Evening discussions — re-writing Bourbaki project based on category theory (contd.)

0:00 Thank you very much. Shall we take, say, about half an hour for some rest, and then accomplish the very light, you know. I was actually going to just do some sandwiches for everybody, but it's a little bit late now, and also the bread, unfortunately, is a bit stale. Yeah, it makes intense work, it's probably better just to go out. Yeah, I think so. I think it would make sense. We had such a fine lunch that I never thought I'd ever need to pick it up again. So we'll just go out and have that little place on the square.

2:30 Okay. We thought we'd go out at about 8 or so.

5:00 About 8, just to give people a chance to get a little bit of rest if they wanted to. And then tomorrow if we can start a little, well, a little early I think, because I think we are running a little bit behind schedule. This was absolutely fascinating today, but Angus is absolutely right. We didn't even start on the outbreak of the flu. Thank you for your attention. You can see that the problem is that that scum at the end is probably going to be the same no matter where we go, especially with the limited time we don't have left. So then I was glad to have you come over. Well, absolutely. But I think if we can try and concentrate on algebra and geometry widely tomorrow, and then it will work. I think we can't have one general philosophy in that day. We'll do that maybe the second day after the event. I guess anything is worth discussing.

7:30 Well, in general, it's because he wants to be an academic professor. Well, yeah, exactly. It looks like that, but is there any conceptual justification for it? Well, and of course, from a Higgins view. After a first approximation, no, but I mean... Well, we're all from the Higgins view. Of course, he can't be just poor. He can't be just poor. He can't be somebody. Yes, of course. That's it. Go on over to the doctor. The enthusiasm and power that made him think that was feasible. Well, instead of that, I mean, just for, you know, it's psychopedic, for a call, but the SGA, of course, is much less rigid. Yeah, yeah. Oh, it's still. But it's a half a dozen in nature, and another dozen or so in the room. It's very much a collective, only it doesn't have a secret handshake. Yeah, yeah. Whereas Tudor is much more of a kind of judge of the court, summing up all the counsels spoken, and, you know, it sits like this. That's amazing that IHES, the building was built for a small group. It was about, you know, the meeting room was not much bigger than the house, you know. I was amazed, basically, at Chuck, by what, yes, I just said. You know, just as, he said, you know, this is bit like, you can put the parkies.

10:00 Yeah. I'd be good. Rather clever, so, at the moment that he heard that, you know, John didn't ask for an answer. I think I should like to die now. But I'm quite sure that you know what I mean. Yeah, there is a debate around it. People who like categories must not like four by two. That's way too crude. That's way too crude. Oh, no, that's it. That's all. Yeah, so is that your stuff? Oh, yeah, of course you can have it. They're clean. Oh, yeah, yes, yes, of course they'll do it. Yeah, sure, sure, of course they'll do it. I mean, this is, this over here is, well, this is dirty clothing here, but it's rubbish. ...which is never used anywhere else, so the deletion causes no problems, so delete it. Now, that hasn't changed anything in the rest of the world. Then there's a step where you introduce basic ideas, monomorphism, epimorphism, quotient, and use them in a very light way to organize the same material. That wouldn't be hard to do, but then it's really hard to reorganize it fundamentally in one way or another. Do you think historically, if this debate is still weathered to go for a rewrite, the category theory is... There's the framework for it, or not, had taken place not in 54, 55, but three years later, so after Khan, after Yanida, after the Android project. They would just have had to do it. No, because like he says, they took that on the program. They already knew it was in front of them. Yeah. And in that sense, these things were just affirmations. The reason that they didn't do it was not because they didn't think it was important. Well, they were faced with a hard choice about priorities. Of course, they had different priorities within the name.

12:30 It's a fascinating illustration of what you said. I spoke yesterday, I think it was in the highest terms, that they believe that it's unfollowing. And I guess these groups are always in contact. And of course the Russians did the money-building mortgage very, very early on. I guess they didn't go, that's all. They're not interested in talking that way, especially, but there's Gauffin and Mann and Homolov-Claude. Absolutely, 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. When you talk to him, you find that the ideas you thought were original say the logic. He had something like it. Of course, I guess it's always a matter of modality and stuff. He told me points that I noticed at the time, but Lang had also tried this a bit later to invent non-standard finite fields. Lang thought, I mean Lang occasionally doubted him, seriously doubted him, he didn't know he was doing it. He felt that by creating a set of objects, since it had a liquid zone, it would somehow relate to the structure of the Maxwell-Hewitt extension. And they do link. Sometimes one knows not what it does, and some date may, but it's not tight enough. And Gauffin, of course, was great at it. Which we were really dealing with, all the products. I mean, not really explicitly, but it sounded difficult at the moment. But I mean, the factorial approach didn't seem to... I think to some extent it's a bit like Sarah. I asked him, you know, in the seminar at Cartao were people influenced by the category theories. He said no, absolutely nobody was into the category theories.

15:00 Now, evidently, that means he doesn't count Eilenberg as a category theorist. He probably didn't count Maclean as a category theorist. What he means is we weren't calling it category theory when we learned it from him. And the Russians, there is sort of a bias in, I think, mid-20th century Russian mathematics against calling your method anything. There's no method here. You just did this. And Serres went that way, too. In fact, he has all these methods, but he doesn't like to think of himself as making them. He likes to think he's solving problems. Yeah, they probably didn't want to become a follower of any of this guy. There was this Kolman crossroads, which was very influential. Like you say, Marxists, philosophers, scientists. There was one talk by this Kolman, and somehow that became the only text that both East and West So, therefore, if you can call Stalinist and sort of have nothing to do with Stalin, if you relate it to any being or figure, it would have to be Bukharin, a Bukharin organist, as I think this talk was run, I mean, flimsy, but on the other hand, but on the other hand, he's like, like Senko and...

17:30 It was the only one that Stalin actually talked about, was the fact that Marr had set up this academic dictatorship, and it was a terrible thing, you know, but people did that sort of thing, and I guess probably it's the opposite of the entire universe. Stalin was probably largely occupied with defeating the Nazis, and these characters are roughly a little empire in the field of philosophy of mathematics. So, I'm just conjecturing now what you say, that maybe an mathematician is still a mathematician. He was actually a Czech citizen. I'd certainly heard of him. There's a long article in the History of Mathematica. That's original. About him a few months ago. Oh, uh-huh, uh-huh. I get a lot of facts, of course, calling him a Stalinist, which would be the highest investigation. Well, that's just shallow. It's just because he was writing in 1931 and called himself a Marxist. There we go. Yeah, but I hadn't heard of his contribution to this conference and I would like to read it, but I certainly knew about the conference. It was the one where this guy Christopher Caldwell emerged as one of the leading Marxists and the great theorists in England and the literary arts theorists and also critics. It was either one who stood up and said, well, this subjective idea isn't entirely right. Isn't that represented by Convessel? I don't agree with Convessel. He died very young. But I mean, for example, in the U.S., he, all his writings on the philosophy of mathematics were derivative from Kolbein.

20:00 I know Kolbein and he were close friends and very late in life. I don't know about whether they actually met early on, but certainly they did. That one article in that book was also Stewart's. It's a kind of very mechanical materialist that, you know, Newton couldn't have done possible unless this, this, and this technology had been developed. It's very anti-dialectical in that way. It overlooks the incredible dialectic between science and technology. Much more complex ways than that, but that would give them the style in which Shurik would talk about, you know, about Yankee science, you know, so he would go through the different sciences. He led to a very mechanical sort of way of doing history and philosophy of science. And there were many others less well known than Shurik. Shurik was originally Dutch. Yes, Shurik. I was wondering whether he had ever had any relations with Planck. Thank you for your attention. Thank you very much for your time. Well, I had seen that she worked on it, but I have to admit, I mean, it's probably a better book than the Tarski book, in a sense, but it's written the same, so it's slightly gushing.

22:30 Do you know what I mean? I gave a talk at Tufts University. I think that is. I don't think one is going to be able to look at the books, but I mean, The reason why we say it's there is that instead they were looking for really ghastly, exotic models of it. I mean, Hellmuth's toyed with it too. Hermann Baas, apparently, toyed with it. It's a monadic version. Yeah, that's right. So, that didn't work, right? There's a fundamental mismatch between both of those. The conceptions of first-order logic, because of the way in which they use the infinite set of variables, as I pointed out in my Siena talk, is that basically it's the category of finite sets that plays a role, not a single infinite set. They had to then impose, on top of the algebra, this extra conditional, totally non-equational, that the things were a finite support.

25:00 The odd thing is I meet people, I met somebody in Slovakia a long time ago, Slyndri Galbige, where he said they were clear. One couldn't understand categories, one couldn't understand categories. Slyndri Galbige said that because he said... Well, Piers actually just got in his car and he's about to drive on somewhere. Sorry, we were looking for you. Are you ready to come to eat now, or did you need to go and get something first? No, no, no. I'm sorry. Oh, did you need to, did you just want to get 40 wins? No, no, no, I just came to check. I'm sorry, didn't mean to disturb you. Yes, I could see that something strange was going on in the street. Okay, well, we'll wait until after the break. Thank you very much for your time, and I hope to see you again soon. I just want my family, finally I will have to be one Tuesday at noon. At noon? Okay. I mean obviously we appreciate your family has to come to the studio. I call my daughter and finally, I mean I made a deal with her, I mean, of course, so I have to do it. I completely understand your family, especially when she's long gone. Can you tell me his name? I'll tell you why I ask, because I have a, it's a slightly involved story. There is a friend of mine who is organising a conference in Sweden next month, who happened to speak to me about his father, who is the director of a French speaking medical institute in Hanoi, and I'm just wondering what he's saying.

27:30 It's a new thing. This is also a new thing. What is his name? No, it's not. Oh, no, he's a Vietnamese, this man. Oh, no, the man I'm speaking about is French. And so what happened, the Vietnamese head of the Institute Pasteur, and then I made a friendship with him, and while I'm considering, I think it was typical of his reform comments. The best of whom were the best of whom were the best of whom were the best of whom were the best of whom were the best of whom were the best of whom were the best of whom were the best of whom were the best of whom were the best In a practical way, it is good enough. He was vice minister of health.

30:00 I can take it on my shoulder, I can take it on my shoulder. Anyone has to be blamed, it's me. But don't have to, please don't have to. And if you are not afraid, long hours to spend the night in rather primitive conditions, if you are not afraid, I say, are you afraid for yourself? Okay, so if you are not afraid for yourself, I'll join, I'll join the party. So, it was a little, of course. So, about halfway, he explained to me that, like in old China, there's a motto, there's nothing inside the gate of the small town, which means that people are the center of everything, and the government asked me, like Renaissance, it's in the other side of the fringes, exactly, he explained to me that.