A company of heroes assembles here. Men long dead and others living still. In this corridor, where honor is paid the deeds of men who through a century of wars have earned the medals and decorations of the nation's military services. Ghosts whose bodies sleep at Shiloh and beneath coral beaches on islands burning in the sun. And the spirits of other men who live today to remember what it was like at Bastogne or on a carrier at Laity Gulf or in the skies above Korea. All are represented here in this hall where heroes walk, wearing the proud symbols of service with distinction, symbols lustered with the gleam of gallantry, commemorating courage under the pressures of combat, spanning the spectrum of human bravery in its severest tests, culminating in the greatest symbol of all, the Medal of Honor awarded in two versions for gallantry and intrepidity at the risk of life above and beyond the call of duty. He weeps and feeds on the insubstantial stuff of dreams. But there's also an ability in him, a clean hard gem of splendor packed into the frail clay by the hand of God. The source of those virtues which are his special glory and which enable him to raise his eyes to the stars even when his feet are in the mud. Such a virtue is his power to love. Such is his knowledge of beauty. Such is his courage. Men in their tribes and the societies they've built, in their homes and nation states and in their armies have always honored courage when they found it among their own. For this quality, courage, bravery, whatever name we call it by, is the royal virtue. And men, when they see it, glimpse the nobility of their line. In its reflected glow, all men are king. History gave us as a nation, particular reason to prize this virtue when it imposed upon us its special challenge to win independence in a test of fire. Beginning with the Tattered Army, which wrote the word Patriot in steel and smoke on the emerging mind of a young nation. Beginning there, brave men carried the American dream in their stout hearts and fought for it and died for it in every test of strength and will our nation faced in its first century. They were unsung most of these early heroes. No medals were forged in their name or their honor. For we were still rebelling in those days of our lusty youth against our old world heritage and medals we thought were the trappings of Europe's armies, not those of a young democracy. Before that first century was over, came the conflict which shook this nation to its fundamentals and marked in deep suffering the beginning of its maturity, the civil war. Hopefully conceived, so proudly constructed, the American Union now lay bleeding and perhaps dying. Searching in its agony for the promise of its future, it found itself looking into the eyes of its sons. For here now, more than anywhere else, lay the meaning and the hope of the American experience. The nation had shaped the man and now in a moment of historic crisis, the man carried whatever hope existed for the nation's continued life. Whether the Union endured would depend heavily on his personal faith in the Union's cause and his ability to prove that faith in the most demanding of all tests. And a grateful people in the midst of war forged a medal to honor that courage. In the swirling fury of battlefields which scarred the American heart, the Medal of Honor was born. The civil war was deeply felt on both sides. The cause to each was sacred. Bravery wore a gray uniform as well as blue. But in the perspective of history, the preservation of the Union was the greater cause. And the Medals of Honor awarded to the Army, Navy, and Marines in that war are testaments to brave deeds which gave us the Union forever. In the War of its Birth, the Medal of Honor was the only award for gallantry in action. Later, other medals would be created to commemorate bravery in all its forms. And in the process of this distillation, the Medal of Honor would emerge as the supreme award, earned only by gallantry and intrepidity above and beyond the call of duty. With the tragic war over, the nation took up the heavy task of binding its war. The guns of the big war were silent now. But on the Western frontier, the fires of another kind of war still flamed. Charged with the task of making the frontier safe was the regular army. Out West, that meant the cavalry. The enemy was no soldier in gray now, but a bronzed warrior in buckskin lashing out suddenly against the beleaguered stockade. In the hot and dusty Arizona sun, in the biting, freezing Nebraska snows, into the face of danger hundreds of times the cavalry rode. Rugged leather-skinned soldiers on horseback, in their defense of the frontier, they bore the brunt of the attacks of hostile tribes. Many men who fought their lonely battles and died their lonely deaths in this distant America, which has passed into legend, won medals of honor. The names of their battlegrounds are obscure now, most of them. But some still ring in our national memory and always will. Names like Little Big Horn, where a saber-wielding cabaretman outnumbered but not out forth went down to the onslaught of the Indian charge. In the hard, grinding years of the Indian wars, 415 army men who fought America's battles on those distant plains were to receive the medal of honor. Not all of these heroes lived to hear about it, but for those who came after them, their names had passed into golden legend. It's 1898 now. The century of consolidation of cataclysmic change, of division and re-appamation, is drawing to a close. The nation hears the first faint echo of history's insistence that it looked beyond its own shores and take its place in the world at large. In Cuba, Havana Harbor is shaken by an enormous explosion, one whose thundering reverberations sound from shore to shore in our land. The explosion is caused by the sinking of the United States battleship Maine, sent to Cuba to protect Americans during the Cuban battle for liberty against Spain. The cry, remember the Maine, sweeps the nation. And men shouted it louder than a band of rugged men called the Rough Riders. Led by Fioro Roosevelt, they were to be in the vanguard of the force to land in Cuba as allies of the Cuban people against their Spanish rulers. Roosevelt and Colonel Leonard Wood recruited about a thousand men who were to be good shots and good riders and a tough and hardy lot they were. Their greatest day was July 1st, 1898. Their objective was a crucial hill in enemy hands. To reach it, they had to advance under deadly fire every bit of the way, headed to the top. And history recorded the George Upsan Juan Hill as one of its most stirring chapters of courage and combat. 30 army men were to be paid our nation's highest tribute in that short but fiercely fought war. Together with 81 Navy and Marine fighting men, they were the first to win medals of honor on foreign soil. The Spanish American War wouldn't be the last time America's soldiers would fight on land far removed from their own. The end of that war brought international responsibilities. And over the years, these responsibilities would grow. And an America which had believed it could lock its interests behind its own frontiers would be shocked into an awareness that trouble in a far away place might well signal a new challenge for American troops. We who live in this tense and global day have learned to live with that idea. But to those of an earlier time, suspicious of foreign entanglements and foreign adventures, the idea was shattering. Consider, for instance, the shock to America in the first year of the new century when it found that developments in far off China called for the presence, the fighting presence, of United States troops. Thousands of fanatical Chinese laid siege to foreign embassies in the capital city of Beijing. As engagements go, the Boxer Rebellion was a minor one. It occupies little more than a footnote in our military history. But brave men fought there. And some of them won the Medal of Honor. And of these winners, one man's courageous action has come down through the years as a symbol of the kind of courage which the bravest of the brave have displayed in all wars. He was a bugler with an infantry regiment. The Americans and other forces trying to relieve the besieged embassies were blocked by a 30 foot wall. The buglers company commander called for a volunteer to scale the wall. And the young soldier's ringing response, I'll try, sir, has become an example of high courage and an inspiration to infantrymen ever since. Curiously a decade after the Boxer Rebellion, United States Army soldiers were riding through the dry desert dust south of the Mexican border. A Mexican bandit named Pancho Villa had stirred up deep trouble by destroying American lives and property. An American expeditionary force had been sent in to eliminate the trouble. And America's fortunate to have that man, that member of a special breed who served beyond the call there at the moment he's needed. But if the nation had felt the need of him up to this time, and certainly it had, it could hardly face the challenges that lay ahead without him. For now the door to the new world, the world we live in today, was opening wide. And events beyond our control, but not beyond our interests, were driving us irrevocably into it. The shape of this world would be determined largely on fields of battle, reluctantly but inevitably. For now we could do no other. We would take our position on those fields far removed from the American continent. The war America entered in 1917 was a new kind of war. The truck and the tank and the machine gun had come and combat was never to be the same again. The war that lay waiting for the dough boy was one of massed firepower and long trench lines basing each other across the graveyard of a no man's land. Americans fought a vigorous offensive of small units sweeping through fortified German defenses taking the war out of the trenches in which it had been stalemated. What kind of face does courage wear in such a war? The one it has always worn. For the face of courage does not change, however much the weapons and tactics change with which the courageous man fights. In World War I, that special courage, summoned by the man who takes his life in his hands to do what must be done above and beyond the call of duty, wore the faces of 95 brave men of all surfaces. Courage and battle did find a new proving ground in World War I. The air. The airplane had barely emerged from its experimental status and now it was a formidable weapon of war. And the ranks of Medal of Honor winners who had fought on land and sea were increased by men who wrote their records of bravery in the sky. World War I, with its particular call on bravery and a kind of war new to the world at that time, saw the introduction of the airplane in combat. Scared me a generation later, a Second World War came to America on the wings of the same machine. Now a highly developed weapon of destruction. 14 million Americans served in uniform during this greatest and most destructive war in history. 430 of these would earn the right to wear the Medal of Honor in virtually every spot on the globe where Americans fought. And how would each man win? By standing for a moment in time alone, lighted by a fire which kindles in all men but rages in a special few in special times. Who was he? The man who served above and beyond the call of duty in World War II. He was a Marine from Ohio, a private first class serving on Guadalcanal. His machine gun emplacement took the full brunt of an all out assault. His orders were hold the position. Through the night he held off the Japanese. Weary and exhausted toward morning, he did not see an enemy soldier approach until too late.  He was an army platoon leader whose unit was pinned down by the Germans locking in American advance. Ordering his men to cover him, he went forward alone and destroyed the enemy's stronghold. When his job was done, he brought his men forward. And in the process memorialized the heroic stance of leadership wherever men fight. He was a naval officer. Commander of the submarine coordinated attack group off Truck Island. He alone of the group possessed secret intelligence information of our submarine strategy. He carried out his secret orders and the enemy paid dearly. Once his own flag submarine was rocked and battered by Japanese depth charges. The damage was soon beyond repair. The commander decided to surface the flagship and engage the enemy in a gun fight so the men might have a chance to abandon ship and live. But for himself, the decision he made was considerably different. Rather than risk capture and possibly reveal secret plans under enemy torture or use of drugs, he decided that he would remain aboard the vessel. He would stay with it in its final plunge to the bottom. He was a flying colonel who led a mission which seemed incredible in 1942. One which started with bombers being lifted from the deck of an aircraft carrier. For these planes were destined for Japan and the Air Force then had no suitable airfields close enough for them to leave from. In those dark early months of the war, the mission of these volunteer airmen electrified the country with a thrill of hope and pride. They carried the war to the enemy to a confident Tokyo which then believed itself invulnerable to attack. So audacious was the mission, so daring in conception and performance, the Japanese defenders were caught by complete surprise. The attackers came roaring in over the Japanese mainland and first blood, the first of much to follow, was drawn from the enemy. He was a general of the army who sent a thrill through the allied world by returning victorious as he had promised to a land he had been forced to withdraw from in the face of overwhelming forces. Not many general officers had won the coveted medal, but it is meaningless to talk of the Medal of Honor in terms of rank. Generals can win it and corporals can win it and admirals and seamen. Bravery knows no rank and it knows no station. The medal can be and has been won by every kind of man our society has produced. It can be won in wars of all kinds as it has been in our time, from the mighty epic of a war that stretched across the world to one localized on the narrow peninsula of Korea. In the hills of this divided and far off land, Americans faced communist guns for the first time. Korea was a war of symbol. It was freedom itself that was attacked and it was in the cause of freedom that men stood and fought. Behind the symbol, it was a war of flesh and steel. The fighting was bitter and intense. 131 Americans who fought here joined the select ranks of the bravest of the brave. Some fell, some lived. Some understood clearly the contribution to freedom's defense they made. Others perhaps saw the issues dim. But each of them reached the summit of America's pyramid of honor by a supreme act of bravery above and beyond the court. The Korean armistice, the guns of Americans in war were silenced. The braved deed in combat was recorded. And thus, in a sense, the story of the Medal of Honor to this day is closed. The heroic adventures of the 3,156 who have won it in a century of wars are preserved between the bindings of official history and all are woven into the living legend of a people and a people spirit. For this very reason, the story of the Medal of Honor is not ended. And indeed cannot end. But the particular essence of the Medal is not what it is or even the epic tales of those who've earned it. But more than anything else, what it represents. Precious quality which Lincoln called devotion, transformed in an atmosphere of danger into a courage whose presence and noble man, such a quality does not die. It lives unflowered and unseen. But if it's needed, it's there. Once more, America stands in crisis. And as in other days, searching for the promise of its future, it finds itself looking into the eyes of its sons. Their defense of freedom is a silent one, but most solidly real. Their mission, urgent in the eyes of mankind, demands more of patience and skill of effort and adjustment and quiet determination than it does of courage. They train so that war with its special call for bravery will never come. The seeds of bravery lie there and they will blossom if they must in fields where they have grown before, where they have always grown, in the stout parts of men. The links in the soldier's tradition are strong and the heritage of those who serve today reaches far. And most prized of all in this heritage is the tradition of courage, refined into the special quality whose presence is felt here in this hall of glory, where ghosts of heroes walk, keeping vigil on a nation's pride.


So there's one thing I wanted to say before we get back to the compactness. So we saw that there were slices for the action of the gauge group, which gives the quotient space a nice structure. And then we can restrict that picture to the space of anti-self-dual connections, which are the zero set of the mat that sends A to F A plus. There's zero. Here's lambda plus. So inside this slice, where's my? Maybe the slice has acquired some dimension now. Inside the slice, there's a local model for what actually the anti-self-dual connection looks like anti-self-dual connections look like modulo gauge. And it's a fundamental fact, which you saw a version of in the lectures on the first week, that if you kind of linearize this picture, what you get, linearizing the gauge group action gives you the map that sends adp value of 0 forms to 1 forms dA.  You notice that A is d. That implies that d plus, this composition is F plus, is 0. So this is a complex. It's an elliptic complex, as you saw. And it's index. Well, I'm going to write it's negative index. Index is the alternating sum of the dimensions. We're really interested in the dimension of h1, so minus the index. And it's 8k minus 3 halves, the Euler characteristic of x. So this is in the case of a closed manifold, or 8k minus 3 times 1 minus b1 plus b plus. So this picture kind of gives you, so this is an elliptic complex. In particular, this tells you that if I restrict to the slice, then the curvature map is a nonlinear Fredholm map. And that gives you a nice package of stuff that tells you that the moduli space is locally, at least finite dimensional, if it's a differential surjective. Then of course, it's a smooth manifold of some dimension, dimension given by this formula, at least if the connection you're looking at is irreducible, has no stabilizer. OK, so that's something I maybe should have said a little bit earlier in yesterday's lecture. I'm going to go back to Ulinbeck's fundamental lemma. I'm not going to prove it. And I stated a slight generalization of it. So the statement I said at the end of the last lecture was the case where I just looked at one connection that has small curvature. But it's easy to prove using the same techniques. I'll say a little bit about that. If you take a pair of connections, each of which has small curvature, so there's some bound that Ulinbeck's argument gives you, epsilon, then, well, you can put both of them into this good gauge, Coulomb gauge with this boundary condition. But the interesting thing about looking at a pair of connections is that you can prove that the difference of the L21 norm of the difference of the connections is controlled by the difference in the L2 norms of the curvature. So the statement I had last time was, say, A2 is 0. So we're just saying that the L2 norm of the curvature controls the L21 norm of the connection in the good gauge. Here, we're saying something slightly sharper, and we'll see that that has a nice consequence. But let's, again, I'm not going to prove that in detail, but just go through one part of it. So a lemma on the way to the proof to kind of get you the feeling for what special in dimension 4, et cetera, is that, well, Ulinbeck's lemma holds, if we assume, actually, let's call this 1 and 2. So we're going to assume 1 that we've already got it in a good gauge. And instead of, maybe, 0, instead of 0, we're not going to assume that. We're going to assume something stronger. We're assumed that the L4 norm on the ball of both connections is less than some epsilon prime. Then that implies that 2 holds. So just to get you some feeling for why this lemma is useful in proving Ulinbeck's theorem, well, if you have control over the L21 norm, so in dimension 4 or less, that L21 embeds into L4. So this assumption holds if you know this. So if the curvature actually is controlling the L21 norm and is sufficiently small, then the L4 norm is sufficiently small. And then the idea, once you know this lemma of proving its theorem, is that you compare the set of connections that satisfy this conclusion of the lemma with a given hypothesis. You compare that with all connections that have small curvature. And you prove that the set that satisfies this hypothesis once the curvature is sufficiently small is closed and open inside the space of connections that have small curvature. And you prove that space of connections that have small curvature are connected. So all of them satisfy it. So somehow there's a thoughtful argument that goes from this lemma to proving both statement. And we'll see in this lemma where we use this. So this is just a straightforward computation exploiting the fact that we need to know that if we integrate over the foreball d plus d star of A, or this doesn't matter what the dimension is, then this is equal to the covariant derivative squared plus the integral of b squared on the boundary if the boundary conditions are satisfied. In particular, this is positive so I can get rid of it. So if I know this, so if the boundary conditions have to be satisfied and then I have this estimate. So on the other hand, if I look at, so again I'm assuming these guys are in good gauge, I look at the difference in the curvatures. In good gauge, this is one. That's what everybody has called it forever. It's a good gauge, it works. So you have to ask Greg. I would call it a gauge fixing condition. Maybe Greg would call it that. But somehow physicists are much less careful about language than we are, sorry. And it's true and we've adopted that language. I mean this is a gauge fixing condition, it's just meaning, just means that we're taking a slice. That's all it means. Anyway, this one. So there's another term, I mean if you write, this is sort of the Weissenbach formula in a manifold with boundary, there's another boundary term in fact. Well, the ball is flat so there's no curvature term. There's another boundary term which vanishes under the boundary condition assumption. So it's particularly simple. Actually let me, I don't want to do the calculation here because I'll run out of room. So we look at FA1 minus FA2 squared. That's equal to DA1 plus that minus DA2 minus D. And well it's in good gauge. So this is, let me say, yeah. Well first of all, this is up to some constant. I can write this as DA1 minus DA2 squared and then minus A1 minus A2 times A1 plus A2. Integrated over the ball. So I collect these terms together here. I collect these terms together. This is sort of a difference of squares. Sorry, I wanted to write this. A1 plus A2 and well this controls the covariant derivative by the Weizenbach formula over there. What about this term? Well, we use Cauchy-Schwarz inequality and we get that A1 minus A2 L4 squared times A1 L4 squared plus A2 L4 squared. And here you see the L4 norm coming in to play. But when we apply the Cauchy-Schwarz inequality, Holder inequality I guess. Anyway, so we're assuming these guys are small, right? And this is controlled by the L2 1 norm up to some constant, right? So what we learn is that this stuff we can control by the L2 1 norm times some epsilon that sucks a little bit away from this guy. The covariant derivative of the difference controls the L2 norm of the difference as well, as you can check easily. And that means that this is greater than or equal to some constant times A1 minus A2 squared plus A1 minus A2 squared. That's it. So it's a simple computation. The key is just this kind of rearrangement in here using the fact that the L4 norm is small. And one nice corollary of this, what? I could have used stronger norms. I couldn't have used weaker norms in dimension 4. The key thing is that I was using this bound, right? Which is true up until dimension 4 and then past dimension 4. Well, it just doesn't work, right? OK, so now a nice corollary of this is that if I look at the space of small curvature connections in a slice, so look at a set of gamma plus A so that gamma plus A is in the slice for some small epsilon. And well, that's sort of redundant. But anyway, then the curvature map, mapping to two forms on the ball, so I think of this with this as this is in the L21 topology. So let me state this. This is L21 topology, L2 topology on the ball values in SU2. This is a proper map, right? Well, that follows immediately from this estimate if I have small curvature, so in the set of connections with small curvature, I get control of the L21 norm. And then if the curvatures are Cauchy and L2, this tells us that the connections are Cauchy and L21. So it's a proper map. And that's kind of the precursor of compactness. So this is, we want to know something about sequences of anti-self-dual connections. And what this shows is that what I need to do to prove compactness, at least locally, is that I need to prove that for a sequence of anti-self-dual connections, I can pass to a subsequence where the curvatures are converging strongly in L2. That's all I need to prove. I only know that half of the curvature, F plus is 0. But anyway, I'm not going to, well, let me just state a version of compactness that's good enough. I won't prove it. Again, I think that simple calculation starts to give you a feeling of what you need to know. And one nice way to kind of set up compactness is to note that if you look at the small energy moduli space on the ball, it's a set of gauge equivalence classes of connections on the ball so that F plus equals 0. And the curvature is less than this magical epsilon. And what you can prove is that there's a restriction map to sub-balls that this is actually a compact map. And several different ways to prove this. I mean, you can think of this in the sort of maybe most standard way to prove this is to just show that once you put connections, anti-self-dual connections in a good gauge, then on sub-balls you have control over higher norms. And then this would follow from, let's say, less goalie theorem. There's kind of, in some sense, a more elementary proof that just uses this properness eventually. But so what this is telling us is that once we have a sequence of connections and we can find a ball where all those connections have small curvature, then on a slightly smaller ball we can assume that they converge after passing to sub-sequences. And so the interesting thing that happens in dimension 4, let's first think about a compact manifold. So let's take a sequence of connections, so ASD connections in a principal bundle P. So first of all, the energy of the AI is always, it's this with our conventions for pi squared k. So it's bounded uniformly.  So here's x. And we want to do it carefully, so fixed size, but so that we want to make sure we choose the cover carefully so that no point, there's a uniform bound for the number of balls that meet any point. All right, so then if we have that, then the number of balls that violate this, the size of the balls doesn't matter because we're in dimension 4. We'll index statement in dimension 4 scale invariant. So the number of balls that violate the requirement for any given connection is finite. And so we can pass to a subsequence where all the connections satisfy the hypothesis of Ulland-Beck's theorem on all the balls, but finitely many of the same ones. Yeah, but the key is that no matter what scale, it'll be the case that there are only a given bounded number of balls for which that fails. Because the total energy is bounded uniformly always. So there are at most 14 balls no matter what scale, say, which violate the inequality. Only 14 balls for any given connection, so you pass to a subsequence where the failure is only on a fixed 14 balls. At some scale, you pass to the next scale just looking, observing those balls. Again, there are only 14 that are bad. And you keep going, and eventually you get convergence. So it's just like Gromov compactness. Is it Gromov compactness? Yeah. What's the first one I'm saying? Well, it's this epsilon. That epsilon is given to you. We prove that for a four ball. For the flat four ball, there is a constant. It doesn't matter what the radius because of scale invariance is. It's exactly the same as in Gromov compactness. I mean, because the energy scale invariant, you prove an estimate on the unit ball once. Then you know it for balls of any scale. And as long as you're below that energy scale, no matter how small a ball you have, you're in good shape. So that's exactly the same. And they're only 14. No, no. I mean, you could prove a sharper statement where epsilon is the energy of the instanton on the four ball, on the four sphere. This is epsilon's, you know, the epsilon that you get out of the argument is much smaller. And it's a technical story, which, you know, first you go by proving that for the given epsilon that you get out of this mess, which is just, you know.  That's all it notices. But then you could prove a sharper statement that says that, well, actually, you don't have any problem if your energy is below the energy of an ASD connection on the four sphere. So anyway, yeah. OK, so we happy with that? So we get eventually out of this, we get convergence away from, finally, many points. Yeah. That's just, it fails, well, because we don't, you know, we don't have, you know, if we have a uniform bound on the L2 norm, then we kind of lose on, you know, the scale and variance as I shrink the ball in dimension five or higher, the energy increases, right? So you don't really, no, no, no, I mean, this, well, this is solving this equation. And this is kind of general nonsense.  What? Which, it goes wrong here. There's no, because we don't, that epsilon doesn't, you know, it's not scale and variance, the size of the ball matters, right? So it just doesn't start. Yeah, yeah, yeah. To localize where the, where the, yeah.  So I get convergence everywhere else. Now I cover this ball by smaller balls. There are, again, only fixed number of balls, there may be two, but no more than 14, inside here. And then I do it again. Okay? Okay, okay, great. Yeah, it just gets worse, life gets worse and worse. I mean, like I said, there are statements you can prove in that context. And the statements are trickier. You get convergence away from a subset of Hausdorff co-dimension four, stuff like that. And again, trying to analyze the structure of what that subset actually looks like is an interesting topic of current research. Okay? Okay, I'm worried that if Vivek and Greg don't understand, then oh dear, I don't know how many other people understand, but my students do, right? Right? Okay, okay. So we've kind of sketched why Lundbeck and Packness holds. And then there's one more key step, which is, let me just put it here. We get convergence away from finally many points. And then we need, as we saw in the four sphere, when we looked at that sequence of connections that bubbled, we observed that we could actually fix what happened at the limit. So there's a removable singularities theorem. So if A is ASD on the punctured four ball and has finite energy on the punctured four ball, then there exists a gauge transformation for G from the punctured four ball to G so that G star A extends to an ASD connection. So G need not extend. As we saw in that example, the gauge transformation that does this job may not extend over the four ball. So what this means is we have a sequence of connections that are converging away from a finite set of points. We get a limit, which is defined away from that finite set of points. This is saying we can fix it, but in fixing it, we're gonna change the topology of the bundle. So P changes. All right. So now let's get back to the cylinder and I need to explain one more important thing before we can kind of sketch the construction of floor homology. So now let's think of R times Y. And I'm gonna say it. Yeah, so the behavior of the moduli space on a closed-form manifold was kind of controlled by local behaviors controlled by these two operators, D plus and D star. D plus gives us the linearization of the curvature equation. D star gives us the gauge fixing. And what I wanna do is, so it's nice to just package them into one package. We're gonna look at this operator on the cylinder and let me tell you what it looks like. So I'm gonna write my connection as some pullback connection from Y. So gamma lives here, it's not necessarily a trivial connection. Plus a one-form time-dependent one-form on Y plus a time-dependent zero-form times DT. So I can write any one-form as a bit with it, out of DT component and a bit with a DT component that I choose to do it that way. And then this operator, in terms of these guys, becomes this guy. So BC goes to, okay. So on the cylinder, I'm gonna write it in this particular form. What's important about this form is, first of all, it looks like D by DT plus a self-adjoint operator. This is self-adjoint. You looked at, one of the homework problems was to look at this operator on the three torus and you observed, I hope, that its spectrum was infinite in both positive and negative directions. Now, if you look at, sorry.


It's not necessarily a talk, it's more a performance, and it's titled A Webpage in 3x. It's done by Joanna Cicco, a graphic designer, a researcher and a performer with a background in dance. Thank you for being here. I'll start by sharing some of these choreography code. Yeah, I hope you enjoyed the dance, and there will be time for questions afterwards. First act. Warning. Theatrical actions are not necessary to the performance piece. Avoid if at all possible. Warning too. Please switch off your mobile phones. Remove. Remove. Remove. New sequence or phrasing. Phrase as a metaphor. For a long or total duration containing beginning, middle, no end. Eliminate or minimize. Keep mindful or be aware of your breathing. Behalte deiner Atmung im Kopf. Choreografie als eine mobilisierende Sprache. Ritualistik. Substitution. Simulate. Element das Zufalls. Kein Zeit in der Akkumulation. Ich höre nicht aufzuspricht. Atmen realistisch. Substitution. Ritualistik. Wiederholend. Gleichzeitig. Simulierend. Akkumulierend. Keine Zeit zum Atmen. Ritualistik. Variation. Erweitern und zusammenziehen. Oder so zu lassen, wie es zu sein scheint. To accept the position of elements and their aleatory influence. Aneinanderreihung von Elementen und verschiedener Einfluss. Ein Ding, das sich Körper nennt. Chance modifies perception. Destroying the idea of sequencing. Accuracy changes perception. Destroying the idea of... beginning, middle, no end. Beginning, middle, no end. Words that define and define. Space and time. Expand and combine. Or everything remains as it seems. Choreography is the organization of tensions. Choreography is a combination of contradictions. Leave the stage. Leave the stage. Accumulation, superimposition, kitalisik, I think all about it. Simultaneously accumulation, superimposition of rhythms. Not that for breathing, accumulation. Simultaneously everything is interesting. Accumulation, re-tailisik, re-tailisik, re-tailisik. Variation, think all about it. Not that for breathing, accumulation, variation, variation. I think all about it. Variation, re-tailisik, re-tailisik. Rhythms, accumulation to the body, somebody position, not utalistic, I think all about accumulation of variations, which is to think all about the repetitive, reading until the end of the utalistic variation, and to really pursue simultaneously, I think all about the utalistic, reading until the end of the utalistic, simultaneously, leave the stage. Verlas di Bühne. Second act. Zweite act. Pause. Pause. The circle suggests the infinity of perpetual motion, repeating itself, internally. The circle shows the repetition of a movement. Or inertia. Movement. There are as many spatial temporal experiences as there are distinct movements. There are as many spatial and temporary differences as there are distinct movements. Spatializing time in multidirections. Multiple speeds and orientations. Different orientations. Between geometry and gesture. Between geometry and guest guests. Our world organizing. Remove. And fernon. Remove. And fernon. Breathe. Undefined. Circle. Like the clockwork. A stronger circle. Undefined. Public area. Rotation. Rotating wheel. Geometry of time. Undefined. The private circle. Rotating. Repeating itself. Undefined. As always in motion. Breathe. Rotation. Rotation. Rotation. Kugeln. Rotating. The private circle. Breathe. Breathe. Breathe and delete enough. Breathe until it's enough. And rotate. And rotate. Pause. Pause. Leave the stage. Final act. Last act. By moving or by opting to remain still, choreography demonstrates how its decodings are not mere conceptual propositions, but actual possibilities for action. By moving or by opting to remain still. For the people in the stream, it's about the room that you probably don't see. And now you're in the second row breathing heavily on a chair. Thank you. Thank you. Thank you for being here until the end. Thank you. Thank you. Thank you. Thank you for being here until the end. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you for finally staying up. Or not sleeping in, and by doing something like that. So, yes, I am open to asking questions. I have a few notes with me, and I'm happy to share a little more about this project. So, yes, I am starting to ask questions. ideas. And I can share more of my choreographic ideas. I read something from Michael Klein and other choreographers. It is something that I brought into the design and the programming world. I think it also helps to explore what happens behind the interface. Maybe that is just a very basic definition. And you also know that choreography for writing movements is. So here you have the tool of a language that was constructed over many years, which was developed by different people and movements in different times. The audience, even if there are Greek-speaking people here who also read it, speaks of written movements, especially this notion of a hand, which goes very physically back to the notions of writing and the movement in writing. The space is not defined beforehand, but something that we define ourselves. And this idea of making space, not giving space, but taking space as a collective is pretty much how I sort of my own formula. That is my own formula, that I have decided to deal with choreographic languages and programming and web programming. And to do different things can be a demonstration or a live performance. For me it is not just an appropriation or trying to... through these performative adherents of code, but it is also a way of thinking critically and thinking differently and also to react to critical voices. There were also other projects in other genres. What you just saw was based on post-modern dance, which has its origin in the 50s. Maybe you know a few names. For example, Yvonne Rayner, Merce Kenningen, Trisha Brown, these are the stars. Many of these voices also fought for other fighters, for example, for women movements, to fight for their own rights and also to fight for their own views, to be performed by them. With all these different projects, I have worked with other choreographers. My background is ballet and contemporary and classical ballet. And that you just saw a little bit. I also worked with other, for example, with Ashka Watson, Movement Notation and finally with Putton. Many of them you can find online. You can find videos or you can find the source code that you have. But I could obviously just have the code in itself. But I could have the code alone, of course, but I also think it's important to perform the code in these moments. Here is a quote. And the way I make the words and the code and everything to my own, in which I bring them together and for example, I am on stage, but also can be a public. And it is for me a kind of physical work that is otherwise not so direct, because normally it is programming, but it is more hidden or only the screen. Here is another reference from Miriam from Emschut. And how the flesh is also something, but also the language with the devices, the body, the flesh is dynamic and always in connection with the environment and with different agents. That was different things that I found out and that I would like to share with you. And I see these programmers and these choreographies as developing and not as static. I wanted to show you some of these projects, but please don't interrupt me, if you have questions. But then I would like to continue. If you want to interrupt, you can like to run to the microphone and interrupt. That was a short experiment. It is an interesting 3D environment and it is an interesting 3D environment. In this gallery, every few months, different artists are invited and I was able to insert my code and made public access to it and created it for Google Maps. This code was created specifically for Google Maps. And I demonstrated the whole thing in the Moon Gallery. I don't always perform alone. I have a collaboration and I am always happy about collaboration. Some of the guests have already worked with me. I am not only a choreographer, but I am also very interested in theater. Traditionally, well, if you can speak of tradition, there is a great connection with music with live coding. I have started a collaboration with Rannick Bell. You can find our platform online if you want more details. I think it is very interesting to have these dual interface performances. When we work on them, I make the sound and someone changes the visual side. Hello, thank you very much for this presentation. It was very moving. When you are around us, I have the feeling that it is a moving movement that pulls us together. If you are around us and have a good idea of what you want to do, you want others to continue to change this code, to develop it and to practice it a little bit as a movement. Do you see it as how it is with people who are not so good at the movement? One thing is sure, we are all in movement. Even if we are still, everyone could take part. We are also part of many choreographies. I was hoping that someone would work. If you want, please come to work with us. It was a great performance. I wanted to talk about what your idea was. I am looking for the visualisation of beauty. Do you look for a personal experience of a room that you want to share? In what direction do you go when you write the code? I don't really know what to say about beauty. I don't know what I could say about beauty. That is something different for me. I wouldn't think about it while I perform. But I think about aesthetics and sense and sensual experiences with movement. In the body, in the flesh, in the sweat and all of that together. And to bring that into the space of codes. I think we are all in this circle. But I don't really think about web design in terms of beauty or ugly. This is a very technical group. Are technical visitors different from those who see the entire interface from the front? I think I had really different comments and I heard really different feedback actually. I got a lot of different feedback and comments. But after a while they really realised that there is actually a head in the body. And some people always see the same code and realise later that there is a head and a body. And they see this differentiation later. So it's quite surprising for me. I always think that what I do is something new. That there is an existing interface. But it's possible to see and read this code differently. In more technologically oriented environments it happens more. People who actually know how to program know more functions and terms. And find more in the code. And I think that's another experience that you have. This is the end of this talk. We will continue at 2150. That was the German translation of this talk. A web page in three acts. I hope you enjoyed it. That was Escarina and Franz T. Have a nice day. If you had feedback it would be great. If you liked this video please leave a comment. Or send us an email at c3lingo.org. See you next time.


So what I'll be showing is a very basic hello world application that will be deployed in a container to the OpenShift container cluster management solution. And essentially, we're going to build it and pretend we're testing it and deploy it and show how it works with our GitLab integration. So I've just imported a very basic application here into GitLab. So it's made up of two files, a server, RRB, which is just a Ruby server sitting out hello world, and a Docker file, which is what we're going to use to bundle up the application into a container. So it contains our base image that we're going to use to bring in all those dependencies we need to run our application. So in this case, the Ruby base image, it's going to copy in our files. It's going to expose our web application on port 5000, and then it's going to actually run our server. So in this demo, everything is blank, but we're going to assume that this is our application that we've been iterating on for a while within GitLab. We've been working on creating new merge requests. We've made new issues, iterated on work, created some branches, and maybe released some tags already. So we're going to pretend this is like a already, we've already done some work in this application. Next what we need to hook up is our testing solution, our continuous integration solution. So we're going to go ahead and do that next. So under the Settings tab in GitLab for your project, under the CI CD pipeline, we have this page where you can set up your CI runners. Now if your company had already set up shed runners, you may not have to do this. In this case, we're going to set up a very specific runner for this project. And we're going to make use of OpenShift to run our CI build. Using OpenShift or any Kubernetes cluster is pretty advantageous for our CI runners, because it's very easy to set up. And then you get the ability to run parallel CI jobs with very minimal setup. So here's my OpenShift Origin UI. I'm going to log into it. And here, I've already created two namespaces, the www namespace, which is where I'm going to be deploying our Hello World application. And it's currently blank. And the GitLab infrastructure namespace, which is where I'll be deploying my CI runners. And it's where the jobs will be running. The namespaces are separated so that we can keep the permissions of the different pods running separate more easily. So I've already added the GitLab runner template as a template to OpenShift, so any namespace could add a runner to their namespace here. So I'll just load it up here. In order to run it, I just need a few input variables. So I need the address of the GitLab instance, which I can find from the Pipelines page here. And I need the registration token that tells the runner which project it's allowed to associate with and identifies it to GitLab. So here's the deployment running for the GitLab runner. So OpenShift has taken our deployment config, and it's creating and booting up a pod, which has our container within it. So if I go into the pod, we'll see that the container is running a Docker image, which is our GitLab runner application. And here in OpenShift, it's assigned a few other things, like it's given a cluster IP address. It's monitoring the state. And we've also have various mounts and sequence mounted automatically. So this runner has registered itself with GitLab. So if we refresh the page, we'll see it show up. So what this runner does is it's going to be polling GitLab for any CI CD jobs to run. And then what it'll do is it'll bring up new pods here in this namespace to run those jobs. So now that we have a runner, we can set up our CI CD jobs. There's a set up CI button in GitLab. We'll click on that, and we get this GitLab CI YAML template, which is where we define the various build stages and define the jobs that make up our continuous integration pipeline. I'm going to show off the bash example. You know, this isn't a bash application. This kind of shows the easiest example here. So you're able to define an image, a Docker image specifically, to use as the default for all the different tasks. So that's going to define all the dependencies to run your CI task, not necessarily your application, but the dependencies needed to run your jobs that will define below. We have a before script. The runs before each job and after script. We have a build stage in this example with a single job to build your application, and then we have a test stage that we've defined two test jobs in that will run in parallel, and then a deploy stage that just has a single job at the end. So the example template I'll show off is the Docker one to just show an example of how you can build a Docker image using CI. So the dependency here is Docker, the Docker image itself, which brings in the Docker binary. And this does a Docker build and pushes it, in this case, to GitLab's own built-in registry in this example.  And I actually had a little bit out here, but all I did was change the images to a Ruby image and the deploy image to the Docker image. So I'll create a new branch and commit this. And we're just going to use this as an example of a CI pipeline. So over here in OpenShift, the runner picked up the fact that there was a job and brought up a new pod that had the Ruby image. If we go back and we look at our pipelines in GitLab, we can see we have one running pipeline. The build is finished in two parallel test jobs that kicked off, which we can see in OpenShift. And then the final, with the Docker image, is the deploy job. This was just echoing things, so it wasn't really doing anything, but it shows the whole pipeline in a way that you can make use of the parallel jobs and easily set up CI. So next, we're going to set up the actual integration we have with Kubernetes and OpenShift. So we have a Kubernetes OpenShift integration listed here. So we're going to, say, define which namespace we want to deploy our application to. We're going to put in the API URL of the Kubernetes cluster or in OpenShift's case, the OpenShift cluster. And we need a service token to give GitLab access to make new pods and deploy. In this case, we're going to just grab it from the UI. This is just an example case. You would want to create your own service user and grab a service token that lasts a little longer. The UI one expires when I log out. So now that is set up. We should be able to go back to our project. And now there's a set up auto deploy button beside our set up CI button. So we can click on that. And we're back in our GitLab CI YAML. And this time, we have both an OpenShift and a Kubernetes example. So the OpenShift one includes a dependency on an image that has the OC binary. But we're not going to show this one today. That one makes use of the OpenShift build pipelines. But we're going to show just raw Kubernetes, which also works with the OpenShift image. So we have the image defined as the, in this case, Kubernetes deploy, which basically is just bringing in the cube CTL as our dependency. I'm going to change it here to OpenShift deploy, which also has the OC binary to this example image. And then these images are meant as examples. And we want you to be able to take them and change them and make them your own for your own needs for deployment. So I switched to my own, which had an updated binary for the version I'm running. The only other thing I have to change in this example is the cube domain to be a wildcard domain that I'm using. In this case, apps.yourdomain.work. So that's where I'm going to deploy my various versions of the application. I'll just create this as a merge request so I can show off the merge request UI. So we have a pending pipeline, and we have our changes that we can comment on. Over in OpenShift, our pipeline is kicked off, and we're running our build image, which we can see if we come in and look at the pipeline in GitLab. We have build running, and then in this case, we're going to be running review deployment next. So the review job is kicked off to make the deployment. If we jump in, we can see it's going to create the new application, deploy it, wait for it to roll out, and then expose the route in OpenShift to the router and load balancer. So to go back into our namespace where we're deploying these, we can see we now have a service that's config and our pods started. In GitLab, if we look at our merge request that we had set up, we see we now have our pipeline having passed. We have a third stage that didn't run, which is actually the cleanup stage which closes this deployment, and it will run when the branch is removed. Because in this case, what we've done is we've deployed a review application. So the URL has been somewhat generated. It's not your final URL. And it's specific to this branch, this merge request. This isn't our master branch. So we're able to now review this application using OpenShift and leave comments, stop the environment when we want to. And there's a couple of other things we can do. So we can actually go into the environment tab and we can access the terminal from GitLab as well. You can do this directly from OpenShift as well, but we can debug the running application from GitLab. So if I go in, what we're going to do is we're going to show an updated deployment. So we're going to go into the branch and edit the server.rb and change what it's going to output from Hello World to be just Hello Open. We'll deploy that to our same branch so it shows up in that merge request. We can see a new pipeline has started. Under our changes, we have two commits. We have our old BI YAML file that we added before and our new change. And in our pipeline, we're running another build of the Docker file and then another push to deploy the review app. The back in our infrastructure namespace, we have the build just finished. Next, it'll pick off the task that will be responsible for doing the deployment of the review app. And over in our actual namespace where we're deploying this application, we should see the old application start to shut down. The new one, the triggered for starting up. So there it goes. So now it has two pods that it's running, one with the old image, one with the new, and it's actively working on scaling down the old one. And OpenShift has already taken care of removing the old one from the load balancer. So even though the pod isn't shut down, it's not accessible at this point. So if I refresh the domain where we had our review app, we see it's been updated and our pipeline is finished. We can go ahead and merge this in and we'll see the review app close. So this will trigger the cleanup job, which will take care of shutting down this particular review app.


Never in a million years did I ever think that I'd be adding to the conversation about the happenings in the chess world, but here we are. Earlier today, I saw that Magnus Carlson released a statement about resigning when playing Hans Nieman and although I had no clue who either of these guys was, my recovering attic brain got hooked. I ended up going down a rabbit hole to learn everything I could about the situation and now know more about professional chess than I ever thought I would. This is a story of cheating, past behavior, the pseudoscience of body language reading, due process and so much more. Although I'm not someone in the chess world, I think it's important to get an outside perspective. Oftentimes, someone who isn't quote-unquote in it can provide a different angle of thought to a conversation and that's why I decided to sit down and discuss this story that's been dominating headlines. This seems like the consensus is that Hans cheated, I'm going to be taking the opposite end of the argument. I come from the world of debunking conspiracy theories and trying to teach people how to become better thinkers.  So it is 100% possible that Hans cheated, but we need to put the quote-unquote evidence up to scrutiny to see how it holds up and also see if there are alternate explanations. And the reason I'm saying this is because I don't want anybody coming across this video to assume that I'm saying Hans is innocent. I'm not saying that, I'm getting that out of the way early, so please do not leave a comment that says you're defending Hans and saying he hasn't cheated. What I'm going to argue is that we do not know and there are details of this story that we need to take into consideration. Because another topic that I am extremely invested in is wrongful convictions and most of the time wrongful convictions happen because entire juries and even prosecutors can't think of any alternate explanations. Well, prosecutors can sometimes just be trying to get a conviction, but oftentimes they are overlooking alternate explanations. For those of you who are unaware, let's get you caught up to speed. Magnus Carlson is one of the best chess players in the world, if not the best. While getting caught up on this story and the main characters in it, I also learned that Magnus's mental health hasn't been doing well. This is important to note and we'll come back to it soon because there are some things going on that definitely need to be taken into consideration when stepping back and getting a full view of this story. The other main character in this story is Hans Nieman, an extremely young chess player who has been seeing a meteoric rise in success. What I didn't know about Hans is that he admitted to cheating when he was about 12 or 13 years old. While this may seem like it was a long time ago, Hans is currently only 19. So this is something to note as well. Not long ago, Hans and Magnus played in a quote-unquote over-the-board match, which to my understanding is basically just a live match because now in the internet age a lot of matches are taking place online, so over the board they were playing live and in person. During this match, Hans wins and rather than continuing in the tournament, Magnus decides to just straight up end his run and leave. As you know, this story involves cheating accusations, but there's also something to be said about someone like Magnus Carlson leaving the tournament after losing. It's important to ask questions when viewing this story in order to get closer to the truth. After his loss, it's easy to say Magnus left because Hans must have been cheating and Magnus has been suspicious for a while. But more importantly, we need to ask, would Magnus have reacted the same if the match was closer or would he have acted the same if someone else had beaten him? We don't know, but is it possible? Magnus is a multi-millionaire world champion chess player. It's hard to imagine not having a massive ego when that's what you're working with. Magnus is a sort of celebrity and hangs out with billionaires. But we may not know how he would have acted if the loss played out in a different way. I'm not sure how well he would have taken the loss against someone as young as Hans in any other situation. After this, Hans and Magnus played in a different tournament online. Based on how the system is set up, Magnus had to play at least one move before leaving and that's exactly what he did. He resigned from the tournament after one move and then he went silent. Today, at the time of recording this, after a lot of silence and speculation from the public, he released this lengthy statement. And if you've already read this, feel free to skip to the next part. I'll leave it at timestamp code down below. But for those of you who haven't, I'm going to go through and read this real quick. Dear Chess World, at the 2022 Sinkfield Cup, I made the unprecedented professional decision to withdraw from the tournament after my round three game against Hans Nieman. A week later, during the champion's chess tour, I resigned against Hans Nieman after playing only one move. I know that my actions may have frustrated many in the chess community. I'm frustrated. I want to play chess. I want to continue to play chess at the highest level in the best events. I believe that cheating and chess is a big deal and an existential threat to the game. I also believe that chess organizers and all those who care about the sanctity of the game we love should seriously consider increasing security measures and methods of cheat detection for over-the-board chess. When Nieman was invited last minute to the 2022 Sinkfield Cup, I strongly considered withdrawing prior to the event. I ultimately chose to play. I believe that Nieman has cheated more and more recently than he has publicly admitted. His over-the-board progress has been unusual and throughout our game in the Sinkfield Cup, I had the impression that he wasn't tense or even fully concentrating on the game in critical positions. While playing me as Black in a way I think only a handful of players could do. This game contributed to changing my perspective. We must do something about cheating and for my part going forward, I don't want to play against people that have cheated repeatedly in the past because I don't know what they're capable of doing in the future. There is more that I would like to say. Unfortunately at this time I am limited in what I can say without explicit permission from Nieman to speak openly. So far I've only been able to speak with my actions and those actions have stated clearly that I am not willing to play chess with Nieman. I hope the truth on this matter comes out whatever it may be. Sincerely, Magnus Carlson, world chess champion. This is when I became interested in the story because I saw multiple people talking about it. I became extremely curious about what's going on. The primary question that I had as an outsider was how do you cheat at chess? So quick little backstory. In my younger days, I was there for the start of competitive esports with the game Counter-Strike. This game came after some others like Quake, but it's really what started taking esports to the next level. I used to travel around the world to different tournaments and all that fun stuff. So due to these games being played on computers, there were various ways to cheat. I was a writer, but I eventually became the coach of one of the best teams in the world. So I needed to know about the different ways people could cheat in the game. Of course, it was a lot easier to cheat online, but most international tournaments were in person on LAN, a local area network. Still, people would cheat. I will never forget going to a tournament where a team from Kazakhstan was caught cheating. If I remember correctly, they were either using thumb drives to try and upload illegal configs or their coach or somebody affiliated with the team was up in the stands behind opponents and signaling to them. Chess is completely different. When you play in person, it's just two people and a game board. So I had to learn all the ways a person could possibly cheat. As I dove into this story, the first thing that shocked me by the way was just how many people love chess. Every video I came across about this story on YouTube had tens of thousands or hundreds of thousands of views. Some of these channels discussing chess even had hundreds of thousands of subscribers, and one even had over a million. I don't know if this has been going on for a while or if like the Queen's Gambit really made chess more mainstream. But the first video that I came across had the strongest quote unquote evidence that I found of cheating. And it made a little bit more sense to me about what's going on. And I'm going to do my best to explain it to my capability. But I'm going to link the video down in the description below, just in case you care to watch because I'm sure that they probably explain it a lot better than I ever could. So basically humans can only be so good at chess. Computers, on the other hand, can do all sorts of math much faster than any human. Computers can come up with probabilities and all that jazz. Well, this program can check how a human played and compare that to a computer. It gives a correlation percentage. And to put it into perspective, here's the correlations for some of the best matches and the best people in the world. Bobby Fisher during his 20 game consecutive winning streak had a 72 percent. Magnus Carlson, the guy we're talking about today at his best had 70 percent. Super top tier players, aka grandmasters, get about 62 to 67 percent. And the average top tier players in the grandmasters, they average about 57 to 62 percent. One guy named Sebastian Feller got a 98 percent correlation in Paris 2010 and that guy was caught cheating. Well, when they did this for Neiman, they found that this dude was getting 100 percent on quite a few games, which is insanely suspicious. And I will fully admit that, but albeit suspicious, we need to also take a look at the probabilities. Anyone who's read a single book on probabilities has probably heard of Nasim Taleb's bestselling book that everyone and their mom references, The Black Swan. The subtitle of this book is The Impact of Highly Improbable Events. Why, you may ask? Well, up until a certain point, people thought that there were only white swans. Then, boom, someone saw a black swan. We need to separate the difference between impossible and improbable. Throughout this book, Taleb lists a slew of quote-unquote black swan events that nobody expected nor prepared for. Well, I'm not a mathematician. I think we can all get the basics down for probabilities. Do you have any idea how many people believe in the supernatural and other strange things because they don't understand probabilities? They think that just because they thought about an old friend the other day and then that friend calls them that it's some kind of sign. They don't take into consideration all the times that they thought of a friend and they never got a phone call. The best way that I heard this explained was someone saying that there are over eight million people in New York City. That means that every single day, something happens to somebody that had a one in eight million chance. Now, with chess, this is different. Accidentally stumbling into such a crazy correlation rate isn't the same as a coincidence. But I don't see anyone asking if this is even possible. As an outsider, I'm curious about how this algorithm works. What's it comparing it to? Does it need to be updated? Is it updated? And is it possible that it's outdated? I know nothing about how this software works and maybe it's bulletproof. But again, we need to come back to asking how does one cheat at chess? Chess is massive and it gets a ton of viewers. They even checked Hans to see if he was smuggling in some kind of device into the tournament area, but nothing was found. Hans admitted that when he was 12, he cheated using a chess engine. Now it's seven years later and nothing was found on him when he played this over the board match. And what's funny is I'm now learning why I saw anal beads trending on Twitter the other week. There's speculation that Hans must have used some sort of anal device to cheat. If this were the case, it involved a second person who could morse code moves to him. While possible, I personally cannot imagine asking a friend to control that sort of device for me. So as of now, the best evidence we have is Hans' chess engine correlation and the speculation of this guy using some next level efforts to cheat at chess. What I also learned is that Hans has made chess his life and it's pretty much what he eats and breathes. The same is obviously said for Magnus, but since Magnus has been in it for so long, it's getting to him when he's not at his best. This is common amongst anyone who is playing at the highest level of any sport and we regularly hear stories of top athletes having mental breakdowns. When I came across this one video, I saw a clip of an interview Magnus did where he discusses how he's been questioning his abilities since 2017. He also discusses how this led to a deep depression which resulted in him curling up in a fetal position and just not knowing how he's going to manage going forward. By the time these two played, you have Magnus on the decline and Neiman on the rise. I don't think it's too crazy to think Magnus wouldn't take the loss very well in any circumstance. What I also learned while researching this story was that Magnus was the owner of Play Magnus which was bought out for $85.5 million by Chess.com. Chess.com is another big character in this story and they banned Hans shortly after he beat Magnus. As someone who has very little trust for the rich and anyone dealing with tens of millions of dollars, this all seems extremely shady to me. And as a top player, Hans clearly brings in a lot of money whenever he plays at these events. I think everyone should be fairly skeptical as they learn about these details. Let's say that we're 100% sure that Hans cheated. Even if that's the case, this is beyond unethical. I'm starting to wonder how Magnus can even be a player with such a massive conflict of interest. For anyone in the chess community, I'd be extremely concerned that Magnus has so much sway that he can get people banned without evidence. I don't know much about this guy's character but that doesn't even really matter. Anyone with that much power that can influence decisions is never a good thing. It's why I'm strongly against financial capitalism. Do we really want billionaires in control of who gets resources and who needs help? No thanks. It's never good when that much power is concentrated. What bothers me the most about this story is the body language reading and mind reading going on.  Does body language prove that Hans Nieman cheated to beat the reigning chess champion? Find out next. And we're back shakers. Time and time again, it's been proven that even experts barely fare better than chance when trying to detect deception. And if you don't believe me, I highly recommend you go read the book Duped by Tim Levine as well as How Emotions Are Made by Lisa Feldman Barrett. While researching the story, I kept coming across amateur body language experts and human lie detectors pointing at different things Hans has done or said as their quote unquote evidence of cheating.  Chess players are seen as being extremely intelligent, which they are, but if you're in the chess community and thinking that you can read body language, you really need to widen your scope of knowledge. Even in Magnus's statement, he points to body language reading. In his statement, he says the following, his over the board progress has been unusual. And throughout our game in the Sinkfield Cup, I had the impression that he wasn't tense or even fully concentrating on the game in critical positions while outplaying me as black in a way I think only a handful of players can do. If I'm being honest, what made me sit down to record this was seeing a tweet with thousands of likes saying something along the lines of, imagine thinking you have better intuition than Magnus Carlson and that he wouldn't know when someone's acting strange. Like, do you people realize that some of the smartest people in the world believe in conspiracy theories?  Throughout the entire COVID pandemic, we have seen people with literal medical degrees push conspiracy theories. There are stories of Nobel Prize winners believing in insane things and geniuses getting conned by their long distance girlfriends that they've never even met who turned out being dudes who were scamming them. So yes, Magnus has years of experience in countless hours playing against people, but there's also a little thing called confirmation bias that nobody is immune to. Walking into a match against someone you already assume is cheating, everything they do is going to look like cheating. Why do you think the cops focus on the wrong suspect for 12 hours straight of interrogations? They lock in on someone and then everything the person does is just further evidence that they did the crime. Let's also think about this for just a minute. Sit back and I want you to get into the mind of a cheater. Magnus says that Hans wasn't quote unquote fully concentrating during their match. Now, if it were you, if you were going to cheat against one of the best players in the world, don't you think that you'd be concentrating? And if you were cheating, would you make it this blatantly obvious? Not only would Hans need to be the best cheater in the world, but he'd also need to be the dumbest. This really reminds me of conspiracy theorists thinking that these shadow organizations and the Illuminati are hiding clues in plain sight. If these people were actually trying to take over the world, why would they leave clues to get caught? Yes, it is possible that Hans cheated, but the guy would have to be a certified moron to be that obvious when knowing that the entire chess world would be looking and scrutinizing this match repeatedly if he won against Magnus. As mentioned earlier, I'm a recovering addict, so I get what it's like to royally screw up. Hans screwed up when he was 12 and I saw one YouTuber actually bring up the point that people grow and change. It's one of the reasons that I'm very pro-prism reform. We have this crazy idea that people can't change. Meanwhile, even you, yes, you can recognize how much you've changed over the years. Should someone be banned from chess forever for cheating when they're 12? Let's say even if they cheated when they were in their 30s or 40s and quote unquote, no better, is it justified to ban the person forever due to the crazy idea that they can't change? I saw some people say that if you don't have harsh punishments, it won't deter other cheaters. That's a terrible argument. In the United States, we have capital punishment, yet murders still happen. Clearly punishment isn't the best deterrent.  And I doubt it'd be much different if you did it with chess. Again, it's 1,000% possible that Hans cheated.  But as a stand, there's no evidence.  The burden of proof has somehow been shifted to the accused rather than the accuser. And that is scary. Maybe you haven't been in that position before, but I sure have been and it's awful. So hopefully you gain some new perspective on the situation and hopefully people can chill out before assuming this kid is guilty without any real evidence. All right, everybody, I hope you enjoyed that video. If you're new here, make sure you subscribe. I make a ton of videos, a bunch of different video essays. I'm very curious and interested in a lot of topics. Like I said, I just happened to go down this rabbit hole and wanted to talk about it, so make sure you're subscribed. And whether you're subscribed or not, make sure you follow me over on Instagram and Twitter at the Rewired Soul. That way you don't miss any updates. Aside from creating these YouTube videos, I also write a ton and I work on other projects. So follow me on social media and more importantly, I love chatting with all of you. So make sure you follow me at the Rewired Soul. All right, but anyways, that's all I got for this video. Have an amazing rest of your day and I'll see you next time. You next time.


Next question is from Derringer Thomas. What are the best stretches for flat feet? Well, you're looking at stretches, mobility, and strengthening, right? So, flat feet can be caused by poor ankle mobility, but also from just having weak feet. It's funny, for 99% of my career as a trainer, I totally didn't even think about the fact that the bottom of your foot is covered in muscles. I didn't even think about that. It was like... And like 7,000 nerves. Oh, yeah. I mean, I didn't even look at anybody's foot. When I assessed people, it was the knee was the lowest that went. Might as well be covered in concrete. Totally, right? So, I didn't pay attention to that at all. So, there are muscles on the bottom of your foot that can be strengthened. There's a movement called short foot, which helps you contract some of the muscles that create an arch. In fact, that's the movement. Short foot is giving your foot an arch. When I first tried short foot, I couldn't even do it. You might as well tell me to fly. It's like I didn't even know what I was doing. I had no connection to those muscles. But through practice, I can now do short foot and I've given myself a little bit more of an arch. The other thing I said was ankle mobility. Combat stretch is a great mobility movement to help improve mobility ankles. Those two things for a lot of people help fix flat feet. Yeah, and just getting more connection there to your foot and activation is articulating each one of your toes individually, which sounds really simple and basic, but it's pretty challenging, especially so hard. Yeah, for anybody who's been stuffed in shoes forever, and I know, like, so I have a hammered toe and so I have a tendency to really grab in. And so I have a really hard time flexing my toes. And this is a very challenging exercise for me that I had to go through, but it totally made a difference in terms of my connection, my grounding and my force production from my feet. Sounds like a pro wrestling move. Here comes Justin with the hammer toe. I don't know if my son is here right now or not. I think Katrina and him are coming down here, but just since we're talking about this, and I was just thinking about this yesterday, is like, so he is now, I've trained him so well with no shoes. I know, you're so proud of it and you do such a good job. I am proud of this because it's so funny because now like other family members, and they watch him, he won't put his shoes on.  So he doesn't wear shoes ever. Ever, ever, ever. Only time I can get him to put them on is if we are like out in the snow, up in truckie or something like that. And it is to see the dexterity that he has in his toes. Like his feet and toes move like my hands do. It is, I'm so jealous of watching, and I'll like play with him and tickle him and mess with him. And he can spread his toes all the way out and move them all. Oh, that's awesome. Oh, and it's so awesome. And I feel like when I look at the way he moves, you know, I know we were joking in the other podcast today when I said, how'd you see his footwork when he was playing best. But his, his control and stability, like he really didn't go through. I watched my other two friends and they, I remember when they said like, when he first started kind of walking and running around, they're like, oh my God, you're going to go crazy because you're going to be so worried. He's going to hit his head here and fall there. And I really didn't go through a phase like that as soon as he could get to a place where he could walk pretty well. Of course we had a first couple of weeks, the stability of like learning to walk. Once he had got it down, he's got great control where he does not stumble. And the only times that we've had issues is when we've put shoes and have that feedback. Yes. We've given, we've put shoes on him that one time when he fell and he hit his head and Katrina freaked out cause blood came out and everything was she put shoes on him and he, he best, he squatted down to pick up a rock and he fell forward cause of the instability. So anyways, the reason I want to share just the importance of, you know, walking around barefoot.    Then I would do it barefoot. I get out, I take him out on the grass and I'd walk around and just start to get that connection again. I took one out of one of my buddy who's a, who's a PT, he used to do this exercise that is really challenging, but seems so basic. You can do it while you're watching TV and you throw a towel or some tissue paper on the ground and you just, you try and pick it up and you move it. Then you take the other, the other foot, pick it up and you move it. And just like Justin was saying is, is re-establishing that connection to being able to articulate the toes and the foot. To me, that's the kind of the laying the foundation. And then once you start to kind of get that and you start to progress that, now we can really try and strengthen, which I, then I think of things like short foot or I love tippy toe squats. I love that because I'm always trying to practice squatting anyways and getting better. And that addresses both ankle stability and strength in addition and your forefoot, all in one movement. And there's good video. I think I, I think I've done a video on my Instagram way back when I believe squat university. I think I stole some content from them that I thought was really good where you take a quarter and you put it on the ground.  Under where you're, yeah, where the big toe is and you're, and you're trying to think of driving up from that. And when you drive up onto your tippy toes, the thing you're looking for is that you can keep the ankle neutral. What you'll see is a lot of people when they drive up on their tippy toes, they break out or in. And so you want to keep that stability while you're up on your tippy toes. And so that just doing it. You can also get a lacrosse ball to put between. Oh, there you go. Yeah. So between like above your ankles, but like you're squeezing it in between your feet and you're raising your heels like that. So I've done and performed some, some tippy toe squats like that as well. One other thing too with the flat foot, I've noticed like when I, I used to get this every now and then when I'd gain weight, like going into the off season and I would go back to running and I would find myself like really running it on a flat foot and, and losing that connection. So, you know, that might be another contributing factor is the gain of weight. It's so crazy how Ma and Sal alluded to this about when it was, it was Dr. Brink who like, I think just like shattered all of our paradigms with, with how important the foot is and really looking at that because, and now I can't help but walk behind somebody and just look at the wear on their soles or their shoes and like know what's probably going on with them because if you've got flat feet and you've got your pronating more on one side or the other, you can just basically, you know, ping pong up the kinetic chain and know that, oh, they're left knee probably bothers them here. Oh, their right hip has probably bothered them here. Oh, they're low back on this side and then show it's crazy how much that if you are not, if you're not really on that tripod and balanced well on your feet, how that could be causing pain in areas in your body that's way away from it. And so you would be, and even as a trainer, I would just, a client told me they had a, you know, shoulder or hip or low back issue. I would never think to go look at their feet where now, that's the very first thing that I look at when someone tells me about any pain is I first look down there and see, is this where it's stemming from? And then it's causing it all the way up.


This 2019 Ram 2500 Megacab Short Box Big Horn Level 1 is stock number 12177Z. We are here at Summit Automotive in Fond du Lac, Wisconsin. Your new and used Ram and heavy-duty truck headquarters. This 2019 Ram 2500 Megacab has the 6.4 liter V8 Hemi engine. This truck has been fully safe and inspected by our service shop as a fresh oil and filter change. All the fluids have been checked and topped off and it is super clean inside and out all the way around. We're going to check out the whole vehicle inside, outside, all the way around and make sure that you get the best representation possible. We shoot all of our videos in 1080p, 60 frames per second. So if you have HD capabilities on your computer, tablet, smartphone, or television, turn them on right now because it is your best way to check out the quality, condition, and options of the truck before seeing it in person. If you like the video and want to subscribe to our YouTube channel where we do videos of our new and used inventory each and every day, in the lower right-hand part of the screen is a subscribe button. Click that and then click the bell notifications. You'll get updates on the videos we do each and every day here at Summit Auto. It comes with the 20 inch polished aluminum rims. They're in really nice shape. And it has Firestone TransForce LT285 60R20 tires and they got right around half the tread left on them. Frame and underbody is in really nice clean condition. Other than a little bit of tire shine on there. Didn't see any corrosion. Front fenders in excellent condition. This one does have the LED lighting. So you get the LED headlamps, LED running lights, and LED fog lamps. Stick around to the end of the video. We'll turn all those lights on so that you can see just how nice and bright that those lights are. Lower valance is in nice shape. Headlight lenses are nice and clear. And the hood is in really nice condition as well. Passenger side front fender. No dents or dings on there. And the passenger side rim. Excellent condition as well. Really like these 20 inch polished aluminum on this truck. Coming down this side of the truck. Take note of how clean the body is, how reflective and mirror like that paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down but you're still interested in purchasing the vehicle you can see the truck here, the truck. And of confidence in the vehicle that you're looking at before you even get here. So when you do get here there's absolutely no surprises and you can make a smart and informed buying decision from wherever you're at. And if this video helps you make that buying decision, let your salesman know that you saw the video and that Brett sent you. Back rim. Excellent condition. No scuffs or scrapes. And the back tires have just about as much tread as the front tires. Frame and underbody. Just like the front. Absolutely perfect. Has all the remaining factory exhausts. And all the lower rockers look really good on this truck. Coming around to the back of the vehicle has the LED tail lamps. Rear bumper is in nice shape. I didn't see any dents or dings in there. This one does have the full towing package which includes a receiver hitch four pin and seven pin wiring. The tailgate is in really nice condition too. Didn't see any dents or dings in there. And the bed is in pretty nice shape. Does have a little bit of scuffs and scrapes. A little bit of light duty usage but that's what happens to trucks when they're used as trucks. Nothing that a bed liner couldn't fix. Coming down to the driver side. Just as clean as that passenger side. No dents or dings on the box. And this back rim is in excellent shape as well. Down the rest of the side of the truck doors look really good. Didn't see anything wrong with them. Has the heated fold up tow mirrors. They have blind spot monitoring, directional signals, 360 cam, and then LED side lights. They do fold up like so. They also power fold in. Inside the big horn level one package gives you the two tone gray cloth interior. No rips, no tears on the seats. They're in really nice shape. Does have a power driver seat. Both these front seats are heated. You do get driver side lumbar, factory all weather floor mats, auto headlamps, and power pedals. You do get audio controls on the back of the steering wheel. Power windows, power locks, power mirrors. You get the cloth bolster and wood grain trim on the doors. And these mirrors do power fold in. I was like showing both sides so that you know that both sides are working properly. Last thing on these mirrors is you get the power blind spot mirror. If you look at that outside mirror on the left there is power. So that's kind of cool. And it's really helpful when you're adjusting the passenger side mirror. We'll turn the ignition on and check out the miles and the radio and everything that this truck has to offer on the interior. 42,316 miles digital speedometer time display. Instrument cluster is very nice and clean. Comes with a leather wrapped steering wheel. This is a heated steering wheel as well. You do get cruise controls on the right, gear selector, Bluetooth and information center controls on the left. And remember it has the audio controls on the back of the steering wheel. This one has the 8.4 4C radio, AM, FM and Sirius XM radio capabilities. You also have your heated seats and heated steering wheel controls. You also have your backup camera, which is right there. You have your cargo cam and you can zoom in on that cargo cam and you can zoom in on the receiver hitch to get hooked up to your boat camper trailer first time every time. There are your side mirrors to park trailers and stuff and you can adjust those to go to either side of the truck, which is really handy if you're back in some trailer or camper or boat up. And then lastly it does have your projection manager and all your other different apps where you can project your cell phone to the screen via Android Auto or Apple CarPlay. And if you have a navigation system on your cell phone projected to the screen and it's like you have the nav right on the screen. We actually did a demo on Android Auto on an 8.4 if you want to check that out, it's in the upper right hand part of the screen. So click that and check us out there. Anyways, you have your heated seats and heated steering wheel buttons down here.  You have your 8 speed automatic transmission, push button 4WD, factory brake controller. Stability control to a haul does have two USBs, two USB-C's and an AUX jack. You get the keyless entry right here with the remote start and sliding storage tray. Passenger side, floor mat and seat are in excellent condition. I didn't see any rips or tears on there and the headliners in really nice condition on this truck. It smells very clean in here. I'd be shocked if it was ever smoked in. You got your map lights up there, home link buttons for your garage door security systems and lighting systems. We'll take a quick look at the back seats and then we'll start it up and check out under the hood. Back seats are just as clean as the front seats, no rips or tears back here. It does have the latch child safety system for any child car seats you may have. Fixed glass rear window. Seats are in great shape, all weather floor mats back here. So these seats go down in two different ways. The first way is that backrest goes down like so, you get a nice high load floor. You also get a storage area back here. Here's a factory carpet floor mat for the back seats or back flooring, I should say. And then you get latch tether anchors and stuff back here. There's also a storage bin underneath there. And then the other way is that these seats hold all the way down when this front seat is up. Let me pause it for just a second and I'll adjust. All right, you can see that I got that seat down. Now I just had to move that front seat up just a little bit. But you can see how it goes down really nice and flat. You get a really nice flat area all the way across back here. So if you actually needed to take a nap or if you've got pets or something that need a nice flat area, that's a great thing to have there as well.  You get child safety locks on the back doors. Bottoms of the doors all look really good. And we'll start it up and take a look under the hood. Starts right up. No check engine lights or anything like that. I would personally like to thank you for checking out the video today and hopefully from this HD video. You've been able to tell just how clean this truck is all the way around inside and out. There are those ultra bright LED headlamps, running lamps and fog lamps. Under the hood we have the 6.4 liter V8 Hemi engine. 410 horsepower engine base very clean, runs very smooth. Once again this truck has been fully safety and inspected by our service shop as a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100%. Ready to go. There is your mission sticker. I'd highly recommend this truck from a quality and condition standpoint. And to see more pictures of this truck or one of our other 450 new and used cars, trucks, SCVs, minivans, Wranglers, halftones, three quarter tons, one tons. You name it. We've got to go to that website right there. www.summitauto.com. Full pictures and descriptions of every single vehicle from two locations all at www.summitauto.com. And if you'd like to check out more HD videos, you can go to www.youtube.com. Remember to like, subscribe, and share on this video and all the videos that you see there. In fact, in a second you'll see a link to subscribe to our YouTube channel in the upper left of the link to more Ram 2500 truck videos. Like this one in the upper right of the link to this vehicle on our website in the lower left of the link to one of our latest YouTube videos in the lower right. Click those, check us out. We hope to help you with this Ultra Clean 2019 Ram 2500 Mega Cab Short Box Big Horn Level 1 in bright white clear coat. Thanks again for checking out the video.