Discussions (contd.)

0:00 This is the first one equation. Before that there were two, six, seven, eight. The idea was that you wanted to do really, really the same thing. Exactly. The other one has a conspiracy theory. Bodies really do contract. Facts really do throw you out, but things are made in such a way that you never really need to. I'm taking it back. So really the idea of asymmetry is the critical part. I can understand why there is a conflict between... The failure of all attempts to detect motion to the equal. A dynamical group of mechanics will really prevail once you get many much more experimental results. So it's the thing I read in the book that... Crazy Reg Cahill should be right. So it's the book that I read from that said that he'd actually proposed a formal Michael C. Martin sermon when Mr. Truman was turned down because they told him he was an already good son. So is that wrong, Truman? No, that's not. Huh? That's right. He proposed it. We have a letter about whether it was turned down for that reason. But even there, the idea of that experiment would reveal a few other experiments, by the way, as already proposed by Aragol, I think, or one of the French, Dominique de Saint-Cyprien, in 1992. I think it's better than the old one. Do you have a tech motion? What is your take on why he didn't get a job? It just seems mysterious and... Oh, you mean initially? No, no, I'm sorry. Yes, I mean initially. Yeah, what was the... When you graduated. Yeah, it was ten years before they finally operated here. That was five years after Special Relativity.

2:30 What was the... In fact, Special Relativity was probably the most important thing. What, Special Electric, correct? No, not even Special Electric. It was quite a serious topic. Few people would think about it. Less than it is given in Special Electric. So why did he give the general answer test to the student in the first place? What we would call experimental physics, where we're rating some young woman for the way Einstein looked at her age. It seems an interesting man died of some illness in a couple of years or so. She just gave me the results, and I'll take care of it. She took her results. She fiddled with the things, and she gave it to me. The writer turned in, and the professor said, You see? Put your mind to it. You couldn't really do anything with it. But I turned to the professor and found out about it. Because this is the only course he took. What you've got to recommend is the lack of villages. So he did alienate the fact that he was Jewish since he was studying Pembroke. He was involved in an affair with fellow students, you know. Yes, but ethically.

5:00 To have a child was not a good luck. How much the school moved out did. It was a kind of heretic. It was a kind of heretic. And he had a tremendous Swiss, I was a Swiss, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, Gardner, in his case, said, where's your ticket? He said, well, I am the speaker. I said, okay, Mr. Sladey, well, he's my cousin. I'm sorry, I'm not stuck as well. So, in that case, I'm leaving. So, Gardner said, okay, I admit you, but under protest. The next day, again, the head of the AATAC, I'll quote him in, you did what's not right. Gardner's other instructions have fallen to the order you should not protest. I came here, I didn't charge you anything, I gave this free lecture, and you refused to let my cousin in, and what do you think the hell did I get out of it? Let's think of the heating course. The Switzerdeutsch, the Switzerdeutsch have not changed in a hundred years. Yes, they have, that's true, but... Were they charging admission? I told you the Switzer-Deutsch haven't changed!

7:30 There's still something very strange between us. I know my wife's family lives 100 kilometers from Switzerland, so you might want to walk with your friends. So I said to them one day, why don't we go to Switzerland? It's only an hour. And they said, oh, we've never been to Switzerland. Have you ever been to Switzerland? No, we've never been to Switzerland. How come? They hate us there. Well that's okay, they hate everybody. You know, it's true, I said, it doesn't matter how you treat people, you treat everybody the same way. Actually, I finally win, so. Excuse me? Ah, yes, yes, that is very true. I've never seen a more miserable looking people. The next case, and here there's a tunnel. It's just that there was a little bit more debate and more than a thousand years ago. And yet it's very curious because if you go a little bit further south in Belgium, you've got the German speaking, the small German section speaking of Belgium, the section of Belgium around Malmedy, which is, you know, is German speaking. Then you've got the immediate transition to the French speaking part. Which is much further over, which of course is a continuation of the Dutch-speaking part, which of course is not contiguous with the German-speaking part at all. There's a big gap of about 100 miles between them, which is all the French speak. No, I don't. No, they'll come to a deal after the politicians have continued to throw their rattles out of their prams for another few months

10:00 and made themselves look even more ridiculous. The total indifference of the Belgian people and the fact that, you know... All the essential institutions are still functioning. We'll just bring them to their senses and realize how redundant they are, and they'll come to some sort of face-saving deal. There's still government? There hasn't been a government for 96 days. No, actually more than that now. It's 102 days. Sounds like very long. I agree. Not only that, but that's what a lot of the Belgians think as well. A lot of the Belgians have woken up to this fact, which is... Yes, of course, the regional, the civil service and the regional administration will continue to function. No, no, no, no. There's no possibility that the French-speaking part would unite with France. That would, I mean, that would not even be on the political agenda. It wouldn't be on the political agenda in France either. The idea, there are no French annexations. Not even the craziest Flemish nationalists claim that... It's a French block. Nobody's believed that sort of thing since about 1910, but I think on the other hand it's just a possibility that if they did in fact separate, but they won't separate as two separate states, there will be some kind of federal, something in between a federal and a confederal solution. Yes, it would actually, it might be a sensible solution, which is one of the reasons I suspect it won't happen, therefore it's unlikely to happen. The interesting thing is Antwerp, if there were a separate Flemish state, the interest, the Vlaamsa Block, which is largely a coalition of more or less unpleasant right-wing parties, including some very unpleasant right-wing parties. would try to form a government but which would probably be prevented by the fact that there is a large solid liberal majority in Antwerp which would of course would be by far the largest city in the Flemish-speaking part. That would contain well over half the population.

12:30 No, I think there are all sorts of reasons why I don't think that Belgium will actually separate into two states like Czechoslovakia did. I can't see that happening. Well, certainly not like that. Well, I'm still waiting for the fate of the Hungarian speaking Serbians. Fortunately nothing happened, but wait. That's exactly where the wife of Einstein was going. Going to Serbia? Oh, with the Hungarians? Yes, Hungarian speaking part of Serbia. There are not many parts of Yugoslavia that were not strong of atrocities, unfortunately, not only in the last war, but in all the wars before that, I mean, they were absolutely, unbelievably atrocious. I have a friend who's a professor at Manchester who's written a standard work on the Balkan wars and it's an incredible story of brutality and atrocity and there was a long long legacy there even before the Astartes and the fascists and got going in 1941 and of course that was an absolutely dreadful... There are Bulgarian horrors about which Gladstone, of course, around which Gladstone constructed the Midlothian campaign and most important episodes in 19th century British politics. Would you like some dessert? Yeah, a coffee would be a good idea. Pierre, may I ask one quick question? What was... I really should know this, but I'm afraid I've forgotten Cyr's first name. Jean-Pierre. It was Jean-Pierre. That's what I thought, but I just wanted to find out. JP, yes. True, true. Are we coming back in here, or...?

15:00 Yeah, we are. One of the things I'd really like to learn about, which I think John knows a good deal about, is actually the developments in Maxwell. In the last period, shortly before the publication of General Relativity, there's a whole volume, it's called something like The Last Phase or The Last Years of Classical Physics, which is in this huge six-volume history of the genesis of relativity, which John has just finished editing, which I would probably very much like to discuss with him. I saw, I had a chance just to glance through this when I was in Madrid because it's just been published by the Boston University Press in the Boston Globe in Syria, and it has the complete facsimile of Einstein's Zurich notebooks with commentary. Because Nathan was the director of the Einstein studies project and the editor of his respective works, so he's obviously still, he's basically been the father of the whole project, and he's very, very knowledgeable about what people like Nernst and Lee and Lee-Kilden were doing in the way of unified field theory, not to mention, thank you comrade, I was going to get to Volterra, not to mention Volterra! Yes, yes. Exactly, yes. Who, of course, also turned out to be rather original and a part of the fruit of calculus, as Bondi did.

17:30 Yes, I think he'll really enjoy talking to us about that. It's fascinating. I've learned a lot about classical and continuous physics from him. Yes, this assumption that, of course, you know, of course space-time is discrete, of course, you know, quantum gravity is at the bottom of everything, I just don't understand why it has become sociologically such a powerful ideology. The funny thing is that young people have their minds run with it. I think it's been said for a hundred years, in spite of no experimental evidence and no coherent theory. Exactly. Isn't that your impression as well? Yes. Well, for what my little impression is, yes it is. We both have limited knowledge. Yes. My answer is yes. Yes, you really are singing to the choir. But if you say this to these people, they will either just ignore you and look blank or... I've certainly not yet heard a coherent answer, whether it's from Kahn or from Rovelli or from, oh yes, it's not even particularly beautiful. I don't think anything beautiful about non-commentative geometry is coming to some people's minds. But this is also coming from the same, it's like a platonic onslaught. You would think that either some kind of coherent theory or some experimental results would have been forthcoming about this. I guess I would say, well, it's below the so-called... Below the Planck level. It's below the Planck scale, or it's at the Planck scale. Perfect buzzword. I even picked it up myself. Planck scale has just become an absolute buzzword, which means, you know, we can sweep everything underneath the cuff. Don't go there from here. You can't go there from here. The Planck scale is just a wonderful label for the carpet under which we're going to sweep everything that we haven't got a clear experience on. I've told people, and I've probably even told you, but it still blows my mind to realize that the Scientific American, three Januaries in succession, had the same cover story with exactly the same article with some small changes, but the same pictures, and it was precisely this. Why space-time is discreet?

20:00 Yeah, that space and time are discreet. And the only reference is Baez. Why am I not someone else? If you look it up, it was written by, of course, by the one from Perimeter. Durland? No, no, Smolin. Oh, Smolin, Lee Smolin, yeah, yeah, yeah. Yes, he's a great popularizer. Yeah, well, apparently it's so great that it wasn't necessary to rewrite the article even, more than a few. Minor adjustments that take account of some recent... They're not, I'm afraid, ma'am. He has been repeating himself for a long time. No, but the magazine itself, and then this reference to Baez, it's to nature, a two-page paper with some mumbling about it. It can't seem incomprehensible, although it does, I think, claim under his breath to reach that conclusion. This is monstrous. I know, this is not science, this is Jiu-Jitsu. There's no theory, and that's the only thing. I know, I know, I know, this stuff is Jiu-Jitsu. It's not science at all. I was trying to get some sense out of Crane this morning for what he works on. It seems that he has got... He believes this stuff, right? His abstract talks about principles of quantum mechanics. They aren't principles, they're just the same onsets. They're just like tiny concepts. On the other hand, he has got, it seems to me, a principled reason for rejecting M-categories. This is a framework. He doesn't like the accountants program. He seems to have quite sensible things to say about that. What program? Well, exactly. I'd say not even a program. To call it a program is to dignify it. It's just a series of buzzwords. It's a bit of a shorthand. And there were two other things he said that seemed to me to be quite interesting. He also had reasons for not being at all happy with the loop quantum gravity program and he seemed to think that, yes, actually there should be a demand that there should be a good proper clear notion of map space between any two spaces. So maybe he's got something worth hearing. On the other hand, he also seems to have come up with all sorts of other things. I don't know, we'll see.

22:30 New York Times still has old-fashioned photography. They take a picture, but men look and capture, and they have photographs that they can look at. And there was a photograph of her and the two assistant males, and she had a smile that looked like she just swallowed something inside. And they were both looking away and grinning at each other. I'm not sure if this is part of the project, but they're all sort of what mostly you face with programs. And I'm not, I haven't studied anything enough to know which program I should submit myself to. And one thing of that entity was Mouchard-Ford. Sorry, John. Became very clear, indeed, shortly afterwards. Yes, absolutely, it was true. No, no. With Hollande, yeah.

25:00 I was never able to complete my curriculum. I could not imagine. I mean, practicing it, when you are recording and then writing, and then they teach a science journal, when you do that, right? Exactly. I have young artists who do theater. Every performance is recorded. Yes. Well, it's not a perfect analogy with mathematics, but I think it's a very strong partial analogy, and of course, of all people, I'm the one who supports you most, because that's what I've devoted my life. This is precisely the project for which I've devoted my life, so... Even if you offer them complete editorial control and say, you know, it will never see the light of day if you're unhappy with it, they're still reluctant. Not I came to the Algerian, but from a friend came to Algeria. My daughter wants to go and then doesn't want to. Where in God? And so when I came in Algeria, I'm in Egypt. And it's interesting that when I came to something I had more confidence in. And then, okay, then there was a real debate. And then I came to some department.

27:30 A department where there was a man. He was, I think, a very proven pastoral politician. I have given the charge to, well, that's the thing to do, that's the thing. That was after the end of the war, after the war, after the end of the war. No, it's a word, I'm on the scene, my dad used to work in India, I was good and all, and all. They can't say they can't make the whole thing, they, they, it's just, the world is different. I mean, there's, what, what to me consists of the world, it's the nation's world. But clear, I don't, no, Morocco, Morocco is the iron rule of the people. In the Arab world, the countries that are happier are the ones that have came. For them, monarchy is... I mean, a republic is just another name for it. That's funny. And Tunisia... That must be why the people in the Congo were so happy under King Leopold. Well, no, no, no. They were... No, I was thinking that was a sarcastic remark, Lou. Sorry. Tunisia, in the time of Bolivar, was a party. And they fought for the government. Well, come on, we can't do two pedantic Sicilian.

30:00 If he'd been a Sicilian, he would have lost count, but four is five in Tunisia. Yes, you would lose count in Sicily. Six legs over ten. Yeah, more like 16 over six below. Yes, exactly. Well, I guess you might subsume them under the Phoenicians, but, you know, however. Yes, exactly. Okay, you want some peace and quiet. Well, so did I, but, no, he's just checking the room and everything. I'll come and clear these up. That's okay. Right, we'll leave you and we'll come and fetch you five, ten minutes before the meeting. Okay, guys, let's go and leave here. Well, I think we'll find somewhere, don't worry. Can you tell me where I should put these, ma'am? Okay. Ah, got it. Thank you, ma'am. Okay. That's great.

32:30 I'm okay. I'm copied out. I'm sorry, I didn't mean to drag you out, but it's just in the sense that Pierre really did want to have a little bit of peace and quiet. No, no, no, I was getting a little confused there because I thought Jen Satchel was going to come back. So did I, but, you know, whatever. I thought you were wrong, yeah. Well, it's okay. He knows where to find us. I missed the cue somewhere along the way. Actually, we could sit here. This is perfect. It's 2.20. Well, exactly. There's no problem at all sitting here. Pierre is one of those people who likes to have just a little bit of complete peace and quiet there. I've rewritten my talk completely about four times now, but I have a feeling if I went over and started it I'd rewrite it again. Oh, don't do that, you'd probably make a mistake. Right. I mean, Kyla is giving a talk that sounds very interesting, titled Geometrogenesis. No, that's not her, that's Martini. Oh, no, that's Martini, of course. I'm sorry, forgive me, I'm out of here. My mind is... I'm still zonked from the 36-hour flight. She's going to come back with a copy, and I'm going to try to ask you to tell us something about her ideas on quantum gravity. What is her name? Her name is Mikaela Iftimi. Do you know what the ethnic origin is? No, I don't. I should have asked her. I think she's part of the Lebanese, but we can always ask her. I think she's... I think most of the Christians are in the way, actually. Go to London, there's an awful lot of restaurants. And I've noticed that if you want to see really, really sexy belly dancing, you go to a... I mean, so somehow they reacted to the Arabs by going in the other direction, to the Muslims by going in the other direction. They already had that, of course. It was known as the Paris of the Middle East for long, long before the Civil War, and had been there for a hundred years, had a reputation of being very laid back. Well, of course, they're very ethnically mixed and cosmopolitan-based. Well, I mean, the ones I saw were like...

35:00 Can I ask you a question? Yes, of course. Just hand it to me, I'll get it. Yeah, we'll do it, ma'am. Thank you. I think I'm going to say I'm going to have a copy available by the end of the day. Well, I'm working on something different. Well, I don't know how different is quantum graphics if you want quantum physics. Okay, okay, okay. I have a different approach. Well, you know, okay, so you know about the Barrett Crane model? Thank you for your attention. I didn't misunderstand. Pierre is just kind of... He's just a little bit spacey. He's commuting with his thoughts. He's commuting. Why do we need... Why do we need quantum physics? Why do we need quantum physics? To understand what's happening behind the events and just in case we all get a new black hole. Why do we need... Okay, you mean practically or intellectually? I'm sorry, there's two different questions. Well, I mean, are there things in physics... Well, there are not things that are very difficult to get to, but if you built a very, very large spherical laser, okay, so that it imploded, like the thing that they used to try to do laser fusion with the size of an asteroid, then the imploding photon wave would at a certain point seem big enough to make a black hole. And we don't know what would happen after that. So that's an experiment that we couldn't do now, but in a couple of hundred years, if we have robots in the atmosphere, that's what we could do. And then it would happen, boom. And then the question is, what would happen after that? I mean, the thing is actually, even, I mean, to be a little bit less operationally, you know, there's theorems that say that in a broad class of initial conditions, you start out with classical general relativity, and in a finite time, you end up in a place where there's no more points at it. The manifold stops, and if you try to even add on points on the boundary...

37:30 Okay, okay, okay. If you start out with doing classical general relativity under a broad class of initial conditions, well, for instance, an imploding star that was massive enough, or if you go back in time, and you can evolve back in time, and expand, and there are the two main cases, either just enough matter imploding, or... If you go back to the universe, if the universe is just consistently expanding, then if you go back in the past, yes? It's got a Cauchy surface that gives you the data. It's in the Penrose garage. The conditions for those holes. In a finite time. So you're talking just in general relativity? Classic, yeah. So if the mass is greater than the limit mass? No, no, no, that's something else. Lou was answering Bill's question, which was why quantum gravity? Why should we assume there is any need, in principle, for a theory of quantum gravity? Then what happens is, at a finite time, the manifold stops. And if you try, there's an end to the manifold. There's a curvature singularity. And it's very generic, you can't help it, it happens. People try to investigate the nature of the... and you cannot even add... A boundary, which is a point set in an attractive way. If you try to do it, you end up with something that's very weird and not how it's supposed to be. So you cannot avoid it? You cannot avoid it, and we cannot describe it. We don't have mathematical tools to describe it. So you can make a perfectly well-designed experiment in classical relativity, and at a certain point, you just cannot say what will happen. The journal, I think, breaks down. We need an explanation. We need an explanation, that's right. It's fairly clear that quantum mechanical effects will be important.

40:00 So it seems like the quantum theory of gravity is going to be the other thing. Now, let me say something else. Suppose you just say quantum effects. Quantum mechanical effects. Exactly. Then there's also the problem, philosophically, that it's very hard to have a universe. Really hard to have? Have a universe. What? Wait, sorry, let me think. It's very hard to have a universe, conceptually and mathematically, that has something which is genuinely classical in it, and something which is genuinely quantum mechanical. Suppose you say, no, I don't believe it, the gravitational field is classical. Now, suppose you have an electron which is in a superposition of two states. So there's a 50% probability of being here and a 50% probability of being here. Okay, what's its gravitational field? Okay, that's easy. It's a linear superposition of this guy and that guy. Okay, now you're not sure where it is. All of a sudden it's here. Well, you're assuming that quantum mechanics can be applied to individual systems. Suppose you only want to use ensembles that will take them out. The problem with half will be one place, half the other. There's no mixture. Well, I'm sorry. I'm not saying... They pretty much want to unify two different words, the deterministic and the uncertainty. That's right. How do you have an interaction between that has a wave that can collapse and one that doesn't? I mean, so that's one argument. Let me try to pursue the purpose. Well, okay. I think that the problem is that you can't use words like real when you talk about quantum processes. You can only use words real after the process is over. You can't say, is this virtual particle really here? If you do the mathematics, that's what it works. If it's a superposition, it works. But the only way we can understand it is through mathematics. What is a track and a snare? Are intuition involved in a classical setting on Earth and do we have to just systematically ignore it and trust the math? The question is what can quantum mechanics do? For me, it can only calculate the amplitude of the process.

42:30 If you try to break up the process, you're talking about a different process. Different, exactly. So that means you can't talk about a wave function and just a device to help you compute the amplitude. Well, I fear it was clear to me that the orbital velocity of an electron must have gone around about 10,000 times in between any two measurements you could make. You can't make measurements closer to the letter. So, in effect, even if it's an ordinary particle, it's going so fast that it's everywhere. I'll make another argument while we should have fun from the ground, ready? I'd much rather you reply to the argument that Bill said. I don't think I quite get the point. Well, go ahead. I've got another argument to lie there. Okay. I want to say that geometry is, in the end, a regularity in the relationships between measurements. And so there's nothing, the only thing that we know geometry is through measurements of relationships between physical objects. And we infer all the properties of space between the elements. Now, the way we now understand it is that measurements of relationships between physical objects, such as particles built at the center of the surface, are really quantum-mechanical, and those are theory-based experiments, but are fundamental theory experiments. And so therefore, in the end of the day, there's nothing except quantum-mechanical relationships for geometry to be regularity of. It has to be a statement about...

45:00 But I feel that our best theory of geometry, our best theory of physical geometry, implies that the gravitational field is highly non-linear. Yeah, it's non-linear, sure. Sure, and here you're saying that you've got to base yourself on a completely linear theory in order to remodel it in terms of... Well, you can have a non-linear Hamiltonian and still have... I mean, the superposition principle is not the same as the law of physics. Okay, so you are, yeah, and that's the problem, I mean, there's something interesting about it. There is, indeed, and I agree you can have a nonlinear Hamiltonian, but... What you were saying before, what you were saying before about the black hole created by the photon, it just seems to me like this is a reversal of what you were saying before, like the black hole is sort of a retro dynamic, and then it's not totally a retro dynamic. Right. So here you can reverse that. Thank you for your attention. Frozen, background, quantized, certain fields. In the case of relativity, it's not really the same. It's a dynamical theory. Yeah, that's right. But you can still couple it to classical or mathematical. It's hard. No, you're right. It's hard to couple it to quantum mathematics. It's hard to couple anything to classical or anything to quantum. But still... I mean, do you think that it's improbable that if you made a large enough imploding weight that the gravitational field would become so strong? And it's certainly an extrapolation that the physicists may understand it, that it would cause a black hole. That's what John, I think, implied. So the theory is we now understand it. The thing is we need to understand it from now. But then we don't know what would happen after that. What's the system that creates this circle? Well, it's a big, a great big laser.

47:30 Then you've got to take into account the gravitation of the laser. As opposed to general relativity, everything is coupled. Yeah, I think the gravitation of the laser would be... That would already have produced a black hole before you... No, no, no, it would be, no, no. So that would be, the laser would be collapsing, too? No, no, no, you have a huge laser. And it's the size of an asteroid. You know, the Church was going to make one with one of the gamma ray lasers, that's right. But it's much, it's way beyond a Churchill ray, so it doesn't collapse. But it makes it the imploding wave, and if you've done it accurately enough, that wave, although it's only a tiny fraction of the total energy of the laser, it gets concentrated in such a tiny region that it eventually creates an anchor on the horizon. And then we really can't say what will happen after that. We don't know if it will radiate, will it disappear, will it leave behind a remnant. General relativity doesn't give us any answers to these questions, but in principle, it's an experiment we can do. And it's very, I mean, and now when this thing is getting down that small, you could no longer treat the light with, you know, ray optics, and it's going to be a wave phenomenon. And questions like tunneling and, you know, all the things that come up in quantum mechanics will certainly come up there. Any theory that could answer that question almost certainly has to at least incorporate quantum mechanics. I know there are some people who would say... That's a different question. Okay, now why am I saying... The fundamental, possibly non-linear theory that incorporates quantum mechanics is not at all the same as what I understand by what those people are talking about when they talk about quantum gravity. Okay, now what I would say is that... I would say is that... Okay, the only way we really understand... And within the structure of mathematics, quantum mechanical theories have a very natural role. It's almost like if you started out just constructing mathematics at some point, you'd be about third or fourth step in theory, not quantum mechanics. Quantum mechanics is just a category. I wasn't indoctrinated in that. I invented it. You invented the very offensive category. No, I said that it's the quantum mechanics is the very offensive category. Oh, I see. I know that's the only fun word. A lot of people use symmetric by monoidal categories as the big bandwagon in rewriting the quantum formula.

50:00 And the interface between the geometry and the structure of the category is meant so the axioms of the category just flow into the geometry. So I would say it's the most likely... Well, could you explain that? Because it sounds a lovely, nice, poetic metaphor, but it conveys nothing to me. How do the axioms... of which category are we talking about? The axioms of which flow naturally into the formalism of quantum mechanics? All right, do you know what the stash of pentagon is? Okay. Well, I kind of understand what that is. The coherence is associated. The coherence is associated. Yeah. Okay. Right. Okay. All right. So it turns out, to make it more concrete, the quantum theory of spin is just a different way of saying the same thing. As the tensor category of representations, spins are representations. Intertwiners in the category are interactions. Period. Everything is just one-to-one. Now, within that, Penrose originally said, okay, we want to think of these diagrams in the category of spins as spinness. We want to think of them as approximations to quantum geometry. Bresci and Pansano then observed that you got back Einstein's equations of motion when you broke everything up. And now every step along the way, particularly the formula that says that the amplitude for a tetrahedron varies as the sign of its regular length, every step of that comes directly under the axiom of category theory. So the same thing will be true for any tetrahedron. The derivation, which is originally done by two physical chemists, of that relationship is just instances of the stagia pentagon, which is so, so all the, you know, the pictures in the books and categories. Yeah, yeah, so it looks like, yeah, that's right, that's right, that's right, that's right. This is what I call the category of the lab. So... It's very close to the fundamental structure of mathematics in its simple and beautiful, and when you just unfold it, it gives you Einstein's equation.

52:30 So I'd say that looks to me like the best place to look, because you should look for the most beautiful mathematics. And when we're starting out, we're doing categories, we're just asking, how can spins combine, or what's the generalization, what are morphisms you'd appropriate against a category, and we can always break them down into combinations of associators, and there's an index of the associators we could use to know what everybody's saying. All quantum mechanics, just suitably abstracted. In fact, any quantum mechanical system is a representation of a reaction. And then the different quantizations actually form the categories. And the only reason people didn't learn this a long time ago is it turns out that the Heisenberg values are only handsome when they're distributed. So people didn't realize you should answer them together because there was only one. But that's really, if you just take ridge and apex, you know, there's a point about it. That's a point about it. Yeah, they're using geometric modernization. So what I want to say is that the nuts and bolts of quantum mechanics, the dispersion from mathematical structure, and you just think about it in generality and then fold it, it looks like a space, and it looks like it's a cataclysmic version of Einstein's equation. So I claim that's the best. I mean, that's why I look there first rather than somewhere else, because I've got a proof of it. The key is under the wing. Yeah, I was going to say, I'm all in favor of looking for morphisms in the appropriate category, but... Okay, so it turned out that in order to get a... Of course, morphisms are not compositions. Okay, okay, no, no, I mean, that is... I'll come up and do it. Oh, yes, all right. Well, we're just getting ready to... Should we go now? No, I think we're probably going to have a fight. Okay, so the answer there is that it turns out that in order to construct an appropriate model for general relativity, the group that you want is the Lorentz group. Now, the Lorentz group is not compact, but its representations are well-known. I mean, Geltine worked on that a long time ago. And it turns out that the diagrams you would try to write using them by analog experiments, you know, they're diagrams on interdimensional Hilbert spaces, but the evaluations of the diagrams tend not to be finite when you make a very simple regularization that doesn't break any of the symmetries. So this was the thing I discovered with John Derrick. So in other words, despite all appearances to the contrary, you get a finite theory when you use it in four dimensions and use it on...

55:00 So that's another piece of mathematical evidence. They are infinite dimensions. They are unitary and they are infinite dimensional. What is it? The traits of a closed diagram. It's a little bit like what they did with dimensional regularization. It reminds you of that a little bit, but the regularization, I mean, it turns out that you can rewrite even an ordinary spin network as an oscillatory unit. So in these cases, you're doing an oscillatory unit to go in a non-compact region, namely hyperbolic space, because it's a non-compact group. So you can rewrite the thing as, by analogy, as a non-compact oscillatory unit. And, you know, hyperbolic space, volume goes up exponentially as you go to infinity, and these things have cut-offs in them and propagators, and it's a very delicate cancellation. But it does sound very reminiscent of what dimensional regularization is all about. It is. It's a regularization that sort of gets everything without destroying the sympathy. I mean, the reason we believe there's a real theory in Neil's theory is because it's a very beautiful regularization. And in fact, it's a multiple integral... Strong structural analogy with Yang-Mills, I see the point, yeah. But it's the multiple integral of hyperbolic space. All you have to do is just take one of the points in the configuration space and fix it, and that's dividing by the volume of hyperbolic space, that's dividing by infinity. Now that they come out finding something of oscillatory behavior, then they oscillate around the solution. So, in other words, it's a bunch of miracles, some of which I don't even know where they're coming from, but it looks like the mathematics looks very common. So, I mean, to be honest, I have all these philosophical reasons why I think we should argue. Okay, I think everybody would agree there should be a theory that encompasses both general relativity and quantum mechanics.

57:30 Now I'm saying I have to build it out as mathematics. The quantum mechanics side also has wonderful tools, some of which may turn out to kick off quantum mechanics.