Evening discussions — re-writing Bourbaki project based on category theory

0:00 I'm thinking of going out about 8. Okay. If you, you know, so if you're, yeah. Okay. And what images should I be forming in my lab? What places are you going? Um, well I had planned just to make sandwiches tonight, but it's too damned, uh, the bread's starting to, you know, the bread's not fresh enough, so we'll just go out and have something very light. That little place on the square, I think will do probably as good as anyone. I mean, nobody wants a big dinner after that lunch, do they? All right? Okay. Well, I don't know. There's nothing like it, you know. Well, that's only for us. You can't get these sandwiches on the square. I'm sorry, I'm struggling to find somewhere nice. Okay, we thought we'd go out about 8 or so. About 8, about 8, just to give people a chance to get a little bit of rest. And then tomorrow, if we can start a little, well, a little earlier, 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. Thank you for watching. Thank you for your attention. Well, absolutely. But I think if we can try and concentrate on algebra and geometry more widely tomorrow, and then it will... I think we've got to have one general philosophy in that day, you know, so we can do that maybe the second day after the event.

2:30 Okay. Okay. Okay. Thank you for your attention. Yeah, and, uh, you know, what I'm saying, I mean, I don't know why, but all of a sudden, you know, it's like, yeah, I'm just like, oh, good. I guess anything he was discussing in detail in general is because he wants to be an academic professor. Well, yes, exactly. It looks like that. Is there any conceptual justification for it? Well, and of course, from a Higgins view. After a reverse approximation, no. Well, we're all from a Higgins view. Of course, he can just form from a Higgins view. He's not just hand-in-somebody. Yes, of course. That's it. Yes. Go on over to the doctor. It was Gibonais' enthusiasm and power that made him think that was feasible. Right. Instead of, I mean, just, you know, psychopedic. That's pretty cool. With the SGA, of course, it's much less rigid. Yeah, yeah. Oh, it's still... But it's a half a dozen in nature. It doesn't make sense. Right. It's wrong. It's very much a collective. It doesn't have a secret handshake, you know. Yeah, yeah.

5:00 Whereas Tudor is much more the kind of judge of the court, summing up after all the council has spoken, you know. It's the kind of thing. It'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. He said, you know, this is a bit like the meetings of the Farquhars. Yeah, that's good. I'd be good. But Kevin said on the moment that he heard that John was an astronaut, he said, I should like to die now. Right, but you know what I mean. Yeah, there is a feeling around it that people who like categories must not like 45G. That's way too crude. That's way too crude. Yeah. Oh there that's it. Yeah, so is that your stuff? Oh really, of course you can have it, they're clean. Yeah, I didn't need it. Oh yeah, yes, of course they'll have it. Yeah, sure, sure, of course you can have it. This over here is, well this is dirty clothing here, but it's rubbish. We thought of my chapter one, which is never used anywhere else, so the deletion causes no problems, so delete it. 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, change things then, but then it's really hard of reorganizing fundamentally in one. Yeah. Do you think historically that if the, if this debating verdict is still weather to go for a rewrite, 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.

7:30 They would just have had to do it. No, because like you said, they put that on the program. They already knew it was important. Yeah. And in that sense, these things were just affirmations for that. The reason that they didn't do it was not because they didn't think it was accepted. We're faced with a hard choice of our priorities, and of course they have different priorities within them. It's a fascinating illustration of what you spoke of yesterday, the highest terms, and I guess these groups are always in it. Of course the Russians did, with money, go to the markets very, very early on. I guess they didn't go at all categorical level, did they? They're not interested in talking that way, especially, but they're still fond of that in homologues, qualitatively. Absolutely, yeah, yeah, yeah, I mean, mining, mining, of course, is a special case, because mining is something, basically, I guess, with a bit of a broadening, you know. And who's the Russian star in Chicago? It's been a slip in my mind, though. I mean, yeah, yeah, no, I'm sure, no, but I'm trying to think of one that doesn't make any sense. Sounding kind of, kind of, when you talk to me, you find, you know, ideas you thought were original, say they were. The logic, he had had something like it. Of course, I guess it's always a matter of modality and stuff. I told him, I said, I know he's a bit dumb, but he had tried it. Because Lange had also tried this a bit later to invent non-standard finite fields. Lange thought, I mean, Lange occasionally doubted him. Serious modality, he didn't know he was doing it. And so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on and so on

10:00 I think to some extent it's a bit like Sarah. I asked him, you know, in the seminar at Cartago, were people influenced by the category theories? He said, no, absolutely nobody listened to the category theories. Now, evidently, that means he doesn't count Eiland-Berg, but probably didn't count Maclean as a category. 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 much that way, too. In fact, he has all these methods, but he doesn't like to think of himself as making methods. He likes to think he's solving problems. Yeah, they probably didn't want to become a follow of any of this guy. They were coming across this Kolman character, about science at the crossroads, which was very influential for them. They'd say, Marx was lost for his science. So, there was one talk by this Kolman, and somehow that became the only text that both East and West ever needed.

12:30 And so on and on and on and on and on and on and on and on and on and on and on and on and Lysenko and two things, Marr, which 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 thing. Stalin was probably largely occupied with defeating the Nazis, and these characters grew up in little empires. The field of philosophy and mathematics was talked about in various ways, so I'm just conjecturing now what you're saying. An athletician is spelled with a H or an S. He was actually a Czech citizen. I'd certainly heard of him. There's a long article in Historia Mathematica about him a few months ago. I give him lots of facts, of course calling him a Stalinist, which would be the highest investigation. Yeah, well that's just shallow, just because he was right in 1931 and called himself a Marxist, there you 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 Marxist literary theorists in England,

15:00 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. Martin Stewart, he put all his writings on the philosophy of mathematics, the derivative from Coman. I know Coman and he were close friends and have been very late in life. I don't know about whether they actually... That one article in that book was also Stewart's source. It's a kind of very mechanical materialist. Newton couldn't have done possible unless this, this, and this technology had been developed. It's very anti-dialectical in that way. It's an incredible dialectic between science and technology. Yes, but in a much more complex way than that, but that would give them the style in which Sturek would talk about, you know, about Yankee science, you know, so he would go through the different sciences. It led to a very mechanical sort of way of doing history and philosophy of science. And there were many others less well-known than Sturek. Sturek was originally Dutch. Yes, I was wondering whether he had ever had any relations with Van Heijenoort. With Van Heijenoort, Trost's secretary, the guy who was there for the history of Lauderdale. I don't know. He was a communist party member. Of course Van Heijenoort was... Oh, was Struik, of course. Yeah. So he wouldn't have obviously... He'd have a reason not to. Yeah, he'd have a reason not to then. Yeah. Well, I knew he was a Marxist, but I wasn't sure.

17:30 You know, on the Carsey period he was suspended from his teaching position, which was regarded as... Parable, but the fact is, he was, the leave was paid, which he could exploit to go around the country handling this particular problem of propaganda, so. Well, are you speaking of Struyck here or Hiawthorpe? Struyck. Struyck. Ben Hiawthorpe. I'm sorry, I always assumed from his name that he must have been touched, because I was assuming, I'm sorry, you could read Mr. Thurkermont's book about how he actually had a stomach. Yeah, well, I had seen that she worked on it, but I have to admit, I mean, I think it's unlikely. It's probably a better book than the Tarski book, in a sense, but it's written the same sort of slightly gushing stuff. You know what I mean, we never talked about it. I think that is. I don't think it's like so.

20:00 Well, there's a fundamental mismatch between both of those and the conception of first order logic because of the way in which they use the infinite set of variables. This I pointed out in my Siena talk. They had to then impose, on top of the algebra, this extra-conditional, totally non-equational, that the things were a finite support. The odd thing is, I meet people, I met somebody in Slovakia, back in the cylindrical algebra, where he said they were clear. One couldn't understand categories. Yeah, well, Piers actually just got in his car and he needs to find out where I'm on somewhere. Is John up? Oh, 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 wings? No, no, no, I just came to check my car. I'm sorry, I didn't mean to disturb you. Yes, I could see that something strange was going on in the street, but I couldn't... Okay, well, we'll wait John up and wait. Thank you for watching. I just want my family to know that finally I will have to be one, two, three, I don't know. I mean, obviously we appreciate your family has to come to the studio.

22:30 I call my daughter and finally I made a deal with her. I completely understand. Well, I first promised your family. Can you tell me his name? I'll tell you why I asked, because I have a... 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 if 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. They reopened the French hospital. And so the Vietnamese head of the institute, and then I made a friendship with him. And while I'm considering, I think it was typical of the reform communist. The best of them were the best of them. The best of them were the best of them. The best of them were the best of them. The tragedy they failed. The tragedy they failed, communists. Well, they are communists because the regime is communist. I don't think they are. They are like communists. But they try to consider them as a liberal, a liberal arm, a liberal wing of the regime. And that's why I did not create one. You reinforced it. I reinforced it. If I gave support, weight is good enough, good enough, so he was vice minister of health at the moment, 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 hustle, please don't hustle, just go tomorrow at 7 in the morning, I will be ready, and if you are not afraid of driving in very rough roads, long hours,

25:00 If you want 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 jump, I jump the path. So, while it was a little, of course, long, painful, of course, it is right under the Laotian border. I expected that, okay. So, but then we don't. I was halfway. Well, so, we went. His goal was to visit some, I mean, he was visiting, you know. There was some plans to create a new regional hospital, something like that, under the control of the Ministry of Health. He explained to me that, like in old China, there is a motto, there is nothing inside the gate of the small town. Which means that people are the central community. And the government has to make the decision. Like Renaissance, it's a little bit like that. He explained to me the principle.