Afternoon Discussions & conversations after P Cartier arrival (contd.)

0:00 All of these are related to mathematics and physics, but they are not related to mathematics and physics. The answer to this question is the following. The answer to this question is the following. The answer to this question is the following. The answer is the following. Discriminator varieties or something like that, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. Well, there is a juice, you know. In fact, we didn't have a grainy flower, had I? We do have a grainy flower. We probably do, but... But loads of grainy granules and salt as well. We'll have to move it. Tomorrow we have more time to move it. We'll prepare for this better. We'll prepare for this better. There's very nice juice in there. You should take some of this. Yeah. Look, you see? Look at the silk. Take some of the juice. You see, but oddly enough, you take the categories. I don't want you to figure out the categorical description of the product. No, I don't want to do that. I'm going to say we identify a new notion. Yeah, yeah, yeah, yeah. We're given two closed sub-objects. We're given two closed sub-objects of a new product. What you play around with is, you know, the simple. You never get anything. You know, you always go back to what they said about the red geometry. They always invoke the kind of real modules alongside it. The theory of atomic theory is the answer to that.

2:30 By and by diagrams, they're just sort of one stage more complicated than the useful ones. Okay, I told them this. They've never developed an idea. They continue to work with it abstractly. Some of the categorists look it up and manage to give a completely empirical formulation of the general theory. If they have to take it, they have to use it in a way. Don't you have a knife, Phil? Phil, you two know how to knife? Well, it's true you're the only man with a beard around the table, but despite that, I think you should have a knife. So let's get back to the commutator, the same as one guy who had worked this out in the general case. You bet. If everybody's got some wine in their glass, I think we should propose a toast to the chef. Seriously. To Mimi and her excellent assistant. Well, you did a great job. Certainly better than anything I could have made.

5:00 I think that's a terrible thing. They don't want to have community development because it's being done by too much mortality. Pure mathematics, as I've said, is some kind of perversion. The idea of pure mathematics, with no connection whatsoever to any kind of objective reality, has been a number of theories and mathematicians. Hem and Ryle for one. Hilbert would do a few things sequentially, but he always thought they were. Well, I mean, he came to physicists, and obviously it must be difficult for the physicists, he said, to do the physicists, he said. But the idea of pure mathematics in that sense, I think, as you know, is a fairly modest conception. I think it was natural philosophy. It was, of course, there were possible factors, but because it was possible to do the long things, it was internalized correctly. I mean, on the other hand, if you actually look at it, a pure algorithm, if you think of that, because people played around with it, and of course, we played around with quantum mechanics. He was actually very sharp at being able to realize that that was what was required for the quantities that you like. As Max Moritz said, he already knew about non-communicability matrices, right, which is something that's already new in modification, yes, yes, and so there were already instances that were suggested by the, you know, the internal structure. One of the most extraordinary discoveries is the double complex numbers that come...

7:30 You know, from, you know, really, from pure algebra. I mean, it comes to a topology, and these guys try to do it. But even there, that is really not entirely abstinence or romantic, perhaps. It doesn't come from quadratic equations, where you can imagine those solutions. It was an irreducible case, because they really puzzled, you know, because they couldn't see how, in an objective situation, in other words, where the equation actually does have a real, genuine solution, how these formulas... Where the reasoning leads you to these ridiculous expressions, and somehow these should actually be equal free, I don't have to guess. That was the thing that really drove it. So in other words, it really wasn't a pure, in some sense, it wasn't a completely set denier. Because otherwise it would simply have been dismissed. Pure imaginaries from Kudrat would simply have been dismissed as non-free. I mean, for a very long time. It's probably the cubic equations that yield to these things. Exactly. It's a very interesting thing where what you might say is a kind of pure, I say, you know, there seem to be within so-called pure mathematics, there are also these levels of abstraction and, I don't know, Yeah, well, the most overt. I know, I know. I don't know, I can't remember what it was. Something we did in number theory actually had some applications. Well, of course. Yeah, but I mean, much later, I'm sure. Now, when mathematicians now talk about the parts of math that are applied versus the parts that aren't, I mean, I ask them, which did you have in mind as not being applied? So this is how the answer always begins.

10:00 I mean, I suppose it was, in a way, a part of the problem was that well, pure mathematics, you know, does actually have applications. I mean, somehow, it already encapsulates. I think it's perhaps difficult to make connections with a brain structure or the actual conditions under which we do experience, you know, we do function, but at least in any sort of detail. I mean, certainly, you know, look at the brain, look at neural, look at neural physiology, there's no explanation, yet there is the brain that's doing this. I mean, how is this simplified? The fact that something is complicated, I believe, I haven't, I haven't. I assume it's complicated. I did go down in chemistry for a time. It's a little bit complicated. How it produces these simplifications seems to have been in mind about cognitive systems, but even the, you know, the sort of everyday simplifications is an extremely difficult problem. And yet it does. And so something has been left. I mean, there's something missing. I mean, the effort, for example, that Rene Tom made in catastrophe theory. You know, I mean, at least it was an elective experiment. But it wasn't enough to try to understand the level of morphology. It's already very difficult to understand the complexities of just the bit of eye in the brain. I mean, specifically how organs actually move into their brain, given this enormous complexity. Well, I mean, that's exaggeration. I don't think it is, actually. I mean, I think at the level of biochemistry, there's this enormous gap. And how to fill it, of course, there's been a serious battle going on over that. Well, given enough time to somehow these structures emerge, there's no explanation at all. I mean, it's combative, of course, the idea of design. But the design answer, actually, is one that the public heard of people initially.

12:30 Indeed, it's the natural answer. It's what Darwin believed. I know, exactly. And so it's still a serious problem. And, of course, there's these vulgar, jealous propagandists like Mr. Dawkins, and I don't think that's true. No, no, no, I don't like that. I don't think that's true. He's definitely a bit of a menace. It's not only that. He doesn't really see what the problem is. There's a certain level at which there really is a problem. And these are really serious questions. I do like Dawkins' insistence that on information-theoretic grounds alone you know something like evolution. I-I know I- You have to be able to predict the whole- You do know on information-theoretic grounds that any of the- Now that doesn't explain why life formed on Earth in roughly two- But that point, the point that something like this, you knew something like this had to happen. Yes, I agree. I do. I know, I know, it's not a new thing, but it's the- it's the- I knew it somehow. Everything can be reduced to that one principle. It's really important. Knowing that really tells you very little, frankly, about it, which enables these principles to be discovered. Now, I agree that a physicist would say, well, yes. We take that point and then we admit that we don't see how it is in other words, but of course, he's a dreadful reductionist, yeah, essentially, no, no, I mean, I mean, among that, I mean, I know, because I talk about evolution with a lot of people, and they almost all believe that the infinitesimal theory is the whole theory of evolution.

15:00 It's very interesting that you can actually have a view of the world to be some kind of

17:30 But in practice, he seems to have been some kind of guru or a guru in that his philosophical views, you know, the idea that the world is an illusion, Maya, and so on, on the one hand, and yet on the other hand, one actually practices things. He has these amazing insights. Well, and womanizing, too. He was very deftly a guru except for a bit of that level, yes. Yeah, the illusion was good, you know. I thought it was hard because he actually did have, maybe he played around with the ideas of the... It seemed to me that was quite much more convincing, somehow, than discrepancy, as Richard Dawkins always will, can't be the way he describes it. Whatever it is, it can't be that. Except there is, surely, some totally convincing argument. I'm not quite sure Dawkins is, frankly, on the same side of my barricade, whatever my barricade is. I mean, maybe, but it's very interesting to compare, let's say, Dawkins and Schrodinger or Hermann Weyl. These are much more serious things, they're like, no, no, but they were, I meant Weyl, because Weyl and Schrodinger were pals. They were very close. There is no genuine bond. There is a very good bond with the intruding in the eye. I can't remember the first name. The last name is Moore. This doesn't have to do with resolving tensor products of representations. This is what I was going to say, that actually in the last maybe 50 years or so. If you're compelled to offer the most shallow explanation possible, you say the outlaw. Information, okay. Just one thing. It is shallow. It's incredibly shallow, and it comes from the culture of the military industrialization. I know, Bill. No, really. Especially like the Rand Corporation regularly produced documents of that sort, and then this became...

20:00 It's shallow when you offer it as the theory of everything. I will say it is important to have the point in mind. We believe that they didn't invent that, it's a lot of people don't know that. Von Neumann may have gone down the tube, you know, in certain ways, and we don't get any of his names here either. But the unusual thing is much more general than that. I don't know why I know that, but even then, they didn't invent it. They actually found it. You would have thought it was a guy who didn't know that. Yeah. Von Neumann really got everything in front of him. But not on information. I know, but the interesting thing, one of the things, of course, that's right, but they use it, they use the advantage of the real, the interesting thing, one of the things, that's where you have genuine guess, you wonder why didn't they do it, there, at that level, you have genuine, stop trying to argue. Thank you for watching. It's like the attitude in the Klan, for example, I guess, you know, towards the, towards the Earth, well, maybe doing different things, but the idea is, all I meant was that even these people get hold of these superficial ideas and they become even more, well, I just said they become even more degenerate and propagandized. I mean, you know it goes back to a serious, a serious battle, a non-trivial battle, I mean, you know, between what I don't know what he's talking about, but you realize that mathematicians have this culture, that's in content, no matter which, you know, it's very, very shallow. But that's because, of course, of the kind of virtual, you know, mathematics, the kind of dazzling business on the surface, isn't it? You could be very clever, without it being a clever mathematician. Look, it's a good like being a flashy pin. Is there music? No, but otherwise, no. I mean, look at the people who are just, you know, problems. You admire them because they can do things, well, frankly, I can't do. I don't think it's the fact that you can solve life a bit like being able to do things quickly. It's a technique that shows up very early when you're young. And that has always been carried through the people of certain capacities, efficiencies, speeds. Come on, one hand, look at these calculating types. I mean, you know, that's a...

22:30 A kind of mathematics, I mean, but that's part of it. Mathematicians themselves get to 10, but there is this great deal of solving problems that are at a, let's call it a superficial level in terms of any real thought about that. And that's true of an awful lot of practices. It's something that's true of mathematics. Just that mathematics is sort of surprising, perhaps, in a way, because mathematics is indeed very concentrated. And the technique that's required even to impress other people with it is already a relatively rare talent. When it then becomes impressive to other people, they say, oh, well, right. Oh, very clever, brilliant. And look, you people, who the hell should play my virtuoso? Even if they do play, you really just do play Paganini. No, I do think that's part of the reason, because there is something impressive about being able to solve problems quickly and cleverly. They are mathematical Indians, what do you think of this? Exactly, exactly, we see the difference. But it is actually part of the mathematical world. That's insane, that's fair. Okay, alright. But it's there. It's always been there. It was these computations that were used at all. That's the point, that it's got much worse. Oh, I don't agree. There is a political... I agree. But in a way, that's always been there. It's always been there. Yes, very much. But they took something that was there already. It wasn't just invented by them. But he said that wasn't the point.

25:00 That would be pretty bad. Well, I don't know. I think one has to take that into account. Otherwise, the impression would be old. There would be people who were going to manipulate it. No, no, no. The business of mathematics is some kind of circuit that detains it, which is what they use. There's always been that element of it which is supposed to impress the public. It wouldn't have been a magic thing. It was that aspect of it, of course. Well, no, indeed, no, I mean, that's my, well, including and now other mathematicians. Very concerned to have a dozen people here. Psychology, I mean, is very important, actually, in fact, in the actual mathematics. And it has been, and it has to be. If that aspect were something that could be exploited, and it has been exploited, of course, very definitely, I agree with you. But it isn't, I know you didn't say that, it's merely that, for me, it's just... But somehow they were already there, and they were always problem-free, and now, yeah, that's hit the superficiality of the level of presentation. Now they're, oh yeah, by the day, oh, these guys are right. These guys say, oh, now we have mathematics. Yes, we can really impress, you know, people with that, including other mathematicians. But then, you know, you did the propellomaths, and there, within mathematics, they were very expansion-sick. Well, yeah, you look at the 1910s, you look at the period of mathematics, and there were a number of them. In fact, they probably were all worth it. Well, I don't know if there was a whole number of them. Well, they were very few, exactly. They really were relatively few. And then the whole thing expanded and, you know, because of genius and no, that's a bad thing, at least prima facie, you know, because of education. And there was a huge expansion. I mean, come on, 20th century still. And solutions to problems and development of concepts. Well, it's sort of unimaginable, obviously, in the 19th century,

27:30 Oh, I think so. Come on, we want to imagine a woman very liberal. Oh, no idea what he's behind all this. And you look at the, of course you see adumbrations, you know, there are no revolutions in that. Mathematics is just suddenly continuing. All I meant was that, at the same time, there's this huge, this enormous efficiency. Yeah, and there's general potential of people to be able to think about that kind of thing without thinking about what they're doing at all. Yeah, that is so. I know I'm in. And yet, I'm in. Yet to be. Well, I mean, why did they back? I know, I know. No, these were, but, but. I mean, there wouldn't be too surprised. No, I agree. No, no, I mean, it would be amazing. Yeah, it would be amazing. But I think on the close scale of the results. I'm not putting myself. But I think that if you were really close. I should have prepared it, but I do think that in the case of. There's a number working, and there always were, of course, and why not? It's an honorable profession. There are, I guess, as in musical composition, the ones you're getting your name, and the music, and it's true of pretty well any practice, if we're doing mathematics, at least in that respect. Well, and of course that involves mathematics because mathematics has been the basis of mathematics. I don't think so. I'm not so sure. I'm not so sure. I'm not so sure.

30:00 Because the idea, there was a kind of liberation demand. No, there is no taxi. I'm sorry, John, I tried everything. I've dialed seven different taxi firms. They all have the phone off the hook.

37:30 I've dialed an English friend of mine. So can we go, why don't you, you come with me to guide me, and I will take Mamie back to the room. And then if I serve, and I put the plates out, and we serve dessert, we'll be back with dessert. Raspberry, raspberry clad, but we've got to get some cream, because next year we'll have to come through. Yes, I'll come with you, absolutely. But do we, do we, do we... Does anybody want another helping of chickens? Well, Lambert... And Lambert knew that? Yeah. One of these things, this is why Cauchy wanted to know about all those things, because of the absolute metric in hyperbolic.

40:00 It's only the case, that's the fundamental difference between the two geometries. Yeah. No, it's okay, I really did try, but I knew it would be a problem getting a taxi, because I had that one guy. Thank you for your attention. The problem is the French don't know the words. That's all right. I'm really sorry. We love it here. It's OK. No, no, no. The downside that you don't seem, that you don't appreciate, is that, you know, I'm so sorry to factor that around, but seriously, you do understand pretty quickly how, after you've lived in France for two years, why they've got the 15% unemployment rate and why... You know, I'm sorry, but they're, you know, it's, you know... No, I'm not, I'm not even going to pretend that, you know, the French is heading for, you know, an enormous bankrupt, collapse of bankrupt, you know, when you will know, you will be, you know... What it's heading for is an enormous boot up the arse from Sarkozy, or whoever will act the role of Thatcher in the French. We shall see. We shall see. No, it's true, I'm sorry, no. The only thing I'm concerned about is that Carter should be, what's the time now? It should be about ten. Have you got time? Ten is ten. Right, well Carter will be here at any moment so I will just tell these guys to listen out for him. Yeah, we won't be long. I'm a speedy driver. No, you don't have to rush.

42:30 Whatever you do. We'll give a ride while we're away. The thing is, I don't even know at this point where I'm going to put it. We're out of your hair in that respect. Yeah, you said you were out of my hair. But there will be things I can do. Okay, so let's go. So to interrupt, Keir Carter will most certainly arrive while we're away, so if you can just listen to the doorbell, it will be him, and obviously your people may be attending. Yeah, yeah, yeah, you'll tell me he's in the right place, definitely. So where are you going? To John and Mimi's hotel and then we'll come back. But I should be here, well, he should be right by here. I could drive and he knows the way. I could do it locally, he could do it locally. There must be some cohomology. Well, I don't know, there's a... You settled something very scary. There's something, yeah. Okay, right, okay, we'll see you shortly. But just keep your head still for the bell in case he doesn't come, which he probably will. That's not a big deal. In fact, if we had ever got rid of the monarchy, if we had, no, seriously, we decided to have a constitutional figure head of state under a public, it would be an opposite candidate. No, I mean that. No, you go around here, and then down. It's going to take you an hour or two. I know, that's probably a serious remark. If you wanted a... Something like Penrose right here would be the obvious candidate if you wanted an absolutely constitutional figurehead who would, you know, bring international renown. It would be extremely sensible. Right here and right again. Right here, right here. Straight up. And then straight back up here. If we ever decided, you know, to go for a presidency out of the French Central Republic, then the sensible thing would be to have a very senior academic rather than someone from politics. I mean, somebody who's also come here socially charming and obviously, you know... I've held a knife and fork and something like Penrose or Atiyah would be perfect for the topic of life.

45:00 I think it's a great subject. Straight on? Yeah, straight on. Yeah. It's interesting. But anyway, it didn't happen. People who learned it from Apostle, or Witten has friends who learned it from Apostle, say that Hegel didn't understand the calculator. That's completely wrong! That's completely wrong! Well, look at the science of it. It's true that he wasn't really interested in that, in that sense. And he never learned Apostle. Yeah. But it was, it's great, it was, it's true. They're all fine, aren't they? No, I think we can just say that Hegel showed no interest whatever in the writing of his work. He's an extraordinary latino in his work, isn't he? Hegel actually showed... I spent all of his work in writing this book, threading the history of the calculus and the notion of the continuous. When I got to the science of logic, Hegel is going to be writing... He knows all of it! It's for his will, you might say. Well, hell, he's got it right! His mill is next to what actually happened in the tricky question. I think, no, really, it's very depressing. It's completely wrong to say that the blind, well, you know, hey, we didn't even know anything, we didn't care about mathematics. Not the contrary. He had other concerns. Well, this is the one, of course, which was... He had other concerns. Ah, I think we have the outcome here. Was it a seminar or a... No, no, no, definitely. No, I just... No, I don't think I've anything. What about your baggage? Yeah, I've got nothing here.

47:30 As Einstein said, you shouldn't repeat a good joke too often. Exactly. Really, I mean, you can't do the same old thing over and over again. Well, although it may turn out, of course, that the same old thing hasn't really been. There's some really fundamental thing that still hasn't been seen. Then you have to go back to it again. It will. It will. I think that's true in the history of mathematics. There were permanent things invented there. They encouraged you to think for yourself. The actual text itself wasn't. It was like I can exercise it. No, I take it. Of course you can do it. But the thing you actually did for yourself in the exercise, the point is, the text had already been written. No, I love this text, but all I'm saying is, yeah, yeah, it's so true. I don't know where I've been. Exactly. I mean, I was about to say that. No, I was about to say that, but I didn't mean it. There was a reason for that. And they're very good. But you know, they're very good. Do you know any one of them? There's ten people picked them up. Yeah, there's no question. Well, I didn't know one of them. No, no, of course. I didn't know one of them. There's one that says, well, I was true and false. That's not so bad. No, there are, but the levels are really, really, the... You are encouraged to do things for yourself, it wasn't the cure-all. In other words, a gentleman seems to have cared about pedagogy, otherwise why the hell do you provide exercise? I don't really know any more about it, but they all did. Oh, sure, there was arrogance there as well, perhaps, but I saw him once. He had a blue suit and he looks like a police chief in Marseilles. He said all that logic is trivial. I remember one time in category 2 he said... In category 2 he said... I did, I did.

50:00 Well, of course, I don't know, they weren't that... Not very mainstream. Not very mainstream. But, no, that's very interesting. I have to revise that thing a bit. I mean, the king's better than the exercisers. That's where you have to revise your thing a bit. Oh, yes, yes. No, I have to do this. But I don't. And he really knew, I mean, he really knew all these musicals by heart. I mean, hence the exercisers, but they really were very nice. They were very nice. Well, he knows. No, no, no. Thank you for your attention.

52:30 I'm getting a little nervous here. I thought you could not talk. This is not the end of this period. I was in Chicago at the time of the meeting for some routine things I had to check. And then I was with some people, of course. Difficult times. Of course, because it was my university and I came. I suppose you know very well who I am. I'm in to make a sample of a thing in a particular place. And so my telephone line is very busy. You can see Bonnie on the cell phone, Peter. I will give you something. I will give you something. Bonnie was there, but he was.

55:00 Do you remember, well, I mean, Pierre-Samuel, do you remember, do you remember when I learned the inconsistencies? He insisted, of course, that Goethe, that, well, you know, actually he hadn't written this. It was a collective decision. It was something that he didn't want, he didn't want this to start, but no, I don't. You sit here and you say, Giordani became very important. I don't think he was going to lie. I mean, Giordani was a chairman of the National Council. He came and the second name came to Washington. He said, it's not the place for you. Finally, after some time, he came and he was the chief. And there was a big street, the first one, and there was a big staircase. What, in the south of the town? The Nescafé. The Nescafé. The Nescafé. Thank you for your attention.