Contradiction in identity (gluons)

0:00 Scripture for today, wherever it is. I'm very glad I signed up for this. I think I may not be able to afford the dinner tonight, but certainly the two lunches seem very well worth it. My problem is that I was supposed to collect, when I saw Freddie Van Oystein yesterday, I was supposed to collect a reimbursed, yes, I'd love to, I was supposed to get, he was going to reimburse my expenses, yeah, stick it down there. I was supposed to cut down the reimbursement for my training, but I didn't get to see it, so now I'm... Thank you for your attention. I was. I'm really just about, in these days, I'm not in anything. I have no official position at all. I'm just a kind of, if you like, I'm a kind of unofficial artist. I've got a project for me. Exactly. I actually run a little private company.

2:30 We do have a couple of grants as well, don't worry about it. That's what we've been trying to do. We've got two sorts of private funding, plus what I'm able to provide myself. I think the big one is for the water and the small one for the wine. Yes, that's very kind of you. So, I have this article which has been going since 1973, which now contains something like 26,000 recordings of interviews with A lot of interviews. I was just in Boston this last week. We also sponsor conferences. We sponsor colloquia and symposia in our places which are in Western France, but we also try to do them in other places as well. We just had one on foundations of category theory. It actually was really a more historical retrospect for the 50th anniversary of Grothendieck, so it's great for the whole group of people. And it's generally about work on all of these ideas, not just in category theory, but in all of the very important areas of mathematics, particularly algebraic, geometry, and some pedagogy theory. It's quite sympathetic though, but I haven't got motivated enough to really find out. Well, it's still involved with other things, don't you think? I mean, it's a perfectly reasonable and valid excuse. I'm not mocking it. I mean, obviously I was lucky enough to get involved with people who were almost from the beginning. I did become very convinced, I became convinced very early on in my career, even when I was an undergraduate, that it really not only clearly was going to provide increasingly the overall conceptual organisation for mathematics, but that it was going to provide almost all the... These are the key ingredient concepts and the deepest tools that you can prove in terms of mathematics. Is that so much the words I have to say for the sake of philosophy of science? I have to say that's a criticism of philosophy of science rather than of category theory.

5:00 It's a criticism of the... What's the criticism? Well, that category theory has been so slow to make any kind of inroads in terms of people's awareness. This is partly because of the... You know, the publish or perish world, and the inevitable intellectual division of labor, but which can be, which at certain phases in the development of science is absolutely indispensable, and in other cases, in other spaces, provides an answer to the block, and it seems to me that these are the foundations of maths and physics. This is one era where, right now, it's that inevitable intellectual division of labor that is acting as a very serious block. Once you have, once you've seen the kind of transformative power of calculus, or any notion of science, or foundation of logic, and indeed on a very conceptual what the subject matter of logic is now, it's in to the rest of math. I mean, it's so powerful, it seems to me. And so, although, basically, it's a kind of social oculon, it's so clearly the way that the 21st century government is going, increasingly. This is a very abstract speculative theory. There are many things like quantum gravity and quantum field theory, but they're actually now using it to do with general relativity and other things related to the subject matter, such as the sweeping reformulation of the Einstein equation on the basis of synthetic differential geometry, which is a very significant thing. ...understanding of the relationship between the metric and the connection, which brings in some very, very interesting ideas, which I think are going to be very, very important. And in quantum theory, there are three...who knows? We obviously have a lot of formalism in standard quantum theory anyway. So, and there are lots of people, including people who are part of the government, who think that the whole thing should be reformulated in terms of symmetries, Also, that turns out to bring in some really deep links with ideas in functional analysis and nuclear spaces and which Banach spaces is a branch, which in fact Gretli was already working on 50 years ago, but which of course is virtually unknown and outside the realm of mathematics because, let's face it, how many philosophers have known about functional analysis?

7:30 There's no corruption of mathematics. Absolutely. There belongs to be a real math theory. Because all they ever teach them is what you can set there. And not just what you can set there, but what you can bring down and prove. I don't know the work of John Bell, but I know John Bell perfectly very well indeed. He's an extremely old friend of mine. In fact, I was just recording a whole series of interviews with him in Paris in June and July. He was over there for about 30 months, and we had some great... Yeah, I've had this very... He's one of... I've had this work pretty well now, I know that. We had a meeting in our foundation in the archives of mathematical science in Boucher two years ago, June 2005. He, Bill Laupierre, Colin McClarty, Jean-Pierre Marquis, who you probably know. Pierre Cartier is a very famous French mathematician, field medalist, and was more or less the directing influence in the Barkeeper about Encephalinius. And a couple of other people all came and spent nearly three weeks discussing foundations and what should the philosophy of mathematics in the 21st century really be about. We've recorded everything, including what we've lived to do. But of course, working through the transcripts of three weeks of discussions and turning them into a book is a massive project, especially when you've got 500 other things to be doing. If I'd had time to do nothing else in the last two years, or if I hadn't needed to do anything in the last two years, I might just about have got it ready for publication by now. But since there has not been, it's a massive project, and we're happy to do everything on the street, street and the lab. We're hoping that, yeah, we've had a couple of these people right here at the Belger Hall Academy, not even just the Belger Hall Academy, but specifically the Lambda, the Flemish wing of it, in January, about the possibility that they might give us some money for a year for a pilot project that starts, I think, the archive for what I call the crowd children, as interesting as a pilot project.

10:00 And of course, you have the archive, yes. Do you have Nick Cricket? I do, but in fact, I saw quite a bit of him. God, he's 30 years old. I'm trying to think in Oxford. I need to see his PhD on relative identity. I knew him, I won't say I knew him well, but I wish I'd known him better. Well, absolutely, I'm completely satisfied. Well, of course, you still keep up an interest in philosophy, foundations of logic, and issues like that. No, nothing, I was born in America's next-door church. So it's much more on the side of political matters. Yeah. And now I'm on the East Coast. During this whole time Nick and I, although we've had the opportunity to work together before, have not had any chance. There was a seminar which Michael Dummett... Thank you for watching this video. Now, he's pretty frail. The last time I saw him was actually about exactly a year ago now. It was in June last year when, in fact, when Cartier, the guy I was telling you about, the French mathematician, who is also a very good thinker. Algebraic geometry is the fifth generation, which is to say that that generation in algebraic geometry in France was the generation of Thierry Grosveny, which is to say that it was almost indisputably the greatest generation of French mathematicians there has ever been, you know, considering what the competition is like.

12:30 I mean, that's including Poincaré, Lagrange, and Descartes. It's incredible. In fact, it's only now really beginning to be felt across the rest of mathematics. I mean, these people really did set the core for the central agenda for much of 21st century mathematics. That's becoming clearer and clearer. Anyway, the point is, he came to London to give a talk, which I've actually, broadly, on the philosophy of geometry, because for the last 20 years, he's the seventh scientist. There's still that, but I don't know what's still in it. He runs the main History and Philosophy of Mathematics seminar at the École des Maths, which is the most prestigious History and Philosophy of Maths seminar in France, and I thought it would be a good idea to expose some British philosophers of mathematics to what, you know, the best French historians of philosophers of mathematics are talking about. They think a great deal more about geometry than people in the math department do. So he came over and gave a talk, which was a very nice talk, and Dummett was there. It was really just my chance. There was a council meeting at the LSE that day. So he stayed after the dinner, and they had a very good conversation. But he does, he is very frail, and of course he hasn't done so many things like kippering his lungs completely by himself, so I'm quite honest, I was amazed when I saw the state he was in, that he's still alive now, 18 months later. Well, I think he's having difficulty walking across this room, I'm afraid he's in a pretty awful shape. But when he was there in the great days, when he used to have his seminar in Oxford, which was when I was a student, I used to go over there and that was where I first started recording the seminar at that period in 1973. We printed and recorded all of the seminars that he and Donald Davis were actually doing.

15:00 This is one of the most valuable things we've probably got. This is why I'm so desperate to try and get some of the data out. You know, we're not talking telephone numbers, we're talking just the simple money we need to start getting stuff online. When it gets to be 30 years old, audiotapes really start to decay quite rapidly, you can't, you know, it won't, it won't, there is technology now, there's a thing called CEDA, Computer Advanced Digital Audio Restoration, which allows you to recover even quite severely, you know, audio. Thank you for watching this video. Audio, it depends on the character. The audio types we recorded back in the early mid 70s are in much better shape than the ones we recorded in the late 80s. So what happened was that the manufacturers, absolutely, they started introducing audio tech with much thinner magnetic coating, much, much, much, much, much, much, much, much, much, much, much, much, much, much, much, much, much, Even CDs and DVDs will stay marked forever. The reason you get everything is not hard drive. The reason is you digitise everything and put it in a dedicated hard drive. Then of course it's safe.

17:30 Then you can make backups of many of what you need. Then it's safe. Look, he might be a man. Yes, I won't. I won't. I can send him a catalogue of some of the goodies. He might even know he wants to buy one of his own. He might even want to buy one of his own. He might be interested in some of our stuff. Oh, this is fascinating. He's absolutely the man for me to speak with. I'm curious. I haven't thought about him for a while, but of course I... That must have been the material archive that he brought. He left every... The main reason I would say about this is because we hate a great big gap. And I have to say, it's very sad because that's largely the reason why Robert Grosdy could knock him off the perch. I mean, he was... The greatest living freshman mathematician in the community. And then again comes the new kid on the block, comes along, you know, completely knocked off by the new genius, who's a bit brash and a bit, you know, rebarbative.

20:00 And Andre Weil, who's a very, very brilliant and sensitive man, but who's never, ever had to handle, in his entire life, ever since he was an infant, ever had to handle the idea that there's anybody else in the world smarter than him, just come and handle it, he goes to sleep. What is the general explanation for their rather idiosyncratic approach to set theory and their idiosyncratic notation? They always had a very, very weird view of... Well, like almost all French mathematicians, they looked down their noses at logic. They really did look down their noses at logic, which is why you've got that incredible stuff in the beginning of the Goethe-Montborea. ...on the Hilbert of time operator, instead of just introducing the active of choice, using it outright and saying, you know, here's ZFC, this is the justification for... But also the notation needs to be used... It's weird that nobody else has ever taken it up. Well, this again came because they wanted to build everything around the epsilon operator, because they didn't want to use... It's a consequence of that, you think. Well, as far as their foundational volume is concerned, it's precisely because they were hung up on this extremely syntactic... They should only use... It's very weird considering the general spirit of the rest of the project, but they have this very Hilbertian, that you could even hold as really the daughter of Hilbert, very formalistic, ultra-formalistic, ultra, not in fact the real Hilbert, but the kind of deprecated spirit of what's after the Hilbert program, and absolutely skeleton Hilbert, and you should do everything in purely syntactic terms that we can't... If we can't touch things like the axiom of the joint directly, we have to do everything via the f-sine operator. I mean, as Adrian Mathias pointed out in his diatribe against, you know, the ignorance of Mubaki, well, yeah, that's fine, except it takes 176 lines to prove that one equals one. The game is clearly not worth a candle, and this is a classic example in the mathematical sphere.

22:30 French jusqu'à boutisme, which is the basic characteristic of the French. No, jusqu'à boutisme, you know, you just pursue the things, you just pursue things for the better end. Which is obviously such a feature of French politics and history. But this is in a way, this is a displacement of mathematics. Having decided to take up this point of view on... We're not going to have, we're going to have a purely equational semantics because that's the only thing that nobody will ever be able to kind of criticise us for, otherwise. They did take it completely ludicrously, and they realised themselves. Plus, as I say, the theory of structure, which is actually really interesting, it's worth studying, which of course came crystallised largely through Weil, just before category theory came along. But Witten's work has never been used by anybody. This was one of the things which we were talking about in Boston. This was one of the main subjects which was not personal. If you ever, I just gave a sort of pre-related in a much more standard way, step-by-step building onto it. So this is basically what you're trying to do with your various structures? No, that's just in my thesis, just as a pedagogical exercise. I'd like to see that, because it is worth doing. No, I haven't. I haven't even seen your thesis. Really? I'm not kidding, I'm sorry, I haven't. Would I not send one copy to you? I don't think so. I don't think you did. Yeah, I'm giving you just these two. I don't have a car, but I'll give you my personal address. Don't let me forget. I really want to read them. No, you shouldn't. No, I really want to read them. Just like the explication of Bob Snow's structure, which is step by step. Really interesting. I'd really like to study that. That a math student can understand it. I'd really like to study that. Have you read...

25:00 I'm actually blank for names, not Ralph. Actually, Ralph Krummeck has written about the Wolbachian period structure in relation to Eilenberg's work. It was really Eilenberg who was questioning one of the, how I said, was the most important thing, the most important thing Eilenberg did was his work in algebraic homology. Well, and Fletcher's work obviously with McLean in developing the theory of categories, but one of the things he did, which certainly was important, was precisely to persuade Mubaki that that was the theory of structures that they haven't chosen, absolutely not going to go anywhere at all, and that they should jump in and they should jump, adopt category theory as the correct... I know, it's an incredible mystery, because they were halfway, you know, they sat down to write that kind of general preface on structures, but that was a long moment in history. Four category theories crystallized from a tool in homology and algebraic typology into a general language for the conceptual context of mathematics, because it was ten years before the adjoint function theory, it was ten years before, and you had the same time. They could see that there was a problem with this theory, and in fact it's really fascinating to listen to these two professors, Cartier, just using these in this last week, on that very subject, on the history, which I will certainly make sure you can copy over. Does Cartier write about these? No, no, he has written. He has written. I mean, he has written about them. There was a question that came up about Plato, the theory of participation in the universal, as it might connect with the idea of a blue... Oh, sorry, sorry, I'm talking to the wrong guy. I'm sorry, that's... So you can see how much I drink. I'm sorry, I'm sorry, I'm sorry. That's grand to ask about that. No, no, no, no, there's a separate thing I want to ask you. Is it possible, if I forget, that I could get your overheads?

27:30 Yeah, okay. I'll make sure you've got my car on. I really want to ask you a couple of questions about, well, quantum space and the universe and some other stuff, but don't worry, we'll get back to you. You're going to be around for a couple of days, I know. That sounds like Bosseux. So, I'm sure that you two didn't like it, but this is the thing on the first hand. And then they ask, this is the thing on the first hand. Do you have any questions? It's the way they used to express it in the law of maths. I'm sure I'll say that these are the pieces from the triumph. You heard about Renault, that he got Magna, what do you call it, Magna Cum Laude, Magna Sulla Cum Laude. The one before it was really nothing, you know, I was ashamed of it, but it says that they gave it to him, and they still give it to him, that's so visually. I haven't heard it yet, of course, but you did record all of my notes, but I sort of need to get those tapes off you. Yeah, but the gap... Yes, well, as I said, if you'll give me a copy, if you give me the original, I'll make a copy, can't I? I will happily do that, but I can only do it if you give me the part of the rendering you want. Okay, we'll do that tonight. This is very grand, isn't it? This is even more grand than the... Have you ever been in the Rolls? No, of course you haven't been to London, have you? You've been in the Rolls this night, haven't you? Well, this is much grander, this is much grander even than the Rolls this night. Much grander. Really? What about? Uh, well, it's one of these quantum computing...

30:00 I think you were at something like that in Paris or something like that. Yeah, yeah. Oh, wow. Basically, you can do four tasks in six days. That's three more, that's, that's, that's... You know the thing, one computer, one map, there's a pure map stuck in Manchester, and one computer. I thought Cartier was doing pretty well to do three in three days, but, you know, that is, that is how I... Well, actually, I didn't want to say that. I passed. No comment, Rob, no more comments. I think you're being a bit hard on yourself, saying that, but... Very good.