridges around here making sure funny business going on with that police presence was stepped up everywhere it becomes much more visible they actually put out some communique is because they didn't want people to get alarmed that some of the police would actually have automatic weapons which they did why do they have that to protect us do we owe them anything well it's their job well that's a good point that's honorable but it's their job yeah I and then when I comes to the military I'm actually that myself and my attitude when I hear people say you know troops shouldn't be put in harm's way is what do you think it signed up for you know you take the money to take the oath you you're probably gonna be put in harm's way it's the same with police or who else firefighters who else is on the front lines you know keeping you safe the organs of society of the coma and about nurses and doctors nurses more than doctors own nurses face you know the chance of getting all sorts of horrible diseases on a daily basis if something comes running we don't think of that as a huge risk like a firefighter please do we owe them anything what do you think it could just be their job we owe them money we owe them maybe we owe that you know we respect our country provides all the stuff what what do we owe well yeah then that's what you eights depending on how much you pay what you guys right now are fortunate most of you I'm guessing in that you're not you know making a lot of money because you'll see the more money to make the bigger the bike gets you don't have to make very much because you're middle class anymore so taxes let's go let's say we do a little bit broader that's providing support to the country there are laws about taxes you have to follow the laws do you have to follow all the other laws sure what if you don't like the laws what does the Credo pulled out as a possibility the laws actually sing this so you can't break us just because you don't like us agreements oh here's your pen okay what should you do if you don't like the laws what do you have a duty to do yeah you could try to you could try to get into politics and change to become one of the rulers the prietto's the dialogue doesn't actually have the laws saying yeah there's another way to change laws though and that's to do

Human Rights: Philosophy and History – Professor Sir Geoffrey Nice QC



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One of the most dynamic aspects of law is that of Human Rights. Sir Geoffrey Nice has spent his career in this area and discusses its origns:

The philosophical and historical development of what may be regarded as essential human rights will be traced. It is essential to understand this development before criticising – or complaining about – modern Human Rights law.

The transcript and downloadable versions of the lecture are available from the Gresham College Website:

Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,500 lectures free to access or download from the website.
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good evening and a special good evening to those of you downstairs student barristers often tell me they want to practice human rights law when asked what's that they have some idea that it's a right that is regardless of race nationality culture background but they're pretty unsure of detail and so are we all I found a short film by an American Action Group that rather made the same point human rights jeez that's a good question Wow I don't even know how to give that a definition I would probably have to do a little bit of homework or something any write that I think any just as a normal you know human maybe the rights that humans have that's a very large debate mr. Larkin two nights ago Abraham preguntar event I personally thought I'd be open until opening on Saturday and I would figure this yeah we just taken for granted there but we don't even consider what they are should I have been down parted my students easy if under informed enthusiasm for the fashionable legal practice of human rights probably not their answer showed at least two things one that they had a feeling that there was something that were attached to the human that was his right and that second thing is they'd like to work in that practice rather than in one that simply dealt with the passage of money from pocket to pocket so quite a happy result I felt but before we part from the film here's a second very short extract which shows there can be rather more serious concern people have the right to food and shelter why are 16,000 children dying of starvation every day one every five seconds if people have freedom of speech why are thousands in prison for speaking their minds if people have the right to education why are over a billion adults unable to read if slavery has truly been abolished why are 27 million people still enslaved today more than twice as many as in 1800 the fact is when it was signed the Universal Declaration of Human Rights did not have the force of law it was optional and despite many more documents conventions treaties and laws it's still a little more than words on a page come back to that conclusion perhaps a little later in this and the next two lectures I hope with you those of you who are good enough to come back to work out something about what human rights may mean for us now as well as to ask what whether they really exist as a separate species of right if they do where do they come from and significantly for us has their development in the last few decades done for the good or for the bad the discussion can hardly have come at a better time fortuitous though that is in light of the fact that there are some politicians and their electors who would seem to like to have no more to do with some forms or formulations of human rights believing them to be worthy of as much regard as our health and safety regulations and other uh Ning glitch things coming from a small continent cut off from the mainland of Britain the rights we consider the rights of men women and cross genders humans that they may have against other humans individually when they exercise kingly or dictatorial power or when they form government's they're not rights against nature or against the animal kingdom and indeed to reverse that and to state the obvious animal kingdom numberless as they are have no rights against men who will of course kill them at will if they find them tasty or imprison them inside some stockade if that suits their purpose equally obvious is that humans do not as a matter of fact have unlimited unqualified rights because they too can be killed in lawful war or by capital punishment and they may be imprisoned lawfully by due process all rights are qualified and they vary over time the founding right of today's human rights the 1948 UN Declaration of Human Rights is sometimes an uncomfortable read is set beside modern Western views or marriage homosexuality rights of women or indeed against the strong views of the Sharia law and indeed sixty-six years after that particular instrument was passed by the United Nations by 58 members the then 58 members of the UN it's pretty unlikely if such a document could now be passed given the increasing diversity and open diversity of 195 members of the UN and the very strongly expressed religious views that there are within that number nevertheless human rights with us they are described as universal and important word because if it is universal if they are universal there's nothing that can change them there's no religion no philosophy no political creed that can be above them that's of course something that some states find unappealing if human rights are universal because they are either part of the humans very being or because they were conferred on us by a God then they will always have existed even if unidentified and will continue forever to exist in roughly the same form and it's this concept that both stimulates an interest in humans rights and also brings about some objection to them early days there are many possible starting points it's a human activity that may reflect human rights some people go back as much as 2,000 years before Christ to the Pharaohs or the Babylonian king Hammurabi but much commentary these days turns to 1/6 century before Christ object as being off critical significance now in 539 BC the armies of cyrus the great there he is the first king of ancient Persia conquered the city of Babylon in modern-day Iraq part of what was a huge Empire under this immensely powerful man a clay cylinder inscribed with the declaration of Cyrus in the Babylonian language was buried beneath a building in Babylon not to surface until its excavation in 1879 very recently the British Museum along with the Iran Heritage Foundation has arranged for a tour of that cylinder there it is it's about the size of an American baseball football bit small writing and they arranged for this to go on hugely publicized and very successful tour of Iran and indeed of America and we can learn the perception of this particular object and its role in human rights from one or two of the things that the curators of museums concerned said so that for example when it was on tour with the Getty Museum in America Timothy Potts the director said even before its discovery that's the discovery of this particular object Cyrus the king the Great had been renowned as a benevolent and Noble ruler the Greek historian Xenophon presented him as an ideal leader in his cria pedia which is a book to a child turn about him in a second while Old Testament texts pray Cyrus for bringing an end to the Jewish exile in Babylon taking control taking control of Babylon he restored religious traditions and permitted those who had been deported to return to their settlements and rather than imposing in Persian practices on its people however he sought to uphold their tradition as is indeed evident from using their language on this little object and it wasn't just what Cyrus the Great said and what he inscribed on the cylinder but it's what he did to an hour thousand and more years ago that makes him a focus for the origins of human rights he freed the slaves he declared that all people had the right to choose their own religion and he established racial equality we can actually see in there's a version of the translation of that I think that companies the document the thing itself when it's on display in the British Museum but what's actually written on the cylinder includes the following and it's quite powerful I announced that I will respect the traditions customs and religions of the nations of my Empire I'll never let any of my governors and subordinates look down on or insult them until I'm alive from now on until God grants me the kingdom favor I will impose my monarchy on no nation each is free to accept it and if anyone has been rejects it I never result I had never resolved on war to reign until I am the king of Persia Babylon and the other nations of the four directions I will never let anyone repress any others and if it occurs I will take back until I am Alive I'm prevent unforced labor today I announce that everyone is free to choose a religion people are free to live in all religions to take up a job provided that they never violate another's rights I will present slavery and my governors and subordinates are obliged prohibit and so on and so forth Wow two and a half thousand years ago this ancient record has been seen by enthusiasts as the world's first known charter of human rights and it's translated into all six languages of the United Nations and there's a facsimile of it given by the sister of the Shah in 1977 I think that sits in headquarters in New York but Cyrus has his detractors notably in Germany where he's said by some to be something of a despot just like any other land grabber and indeed Tom Holland and English historian and author wrote the following about the rise of Cyrus in his book Persian fire he said it's nonsense absolute nonsense it's nonsense he said absolute nonsense the ancient Persians were not some form of early Swedish Social Democrats adding that a conquering a huge Empire in the ancient world didn't come without a list of atrocities and Cyrus staged several salutary atrocities when he invaded but he Tom Holland also moved this quite interesting point to have in the back of your minds he said one of the reasons that the UN is so keen to embrace as an important origin of human rights this particular thing is that it has an Eastern flavor to it and the UN is so heavily under the domination of West they'd like to sort of share the credit well that's a particularly skeptical view of the sincerity of things that the United Nations does but never mind because these criticisms even if they are true may be irrelevant for our present purpose if the way Cyrus was presented in biblical texts for he was and by his decree on the cylinder at agency at the top and those assertions were in fact believed by people despite being self generated untruths of Cyrus and if they were then applied by others then the text may have been for the good however much Cyrus may have been for the bad however the Buried cylinder to be read only by the gods couldn't have affected subsequent thinking but the writings about cyrus did and it's worth having this in mind that even if cyrus was genuinely for the good does another issue arise when we think about rights this so-called first Charter of Rights could have been just good advice for others to follow in the governance of empires and countries or it could have been something that Cyrus chose to give to his people not something that they claimed asserted or grabbed from him and that leads to a question for us to consider as we consider what are our rights are human rights and indeed others can rights be given or must they as a minimum be asserted if not actually demanded or seized now Cyrus is thinking immortalized by Xenophon as I've said in as encyclopedia the site the Cyro pedia which is a fictionalized account of his life was read very widely because Xenophon was Socrates pupil and so these thoughts found their way to Greece and we know also from Cicero that they found their way to Rome Cicero had studied the sorrel pedia and he wrote to one of his relations very favorably about the fictionalized Cyrus who was the subject of the book and so they're rapidly but we'll come back to it briefly our origins of human rights could be depending on your conception things as long ago as 2500 years because of course what Cyrus says is pretty much exactly what you get in the Universal Declaration of Human Rights I think chapters 1 to 4 well now the conception that humans had rights somehow permeated the Middle Ages or the Dark Ages and Europe serve saw the first famously to deal with such things in the Magna Carta in 1215 now that document Magna Carta had little initially to do released by purpose with ordinary men and women only with the rights of barons and their powers nevertheless signed as it was at Runnymede on the 12th of June 2015 so we're in for a lot of celebration next year the king attached his seal signed the document as it were and dealt with the unhappy group of noblemen this first proclamation that the subjects of a crown or the crown had legal rights and that the monarch then indistinguishable from the state could be bound by law became the first document to set out the right of habeas corpus in different wording and set a tradition of civil rights in Britain that still exists today the petition of right comes next at 1628 it ended a bitter contest between Parliament and King Charles the first over the way he was running and funding the 30 Years War as it would become known and this petition called on the team or required the king but relied first of all on a statute from Edward the first reign which dealt with the ability of the King to make to make funding to get taxes without the common consent of parliament it also the document of 1628 looked back to Magna Carta itself and it landed up theirs Magna Carta we needn't trouble with that the petition of right of 1628 landed up with the Parliament saying to the king they do therefore humbly pray your most excellent Majesty that no man hereafter be compelled to make a yield any gift loaned benevolence tax or such like charge without common consent by Act of Parliament and the nun be called to make answer or to take such earth or to give attendance I'll be confined or otherwise molested in any way manner as is before mentioned be imprisoned or detained so that we've we see the notion of rights in individuals and in parliament developing and being built one on the one that had gone before it granted that we then have to move on beyond that actually to the Bill of Rights of 1689 this followed the execution of Charles the first the short reign of James his departure and the arrival of William of Orange whose arrival was conditioned by or upon the Bill of Rights of 1689 now in summary and I'm in a quote from it but in summary the Bill of Rights 1689 keep focusing on the word rights that's what we are concerned with how do they come about do they exist in individuals only in organizations only in Parliament's the Bill of Rights granted freedom from taxation by Royal Prerogative it granted freedom to petition the monarch the citizen could approach the monarch that becomes relevant later it granted freedom to elect members of parliament without interference granted freedom of speech at least for parliamentary purposes and freedom from cruel and unusual punishments and from fine and forfeiture so much for England so far we followed ourselves maybe from Persia Greece Rome England let's go to America and of course it's impossible to understand the development of something like rights in a human being without some regard to the contemporary philosophers and we're entering the age as we turn to America into the 18th century of philosophers who were arguing and discussing what it's were famous among them was the English philosopher Locke who regarded rights as something that would have existed in a state of nature before man entered into society as self evidence rights and those rights he thought were the right to life liberty freedom from arbitrary rule and property now Locke's ideas and there are many other philosophers of the same period who held contrary views or similar views but Locke's ideas and those of the other philosophers lived beyond Locke's death in 1704 and so that when we come to the unanimous declaration of independence in America by the thirteen states what do we find is being asserted hostile to England this is not an English development well we find that in the Declaration of Independence they said this in the course of human events when in the course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another and to assume among the powers of the earth the separate and equal station to which the laws of nature and nature's gods entitle them a decent respect to the opinions of mankind they promised it then this is part of the preamble on the idea of the laws of nature nature's God entitle in them but they then went on to say this we hold these truths famously these truths to be self-evident that all men are created equal and they are endowed by their creator with certain unalienable rights that among these are life liberty and the pursuit of happiness then it goes on a little bit but the concept of rights to things is now central to the development of what is the greatest country if not the greatest the greatest power on earth if I express no qualen qualitative view one way or the other but the greatest power on earth is founded on the concept of rights by which they are prepared to withdraw from the country that have commanded them remember what I said at the beginning our rights things you can give or do you actually have to take them well they took these rights and in taking them they took their country with them now this particular document mustn't let us get overexcited over carried away with the idea that it's all good because in the second part of the document they set out their complaints about the king and how what a Rotter he was and one of the things that they said was this he's excited domestic insurrections amongst us and has endeavoured to bring on the inhabitants of our frontiers read what follows the merciless Indian savages whose known rule of warfare is an undistinguished destruction of all ages we have to bear in mind that at the same time as these people were advancing what might be thought very modern rights they were living with a philosophy which we're not a philosophy with a practice which we now know could have been described as genocide for what they were doing to the Native Americans they were now be called not by the term that's used here is pretty well long controversially described in those terms so to be on the good side of claiming a right doesn't mean to say your entire philosophy is to the good well we move back I think briefly to Persia why well actually stay in America but it's important enough to have in mind that Thomas Jefferson Benjamin Franklin and other founding fathers read ancient historical works in Latin and in Greek and indeed as Julian ray be the director of the Faire and Sackler galleries hosting that turn our thousand-year-old object observed in his explanation of its significance for the American people he said well in the 18th century that model of religious tolerance are based on a state with diverse cultures but no single dominant religion became a model for the founding fathers now why do I mention this at all in getting towards Europe but it's going to take us a bit more time yet because it's here it's important it's not essential to understand that concepts of human rights are complex in their formation and international they draw on whatever you can find that is valuable to the purpose do we want to have that in mind as we consider our possible withdrawal from the European Convention do we want to recognize that there's a big wide history that brings us to the position which we'll come to before very long um shall we now go to France because of course France you may think comes next in 1789 at the National Assembly of France it was declared that the representatives of the French people organized as a National Assembly believing that the ignorance neglect or contempt of the rights of man are the sole cause of public calamities and of the corruption of governments they determined to set forth in a solemn declaration the natural and unalienable and sacred rights of man namely man is born and remained free and equal in rights social distinctions may be founded only on the general good then dealing with political association it says that these rights Liberty property security and resistance to oppression although of course I've been selective in the passages from these various documents I've put before you but I hope I haven't missed represented them in any unfair way and you may think that what you've been reading from history is what is part of your present conception of your rights as a human being in northern Western democracy back to America briefly we have to look at the US Bill of Rights this was the first ten amendments of the US Constitution called the Bill of Rights and perhaps we just ought to look this one amendment one Congress made no law respecting an establishment of religion or prohibiting the free exercise thereof or abridging the freedom of speech or of the press or the right of the people peaceably to assemble it's a slightly less comfortable one for some of us in England because of course by amendment two there was that right of the people to bear and keep kids keep and bear arms which should not be infringed so again you can't assume that because something good is coming out of a particular document or of a particular period of time it's all going to be good but overall by this stage there's a big body of material coming towards us from our history to tell us what our rights might be but does it tell us what sort of rights they are have they been given to us have we seized them are they inherent in being a human Browsing old dictionaries and encyclopedias is sometimes a time-consuming but sometimes an interesting exercise in showing us how words have developed in their daily use the first edition of the encyclopædia Britannica published in 1771 by the Sir a society of gentlemen in Scotland as you may or may not know says nothing at all about the rights of man or indeed as far as I can find about rights I may have failed in searching the index not indexed but searching the topics correctly and this in the age of enlightenment published at a time when the English Philosopher's Locke Berkeley Hume in England Montesquieu Voltaire Rousseau in France were at their height fizzing with ideas about rights I was puzzled by this and I ventured to look something up on the internet as if I don't often do that and I found a clue I haven't been able to take it further but rather interesting clue because I it said that the Encyclopedia Britannica was a specifically an intentionally conservative document brought in defense of the French encyclopedia of Denis Diderot whose encyclopedia was thought to be heretical not least because it included entries by Rousseau Voltaire and Montesquieu and of course covered those issues of the Age of Enlightenment and why do I find that interesting well because if you think of neighboring countries advancing with their philosophies they don't actually advance together they find things to be at odds with one another about and that's why it remains important for us to be open to other influences there's at least the slightest indication here that the first edition of the encyclopædia Britannica was not that willing to be open to the arguments that were going around about rights that had formed the United States of America you see why this might be significant in the decision we have to make now Beaton's dictionary which I've never been able completely to date but I think it's about 1860 from the entries dealing with rights says rights necessarily implies duties for whatever is due to one man or said of men is necessarily do from another and it further defines rights as natural to those which a man NAT Forge would you man has a natural or just claim to such as his life his liberty to produce labor but there are also adventitious rights of the kind derived from appointments for example you thumb the king or he become a general but it's in each case rights implying duties and natural rights Lloyd's encyclopedia of 1895 deals with things much more some early natural rights it says are those relating to life and liberty and went on to say that they are that which is right or in accordance with the laws of God pausing there if I were to be the person with the camera and the microphone that you saw or you didn't see in the little film at the beginning and I were to ask you okay what's a human right even with this very short exposition of history would you be any better able to do more than give some sense of what they were about they are things that we sense they think they there are things we feel but they're a bit willow the wisp ish or on you'll tell me later and in the next two lectures because as you probably know I'm going to hope to get some involvement by you in the next two lectures which will enable us to tease out a bit more of what human rights may really be about the 20th century well we have to move rapidly and I should say this it was interesting to discover given that the Declaration of Human Rights was made in 1948 that the first of two shorter oxford dictionaries that I looked averages are quite big ones but not the biggest had absolutely no entry of any kind in relation to human rights that was one I think was in 1968 so 20 years after the Declaration of Rights not covered in a dictionary not thought of as ordinary parlance by the time you get to 2007 it's got about the most succinct definition of human rights that you can have held to be justifiably claimed by any person held to be justifiably came by any person well it's the 20th century which we must focus on and this Declaration of Human Rights that came in 1948 followed the formation of the United Nations first of all who then set out up a commission to deal with the issue of human rights and it was established under Eleanor Roosevelt the late president's wife herself a formidable figure in this field the declaration the preamble to the United Nations Charter said we the people of the United Nations are determined to save succeeding generations from the scourge of war now when we have the Declaration of Human Rights following so quickly after the original formation of the United Nations it's sure that they had in mind the second extract from the film that human rights are more than just things you give they they're there to stop these terrible things happening again even though as that little extracts from the film showed it doesn't always work or rarely works well when we come to the Declaration of Human Rights itself it said amongst other things this disregard and content for human rights have resulted in barbarous acts which have outraged the conscience of mankind and the advent of a world in which human beings shall enjoy freedom of speech and freedom from fear and want has been Klain is the highest aspiration of all people all human beings are born free and equal in dignity and rights so an extremely important document that focuses on rights as part of a much broader overall international policy what could we say about the Declaration of Human Rights the first thing is its it wasn't a treaty was plans for it to be a retreat but a treaty would of course be something to which people would be bound with consequences if they broke it but they could also withdraw from it the declaration possible all 58 members at the time I think some abstained is something that remains a universal declaration it's quite hard to unmake it and in many ways it's perhaps better that they had a declaration that they had a cut than they had a covenant or a treaty or something of that form the Commission that drafted this was international apart from the Eleanor Roosevelt there was a Frenchman a Lebanese gentleman a China a person from China and Eleanor Roosevelt says in her memoirs how broad the discussion was that they range from Confucius to Thomas Aquinas to the theories of pluralism and it's clear that these people chose them no doubt for the breadth of their experience and intellect didn't look at rights in a narrow basis they looked at it as broadly as they could and surprisingly got this draft through on the 10th of December 1948 and the chill a member of the drafting subcommittee a man called Santa Cruz said this I perceived clearly this was on the day of the signing that I was participating in a truly significant historic event in which a consensus had been reached as to the supreme value of the human person the value that didn't orig in the decision of a worldly part but rather in the fact of existing which gave rise to the inalienable right to live free from want and oppression and to fully develop one's personality and then he goes on to say the emotions he had when it was signed but this you see is approaching the business of human rights at an even more an elevated level really it's saying that the inalienable right right sorry the three lines down the supreme value of the human person it's almost as if people were starting to think of an sometimes when I talk to students I suspect they think of it in these terms that your human rights actually identifies you as a human being in a way that perhaps religion might have done but for some does not so we won't spend too much time with the details of the declaration because it won't come as any particular surprise to you to know now having seen all the other documents which may be part of the lineage of this documents that all humans are being born free everyone is entitled to the rights and freedoms set forth regardless of sex language religion political or other opinion everyone has the right to life liberty and security no one shall be held in slavery no torture so that it's in line with all the documents that have gone before article 25 I'm not gonna trouble with article 25 I because I'm going to come back later to article 22 so don't bother to read it sorry you have an inalienable right if I might say to read whatever you like it would be claimed with you at birth but the the Declaration of Human Rights has inspired eighty or so international human rights treaties and declarations and a great number of regional Human Rights conventions and has been instrumental in the Constitution's of many developed and developing countries and so it is finally that we come to Europe initially after the Second World War the idea of the development of Europe lay with an unofficial body the European movement that pressed for European unity and very soon after the war it said about drafting a human rights convention now these days a great deal is made of the fact in the party politics side of all this that one of the prime movers of this convention Human Rights Convention was a man called Sir David Maxwell Fyfe later of I can't kill Muir head of the chambers where I was for tyranny where I was head of chambers return and a very odd champion of human rights indeed famously he did not encourage the monarch to reprieve people sentenced to death infamously he refused to reprieve Bentley contrary to his advisers advice and course Bentley was ultimately acquitted posthumously in the 1990s the famous case of Craig and Bentley anybody doesn't know about it ask people a bit older than you are and you'll learn now it seems to me but I should also say that that Maxwell Fyfe famously cross-examined Goering when the Americans weren't doing such a good job and he very clearly as a result of the war understood the needs to have some mechanism to bring people together around laws that reflected the rights of humans to live in peace and it seems to me and you might want have this in mind when you hear the debates on the television with the Labour Party praising the man who allowed Bentley to hang and all that sort of thing because these are conservative you might like to think that the more important part is not who he was but the origins of this act this part of European community life was a government process of ours it wasn't some strange imposition on us we were fully engaged in it and what this all led to was something called the Council of Europe nothing to do with the European Commission totally different the Council of Europe still exists today and it was the Council of Europe that established the European Court of Human Rights and dealing quite swiftly with that let me try and explain the position because we will look at this in more detail in the next two lectures but the European Court of Human Rights is a court to which people could go and they could go eventually directly remember I invited your attention to the right of being able to address the sovereign directly in your petition as a citizen how that was part of the developing pattern of human rights well here in 1966 it was possible to go directly to the Commission and to the court and who do you think was the country that held that up put it on paid it was ass we were quite keen on creating that there Commission of Human Rights of the convention well we were very very keen on giving it as much parse as others wanted it to have dragged our feet a bit on that one but nevertheless that's what happened so you can go to the court and you can get if you have exhausted all your English remedies or your national remedies you can get a decision on the court that can come back and affect the decision that's made in England and what you're going to hear discussed in the months and to come before the next election is whether that's something that should be preserved for you country our country or whether it's something that should be changed and there are I think a couple of approaches to this as a problem that I'd like to draw to your attention first of all and I've mentioned him before in a previous lecture I kill you I'll stop you reading that so that I make you listen to me John Laws is a sitting member of the Court of Appeal or an extremely intelligent vastly experienced and very well-read classical scholar and in the debate about how much power Europe should have in the business of law coming back to England he says don't worry too much so if England has always been something were magpie it's picked up bits and pieces from here there and everywhere else he calls it the catholicity of the English law and he says what happened is you you gather it in and you use it and the law changes and you shouldn't be frightened about it and he says and in any event the Parliament the European called can't actually force us to compare to change our laws our laws are still sovereign the convention the convention of human rights which is the subject of so much discussion the convention yes we have to accept as a matter of government and parliamentary decision over the years but in fact when the law comes back to us we can embrace it we can engage with it but we don't have to actually take it into account and that's a very encouraging approach to take especially if it's accurate one as it's likely to be coming from him now let you read his his writing is worth three over on the handout I've given you the reference read the lecture if you're in his lecture in full its it's an easy and and enjoyable read even if you're not a lawyer but this is how he ended his lecture and he said this because our law is constantly renewed by the force of fresh examples because it reflects and moderates the ten of the people as age succeeds age because it builds on the experience of ordinary struggles its principles will always be buffeted by events in their different ways the confrontation of extremism and the absorption of law from Europe press upon the constitutional balance but he ends if we keep faith with it we should enjoy a noble inheritance and may anticipate a tranquil future that's one approach to the debate about human rights there are others who take a different and less positive view in the handout I have given you another lecture or in it I've given you extracts from another lecture which is also given a citation but before I come to that I should at least tell you some of the other criticisms that have been made of the process of development of human rights which has really got quite a head of steam under it since the end of the Second World War and as long ago as 1998 the 50th anniversary of the Declaration of Human Rights you can find people cited in the paper you can find people saying it's time to reform this document because it is a Northern European based exercise because it's concerned with supporting Western democracies it's part of the prasada tizen of Western views and we have to bear in mind that there have been critics of the whole development of human rights at all times and they should be listened to because in the same way as in the Age of Enlightenment you didn't just pick one philosopher and say well that's a good idea I'll follow him you read all of them if you could in order to form your own view now on the contrary side the perhaps best read that you can have is from Roger Scruton who is a lawyer and a philosopher and he makes a number of extremely powerful points in the Lincoln's in lecture that I've left for you to read if you wish to but like laws he's a very easy a very easy read and he is concerned about a number of possibilities with human rights namely he says that what you have is that egalitarians who support the human rights movements and who dislike hierarchies of every kind have begun to insert into the general body of positive rights right to life liberty and so on a list of negative freedoms as he describes them the liberty rights specified by the various international conventions that we've looked at some of them and some of their sources have therefore been supplemented by certain claim rights rights which don't merely demand non encroachment from others which impose a positive duty on others and he says this is particularly apparent in the UN Declaration of Human Rights which begins with a list of freedom rights and then suddenly at article 22 makes radical claims against the state claims which can be satisfied only by a positive action and article 22 of the 1948 declaration said everyone as a member of society has the right to Social Security and is entitled a realization through the national effort and international cooperation and in accordance with the organizational resources of each state and so on and so forth and you can see immediately what's Cruden's point is if you say well not only do I have a right to read what's on the board to breathe to say my mind and so on but I also have a right to be supported by the state that's a bit strange isn't it it's a different category of right it may be a jolly good thing to be entitled to be supported by the state but is it a human right does it feel like one and if there's a sort of rights creep creeping of human rights he says well if that's happening this can't be the right thing it can't really be what was ever intended by philosophers of years ago or the underlying philosophy of age and he says there is a weight of political and social philosophy behind that article 22 contained within this right is an unspecified list of other rights called economic social and cultural which are held to be indispensable not for freedom but for dignity free development of personality and he sets it all out and he sets out a list which I have given you in case you need a crib of some of the things that are fashionably said unfashionably said to be wrong with the consequences of mission creep or human rights creep to which he refers let me start then to draw things to a conclusion and to invite you in due course to ask questions or make a few comments before we close for the evening what if anything can we draw from what I've been able to discuss with you so far what conclusions if any do I feel able to make given that if you look to the conservative party now they are unequivocally going not unequivocally but they are intending to withdraw from the convention to have at most the Court of Human Rights an advisory body and to set up the contents of the convention within the domestic law if you look at UK for example they are even more blunt and shorter in what they're going to do which of course involves withdrawing from the convention indeed involved I express partly because I have no view but it is right isn't it to ask yourself the question or is it to ask yourself the question you have a freedom to choose a right to choose I pick a fight is it fair to say look where we are now goes back either hundreds of years if you want to start at magna carta or thousands of years and we've drawn on sources from all around at least part of the globe if Confucius is apprised as well even more of the globe and sometimes we've been drawing material from our enemies I guess the average Briton when America was declaring human rights would have said well that's a that's a wicked thing to say and yet now we'd all agree with it when they did describe what the rights were that they are suited for themselves and so conclusion number one it seems to me is that in making our decision about where we go with human rights we should recognize this rich complicated history the second thing is I I feel that the students and the people in that film right at the beginning are probably pretty much like we would still be right now because as I said earlier on it's something that we sense and we can feel but we can't necessarily describe and if at the end of it I was have to ask you is is a human I'm not going to do one of those so for any questions hands up polls but if I was to ask you is it something inbuilt in the human that you have these riots or is it something that's been given you by a state who knows but your hands off and hands down would be the next thing is it seems to me that those who have complained that these rights are over contextualized in the Western democracies may well have a point imagine a tribe in Borneo or possibly in Africa untouched by Western society or indeed the occupants of North Korea who have lived for a long time under an authoritarian regime parents and children or indeed the Chinese students who I saw being interviewed by Jonathan Dimbleby on his tour to China and these were students all postgraduate students speaking impeccable English saying no mr. BB you're wrong we don't want the rights that you say are so important we have a different culture now do we have to take note of the fact that there may be cultures who would simply say no thanks very much those are not things we want and if they say that or they might say that what does that say about the true nature of a human right well you could answer that with a yes but yes you might be right but in fact many of the developments you've pointed to not necessarily Cyrus because he may have given the benefits to his people but the Americans and the French they were taking things they were people previously under control that was not democratic and they chose to seize these rights for themselves so you could say well it looks as though some of these rights are in any event inbuilt in us the things we desire but you can't really go much further than that I would have thought I would have hoped that you would think that there must be something worth thinking about in John Laws a little justice laws point that a law like ours that we many people pride for its longevity and its flexibility has drawn on sources for all around the world and should continue to do so and that by implication although of course he expresses no political view or implies any and that it would be unwise having got a body that's providing answers to questions of human rights simply to abandon it or effectively abandon it even if it's not bringing quite the results you want at the moment might it not be better to stay with it in order to work it through because then you have the benefit of a broader input to your own knowledge and then as to Roger Scruton on the other hand is is there not a pretty strong argument that he makes that once you start talking of rights that beyond the right to life or light to freedom that you you really do run the risk of muddying yet further our understanding of what a human right is and diluting what it is but those questions and none of them answer the question sorry those observations and none of them answer the question but in the next couple of events if you'll join me I hope that we may be able to look at what you may regard as the bad sides of human rights in the next lecture if you tell me what you think they are I'll select some or all of them and I'll do what I can to research them between now and then so that I can present some analysis of the things that are concerning you and then on the last one to look at the good things that human rights supporters in the period since the Second World War human rights law as understood so that we can perhaps leave these three lectures with if not an understanding of what a human right is a better understanding of the reason for our ignorance and let me finish as I forecast I would with a back reference to the second little film clip do you remember the one that showed the terrible things that happen well human rights are not just intellectual construct they are said to be things that people have and should be fought for and there are all these God is the United Nations and the United Nations Human Rights Council and the United Nations Human Rights Commission who have functions plentiful to do in relation to the state of the world and so coming back from the academic if it is of the theoretical if it is this is what the outgoing Human Rights Commissioner Navi Pillay said this very year about the present position this is the Human Rights Commissioner leaving office she said short-term geopolitical considerations and national interests narrowly defined have repeatedly taken precedence over intolerable human suffering and grave breaches of and long-term threats to international peace and security I firmly believe that greater responsiveness by this council that's the Security Council would have saved hundreds of thousands of lives an extraordinary and I suppose brave thing for somebody in that position to have said and focusing our minds as we look at what lies ahead on the need to get the identification of human rights right and then to recognize that doing nothing about it is wrong you

Feynman: Knowing versus Understanding



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Richard Feynman on the differences of merely knowing how to reason mathematically and understanding how and why things are physically analyzed in the way they are.

Einstein's General Theory of Relativity | Lecture 1



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Lecture 1 of Leonard Susskind’s Modern Physics concentrating on General Relativity. Recorded September 22, 2008 at Stanford University.

This Stanford Continuing Studies course is the fourth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on classical mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

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this program is brought to you by Stanford University please visit us at stanford.edu gravity gravity is a rather special force it's unusual it has different than electrical forces magnetic forces and it's connected in some way with geometric properties of space space and time but before and that connection is of course the general theory of relativity before we start tonight for the most part we will not be dealing with the general theory of relativity we will be dealing with gravity in its oldest and simplest mathematical form well perhaps not the oldest and simplest but Newtonian gravity and going a little beyond what Newton certainly nothing that Newton would not have recognized or couldn't have grasped Newton could grasp anything but some ways of thinking about it which will not be found in Newton's actual work but still lutonium gravity the Toney and gravity set up in a way that that is useful for going on to the general theory ok let's begin with Newton's equations the first equation of course is F equals MA force is equal to mass times acceleration let's assume that we have a frame of reference a frame of reference that it means a set of coordinates and as a collection of clocks and those frame and that frame of reference is what is called an inertial frame of reference an inertial frame of reference simply means 1 which if there are no objects around to exert forces on a particular let's call it a test object a test object is just some object a small particle or anything else that we use to test out the various fields force fields that might be acting on it the inertial frame is one which when there are no objects around to exert forces that object will move with you for motion with no acceleration that's the idea of an inertial frame of reference and so if you're an inertial frame of reference and you have a pen and you just let it go it stays there it doesn't move if you give it a push it will move off with uniform velocity that's the idea of an inertial frame of reference and in an inertial frame of reference the basic Newtonian equation number one I always forget which law is which there's Newton's first law second law and third law I never can remember which is which but they're all pretty much summarized by f equals mass times acceleration this is a vector equation I expect people know what a vector is a three vector equation will come later to four vectors where when space and time are united into space time but for the moment space is space and time is time and a vector means a thing which is like a pointer in a direction in space as a magnitude and that has components so component by component the X component of the force is equal to the mass of the object times the X component of acceleration Y component Z component and so forth in order to indicate that something is a vector equation I'll try to remember to put an arrow over vectors the mass is not a vector the mass is simply a number every particle has a mass every object has a mass and in Newtonian physics the mass is conserved that does not change now of course the mass of this cup of coffee here can change it's lighter now but it only changes because mass has been transported from one place to another so you can change the mass of an object by whacking off a piece of it and but if you don't change the number of particles change the number of molecules and so forth then the mass is a conserved unchanging quantity so that's first equation now let me write that in another form the other form we imagine we have a coordinate system an X a Y and a Z I don't have enough directions on the blackboard to draw Z I won't bother there's x y and z sometimes we just call them x1 x2 and x3 I guess I can draw it in x3 is over here someplace XY and Z and a particle has a position which means it has a set of three coordinates sometimes we will summarize the collection of the three coordinates x1 x2 and x3 incidentally x1 and x2 and x3 are components of a vector the components they are components of the position vector of the particle position vector of the particle I will often call either small R or large are depending on on the particular context R stands for radius but the radius simply means the distance between a point and the origin for example we're really talking now about a thing with three components XY and Z and it's the radial vector the radial vector this is the same thing as the components of the vector R alright the acceleration is a vector that's made up out of the time derivatives of XY and Z or X 1 X 2 and X 3 so for each component the compose for each component one two or three the acceleration which let me indicate well let's just call it a the acceleration is just equal the components of it are equal to the second derivatives of the coordinates with respect to time that's what acceleration is the first derivative of position is called velocity we can take this to be component by component x1 x2 and x3 the first derivatives velocity the second derivative is acceleration we can write this in vector notation I won't bother but we all know what we mean I hope we all know we mean buddies by acceleration and velocity and so Newton's equations are then summarized and summarized but rewritten as the force on an object whatever it is component by component is equal to the mass times the second derivative of the component of position so that's the summary of I think it's Newton's first and second law I can never remember which they are Newton's first law of course is simply the statement that if there are no forces then there's no acceleration that's Newton's first law equal and opposite right so this summarizes both the first and second law I never understood why there was a first and second law it seems to me there was just one F equals MA all right now let's begin even even previous to Newton with Galilean gravity gravity as Galileo understood it actually I'm not sure how much of this mathematics Galileo did or didn't understand he certainly knew what acceleration was he measured it I don't know that he had thee but he certainly didn't have calculus but he knew what acceleration was so what Galileo studied was the motion of objects in the gravitational field of the earth in the approximation that the earth is flat now Galileo knew the earth wasn't flat but he studied gravity in the approximation where you never moved very far from the surface of the earth and if you don't move very far from the surface of the earth you might as well take the surface of the earth to be flat and the significance of that is to twofold first of all the direction of gravitational forces is the same everywhere as this is not true of course if the earth is curved then gravity will point toward the center but in the flat space approximation gravity points down down everywhere is always in the same direction and second of all perhaps a little bit less obvious but nevertheless true then the approximation where the earth is Infinite and flat goes on and on forever infinite and flat the gravitational force doesn't depend on how high you are same gravitational force here as here the implication of that is that the acceleration of gravity since force apart from the mass of an object the acceleration on an object is independent the way you put it and so Galileo either did or didn't realize well he again I don't know exactly what Galileo did or didn't know but what he said was equivalent to saying that the force on an object in the flat space approximation is very simple its first of all has only one component pointing downward if we take the upward sense of things to be positive then we would say that the force is let's just say the component of the force in the X 2 direction the vertical Direction is equal to minus the minus simply means that the force is downward and it's proportional to the mass of the object times a constant called the gravitational acceleration now the fact that it's constant Everywhere's in other words mass times G doesn't vary from place to place that's this fact that gravity doesn't depend on where you are in the flat space approximation but the fact that the force is proportional to the mass of an object that is not obvious in fact for most forces it's not true for electric forces the force is proportional to the electric charge not to the mass and so gravitational forces are rather special the strength of the gravitational force on an object is proportional to its mass that characterizes gravity almost completely that's the special thing about gravity the force is proportional itself to the mass well if we combine F equals MA with the force law this is the law force then what we find is that mass times acceleration the second X now this is the vertical component by DT squared is equal to minus that's the minus M G period that's it now the interesting thing that happens in gravity is that the mass cancels out from both sides that is what's special about gravity the mass cancels out from both sides and the consequence of that is that the motion of an object its acceleration doesn't depend on the mass it doesn't depend on anything about the particle a particle object I'll use the word particle I don't necessarily mean the point the small particle or baseb as a particle an eraser is a particle a piece of chalk is a particle that the motion of the object doesn't depend on the mass of the object or anything else the result of that is that if you take two objects of quite different mass and you drop them they fall exactly the same way our Galileo did that experiment I don't know if they're whether he really threw something off the Leaning Tower of Pisa or not it's not important he yeah he did balls down an inclined plane I don't know whether he actually did or didn't I know the the the myth is that he didn't die I find it very difficult to believe that he didn't I've been in Pisa last week I was in Pisa and I took a look at the Leaning Tower of Pisa galileo was born and lived in Pisa he was interested in gravity how it would be possible that he wouldn't think of dropping something off the Leaning power tower is beyond my comprehension you look at that tower and you say that I was good for one thing dropping things off now I don't know maybe the Doge or whoever they call the guy at the time said no no Galileo you can't drop things from the tower you'll kill somebody so maybe he didn't but he must have surely thought of it all right so the result had he done it and had he not had to worry about such spurious effects as air resistance would be that a cannonball and a feather would fall in exactly the same way independent of the mass and the equation would just say the acceleration would first of all be downward that's the minus sign and equal to this constant G excuse me that mean yes now G is a number it's 10 meters per second per second at the surface of the earth at the surface of the Moon it's something smaller and the surface of Jupiter it's something larger so it does depend on the mass of the planet but the acceleration doesn't depend on the mass of the object you're dropping it depends on the mass of the object you're dropping it onto but not the mass of the object that's dropping that fact that gravitational motion is completely independent the mass is called or it's the simplest version of something that's called the equivalence principle why it's called the equivalence principle we'll come to later what's equivalent to what at this stage we could just say gravity is equivalent between all different objects independent of their mass but that is not exact were the equivalents an equivalence principle was about that has a consequence an interesting consequence supposing they take some object which is made up out of something which is very unwritten just a collection of point masses maybe maybe let's even say that not even they're not even exerting any forces on each other it's a cloud a varied a few diffuse cloud of particles and we watch it fall let's suppose we start each particle from rest not all at the same height and we let them all fall some particles are heavy some particles are light some of them may be big some of them may be small how does the whole thing fall the answer is all of the particles fall at exactly the same rate the consequence of it is that the shape of this object doesn't deform as it falls it stays absolutely unchanged the relationship between the neighboring parts are unchanged there are no stresses or strains which tend to deform the object so even if the object were held together by some sort of struts or whatever there would be no forces on those struts because everything falls together the consequence of that is the falling in a gravitational field is undetectable you can't tell that you're falling in a gravitational field by you when I say you can't tell certainly you can tell the difference between freefall and standing on the earth that's not the point the point is that you can't tell by looking at your neighbors or anything else that there's a force being exerted on you and that that force that's being exerted on you is pulling you down word you might as well for all practical purposes be infinitely far from the earth with no gravity at all and just sitting there because as far as you can tell there's no tendency for the gravitational field to deform this object or anything else you cannot tell the difference between being in free space infinitely far from anything with no forces and falling freely in a gravitational field that's another statement of the equivalence principle for example these particles could be equipped with lasers lasers and optical detectives of some sort what's that oh you could certainly tell if you was standing on the floor here you could tell that something was falling toward you but the question is from within this object by itself without looking at the floor without knowing the floor was it well you can't tell whether you're falling and it's yeah yeah if there was something that was calm that was not falling it would only be because there was some other force on it like a beam or a tower of some sort of holding it up why because this object if there are no other forces on and only the gravitational forces it will fall at the same rate as this all right so that's another expression of the equivalence principle that you cannot tell the difference between being in free space far from any gravitating object versus being in a gravitational field that we're going to modify this this is of course it's not quite true in a real gravitational field but in this flat space approximation where everything moves together you cannot tell that there's a gravitational field or at least you cannot tell the difference I will not without seeing the floor in any case the self-contained object here does not experience anything different than it would experience far from any gravitating hating object standing still or uniform in uniform motion no you're accelerating if you go up to the top of a high building and you close your eyes and you step off and go into freefall you will feel exactly the same you feel weird I mean that's not the way you usually feel because your stomach will come up and you know do some funny things you know you might you might lose it but uh but the point is you would feel exactly the same discomfort in outer space far from any gravitating object just standing still you feel exactly the same peculiar feelings one of those peculiar feelings due to they're not due to falling they do to not fall well they do to the fact that when you stand on the earth here there are forces on the bottoms of your feet which keep you from falling and if the earth suddenly disappeared from under my feet sure enough my feet would feel funny because they used to having those forces exerted on their bottoms you get it I hope so the fact that you feel funny in freefall is because you're not used to freefall and it doesn't matter whether you're infinitely far from any gravitating object standing still or freely falling in the presence of a gravitational field now as I said this will have to be modified in a little bit there are such things as tidal forces those tidal forces are due to the fact that the earth is curved and that the gravitational field is not the same in every same direction in every point and that it varies with height that's due to the finiteness of the earth but in the flat space surprise and the Flat Earth approximation where the earth is infinitely big pulling uniformly there is no other effective gravity that is any different than being in free space okay again that's known as the equivalence principle now let's go on beyond the flat space or the Flat Earth approximation and move on to Newton's theory of gravity Newton's theory of gravity says every object in the universe exerts a gravitational force on every other object in the universe let's start with just two of them equal and opposite attractive attractive means that the direction of the force on one object is toward the other one equal and opposite forces and the magnitude of the force the magnitude of the force of one object on another let's let's characterize them by a mass let's call this one little m think of it as a lighter mass and this one which we can imagine as a heavier object will call it begin all right Newton's law of force is that the force is proportional to the product of the masses making either mass heavier will increase the force or the product of the masses begin tons of little m inversely proportional to the square of the distance between them let's call that R squared let's call the distance between them are and there's a numerical constant this for this law by itself could not possibly be right it's not dimensionally consistent the if you work out the dimensions of force mass mass and R will not dimensionally consistent there has to be a numeric constant in there and that numerical constant is called capital G Newton's constant and it's very small it's a very small constant I'll write down what it is G it is equal to six or six point seven roughly times 10 to the minus 11th which is a small number so in the face of it it seems that gravity is a very weak force you might not think that gravity is such a weak force but to convince yourself it's a weak force there's a simple experiment that you can do week week by comparison with other forces I've done this for car classes and you can do it yourself just take an object hanging by a string and two experiments the first experiment take a little object here and electrically charge it electrically charge it by rubbing it on your sweater that doesn't put very much electric charge on it but it charges it up enough to feel some electrostatic force and then take another object of exactly the same kind rub it on your shirt and put it over here what happens they repel and the fact that they repel means that this string will shift and you'll see a shift take another example take your little ball there to be iron and put a magnet next to it again you'll see quite an easily detectable deflection of the of the string holding it next take a 10,000 pound weight and put it over here guess what happens undetectable you cannot see anything happen the gravitational force is much much weaker than most other kinds of forces and that's due to the or not due to but the not due to that the fact that it's so weak is encapsulated in this small number here another way to say it is if you take two masses each of one kilometer not one kilometer one kilogram kilogram is a good healthy mass right nice chunk of iron mm and you separate them by one meter then the force between them is just G and it's six point seven times ten to the minus eleven the you know the units being Newtons so it's very very weak force but weak as it is we feel that rather strenuously we feel it strongly because the earth is so darn heavy so the heaviness of the earth makes up for the smallness of G and so we wake up in the morning feeling like we don't want to get out of bed because gravity is holding us down Oh Oh the equal and opposite equal and opposite that's the that's the rule that's Newton's third law the forces are equal and opposite so the force on the large one due to the small one is the same as the force of the small one on the large one and but it is proportional to the product of the masses so the meaning of that is I'm not heavier than I like to be but but I'm not very heavy I'm certainly not heavy enough to deflect the hanging weight significantly but I do exert a force on the earth which is exactly equal and opposite to the force that they're very heavy earth exerts on me why does the earth excel if I dropped from a certain height I accelerate down the earth hardly accelerates at all even though the forces are equal why is it that the earth if the forces are equal my force on the earth and the Earth's force on me of equal why is it that the earth accelerates so little and I accelerate so much yeah because the acceleration involves two things it involves the force and the mass the bigger the mass the less the acceleration for a given force so the earth doesn't accelerate quickly I think it was largely a guess but there was certain was an educated guess and what was the key ah no no it was from Kepler's it was from Kepler's laws it was from Kepler's laws he worked out roughly speaking I don't know exactly what he did he was rather secretive and he didn't really tell people what he did but the piece of knowledge that he had was Kepler's laws of motion planetary motion and my guess is that he just wrote down a general force realized that he would get Kepler's laws of motion for the inverse-square law I don't believe he had any underlying theoretical reason to believe in the inverse-square law that's correct he asked a question for inverse square laws no no it wasn't the ellipse which was the the the orbits might have been circular it was the fact that the period varies is the three halves power of the radius all right the period of motion is circular motion has an acceleration toward the center any motion in the circle is accelerated to the center if you know the period in the radius then you know the acceleration toward the center okay or we could write let's let's do it anybody know what if I know the angular frequency the angular frequency of going around in an orbit that's called Omega you know a–they and it's basically just the inverse period okay Omega is roughly the inverse period number of cycles per second what's the what is the acceleration of a thing moving in a circular orbit anybody remember Omega squared R Omega squared R that's the acceleration now supposing he sets that equal to some unknown force law f of r and then divides by r then he finds Omega as a function of the radius of the orbit okay well let's do it for the real case for the real case inverse square law f of r is 1 over r squared so this would be 1 over r cubed and in that form it is Kepler's second law remember which one it is it's the law that says that the frequency or the period the square of the period is proportional to the cube of the radius that was the law of Kepler so from Kepler's laws he easily could have that that one law he could easily deduce that the force was proportional to 1 over R squared I think that's probably historically what what he did then on top of that he realized if you didn't have a perfectly circular orbit then the inverse square law was the unique law which would give which would give elliptical orbits so who's to say well then of course there are the forces on them for two objects are actually touching each other there are all sorts of forces between them that I'm not just gravitational electrostatic forces atomic forces nuclear forces so you'll have to my breaks down yeah then it breaks down when they get so close that other important forces come into play the other important forces for example are the forces that are holding this object and preventing it from falling these we usually call them contact forces but in fact what they really are is various kinds of electrostatic for electrostatic forces between the atoms and molecules in the table in the atoms and molecules in here so other kinds of forces all right incidentally let me just point out if we're talking about other kinds of force laws for example electrostatic force laws then the force we still have F equals MA but the force law the force law will not be that the force is somehow proportional to the mass times something else but it could be the electric charge if it's the electric charge then electrically uncharged objects will have no forces on them and they won't accelerate electrically charged objects will accelerate in an electric field so electrical forces don't have this Universal property that everything falls or everything moves in the same way uncharged particles move differently than charged particles with respect to electrostatic forces they move the same way with respect to gravitational forces and as a repulsion and attraction whereas gravitational forces are always attractive where where's my gravitational force I lost it yeah here is all right so that's that's Newtonian gravity between two objects for simplicity let's just put one of them the heavy one at the origin of coordinates and study the motion of the light one then Oh incidentally one usually puts let me let me refine this a little bit as I've written it here I haven't really expressed it as a vector equation this is the magnitude of the force between two objects thought of as a vector equation we have to provide a direction for the force vectors have directions what direction is the force on this particle well the answer is its along the radial direction itself so let's call the radial distance R or the radial vector R then the force on little m here is along the direction R but it's also opposite to the direction of R the radial vector relative to the origin over here points this way on the other hand the force points in the opposite direction if we want to make a real vector equation out of this we first of all have to put a minus sign that indicates that the force is opposite to the direction of the radial distance here but we have to also put something in which tells us what direction the force is in it's along the radial direction but wait a minute if I multiply it by r up here I had better divide it by another factor of R downstairs to keep the magnitude unchanged the magnitude of the force is 1 over R squared if I were to just randomly come and multiply it by r that would make the magnitude bigger by a factor of our so I have to divide it by the magnitude of our this is Newton's force law expressed in vector form now let's imagine that we have a whole assembly of particles a whole bunch of them they're all exerting forces on one another in pairs they exert exactly the force that Newton wrote down but what's the total force on a particle let's label these particles this is the first one the second one the third one the fourth one that I thought that thought this is the ithe one over here so I is running index which labels which particle we're talking about the force on the eigth article let's call F sub I and let's remember that it's a vector it's equal to the sum now this is not an obvious fact that when you have two objects exerting a force on the third that the force is necessarily equal to the sum of the two forces of the two are of the two objects you know what I mean but it is a fact anyway obvious on how obvious it is a fact that gravity does work that way at least in the Newtonian approximation with Einstein it breaks down a little bit but in Newtonian physics the force is the sum and so it's a sum over all the other particles let's write that J not equal to I that means it's a sum over all not equal to I so the force on the first particle doesn't come from the first particle it comes from the second particle third particle fourth particle and so forth each individual force involves M sub I the force of the ice particle times the four times the mass of the Jade particle product of the masses divided by the square of the distance between them let's call that R IJ squared the distance between the eigth article his I and J the distance between the earth particle and the J particle is RI J but then just as we did before we have to give it a direction but a minus sign here that indicates that it's attractive another R IJ upstairs but that's a vector R IJ and make this cube downstairs alright so that says that the force on the I've particle is the sum of all the forces due to all the other ones of the product of their masses inverse square in the denominator and the direction of each individual force on this particle is toward the other all right this is a vector sum yeah hmm the minus indicates that it's attractive excellent but you've got the vector going from like a J oh let's see that's a vector going from the J yes there is a question of the sine of this vector over here so yeah you know absolutely let's yeah I actually think it's yeah you're right you're absolutely right the way I've written that there should not be a minus sign here all right but if I put our ji there then there would be a minus sign right so you're right but in any case every one every one of the forces is attractive and what we have to do is to add them up we have to add them up as vectors and so there's some resulting vector some resultant vector which doesn't point toward any one of them in particular but points in some direction which is determined by the vector sum of all the others all right but the interesting fact is if we combine this this is the force on the earth particle if we combine it with Newton's equations let's combine it with Newton's equipped with Newton's F equals MA equations then this is F this on the ice particle this is equal to the mass of the I particle times the acceleration of the ice particle again vector equations now the sum here is over all the other particles we're focusing on number I I the mass of the ice particle will cancel out of this equation I don't want to throw it away but let's just circle it and now put it over on the side we notice that the acceleration of the ice particle does not depend on its mass again once again because the mass occurs in both sides of the equation it can be cancelled out and the motion of the ayth particle does not depend on the mass of the earth particle it depends on the masses of all the other ones all the other ones come in but the mass of the iPart achill cancels out of the equation so what that means is if we had a whole bunch of particles here and we added one more over here its motion would not depend on the mass of that particle it depends on the mass of all the other ones but it doesn't depend on the mass of the i particle here okay that's again the equivalence principle that the motion of a particle doesn't depend on its mass and again if we had a whole bunch of particles here if they were close enough together they were all moving the same way before before i discuss lumo mathematics let's just discuss tidal forces what tidal forces are once you set this whole thing into motion dynamic young we have all different masses and each part what's going to be affected by each one is every particle in there is going to experience a uniform acceleration oh no no no no no acceleration is not uniform the acceleration will get larger when it gets closer to one of the particles it won't be uniform anymore it won't be uniform now because the force is not independent of where you are now the force depends on where you are relative to the objects that are exerting the force it was only in the Flat Earth approximation where the force didn't depend on where you were okay now the force varies so it's larger when you're far away it's sorry it's smaller when you're far away it's larger when you're in close it changes in a vector form with each individual particles each one of them is changing position yeah and and so is the dynamics that every one of them is going towards the center of gravity of the fire not necessarily I mean they could be flying apart from each other but they will be accelerating toward each other okay if I throw this eraser into the air with greater than the escape velocity it's not going to turn around and fall back changing with what with respect to what time oh it changes with respect to time because the object moves moves further and further away it's not uniformly the radius is changing and it's yeah let's take the earth here's the earth and we drop a small mass from far away as that mass moves in its acceleration increases why does its acceleration increase the deceleration increases because the radial distance gets smaller so in that sense it's not the alright now once the gravitational force depends on distance then it's not really quite true that you don't feel anything in a gravitational field you feel something which is to some extent it different than you would feel in free space without any gravitational field the reason is more or less obvious here you are his is the earth now you're you or me or whoever it is happens to be extremely tall a couple of thousand miles tall well this person's feet are being pulled by the gravitational field more than his head or another way of saying the same thing is if let's imagine that the person is very loosely held together he's just more or less a gas of we are pretty loosely held together at least I am right all right the acceleration on the lower portions of his body are larger than the accelerations on the upper portions of his body so it's quite clear what happens to her he gets stretched he doesn't get a sense of falling as such he gets a sense of stretching being stretched feet being pulled away from his head at the same time let's uh let's all right so let's change the shape a little bit I just spend the week two weeks in Italy and my shape changes whenever I go to Italy and it tends to get more horizontal my head is here my feet are here and now I'm this way still loosely put together right now what well not only does the force depend on the distance but it also depends on the direction the force arm my left end over here is this way the force on my right end over here is this way the force on the top of my head is down but it's weaker than the force on my feet so there are two effects one effect is to stretch me vertically it's because my head is not being pulled as hard as my feet but the other effect is to be squished horizontally by the fact that the forces on the left end of me are pointing slightly to the right and the forces on the right end of me are pointing slightly to the left so a loosely knit person like this falling in freefall near a real planet or real gravitational object which has a real Newtonian gravitational field around it will experience a distortion will experience a degree of distortion and a degree of being stretched vertically being compressed horizontally but if the object is small enough or small enough mean let's suppose the object that's falling is small enough if it's small enough then the gradient of the gravitational field across the size of the object will be negligible and so all parts of it will experience the same gravitational acceleration all right so tidal for these are tidal forces these forces which tend to tear things apart vertically and squish them this way tidal forces tidal forces are forces which are real you feel them I mean certainly new the car the cause of the tides yeah I don't know to what extent he calculated what do you mean calculated the well I doubt that he was capable I'm not sure whether he estimated the height of the of the deformation of the oceans or not but I think you did understand this much about tides okay so that's the that's what's called tidal force and then under the tidal force has this effect of stretching and in particular if we take the earth just to tell you just to tell you why it's called tidal forces of course it's because it has to do with tides I'm sure you all know the story but if this is the moon down here then the moon exerting forces on the earth exerts tidal forces on the earth which means to some extent that tends to stretch it this way and squash it this way well the earth is pretty rigid so it doesn't it doesn't deform very much due to due to these two the moon but what's not rigid is the layer of water around it and so the layer of water tends to get stretched and squeezed and so it gets deformed into the a the form shell of water with a bump on this side and the bump on that side alright I'm not gonna go any more deeply into that that I'm sure you've all seen okay but let's define now what we mean by the gravitational field the gravitational field is abstracted from this formula we have a bunch of particles don't you have need some some coordinate geometry so that would you have the four kind of middle is being pulled by all the other guys on the side I'm not explaining it right it's always negative is that what you're saying doesn't know I'm saying so she's attractive all right so you have but what about the other guys that are pulling upon him a different direction here and we're talking about the force on this person over here obviously there's one force pressing this pushing this way and another force pushing that way okay no the cone no they're all opposite to the direction of the object which is pulling on that's what this – sorry instead well you kind of retracted the minus sign at the front and reverse the ji yeah so it's the trend we can get rid of a – like a RI j and our ji are opposite to each other one of them is the vector between I and J I and J and the other one is the vector from J to I so they're equal and opposite to each other the minus sign there look as far as the minus sign goes all it means is that every one of these particles is pulling on this particle toward it as opposed to pushing away from it it's just a convention which keeps track of attraction instead of repulsion yeah for the for the ice master that's my word you want to make sense but if you can look at it as a kind of an in Samba wasn't about a linear conic component to it because the ice guy affects the Jade guy and then put you compute the Jade guy when you take it yeah now what this what this formula is for is supposing you know the positions or all the others you know that then what is the force on the one additional one but you're perfectly right once you let the system evolve then each one will cause a change in motion and the other one and so it becomes a complicated as you say nonlinear mess but this formula is a formula for if you knew the position and location of every particle this would be the force something you need to solve some equations to know how the particles move but if you know where they are then this is the force on the particle alright let's come to the idea of the gravitational field the gravitational field is in some ways similar to the electric field of our of an electric charge it's the combined effect of all the masses Everywhere's and the way you define it is as follows you imagine an one more particle one more particle amount you can take it to be a very light particle so it doesn't influence the motion of the others and one more particle in your imagination you don't really have to add it in your imagination and ask what the force on it is the force is the sum of the forces due to all the others it is proportional each term is proportional to the mass of the sec strip article this extra particle which may be imaginary is called a test particle it's the thing that you're imagining testing out the gravitational field with you take a light little particle and you put it here and you see how it accelerates knowing how it accelerates tells you how much force is on it in fact it just tells you how it accelerates and you can go around and imagine putting it in different places and mapping out the force field that's on that particle or the acceleration field since we already know that the force is proportional to the mass then we can just concentrate on the acceleration the acceleration all particles will have the same acceleration independent of the mass so we don't even have to know what the mass of the particle is we put something over there a little bit of dust and we see how it accelerates acceleration is a vector and so we map out in space the acceleration of a particle at every point in space either imaginary or real particle and that gives us a vector field at every point in space every point in space there is a gravitational field of acceleration it can be thought of as the acceleration you don't have to think of it as force acceleration the acceleration of a point mass located at that position it's a vector it has a direction it has a magnitude and it's a function of position so we just give it a name the acceleration due to all the gravitating objects it's a vector and it depends on position here X means location it means all of the position components of position XY and Z and it depends on all the other masters in the problem that is what's called the gravitational field it's very similar to the electric field except the electric field and the electric field is force per unit charge it's the force on an object divided by the charge on the object the gravitational field is the force of their on the object divided by the mass on the object since the force is proportional to the mass the the acceleration field doesn't depend on which kind of particle we're talking about all right so that's the idea of a gravitational field it's a vector field and it varies from place to place and of course if the particles are moving it also varies in time if everything is in motion the gravitational field will also depend on time we can even work out what it is we know what the force on the earth particle is all right the force on a particle is the mass times the acceleration so if we want to find the acceleration let's take the ayth particle to be the test particle little eye represents the test particle over here let's erase the intermediate step over here and write that this is in AI times AI but let me call it now capital a the acceleration of a particle at position X is given by the right hand side and we can cross out BMI because it cancels from both sides so here's a formula for the gravitational field at an arbitrary point due to a whole bunch of massive objects a whole bunch of massive objects an arbitrary particle put over here will accelerate in some direction that's determined by all the others and that acceleration is the gravitation the definition is the definition of the gravitational field ok let's um let's take a little break we usually take a break in about this time and I recover my breath to go on we need a little bit of fancy mathematics we need a piece of mathematics called Gauss's theorem and Gauss's theorem involves integrals derivatives divergences and we need to spell those things out there a central part of the theory of gravity and much of these things we've done in the context of a lot of electrical forces in particular the concept of divergence divergence of a vector field so I'm not going to spend a lot of time on it if you need to fill in then I suggest you just find any little book on vector calculus and find out what a divergence and a gradient and a curl we don't do curl today what those concepts are and look up Gauss's theorem and they're not terribly hard but we're gonna go through them fairly quickly here since they we've done them several times in the past right imagine that we have a vector field let's call that vector field a it could be the field of acceleration and that's the way I'm gonna use it well for the moment it's just an arbitrary vector field a it depends on position when I say it's a field the implication is that it depends on position now I probably made it completely unreadable a of X varies from point to point and I want to define a concept called the divergence of the field now it's called the divergence because one has to do is the way the field is spreading out away from a point for example a characteristic situation where we would have a strong divergence for a field is if the field was spreading out from a point like that the field is diverging away from the point incidentally if the field is pointing inward then one might say the field has a convergence but we simply say it has a negative divergence all right so divergence can be positive or negative and there's a mathematical expression which represents the degree to which the field is spreading out like that it is called the divergence I'm going to write it down and it's a good thing to get familiar with certainly if you're going to follow this course it's a good thing to get familiar with but are they going to follow any kind of physics course past freshman physics the idea of divergence is very important all right supposing the field a has a set of components the one two and three component but we could call them the x y&z component now I'll use x y&z are X Y & Z which I previously called X 1 X 2 and X 3 it has components X a X a Y and a Z those are the three components of the field well the divergence has to do among other things with the way the field varies in space if the field is the same everywhere as in space what does that mean that would mean the field that has both not only the same magnitude but the same direction everywhere is in space then it just points in the same direction everywhere else with the same magnitude it certainly has no tendency to spread out when does a field have a tendency to spread out when the field varies for example it could be small over here growing bigger growing bigger growing bigger and we might even go in the opposite direction and discover that it's in the opposite direction and getting bigger in that direction then clearly there's a tendency for the field to spread out away from the center here the same thing could be true if it were varying in the vertical direction or who are varying in the other horizontal direction and so the divergence whatever it is has to do with derivatives of the components of the field I'll just tell you exactly what it is it is equal to the divergence of a field is written this way upside down triangle and the meaning of this symbol the meaning of an upside down triangle is always that it has to do with the derivatives the three derivatives derivative whether it's the three partial derivatives derivative with respect to XY and Z and this is by definition the derivative with respect to X of the X component of a plus the derivative with respect to Y of the Y component of a plus the derivative with respect to Z of the Z component of it that's definition what's not a definition is a theorem and it's called Gauss's theorem no that's a scalar quantity that's a scalar quantity yeah it's a scalar quantity so it's let me write it it's the derivative of a sub X with respect to X that's what this means plus the derivative of a sub Y with respect to Y plus the derivative of a sub Z with respect to Z yes so the arrows you were drawn over there those were just a on the other board you drew some arrows on the other board that are now hidden yeah those were just a and a has a divergence when it's spreading out away from a point but that there vergence is itself a scalar quantity oh let me try to give you some idea of what divergence means in a context where you can visualize it imagine that we have a flat lake alright just the water thin a a shallow lake and water is coming up from underneath it's being pumped in from somewheres underneath what happens that the water is being pumped in of course it tends to spread out let's assume that the height let's assume the depth can't change we put a lid over the whole thing so it can't change its depth we pump some water in from underneath and it spreads out okay we suck some water out from underneath and it spreads in it anti spreads it has so the spreading water has a divergence water coming in toward the towards the place where it's being sucked out it has a convergence or a negative divergence now we can be more precise about that we look down at the lake from above and we see all the water is moving of course it's moving if it's being pumped in the world it's moving and there is a velocity vector at every point there is a velocity vector so at every point in this lake there's a velocity vector vector and in particular if there's water being pumped in from the center here right underneath the bottom of the lake there's some water being pumped in the water will spread out away from that point okay and there'll be a divergence where the water is being pumped in okay if the water is being pumped out then exactly the opposite the the arrows point inward and there's a negative divergence the if there's no divergence then for example a simple situation with no divergence that doesn't mean the water is not moving but a simple example with no divergence is the waters all moving together you know the river is simultaneous the lake is all simultaneously moving in the same direction with the same velocity it can do that without any water being pumped in but if you found that the water was moving to the right on this side and the left on that side you'd be pretty sure that somebody is in between water had to be pumped in right if you found the water was spreading out away from a line this way here and this way here then you'd be pretty sure that some water was being pumped in from underneath along this line here well you would see it another way you would discover that the X component of the velocity has a derivative it's different over here than it is over here the X component of the velocity varies along the x direction so the fact that the X component of the velocity is varying along the direction there's an indication that there's some water being pumped in here likewise if you discovered that the water was flowing up over here and down over here you would expect that in here somewhere as some water was being pumped in so derivatives of the velocity are often an indication that the some water being pumped in from underneath that pumping in of the water is the divergence of the velocity vector now the the the the water of course is being pumped in from underneath so there's a direction of flow but it's coming from from underneath there's no sense of direction well okay that's that's what diverges just the diagrams you already have on the other board behind there you take say the rightmost arrow and you draw a circle between the head and tail in between then you can see the in and out the in arrow and the arrow of a circle right in between those two and let's say that's the bigger arrow is created by a steeper slope of the street it's just faster it's going fast it's going okay and because of that there's a divergence there that's basically it's sort of the difference between that's right that's right if we drew a circle around here or we would see that more since the water was moving faster over here than it is over here more water is flowing out over here then it's coming in over here where is it coming from it must be pumped in the fact that there's more water flowing out on one side then it's coming in from the other side must indicate that there's a net inflow from somewheres else and the somewheres else would be from the pump in water from underneath so that's that's the idea of oops could it also be because it's thinning out with that be a crazy example like the late guy young well okay I took all right so let's be very specific now I kept the lake having an absolutely uniform height and let's also suppose that the density of water water is an incompressible fluid it can't be squeezed it can't be stretched then the velocity vector would be the right thing to think about them yeah but you could have no you're right you could have a velocity vector having a divergence because the water is not because water is flowing in but because it's thinning out yeah that's that's also possible okay but let's keep it simple all right and you can have the idea of a divergence makes sense in three dimensions just as well as two dimensions you simply have to imagine that all of space is filled with water and there are some hidden pipes coming in depositing water in different places so that it's spreading out away from points in three-dimensional space in three-dimensional space this is the expression for the divergence if this were the velocity vector at every point you would calculate this quantity and that would tell you how much new water is coming in at each point of space so that's the divergence now there's a theorem which the hint of the theorem was just given by Michael there it's called Gauss's theorem and it says something intuitive very intuitively obvious you take a surface any surface take any surface or any curve in two dimensions and now suppose there's a vector field that the field points now think of it as the flow of water and now let's take the total amount of water that's flowing out of the surface obviously there's some water flowing out over here and of course we want to subtract the water that's flowing in let's calculate the total amount of water that's flowing out of the surface that's an integral over the surface why is it an integral because we have to add up the flows of water outward where the water is coming inward that's just negative negative flow negative outward flow we add up the total outward flow by breaking up the surface into little pieces and asking how much flow is coming out from each little piece yeah how much water is passing out through the surface if the water is incompressible incompressible means density is fixed and furthermore the depth of the water is being kept fixed there's only one way that water can come out of the surface and that's if it's being pumped in if there's a divergence the divergence could be over here could be over here could be over here could be over here in fact any ways where there's a divergence will cause an effect in which water will flow out of this region yeah so there's a connection there's a connection between what's going on on the boundary of this region how much water is flowing through the boundary on the one hand and what the divergence is in the interior the connection between the two and that connection is called Gauss's theorem what it says is that the integral of the divergence in the interior that's the total amount of flow coming in from outside from underneath the bottom of the lake the total integrated and now by integrated I mean in the sense of an integral the integrated amount of flow in that's the integral of the divergence the integral over the interior in the three-dimensional case it would be integral DX dy DZ over the interior of this region of the divergence of a if you like to think of a is the velocity field that's fine is equal to the total amount of flow that's going out through the boundary and how do we write that the total amount of flow that's flowing outward through the boundary we break up let's take the three-dimensional case we break up the boundary into little cells each little cell is a little area let's call each one of those little areas D Sigma these Sigma Sigma stands for surface area Sigma is the Greek letter Sigma it stands for surface area this three-dimensional integral over the interior here is equal to a two-dimensional integral the Sigma over the surface and it is just the component of a perpendicular to the surface let's call a perpendicular to the surface D Sigma a perpendicular to the surface is the amount of flow that's coming out of each one of these little boxes notice incidentally that if there's a flow along the surface it doesn't give rise to any fluid coming out it's only the flow perpendicular to the surface the component of the flow perpendicular to the surface which carries fluid from the inside to the outside so we integrate the perpendicular component of the flow over the surface that's through the Sigma here that gives us the total amount of fluid coming out per unit time for example and that has to be the amount of fluid that's being generated in the interior by the divergence this is Gauss's theorem the relationship between the integral of the divergence on the interior of some region and the integral over the boundary where where it's measuring the flux the amount of stuff that's coming out through the boundary fundamental theorem and let's let's see what it says now any questions about that Gauss's theorem here you'll see how it works I'll show you how it works yeah yeah you could have sure if you had a compressible fluid you could discover that all the fluid out boundary here is all moving inwards in every direction without any new fluid being formed in fact what's happening is just the fluid is getting squeezed but if the fluid can't squeeze if you cannot compress it then the only way that the fluid could be flowing in is if it's being removed somehow from the center if it's being removed by by invisible pipes that are carrying it all so that means the divergence in the case of water would be zero there was no water coming it would be if there was a source of the water divergence is the same as a source source of water is the source of new water coming in from elsewhere is right so in the example with the 2-dimensional lake the source is water flowing in from underneath the sink which is the negative of a source is the water flowing out and in the 2-dimensional example this wouldn't be a 2-dimensional surface integral it would be the integral in here equal to a one dimensional surface and to go coming out okay all right let me show you how you use this let me show you how you use this and what it has to do with what we set up till now about gravity I think hope a lifetime let's imagine that we have a source it could be water but let's take three dimensional case there's a divergence of a vector field let's say a there's a divergence of a vector field del dot a and it's concentrated in some region of space that's a little sphere in some region of space that has spherical symmetry in other words doesn't mean it doesn't mean that the that the divergence is uniform over here but it means that it has the symmetry of a sphere everything is symmetrical with respect to rotations let's suppose that there's a divergence of the fluid okay now let's take and it's restricted completely to be within here it does it could be strong near the center and weak near the outside or it could be weakened near the center and strong near the outside but a certain total amount of fluid or certain total divergence and integrated there vergence is occurring with nice Oracle shape okay let's see if we can use that to figure out what the field what the a field is there's a Dell dot a in here and now let's see can we figure out what the field is elsewhere outside of here so what we do is we draw a surface around there we draw a surface around there and now we're going to use Gauss's theorem first of all let's look at the left side the left side has the integral of the divergence of the vector field all right the vector field or the divergence is completely restricted to some finite sphere in here what is incidentally for the flow case for the fluid flow case what would be the integral of the divergence does anybody know if it really was a flue or a flow of a fluid it'll be the total amount of fluid that was flowing in per unit time it would be the flow per unit time that's coming through the system but whatever it is this integral doesn't depend on the radius of the sphere as long as the sphere this outer sphere here is bigger than this region why because the integral over that there vergence of a is entirely concentrated in this region here and there's zero divergence on the outside so first of all the left hand side is independent of the radius of this outer sphere as long as the radius of the outer sphere is bigger than this concentration of divergence iya so it's a number altogether it's a number let's call that number M I'm not Evan let's just Q Q that's the left hand side and it doesn't depend on the radius on the other hand what is the right hand side well there's a flow going out and if everything is nice and spherically symmetric then the flow is going to go radially outward it's going to be a pure radially outward directed flow if the flow is spherically symmetric radially outward direct directed flow means that the flow is perpendicular to the surface of the sphere so the perpendicular component of a is just a magnitude of AE that's it it's just a magnitude of AE and it's the same everywhere is on the sphere why is it the same because everything has spherical symmetry a spherical symmetry the a that appears here is constant over this whole sphere so this integral is nothing but the magnitude of a times the area of the total sphere if I take an integral over a surface a spherical surface like this of something which doesn't depend on where I am on the sphere then it's just I can take this on the outside the magnitude of the the magnitude of the field and the integral D Sigma is just the total surface area of the sphere what's the total surface area of the sphere just 4 PI 4 PI R squared oh yeah 4 PI R squared times the magnitude of the field is equal to Q so look what we have we have that the magnitude of the field is equal to the total integrated divergence divided by 4 pi the 4 pi is the number times R squared does that look familiar it's a vector field it's pointed radially outward well it's point the radially outward if the divergence is positive if the divergence is positive its pointed radially outward and it's magnitude is one over R squared it's exactly the gravitational field of a point particle at the center here that's why we have to put a direction in here you know this R hat this art will this R over R is it's a unit vector pointing in the radial direction it's a vector of unit length pointing in the radial direction right so it's quite clear from the picture that the a field is pointing radially outward that's what this says over here in any case the magnitude of the field that points radially outward it has magnitude Q and it falls off like 1 over R squared exactly like the Newtonian field of a point mass so a point mass can be thought of as a concentrated divergence of the gravitational field right at the center point mass the literal point mass can be thought of as a concentrated concentrated divergence of the gravitational field concentrated in some very very small little volume think of it if you like you can think of the gravitational field as the flow field or the velocity field of a fluid that's spreading out Oh incidentally of course I've got the sign wrong here the real gravitational acceleration points inward which is an indication that this divergence is negative the divergence is more like a convergence sucking fluid in so the Newtonian gravitational field is isomorphic is mathematically equivalent or mathematically similar to a flow field to a flow of water or whatever other fluid where it's all being sucked out from a single point and as you can see the velocity field itself or in this case the the field the gravitational field but the velocity field would go like one over R squared that's a useful analogy that is not to say that space is a flow of anything it's a mathematical analogy that's useful to understand the one over R squared force law that it is mathematically similar to a field of velocity flow from a flow that's being generated right at the center at a point okay that's that's a useful observation but notice something else supposing now instead of having the flow concentrated at the center here supposing the flow was concentrated over a sphere which was bigger but the same total amount of flow it would not change the answer as long as the total amount of flow is fixed the way that it flows out through here is also fixed this is Newton's theorem Newton's theorem in the gravitational context says that the gravitational field of an object outside the object is independent of whether the object is a point mass at the center or whether it's a spread out mass or there it's a spread out mass this big as long as you're outside the object and as long as the object is spherically symmetric in other words as long as the object is shaped like a sphere and you're outside of it on the outside of it outside of where the mass distribution is then the gravitational field of it doesn't depend on whether it's a point it's a spread out object whether it's denser at the center and less dense at the outside less dense in the inside more dense on the outside all it depends on is the total amount of mass the total amount of mass is like the total amount of flow through coming into the that theorem is very fundamental and important to thinking about gravity for example supposing we are interested in the motion of an object near the surface of the earth but not so near that we can make the flat space approximation let's say at a distance two or three or one and a half times the radius of the earth well that object is attracted by this point that's attracted by this point that's attracted by that point it's close to this point that's far from this point that sounds like a hellish problem to figure out what the gravitational effect on this point is but know this tells you the gravitational field is exactly the same as if the same total mass was concentrated right at the center okay that's Newton's theorem then it's marvelous theorem it's a great piece of luck for him because without it he couldn't have couldn't have solved his equations he knew he meant but it may have been essentially this argument I'm not sure exactly what argument he made but he knew that with the 1 over R squared force law and only the one over R squared force law wouldn't have been truth was one of our cubes 1 over R to the fourth 1 over R to the 7th with the 1 over R squared force law a spherical distribution of mass behaves exactly as if all the mass was concentrated right at the center as long as you're outside the mass so that's what made it possible for Newton to to easily solve his own equations that every object as long as it's spherical shape behaves as if it were appoint appointments so if you're down in a mine shaft that doesn't hold that's right but that doesn't mean you can't figure out what's going on you can't figure out what's going on I don't think we'll do it tonight it's a little too late but yes we can work out what would happen in the mine shaft but that's right it doesn't hold it a mine shaft for example supposing you dig a mine shaft right down through the center of the earth okay and now you get very close to the center of the earth how much force do you expect that we have pulling you toward the center not much certainly much less than if you were than if all the mass will concentrate a right at the center you got the it's not even obvious which way the force is but it is toward the center but it's very small you displace away from the centre of the earth a little bit there's a tiny tiny little force much much less than as if all the mass was squashed toward the centre so right you it doesn't work for that case another interesting case is supposing you have a shell of material to have a shell of material think about a shell of source fluid flowing in fluid is flowing in from the outside onto this blackboard and all the little pipes are arranged on a circle like this what does the fluid flow look like in different places well the answer is on the outside it looks exactly the same as if everything were concentrated on the point but what about in the interior what would you guess nothing nothing everything is just flowing out away from here and there's no flow in here at all how could there be which direction would it be in so there's no flow in here so the distance argument like if you're closer to the surface of the inner shell yeah wouldn't that be more force towards that no you see you use Gauss's theorem let's do count system Gauss's theorem says okay let's take a shell the field the integrated field coming out of that shell is equal to the integrated divergence in here but there is no divergence in here so the net integrated field coming out of zero no field on the interior of the shell field on the exterior of the show so the consequence is that if you made a spherical shell of material like that the interior would be absolutely identical to what it what it would be if there was no gravitating material there at all on the other hand on the outside you would have a field which would be absolutely identical to what happens at the center now there is an analogue of this in the general theory of relativity we'll get to it basically what it says is the field of anything as long as it's fairly symmetric on the outside looks identical to the field of a black hole I think we're finished for tonight go over divergence and all those Gauss's theorem Gauss's theorem is central there would be no gravity without Gauss's theorem the preceding program is copyrighted by Stanford University please visit us at stanford.edu