 All right. Let's get started. He did it. Yasha got tenure and we're here to celebrate his achievement. Just a short introduction about starting from the beginning. Yasha was born Victory Day 1986 in Moscow, which was then the USSR. A small and sickly child, Yasha was was reading at age two, but only really speaking at age four. When the USSR collapsed, Yasha's family moved to Israel when he was four. And by age eight, he decided that school was not for him. So for by in age eight to nine, he did not leave the house or go to school and was only convinced to start school again at age 11, where he started high school. And at age 12, he started college. And at this point, he through the help of a private tutor and friend, he became interested in physics and joined the physics Olympiad. He was the youngest winner at the time of the Asian Physics Olympiad. Here he is. And then he at this point became somewhat of a celebrity in Israel for being a child prodigy. So here's in the the paper of record. He graduated with his first bachelor's degree at age 17, before he graduated high school. And this created a bit of a problem. He had to write an essay. And so after in order to graduate high school, after graduating college, and the essay he chose to to write was how the Israeli or the Hebrew translation of the Lord of the Rings was bad. And the word of this essay got to the translator, who was a professor at the Hebrew University, who summoned Yasha to his office to say, what are you doing? How can you object to my translation? And after yelling at him for an hour, he offered him to do a PhD with him in literature. But Yasha said no, physics was for him. And so literature's loss is our gain. He then joined the military and got his PhD. And at this point grew up, you know, a little bit. Met Yad Vrata at age 21, married at 24, then moved to do the his first postdoc at Penn State in the US in 2013. In 2015 moved to do a second postdoc in the Perimeter Institute in Canada before coming to OIST in 2017. And in every one of his postdocs and now as faculty position, he had one wonderful child. I became friends with Yasha after hearing one of his introductions to someone's talk, which is very a combination of idiosyncratic, intelligent, kind of amusing, and slightly offensive. And I think this is really Yasha in a nutshell. Yasha works on quantum gravity. This is a particularly esoteric branch of physics. And I think this esoteric nature of the topic really attracts Yasha. I would say in our conversations, the 11th century Jewish philosopher, Maimonides, comes up like way more when I'm talking to Yasha than I'm talking to my other friends. So Yasha's work is basic research, right? So we hear a lot these days about tech transfer and academic industry collaborations and general applications. Yasha's work gives us none of these things. But I'm proud to be one of the very few places that would celebrate someone like Yasha. Some place that will celebrate someone pushing the boundaries of what humanity knows and getting knowledge for its own sake, free of any other gains. You know, you could ask, what's the point? But I think in a certain frame of mind, you could also ask, what's the point of doing anything else? So Yasha. Yeah, thank you, Sam. That was quite bad. All right. Can we turn off the projector, please? Okay. So let's talk about some physics. Now, the most important thing in physics is the Pythagoras theorem as it turns out. It took us a while to figure that out. But okay, so it's this. If you have a right-handed triangle, then there is a squared plus b squared equals c squared. And it's like a prime example of Greek science. And it's really cool. In case you've never seen the nicest proof of the Pythagoras theorem, so here it is. The two big squares are the same. The little orange garbage is the same in both ones. So a squared plus b squared is in fact c squared. So it's very nice, but largely useless and doesn't seem to apply to anything in the world. Like until you come and draw lines in the sand, we don't have right-handed triangles just lying around. And so it took 2,000 years for Greek science to develop into modern science, which takes things quite a bit more seriously. And I think this happened through an injection of really Jewish intellectual culture. And yeah, many of this is relevant to that. Because in Jewish culture, you see, in Greek science, this would be the domain of some small number of nerds who would care. In Jewish culture, everyone is a nerd. And by combining that with the thinking of the Greeks, we got modern science that really managed to eat everything and to transform everything it touched. So in particular, it turned out that the Pythagoras theorem is everywhere. And the way that happened is there was this guy called Descartes. And Descartes, he imagined little fairies flying around everywhere in space and sprinkling fairy dust. And painting with their fairy dust, this fairy dust grid that you can see only if you're a little child and you wear the fairy dust glasses. So there's a grid everywhere in space. And to every point on the grid, the fairies come and attach a label with some numbers on it. So every point has numbers x, y, and actually the grid is in 3D space. So there's also z. And here's another point, x, y, z. And so for every line, you must think just the line. But if you put on the fairy dust glasses and you can see the imaginary grid, then it turns out that for every line in the world, there is secretly a right angle triangle. And the length of the line then turns out to be the square root of this. So the difference in x, which is this side, and the difference in y, which is that side. And if there's also a bit of z, then we can add that in. Okay. So the Pythagoras theorem is actually telling us the length of every line in the world. Well, okay, fine. Smart guy. But how many straight lines does the real world actually have in it? Right? The real world, last time I checked, is made of some, you know, floppy, floppy things like this. Okay. How are you going to eat that? Well, okay. Then came another fellow called Newton and came up with another bright idea, which is for every floppy, floppy complicated thing, we can chop it up into infinitely many little pieces like this. Okay. And then every little piece is itself a little bit of straight line. Okay. So we can do the same thing as before. Okay. We can say the length of this whole thing is, so for every little piece, there will be some very little dx. And then to get the length of it, we'll do dx squared plus dy squared plus dz squared and take the square root. And that will be the length of every little piece of line. And now we need to add them together. So we invent a new fancy symbol for adding things together. We call that an integral. Okay. And now the Pythagoras theorem tells us the length of any line of any shape in the world. Okay. So that's one achievement unlocked. Let's try to write that. So a squared plus b squared equals c squared leads to any length being an integral of these things. Okay. And this is an example of like the intricate relationship that we have in modern physics between like the real and the concrete versus some imaginary worlds. All right. So again, this grid does not exist. x, y and z do not exist. The little dx's, dy's and dz's do not exist. Okay. It's very easy to convince yourself of this if you're confused because just show me the device that measures x. Okay. Is there an x meter or is there a y meter? And like there's not. Okay. You can only see it if you believe in fairies. But there is a device for measuring length. It's called a ruler. And it just so happens that believing in fairies and in their fairy dust x, y, z's gives you a wonderfully convenient way to arrange all possible measurements that you can make with the real world rulers. Okay. And that's a useful thing to have. Okay. So a little example in case you don't believe me yet that this is physics. So let's start talking a bit about optics. Okay. So optics is about how light rays choose to travel through space. And choose through is a good word to use. So we can say, okay, there's a point A and there's a point B. Okay. What will be the path that light takes from A to B? And it turns out that the universal law that governs the answer to this question is that light will take the quickest path. Okay. This is called Fermat's least time principle. So what is the quickest path? Okay. We can try drawing some paths. Okay. And asking, which one will be the shortest? Then, of course, the shortest one is actually the straight one. Okay. Now, why is it the shortest one? Okay. Well, we can sprinkle some fairy dust and decide that this axis between the two points is called the x-axis. Okay. And then for the length of the line, okay, we have no choice but to travel along the x-direction. So we will always pick up these dx's. But only if the line wiggles up and down, we will also pick up the dy's or dz's. Okay. So the shortest path will be if we avoid wiggling up and down in any direction and only keep the dx's. Okay. So light travels in a straight line. All right. Now, that's maybe a bit too simple, but we can make it more interesting. So suppose there is a mirror. Okay. And then light is trying to get from point A to point B. And the new rule is that it needs to touch the mirror first. Okay. So now, okay, you have all kinds of different paths to try. So we already sort of understand that the segments need to be straight because anything else will be longer. Okay. But there are these different possibilities of going in straight segments. Okay. And say if you go from one possibility to the other, then maybe the first segment gets longer but the second one gets shorter. Okay. So which is the shortest one overall? Okay. So there is a fun way of solving this problem, which is, okay, we zoom in on one segment of the path and ask what happens when we change the path a little bit. Okay. So this segment will get longer. Okay. By how much? All right. Let's start giving names to things. Okay. So let's say the angle between the light ray and the mirror is called theta. Okay. Now, by how much did the path become shorter? So, okay, by this much, okay, the two white lines are the same. The difference in length is the little yellow bit. Now, how much is the yellow bit? Okay. Let's say that this little dx here is by how much we moved the point. Okay. Now, let's maybe draw this triangle a bit bigger. So there's a right hand the triangle like this and this is the dx and this is the same theta as here. Okay. So the amount by which the segment got shorter, got longer is, okay, dx here times cosine of theta. Okay. Now, we can repeat the same exercise for the second part of the segment, right, where, okay, if this one got longer then this one will get shorter and, okay, but from moving by the same dx, okay, except now there'll be some different angle here, theta 2 and this one was maybe theta 1. Okay. So the amount we lose by moving the point a little bit is dx times cosine of theta 1. The amount we win is dx times cosine of theta 2. Okay. And the optimal point will be the one where we don't win or lose much by moving in either direction. All right. So if it's a good idea to move to the left, okay, well, that means that this shortening is bigger than this lengthening. If it's a good idea to move to the right, that means it's the other way around. Okay. If we are at exactly the right point, so we shouldn't really move either way, away from it. Okay. So that means the length shouldn't really change when we move by a little dx here. Okay. So that means these should be equal. Okay. So we get that when light is reflected off a mirror, okay, it does it at equal angles. Okay. Something like this. Okay. That still may be a bit too easy. So let's make it harder again. We said quickest path. Okay. Didn't say shortest. And normally you would say, what's the difference? Quickest, shortest, light always travels at the same speed. There's a speed of light, 300,000 kilometers per second. So, okay, shortest is good enough as a proxy. But sometimes the world is dirty and full of all kinds of materials. Okay. Like water or glass. I don't know what. And inside materials, light can have a different speed. Okay. So when light moves slower in a material, okay, we call that a refraction coefficient. Okay. And label it by the letter n. Okay. So actually the time that it takes light to move from place to place, what we're trying to minimize is now not just the length, but when we're moving slower in some portion of the path. Okay. Then we also need to multiply by this refraction coefficient. Okay. So now what happens when light is trying to get from A to B? Okay. And the refraction coefficient is let's say higher here and lower here. Okay. So that means here we're moving slower. So we want to spend less of our path here in the slow region and more of our path in the fast region. Okay. So probably the quickest route will be something like this. Okay. And that is indeed what happened to light rays. When they move from medium to medium, they get refracted like so. Okay. But by how much? So, okay, we can play the same game as before. Let's say here there is an angle of theta one. Here there is an angle of theta two. Okay. And refraction coefficients are n1 and n2. Okay. And we can play the same game as before. All right. So we need to choose at which point the light ray should switch between the materials. So we choose it by trying to wiggle it a bit to the right or to the left and see by how much the length of the path and then the time it takes to travel changes. Okay. Do the same little calculation as here. Okay. Exactly the same triangles, the same cosine theta and cosine theta, except now on both sides, we need to multiply the length of the path by how long it will take to travel along it. So we need to multiply by the ends here on both sides. Okay. So the angles are no longer equal. And the way to figure out how unequal is that, well, okay, only the dx cancels now. So n cosine theta is n cosine theta on the other side. Okay. And this is Snell's law of refraction. Now, okay, this happens every time we move from high to low refraction coefficient. Okay. We can think of that happening continuously. So suppose there's some direction in which the refraction coefficient decreases. Okay. And now suppose we shoot a light ray, okay, a little bit up like this. Okay. Then what will start happening to it? It will start bending like this continuously throughout its flight. So it will bend, bend, bend, bend, bend. At some point, it will bend all the way horizontally and start falling back down. Okay. That sounds suspiciously like it's actually a ball falling under the influence of gravity. And we will soon see that it's quite similar. Okay. But, right, this is what will happen. Okay. A quick way to see, okay, what is going on here is, okay, we write again the, okay, Pythagoras multiplied by n. Okay. So now if we're trying to get from point A to point B, then we would think, okay, that it would be cheapest to just go only along x without paying this extra penalty of going up and down in y. Okay. But because n is smaller if we go higher up, then it becomes worth our time, okay, to pay in de-wise in order to get to a region of small n where we move faster. Okay. So path becomes something like this. Okay. This turns out to be very relevant to the real world. Okay. So in the Earth's atmosphere, the higher layers, the ionosphere, have a low refraction coefficient for radio waves. So when people started using wireless communication and try to see if they can use it over long distances where the curvature of the Earth becomes important, they had a pleasant surprise. Okay. So you would think that because the Earth is round, then, okay, if you shoot a radio signal, say, from here to here, you'll never manage, okay, because it would just fly off into space. Okay. Possibly this is one of the arguments of Flat Earthers. I don't know if it really is. But what turns out to happen in the real world is that the refraction coefficient behaves like this. So the radio waves actually bounce back down like so, and so wireless telegraph across continents worked much better than people expected. Okay. So we're making good time. We understood all of optics. Okay. So let's call it minimal time. Leads to, okay, the hardest part of optics is n cosine equals n cosine. All right. Okay. Now let's briefly discuss tenure. So, okay, Sam was wrong in almost every particular fact, but, I mean, he's a biologist. But it is more or less true that, yeah, in 2003, I went to the physics Olympiad and as part of the preparation for the physics Olympiad, a good friend explained Maxwell's equations. And from due to a combination of these two things, I decided that I want to be, you know, a world traveling scientist and specifically to do fundamental theoretical physics. Ha-ha. Okay. And I want to be a Hollywood actor. Great. Okay. For some reason, this actually managed to happen and get secured 20 years later. Now, what is important to point out is that left to my own devices, okay, I would have made it. Now, I wasn't too dumb. So I made it more or less 10 years by my own resources, right? So during this time, I did the physics undergrad, did the army, did PhD, got a strange first postdoc. But from then on, I would basically need to find the real job and that was it. Now, the strange thing that happened is that somewhere in the middle of this interval here, okay, I met this absolutely amazing girl, that one, I guess, who has talent for making things happen. So very routinely, she takes problems that look far too complex, like the academic job market or situations that look far too hopeless, like, well, here's this idiot who decided that he wants to do fundamental theory for a living and he doesn't want to be friends with these people and he doesn't want to be friends with those people and he keeps calling everyone names and how the hell is that going to work out, right? But when she sees a complicated problem, she figures out how to make it work. And she can solve things before anyone can even put a name to them and she can clean up messes before anyone will admit that there was a mess or that they made it. And she can generally science the shit out of very complex situations, all right? And for some reason, she decided that her project for the time being is going to be to make my stupid dream come true. I wasn't the only project that was competing for her attention. Okay, so somewhere around this time, she got an invitation from the Institute of which this Institute is an imitation to come and go to grad school there to solve their problems. An invitation must be stressed, she'd not apply, they called her. And she said, no, you know, I found this idiot and he has this dream and I'm going to make that work and we will talk later. And so it kind of happened. Okay, so at this point, we're in America and okay, Tai gets born, low Tai and then because Radu exists and can make things happen, we then find ourselves in Premier Institute in Canada and Gali gets born, hello Gali. And then again, because Radu knows how to make things happen, we find ourselves here and I somehow survive being here where again, because Radu knows how to make that happen. So okay, and now I should I guess carefully point out because this project is largely done, her attention is again divided. And so just to bring it to your attention, if something near you is working and Radu is somewhere in the vicinity, please take very seriously the possibility that she is the reason it's working. Even if you're too stupid to understand exactly why in the moment, just sit quietly and consider the possibility. Okay, back to physics. So X, Y and Z, okay, were fairy dust. Okay, we just invented them, sprinkled them over the space, adults can see them, all the children with the special glasses can. But surely this timeline that I drew here, that's not fairy dust, that is real. X, Y and Z are fake and made up, but T, T is a real axis, right? Because there is no device for measuring X, Y and Z, but there is a device for measuring T, right? There is a clock. We can look at the clock and see, oh, it's 2003. Oh, it's 2023. And two people comparing clocks will always see the same thing and that's how we know that T is real and not made up, right? Well, not exactly right. Okay, so it turns out that, you know, if you take, okay, people like doing this with twins, but, you know, fine, unethical experiment, you take two twins and one of them stays on Earth and the other does around an interstellar round trip, you know, fast, close to the speed of light. The Ender's Game sci-fi series is pretty good at accurately depicting the situation if you want it in story form. Then, okay, then they come back and they compare their clocks and this guy's clock, the one who stayed, might say that it's been a hundred years and the guy who went there and back again, his clock, might say that it's been one year. And of course, not the clock that nobody wears on their wrist anymore and not only these new clocks that we keep in our pockets, but also the biological clock, right? So this guy will be old and this guy will be young and every sense of clock that there is, okay, we'll say that, okay, something different happened here and therefore clocks do not measure T. Okay, T is an imaginary label that we put on events, on points in space-time, just like X, Y, and Z are. So there is an imaginary fairy dust grid of both T, X, Y, and Z and there is not a device that measures any of them. But we do have clocks. What on earth do clocks measure? So it turns out this is the great victory of Pythagoras from beyond the grave that what clocks measure, what we should call clock time, or if you want to be fancy, fancy full, we can talk about the clock inside our brain and call it experienced time, you know, how old the twin is going to live, is going to feel. Any kind of actual true physical time, okay, the physicist's name for it is proper time. And we denote it by the letter tau, okay, so for a while this was kind of a class filter, right, you couldn't submit papers about relativity into journals if you only had a type writer with the regular letters and you couldn't write the letter tau, you would write T and they think that they would think that you're stupid. This actually happened to a good person so this proper time tau is given by, okay, we already know it should be a sum of lots of tiny things and we already know that there should be something like DT here because, you know, in our normal life it does seem like the T coordinate is in fact measuring the same thing as clocks are, but also, okay, we see that if you travel in space, if you travel in XYZ, then your clock time turns out to be shorter than someone who doesn't and there is a formula for this which is utterly astonishing, so it turns out that we take exactly the same thing that we had in the Pythagoras theorem before and you just put it here and you slap it on with a minus sign, okay, or if you like we can just ditch the parentheses and write minus three times, okay, so this is a Pythagoras theorem for space time and this is the thing that clocks really measure, okay, we have thus learned special relativity, okay, honest to goodness, this is all that special relativity is, the rest is, you know, not Rabbi Lele himself, but somebody would comment here that the rest is commentary, right, so special relativity is an activity centered around the worship of this formula and understanding its implications and there are many, okay, so, okay, we learned special relativity, let's write it here that clock time is this four-dimensional Pythagoras theorem with minuses, okay, in particular the difference between space and time and the fact that there's one dimension of time and three dimensions of space and that a clock and the ruler are such different physical objects is, and that you cannot go backwards in time, et cetera, et cetera, is all hiding here in these minuses, okay, but we can also immediately take this formula and apply it into a law, okay, so in the story of the two twins, okay, one of them who stayed and the other who flew, so this is called sometimes the twin's paradox, okay, the reason people call it the paradox is they make it out to be, oh, look, they were the same, you know, this one was doing one thing and this one was doing a similar thing and then they compared the clocks and the clocks didn't agree paradox, okay, but that's of course silly, they were not doing the same thing at all, okay, one of them was dutifully staying put and the other was working a rocket engine, okay, so we don't need to draw the earth here at all, we can just, okay, this guy is here hovering in space, doing nothing, just quietly obeying the laws of physics, okay, so this is, okay, he's doing inertial motion, just doing what he's told, okay, while the other guy is, you know, working hard and burning jet fuel, etc., so we can now write down the law of inertial motion, so just as the central law of optics is that light will take whatever path that would take it minimal time, so here it's a similar but like delightfully backwards version that if you travel from point A to point B in spacetime, right, so this is at some time and some place and this is at some other time and some other place, okay, then you can take different paths between these two points and the one that you'll take if moving inertially, if not cheating, if not using jet fuel, if not using any forces, will be the path of maximal clock time, okay, so if you're just, if we draw the time axis to go straight between the two points, then the longest way to get from here to there, okay, the oldest that you can be when meeting your twin is if you stay put, okay, because if you wiggle back and forth in space, if you turn on your jetpack and start flying to the stars and doing silly things like that, then you will pay here with the negative signs, okay, so the time on your clock will get shorter, okay, so the path that you follow without any forces acting on you is the path of maximal clock time, so in other words, you know, the universe is just trying to spend more time with you as you go from point A to point B and all of your efforts are just working against that, okay, so now, okay, what does all this have to do with gravity, right, so you know, I'm working here for a while and because I got here early enough in the life of the institute, I got to be really shameless and call my group quantum gravity and then everybody else who came later had to invent some longer and more convoluted names and because of this, people keep coming to me and asking basic questions, okay, and for some reason nobody asks what is quantum mechanics, maybe they go to Thomas for that or whatever, but they keep coming and asking what is gravity, so that is the main idea of the stock, to give some sort of explanation of what gravity is in our modern view of the world, so the statement is that motion under gravity, under the so-called gravitational force, is described by exactly the same law as motion without any forces at all, okay, so the time on your clock when traveling from point A to point B is trying to be maximal, gravity just wants to spend more time with you, now, okay, then why does it seem like it's pulling us places and, okay, why is there such a thing called gravity at all? Well, what it does is it hacks into the formula that relates, is the fairy dust coordinates TXYZ to the clock time tau, so just as if you're light trying to go through a material, so there would be some refraction coefficient sitting in front here, but gravity is more subtle than that, so it goes inside the square root and what it does is, so let's keep the x squared, dy squared and dz squared where they are for a second and the dt squared, okay, it puts a coefficient in front, okay, so it's not just one as here, but one plus something, okay, this something turns out to be up to a little factor of two, exactly the same, that exactly the same thing that in Newtonian mechanics we call the gravitational potential, okay, so we have this kind of deformed coefficient in front of the dt squared and, okay, let's leave the others B for a second, okay, so what does that do? Okay, so we have our surface of the earth, say, and, okay, as you go up, okay, there is an increasing gravitational potential, okay, we're climbing up the earth's potential well, so in this direction there's an increasing phi, and, okay, I suppose we want to go to get from some point A to point B, okay, so the longest path without gravity, if it were just like this, would be just to go in a straight line, okay, so suppose, okay, let's draw the t-axis here, okay, so the longest path is to go just along t and not pick up any of these minuses, okay, and this is height, but once we start messing with the formula for the clock time, then, okay, then the path wants to go through the higher regions because time takes faster there, okay, and then it has choices to make, okay, so it wins some longer time by traveling up, okay, but it pays a price, okay, from the minus dz squared, okay, and there's some kind of balance between the two, okay, and it will end up taking a trajectory like this one, so shooting up and then falling back down, okay, and this is what the gravitational force is, okay, I think nobody really says that, they don't say it in high school, they don't say it in undergrad, they don't really say it ever, but this is what it is, so they teach you about the gravitational force, like Newton would talk about it, then sometime much later they maybe teach you general relativity, and then they mention as one of the physical effects, one of the, let's say, experimental successes of general relativity that we can do is, yeah, we can take an atomic clock, okay, put one on earth, put one on an airplane or on a space station, and compare them and find that, yes, clock tick, the clock stick more when they're high up than when they're down here, okay, and we call that gravitational time dilation, right, but the cool point is that this effect is the entirety of the gravitational force that we are used to, okay, so the universe is trying to spend as much time with you as possible, okay, gravity deforms the notion of how much time you're spending with the universe, and you just respond by choosing a new maximal time path, okay, so we learned general relativity, well, kind of, we learned motion in general relativity, so that's exactly the same as special relativity, except there's something else here in front of the dt squared, and minus the stuff from before, so now let's, okay, this is the entirety of the gravitational force that Newton knew about, okay, that everything that is about, you know, apples and the orbit of the moon and the orbit of the planets, and what happens to you when you fall off a 20-story building, but that's not all that gravity in its modern formulation in general relativity knows how to do, because this is only one term inside the square root. If we're messing with one, we really should mess with all of them, so generally, okay, there can be a lot in here, so we talked about the coefficient in front of dt squared, because it's dt squared, we call it like this, g with a tt, okay, and we can also change the coefficient if in front of dx squared, and we can change the coefficient in front of dy squared, and it quickly turns out that if you're already doing this, then you also need to allow yourself to mix them together, so there's going to be an xy, like this, and maybe a yz, okay, so a bunch of terms inside the square root, and because theorists are lazy people, we take all this, and we package it in fancy notation, so we say, yeah, there's a square root, but now there's this matrix of coefficients that multiplies displacements along some axis and some other axis, so we invent a little letter mu in honor of the great Minkowski, who understood this whole picture of what spacetime is, and nu, which is the next letter after mu, and g mu nu here, with the convention, which is maybe Einstein's greatest contribution to mankind, that, okay, we sum over all the choices of axes here, so this literally means all of this sum here, okay, so now the hacked clock formula is written in its full glory. Hacking, now people can come and say, nah, this is too complicated, we don't know how to multiply and take squares, and then you're telling us we need to take a square root in the end, look, if you wanted the force, if you wanted to change the balance of longest time from point to point, and surely there is an easier way to tamper with the formula than going and inventing coefficients inside the square root. We can just do some good old fashioned bias, yeah, so let's just say that, okay, we want to keep maximal, what? Hey, there's time on the clock, which is the t squared minus all these things, but we're going to cheat, and we're going to say, oh, by the way, and if you move too much in the t direction, you're going to pay for that some amount, some coefficient, let's call it AT, and if you're going to move in the x direction, okay, you're going to pay some amount for that. This isn't that simpler, okay, just instead of maximizing the time on the clock, okay, you introduce some extra thing that's added on top of the clock, simply without squares, without square roots, just pay a price for every little motion along t, pay a price for every little motion along x, and that's done, there you have a force, okay, things won't be moving along boring straight lines now. Okay, wonderful, it turns out that the universe does actually do this as well, and that this idea is nothing but the modern picture of what electromagnetism is, okay? So, yes, the simplest way to add something on top of just maximal time turns out to invent electromagnetism, so here we are here, so now the maximal thing is going to be not just clock time, but shifted by, this is still a good trick, packing up many terms in one little formula, so there's going to be coefficients along some axes, times, displacements along those axes, and this is electromagnetism, okay? In particular, this little thing here, a mu, is called the electromagnetic potential. Historically, here this price we pay for moving along the t-axis is called the electric potential, and it is responsible for all the phenomena of electrostatics, okay, of capacitors and sparks, and lightning, and your hair getting spiky when you rub balloons against each other, and so on, and these other terms in front of x, y, and z are called the magnetic potential, and they're responsible for all the phenomena of magnetism, and all the complicated ways in which the two interact that results in objects like electric generators and washing machines. And now important historical note is that, of course, generators and washing machines, the electricity and magnetism were figured out before all the rest of this story, and not only figured out before, but they led to it, okay? So this is a slightly modernized notation, I don't think anyone in the 19th century would have written it like that, but they noticed that there is some funny way in which the t-axis behaves just like the x, y, and z axes, and it makes sense to package them all together into one beast like this, and from figuring out the consequences of what that would entail, we ended up with the four-dimensional Pythagoras, with the, and the Feinstein's understanding of what a clock really measures, and ultimately with the picture of gravity as hacked into clocks. Okay, philosophical little bit to finish, so we already draw twice a picture like this, once for refraction of light rays, once for gravity itself. It's worth noting that there are two opposite ways of viewing this picture. Okay, so if we, if we zoom in on every little portion of it, okay, then it looks like, ah, okay, ball is flying up, and along comes the evil universe with its nasty tendency to maximize clock time, and it's pulling the poor thing back down. It tries to go up, but it comes back down. Okay, but that is not the fundamental way in which the law is written, okay? This is the best formulation of the law. The universe wants to spend as much time with you as it can, and this version of the law, what grown-ups call the action principle, is not talking about any kind of downwards force that is pulling you when you're trying to fly up. No, no, no, it just says, maximize this. Maximize this when trying to go from A to B. Now, when you zoom out and look at the global picture like that, then it begins to seem that you actually got gravity all wrong, because without gravity, the shortest path from A to B is the horizontal line, but because, okay, clocks run faster, up here, what gravity does is it takes that line, and it pulls it up, okay, and shows the way to where we belong, to the stars, okay? Now, I'm too sick to do the last bit, so I'm just not gonna do it, just follow the link in the email. Thanks for coming. Well, it's pretty self-explanatory. If there's no questions, I'd like to thank all the people that have made this possible, so the CPR for the filming and the advertisement, the Provost Office for putting this together, and the machine shop for making this special gift, which reads, Dear Yasha, your tenure marking you as a colossus in academia radiates extraordinary brilliance and indomitable spirit, profoundly inspiring our collective journey knowledge. We thank you.