Post-session Discussions

0:00 We'd like to put our little brick in the wall to help that, particularly by creating this resource, and of course the aim is to eventually put it online. We've been recording stuff... ... since 1973, so 34, 35 years now, and there are 26,000 recordings in the archive, including recordings of Gerard, Deaver, Wigner, and the really important and interesting philosophy of math recordings, which you may date from about 1889, when I came in and told Charlie, we are a bit interested in... ...as well, particularly when it's stuff that is really basic to the conceptual organization of math. But we've been recording quite a lot of interviews with just secure mathematicians. He's a vegetarian, and he's a non-vegetarian. I know who he is, yeah. I've never met him, but I know who he is. I must get in touch with him. Do you think he'd be interested? Because we, you know, we're always getting in touch with him. A bit like Roger Penrose by the sound of it, you know. I remember I called him over the morning and he said, well, I didn't have a legal career. Uh-huh. Got it. Where is he based? Oh, in SUNY, right, right. Which one? But SUNY where? Oh, in SUNY Book, right. Because I know SUNY Book very well because of Bill, of course, but I don't know SUNY and SUNY Book. He might be interested, if I sent him a kind of general, you know... Well, right now, as I say, we have 26,000 students, about one-third math, about one-third philosophy, about one-third philosophy, and most of the math, particularly. That's stuff which has brought the philosophy of math into it. And, for instance, we had a meeting in our archive in New Jersey two and a half years ago, and Bill Moore came together with Colin and three or four other people, and we spent two weeks chewing fat, where we spent a year preparing the discussion on exactly what would be the topic of the lecture. But that was a magic exercise.

2:30 And we've recorded all of the seminar for the last ten years or so and quite a lot of other material, not only in France, a lot of stuff. We are trying to get the financial support of us to digitize the whole thing. And get it online so that anybody can just log on and tune in and go to sleep. And that's the motive. But whether it will ever happen, I don't know. Because the funding needed to even using state-of-the-art CEDA, which is a computer-edited digital environment. Which can actually be compared to the other transcripts that we have available on the internet, with the digital time to describe the control set, to record that much material, which of course you couldn't in practice. It's going to be a long three or four year project, we need at least a full four year project, plus the technology, so you're looking at it. We'll have a gamma, I don't know, but in the meantime I just do as much as I can on my own. It's a recording of the conference now. Yeah, go ahead, I was going to suggest my name. But I'd be very interested in, well obviously this won't come up, but I'd love to talk to Jeremy Sullivan, because we've been trying to get links with other archives to merge, especially to see whether they'd be interested in agreeing to have their stuff written on the paper.

5:00 Did you see the Killing Fields? The what? The movie The Killing Fields. I read this last time. Mm-hmm. Well, no. What did it weigh for the movie? Um, I don't know what you're talking about. I read it myself. She's the main collaborator at the Berman Institute. I've got her name now, but the woman at the IHS that he's co-authored a number of papers with, has written a rather good introduction to mathematics geometry. And that was why he did the interview in Iran. I think it was a very influential time. They had a number of people working on categorical mathematics, He wasn't there, but I mean, he was, in fact, in Tehran at the same time, at a separate conference. So, you know, I think it was quite interesting. There's actually quite a lot of people who are very serious about mathematics, and they're very professional. Some absolutely colossal hidden treasures. There is a lot of serious mathematical activity going on there. Obviously they feel very isolated and they're mostly running scared of the lunatic regime. But running even more scared of the totally lunatic regime in Washington. So, you know, I wouldn't be in their shoes for the world. But I know some of them. In fact, one of them is married to a very good friend of mine, Bob Cooker, the University of Oxford. He's a scientist, but he did a re-tread. That's right. He did a lot of operational quantum logic, but he's now learned category theory.

7:30 ...quantum logic, as I say, which I think is an interesting term. His magic wife is a very good one. Yeah. Gosh, I'm trying to think of her first name. She's very good. She's a very pretty girl. Exactly. She's stunning, actually. Mernouche... Hang on. Mernouche... Mernouche Cotletardé. Thank you very much. And she's a mathematician. She actually has a position at the University of Southampton. So it's very interesting talking to her and talking to some of these other guys. God knows what will happen. So now, before I try to get them all together... Yeah, please. What's the wisdom here in my name? I'm trying to think. No, in that case I'm confusing with somebody else. I'm thinking I've had a similar sounding name here with the math guy. Sorry. I'm so sorry. What did he say? He said a lot of things on his web page, including things about me, which you can click if you want to Google me or find me on his web page. Thank you for watching.

10:00 Well, this is a mention of a boy who was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was, was I'd love to get to it. If you don't, I might ask you if you can record it. Sounds really interesting. We interviewed him, actually. Thank you for your attention. The point I wanted to make after Brisbane is that I remember you were saying, why not bring us up to date with what you all are doing right now? Yeah, well, it depends on what you're doing. But I was, I come back to, uh, low base, and, uh, the reason, the writer is going to be, I mean, it's easy for him to say that logic is not based on mathematics or mathematics.

12:30 Yes, in one sense, one dimension of foundations is about intellectual hygiene. I agree. But only one dimension. But it's not the end of it. No, I agree. I mean, the notion of foundations, for me, is one which is very much non-monolithic and has many aspects of what we call kind of variable geometry, and involves at least three quite distinct axes or dimensions, such as one is anthropological, the other is anthropological, in the other it's broadly... Logico-semantics and it might add also a kind of more internal methodological dimension as well. So at least three or four quite distinct dimensions of the notion of being a foundation. All of which, the interrelationships between which it seems to me are very entangled and need to be straightened out. So I'm very, I'm always very cheery when people talk about foundations. Neumann. No, I know Peter Neumann, who's a group theorist in Oxford, but I don't think I know Michael Neumann. I know quite a few people in Oxford. I know John Bell. Thank you for watching. Not as well, not as well as Jean-Pierre here knows. He knows him very well, but yeah, I certainly know him. But the government is thinking about him politically. Yeah, yeah, yeah, because Jim is about 85 now. That's still incredible. Absolutely incredible. I mean, he's amazing, phenomenal. I mean, you know, the last time I saw him was in Oxford about a year ago.

15:00 ...completely shining, shining examples of us all. He's gotten very interested in categorical quantum logic, not surprisingly. He comes to all these conferences that Bob Cooker and Sam Szebranski organize. Yeah, yeah, he was in fact, that's why I met him last. I did a long interview with him about four years ago, about two days of interviews with him. I'd love to talk about more. Sorry to interrupt, but this is not something I know much about at all. I would love to know a lot more about it, but was he at all influenced by Kroll? Was he at all influenced by Kroll? Kroll was this extremely interesting guy who was a lecturer, who was a... I'm talking about Raoul, I'm talking about Raoul. I was wondering whether he'd been told influenced by Kroll. Uh, a guy called Gabriel Krohn. He wrote... Krohn! Sorry, I meant to say Krohn. It's a slip of the tongue. Gabriel Krohn. You must have known about his work. I'm sorry, you'll have to give me, I've just been to a 36-hour, you know, change of time, so, shit, lag, I meant to say Krohn. Yeah. Yeah, there we are.

17:30 Yeah. Oh, you know about Kondo as well, yeah? Well, the guy who runs these conferences in Moscow, I've been attending, recording, is a big Kondo fan. Thanks a lot. So tell me, we were talking about Cron, and Raoul Bargain, and that's interesting. He has very intense knowledge of the re-duals of the world, and it was then that he was invited to a seminar in Hungary, so he organized a graduate seminar. I mean, then, to the argument between Hungarian and Hungarian theorem of violence, there's a lot to do right here, isn't there? Very impressive, yeah, I can imagine. It was very useful to be fluent in Hungarian and IEP those days, considering the number of people the Hungarian extractions were around, taking on time, and, you know... It's a long way from the idea. Exactly. There's a fact around within the picture. Cops who have married each other's sisters. Well, no, no, that was Dirac, I know, but you know... I wrote a really easy paper I picked out of all of you, but I'm sure you'll like it. I think you'll like it. I think you'll like it. I think you'll like it. I think you'll like it. I think you'll like it. I think you'll like it. I think you'll like it.

20:00 I think you'll like it. I'd love to get an interview with him, that would be great. Who, Ralph? Ralph, yeah. I'm not invited. Oh, I'm sorry, I didn't realize. I should keep up with you, thank you. Yeah. So, you know, those are my... If I read all the obituary notes all the time, I'd just be too depressing. So, his daughter is... Oh, right. So probably the least known in my life. Thank you for watching. When I was in London, I was in one of the great colleges. I was probably in the next to the general, yeah. It's like it's a lot of people in London. Sure, say that. I didn't give any of that advice to your mom. Yeah, yeah, obviously. So what was the story? I did that several times. I lived there for about a year. Oh, not very. You mean Hilbert in regard as rigorous.

22:30 ...at that point in 1923. Well, I mean, they have several stationary things. Well, I knew that. I mean, I've read the standards you've got in history of algebraic homology. All I'm saying is that at the point that I was writing the paper in 1923, Flowers obviously created the major theorem in... Well, all I'm saying is that there is only one way to reduce the power of the algebraic homology. That's not, okay, that's not, that's not where it's coming from, okay. Oh, shut up, you tell me where it is coming from, I'm sorry. Yeah, well, I got back all those papers. You made lots of mistakes. You're a great, great man. But the other half. Well, I tell you what, they're half wrong, but they're riddled with gaps. Actually, I'm going in a week, and I'm going to talk to some of my relatives, and I'm going to visit a colleague from the UK, and he was there till I came here, and he was there till I came here, and he was there till I came here, and he was there till I came here. I didn't know that. I didn't know that. Very interesting, yeah. Yeah, I can imagine.

25:00 When did Weil actually go to Princeton now? Ah, 1933. Ah, so he wasn't... Oh, I knew he was a director at that time. I realized that was the reason. So when was he in Zurich? Oh, that's right. So he was with EPR before he went to Göttingen. That's what I thought. Yes, yes. Okay, no, I had got it right. You know, so I've got to start a parallel story. You know, Kershaw, who... Of course. But on the other hand, the creator of such a fantastic concept, incredible, the growth peak of the 1920s, I mean, Kovacan is only human, we're not going to break him. We want other people to have quantum mechanics as well. I'm interested in the differential of things like the polarity level. I would have loved to read that, but morally, it's not very interesting. Stokes' theorem was something he got a version of there. Volterra had a version in 1889. Oh, I'd love to know more about that. You must talk a bit about Volterra, because he's great. He's very interesting. I'd love to... Thank you for watching. Thank you for watching. Thank you for watching.

27:30 Thank you for watching. And so, Rob, who works on the general form of Stokes' Theorem, to establish this idea, he goes down to L.A. Carthage, and he writes a letter to him, and he writes a letter to him, and he writes a letter to him. Why is the real name of Bakers-McCartan? This is mathematics. Which kept you on the phone. Yes, exactly. But the interesting thing is that, who was it you said to him? He's actually much cleverer than people. I'm so confused. I don't think so. I mean, I don't know. For one thing, there's a tape of him making shows on YouTube. Well, despite anything you would imagine, he was absolutely dead, but... Right, exactly. Well, I have to say very quickly, there was an absolutely fascinating conference. Russia was getting a lot of attention. You don't get there, I'm sorry. And we had a wonderful conversation. Well, we've got an election. Sure, and it's what's happened since. The irony is, I think you may realize, because I've got a theory that... Einstein. Well, prove is too strong. We're not going to say prove. But when Cartan said of the Durant theorem that it's all true, I suspect what he had in mind was the contraction of the contours of the torus when you do surgery on it. Einstein, in 1917, published a paper which contains the Duran theorem. It's just absolutely clear, contains the Duran theorem. Absolutely, the Duran theorem is in there. And it was a paper which is really well known.

30:00 I think he was really out of his head when he was talking about quantum mechanics. I mean, he really makes a difference. Although, actually, you know, he did with advice. That's his advice, too. But, you know, he's done a lot of... Purely topological considerations, in terms of the 1970s and the 1970s, the job was basically using these sheer incredibilities and conditions, not just for the time, but the way if you did horizontal and, you know, surgery and similar kind of contra-integration, you'd have... All of these surfaces, you have an obstruction of the contraction of the constant, and therefore two invariants, which in fact is simply as fabulous as the famous Adirondack. This thing, you let, let the go, do it, and didn't, you know, you didn't do it. And so there is a whole history of how Kamyonov, a professor, would have started a lab. Well, I think, to me, this is... You would have thought he was a mathematician. He was a mathematician. Well, he knew what he was doing. So, when he was a physicist, he knew what he was doing. We invented a lab somehow. That's all. Yeah, exactly. But as I say, the wrong cohomology is there in Einstein's treatment of the fourth capital theory. I'm sure it's there implicitly, but it's sort of stuck to the betting numbers now in the Maxwell theory. This is really interesting. Thank you very much for your time, and I look forward to seeing you again soon.

32:30 Well, I mean, if we sign in, we're messing it up. I wish I knew more about this. I mean, you know. I mean, we had a really good talk about Ritz and Hilbert in, uh, we had really heard a good talk about Ritz and Hilbert in the, um... What, what billions of dollars did you not in, uh, Ritz win? Well, I wonder if Ritz won an award or not. R-I-T-Z. Did I ever say R-I-T-Z or R-I-T-Z? Uh, I, I'm sorry, I'm sorry. Yes. Yes. Oh, I thought you said Ritz. No, I said Ritz. I, I was trying to say Ritz. I was trying, trying hard to listen to Colin's conversation out in our area while I was listening to you at the same time. He hasn't said anything, but there's been nothing that he doesn't believe. Well, they voted to cut off funds for Iraq. Okay, and they may or may not get that through. Well, this is the dull problem that, although the Republicans are much worse than the Democrats, the Democrats are much better than the Republicans. We could talk about this more and more. I read a very interesting article about Hilbert and Ritz in Paris about three or four months ago, had lots of questions I wanted to ask, and asked about very, very, very, very, very, very, very, very, very, very, And as I'm trying to use the region, the book is used a lot on linear functions. There's quite a man, and he guarantees it. He ends up with the liberal republic in their hands, and you guys need to have him minimize the secrets. That was an exact truth. Once we're across the ocean, we haven't even had a computer. We have to solve parts of the equation.

35:00 They actually computed these things. And that's all the finite element. I have come across this, and they've come to the conclusion that it seems to be an engineering event. Yeah. So what happens is that when you talk about the Republicans, people are trying to, if the Conservatives want a low-government opinion, this is not one of them. But the Conservatives want a low-government opinion, which is not one of them. The word credit is appropriate here, but yes, I'd love some actually. Certainly, but put it this way, the Israeli intelligence services give them credit for it, which is why they'll never speak to the Bush White House again. One of the unwritten aspects of this saga is the length the Israelis went to save Saddam Hussein's neck. They wanted him to avoid the war? Obviously. Because they're highly intelligent, they're not bloody fools, and they realized it was going to lead exactly to the debacle that it has led to, to a massive shift in power structure in the Middle East, which was extremely unfavorable to them, and to probably to a weakening of American will in other areas, which was also going to present them with very serious problems. It's perfectly obvious that they spent There were a great deal in the way of their political assets to head off the neocons, who they knew were idiots. I don't know anything about Israel, but of course, when your father famously didn't want to go after Saddam, Yeah, well, and from the point of, from the narrow State Department view of these things, he got it right. It would massively move things massively in favor of Iran, yeah. No, the interesting thing is you can accuse the neocons of a perverted kind of idealism, I mean, they don't seem to be very good at realpolitik, but then you can accuse Himmler of a perverted kind of idealism. He really had the ideal of ridding the world of the Jewish race and what have you.

37:30 Well, I don't think the neocons want to rid the world of anybody. Oh, really? I have to say, that's really... Do you think they want to exterminate all people? No, no, no. I grant you they don't do that. They don't think in those categories. I give them credit for that. They probably would like to exterminate poor people if they had the chance. No, I think they'd like to feed the enemy. They'd actually like to go away so they couldn't actually be in view and, you know, present this disgusting spectacle of getting the noses of the rich. But apart from that, yeah, I agree, they're not actually in the business. Well, I think they were very unrealistic. You'd say that again. ...that everybody wanted to be like us, and that we wanted to help them. And, you know, I mean, it's helpless, and I advocate it. I know when, um, Bush came to K-State... The thing that really made me grit my teeth first was he said, oh, everyone in the world wants to be free. Well, what's your definition of free? Well, other people don't have a definition. I mean, maybe they think it's immoral or evil. A lot of people think freedom is wrong. I mean, a lot of people in the West. And with this terrific uphill battle and this democracy season in the West, because a lot of people thought it was wrong. I mean, so it's just hopeless. And no, I just think we'll just walk in and everybody will... Yeah, if they really believe that. I never believe they did actually believe that. I think they were far more cynical. I think they were far more cynical than that. I think that was just rhetoric for the know-nothings. It seems clear to me that she doesn't like lying. She would really rather not have had to lie to Carl. Now, of course, she has to, and she did, because she wished she didn't have to lie. In the same way as Colin Powell, obviously, wished he didn't have to lie to the United Nations. I mean, I've got a trail of horrible people in the world. I have them not very far out. I mean, I live in Kansas, and we've got the Christian life. And they really, I mean, those are fascists. I don't use the word like. I use it to remark. Those are real, un-forgotten things to let you know.

40:00 I'm going to start, he's going to cut his teeth as an engineer, like so many of them, but he still is an engineer, sorry. But I'm organizing a conference in Montreal called the Celebration of the Mathematical There's plenty of stories of Watt not being worthy of being the math department coach to an engineer, but yet he could teach calculus to returning veterans on campus. ...which didn't make my jaw drop because of the algebra part, all right. Fascinating. Thanks, that's a really interesting talk, really enjoyed it. Yeah, you too, really enjoyed it. Well, I'm glad that I got... I'm glad that I avoided the political crap that was going on across the table from me. Well, that probably happened in Princeton. But Hermann Weill is the person who brought him to Princeton in a way. Yeah, but actually the one who taught him was Ernst Specker. He was fond of telling that. I was one of the first people to buy Raoul's collected works. I was on Ann Costner's board special. Yeah, I know when I bought selected works, I realized, I read a good fraction of the papers, I was really relieved, you know, poor volumes, but yeah. So we're both Moodle engineers going back. Oh, yeah. I did a very weird thesis, so I ended up, uh, the engineers thought it was weird. I was implicated in France, but, um, I did a postdoc in it, so 22 years ago, so I had the opportunity to go in on all RELWIS courses, that's for the most part here, fingers, teaching a course on string theory.

42:30 Oh, I just had a wonderful time, learned so much, and then I went back to engineering. I don't know why. Because you're a really honest man, that's why. No, I really felt that if I was going to teach, I could do it in the field of my undergrad. I must be the greatest engineering teacher. I started in engineering myself. Oh great, how long ago? So are you familiar with Fox, Duffin, Simpsons, and all that stuff? No, I didn't get that far. Okay. I was more practical with mathematics. My biggest achievement was to redesign Indiana University's Cyclotron. Oh, wow. In order to be presented to the state police. Oh, so I thought it was nice. I'm applying R-S-3 manifold topologies to problems involving force-free magnetic fields, so how do you build a big magnetic field without a lot of R-N-space, G-S-R-3? And I'll continue to talk about that. Fantastic! Nice to have talked to you. Yeah, see you tomorrow. A really interesting guy, I had a wonderful conversation with him, really sensible, lots of interesting, he knows a great deal of math, clearly, knows Jim Lambeck, very, very interesting character, he really wants to learn, knows what he needs to know, really keen to talk to you, and it was a great blessing because otherwise I would have lost it completely with this. This guy with the Ukraine, he's just coming up with such, I would have lost it completely, he was just coming up with such unbelievable crap, you know, political crap the whole evening. It's bad enough having to be told that, you know, how much the Egyptians would, you know, love to have King Farouk back and how happy they'd be if only they were a monarchy again, but oh my god, he's defending, oh, you know. And you'll realize the surge is working, of course. Bush and Cheney have got it right in Iraq, you know, we're right on top of those terrorist bastards and, you know, just one more push and we'll have, whoo! I just didn't know how to keep my, you know, you talk about people biting their tongue. I mean, I'm afraid I left Colin to soak it all up.

45:00 Well, there's a generally reactionary line there, but there's also the whole maximum imprecision that I was talking about. Oh, God, yes, I mean, I realized that. Oh, God, I mean, when we were talking after lunch, every time I heard something, I'd get another soundbite. Oh, yes, every time. It was just the most incredible. But it's obvious that at the Planck scale, you know, if I hear the words, you know, what's obvious about, it's obvious that time and space are discrete at the Planck scale. I think I've ever heard somebody say that one more time without having even given any thought to what. That's why they believe it, just because it's the soundbite that they've had. I think I'm going to puke halfway, really. It is abstract. He says it's the law of quantum principle and principle of quantum mechanics. As far as I know, this is the law. Yes, it doesn't have any clear principle. People have speculated. I mean, there is a theory of quantum mechanics. Oh, sure, of course there is. People have speculated for a century about this. Yeah. Sure. But nobody has come up with an experimental or theoretical justification. I mean, I thought at first when he was coming up with that business about the thought experiment with the, you know, the circular laser, that there might be something in that. Yeah. I mean, I was taking him seriously then. Yeah, I was too for a moment. Yeah. And there may be something in it, but as I say, okay, I mean, you can be a good mathematical thinker and still be an extreme reactionary. One has to face that fact. But, uh, anyway... I'll let the... No, I don't think it is my strongest intuition that this is not the case of that. No, no. But if I had to listen to any more of this crap about... And of course, you know, the capitalist system is absolutely wonderful. There's never been any... Oh, you know, there was never any genocide of the Native American peoples. It's all lies about the Cherokees and the Sioux and the wounded. No, no, it was all just... First of all, there hardly was a Native American population. I didn't even guess that it was that much. There never was a Native American population, because there were only 100 gatherers. There was only, like, about one person a hundred square miles. And, oh, there might have been like 15 people killed in an Indian war, but they almost all died of smallpox because they were exposed to these diseases to which they didn't have any immunity. Not with any deliberate attempt, of course. I pointed out here that Amherst, you know, the British general, had deliberately gave smallpox-impregnated blankets to the Indians in order to wipe them out.

47:30 One of the best-known early examples of, you know, colonialists using germ warfare to exterminate. But he just denied that. He said, that's got to be nonsense. Nobody knew about the germ theory of disease in the 18th century, so that's got to be a lie. Excuse me, they may not have known of the germ theory of disease, but they certainly had enough empirical knowledge to know what happened if you rubbed blankets against smallpox stores and then gave them to people, you know, for their children to sleep in. I mean, this is just... I have no idea. Because John is a very fine man and a very sensible guy. I think it's all at one remove. He's read some of his papers, been impressed for what reason, I don't know, with some of his ideas about quantum gravity, but I think he didn't know what he was like. Anyway, one has to put up with these things. Well, now we know. Thanks for telling me. I don't have to endure the investigation for myself. Yeah, well, Colin will. Colin will confirm, because he's been soaking up most of it. But you were having a very interesting conversation with Colin, I think, about Eilenberg. Did I pick up something? Well, I heard about his... about Ralph Kramer. He thinks Ralph Kramer has faith in him. Well, well, that's my impression of him too. Yeah, he, I agree that the rhetoric about, you know, the category theory illustrates the virtues of pragmatism in the philosophy of mathematics is absolutely poisonous rubbish, but, and I was very surprised actually when I read his book to find him coming out with that, because I had been impressed with him as a pretty careful scholar. He's no great... You know, he's never going to prove any theorems, he's never going to be a mathematician, but nor am I. It doesn't mean he can't do really useful work in the history, he can't be a serious historian of math, he can't be a serious person who thinks seriously, you know, a reflection about the history and philosophy of math, and he can't do good work on category theory. It might be, it would be better if better people were doing it, but still he struck me as a serious person. I was quite taken aback when I read his book. I always do it because we're meeting and then I'll see it. Yeah, yeah. Because apart from anything, the book is really just a kind of laundry list of references.

50:00 It doesn't seem to have tied, it doesn't seem to have pulled together the various themes. Ah, you have this dispersion, you see, because this is one kind of library work, right? You have a list of references. Yeah, yeah. Yeah, but it's, you know... You can have a big list without actually... ...saying anything in the way of a serious thesis. Yeah, right. Exactly, exactly. I see, that's interesting. Well, that was my impression of it. You used that impression. Yeah, yeah. But I should go back and re-read it, because I think... But what was it specifically in connection with... Well, just the fact that he obviously doesn't say anything like enough about Eilenberg. Well, you know, you think a lot. I know. This is why it's so important to record things. It's so important to record things and get them done. Mentioning which, do please let me have a copy of this interview, and do you have a means... Oh no, you were going to give me the disc to copy, weren't you? Yeah, the audio from Algarve, yes. Could you do that? Sure. Because I should be able to copy that tomorrow. Actually, that young man, Sean Westmoreland, Crane's student, who seems to be far nicer, more... All together a more pleasant piece of work than Craig. It was pleasant, but he was blithering. What I would like to do is to develop a theory without any use of the continuum. I don't know what that would be, but that's what I would like to do. This is his PhD project or whatever. No, I'm sorry, I hadn't heard anything. I'd only just got a very, very superficial personal impression. No, I think the student is following the teacher here. Well, let's hope he'll rebel against it and start to have some serious ideas before long. If he's capable of having them. I'm pretty sure he is. Well, as I say, I haven't had a chance to talk to him about math or philosophy or anything serious, to be honest, until now. But I do know that he has got a CD burner. Well, he's got one. Yeah, that's my point. I mean, whatever his fault, he does have a CD burner, so I could get it done tomorrow morning. My computer has a CD burner, and I'm not sure how to take the information from the audio disk that I have into the computer, and then...

52:30 I know, I have the same problem. Put it back. Don't do this. You don't know how to do that. It's called Anno Domini. It's to do with our age, Bill. We just have to face the fact that you don't get, you don't just get that good at learning to master new technology or you'll hit a certain age. I worry about these steps. Oftentimes, they actually, if you start, then they will guide you through the steps. Yeah, yeah. But not always. Well, I have done it on this. I mean, I would know how to do it on my own computer at home on that CD burner, but whether I know how to do it from your laptop, I really don't know. But give it to me. I'll give it my best shot, and if it doesn't work, I'll give it back to you tomorrow, if that's okay. Well, the interviewer just brought me one blank disc. Subtitles by the Amara.org community I promised to do them by December. I'm trying to run through the wire here. Well, fantastic integrity. Well, I don't know. I think they meant to include it in the December issue of their journal. Well, I really hope that they appreciate your, you know, your efforts. But give it to me. I should be able to... I told them about the tie reference, so I'm still using that as a, well, I think, valid excuse for not having to do all my duties yet. I suppose one could still revise it if you have any objections, by the way. Well, of course not. Of course not. It's your interview.

55:00 No, no, no, no. That's totally wrong. I view it as... it's just an opportunity to properly publicize our subject to the European Maths Union. Well, yes. But if you think it would be better if you revised it further, of course you... go ahead. Well, the beauty of having a... the beauty of having it on... That's what I say, if you have any critical ones. Yeah. Well, if you want to print off a version or just, you know, the version you've got now, and I'd be happy to... It won't be any later. Yeah. Two days from now than it is now. Well, why don't you just do a save on it in your... I presume you've got some kind of package. Can't you just do a save on the present version and then do your revisions, and then you can compare both versions, decide whether... I already sent it in. Oh. Yeah. Well... Well, there'll be two versions then, that's all the better, because it's always useful to compare texts, see where people have revised. That's one case where Cartier's analogy with the musical score, which I think was a little bit overdone in his talk, but that's one case where I think it's spot on, where there's great value in having that kind of detailed record of the various stages. ...construction of mathematics, yeah. We would have waited, hadn't we? Oh, no, we're all right. What time is it? It is... well, this is far... It's just gone nine o'clock. Not so bad, not so late. Yeah, not bad at all. Yes, it's just literally gone nine o'clock on nine o'clock. It does get dark very early, of course, at this time of the year here. Ah, here we are. But, uh... But, of course, we have a very early start tomorrow, as you know. No, do we? Well, we're supposed to be there at 8.30. Oh, no. Well, I hate to say it, but yeah, that's what's at the timetable. Well, you're not speaking till the afternoon. You're on 2 o'clock. He thinks he's talking to Cartier again. Cartier again? He's a...

57:30 Iron Man. Iron Man. I'm a stinted admiration. We were just saying, you know, you had a 12-year-old grandson at a 10-hour hike from the top of the mountain and back to somewhere else. Well, all mathematicians are good mountaineers. Yeah, well, I'm not so good anymore. Oh, you were pretty good, yeah. I remember, what was it called, in Wales? In Bangor, yes. When we went up here, you were jolly good mountaineer then, I remember it well. Well, for that walk with Peter Johnson, didn't we? Of course, it's a very serious, well, not a mountaineer, but a really serious walker. I guess that's more what I meant to say, a serious walker. Yeah. What was the name of that mountain? Yes, I remember it very well. I still can't remember. A mountain. A mountain, yes. It was probably... We were staying, well, we were in Bangor, weren't we? Well, Abba is a generic Welsh name for, actually it's for the mouth of. Abba just means mouth of, usually for a river. Like Abba Conway, Abba Islet. Abba is just the old Celtic prefix meaning the mouth of. So I think it was probably, no, mountain is actually caida in Gaelic. Yeah, yeah. I'm trying to remember it too. But Arva is the mouth of an estuary, the river, that can mean a mountain in other senses. And Kaida is the American term for mountain. And Arfon is an actual river. Arva is the mouth of... So Arvarafon, or Abraven, which remains the mouth of the river. Hang on, have we come into the right entrance? Oh, I think we have to go round... Oh, it's okay, we're just at the side entrance of the lobby, aren't we? Yeah, that's why we're having coffee up there. No, no, we're in the lobby, it's just we've come in the side entrance.

1:00:00 Well, interesting day. I really enjoyed the conversations with you and Pierre and Colin last night. Learned a lot from that. Do you want a nightcap? Yeah, I think. I think. Yeah, let's do that. I think we've earned it. Well, that's all right. Let me just... No, it looks like they're setting up here for breakfast tomorrow. We could... May I help you guys? Yeah, we were wondering if we could get a nightcap, a drink. A couple of drinks? Yeah, yeah. Maybe we should just go to the bar and drink. Is there any way we can just get a table, just for 20 minutes, or would that be possible? Sure, sure. What, this one here that you've already set? No, this one? Well, are you sure? But you've already set it up for breakfast. You're sure? Okay, that's very kind of you. Thanks a lot. What a good idea. I think I might join you in that. Yeah, it was an excellent meeting. Actually, I'll save a cognac for... Perhaps for the conference dinner. Now, I think I'll stick to the beer because I did enjoy that beer last night. I had something very light. I had the soup, the mushroom soup, and then I had a Caesar salad. No, but then I can have that any time. No, no, no. Ah, right, so that's why you felt like Cognac. I enjoyed Cognac, but alas, I do have this very severe ulceration in my esophagus. Which means that if I take a digestif, it tends to be like swallowing red-hot coal. Sometimes it's so it's in a bounce I don't feel it, but the last couple of days just, I guess, stress, worry about the meeting and things.

1:02:30 It's flared up a little bit, so I think I'll go easy on it. Yeah, they look good. They look good. Yeah, they look good. Next time you come to Dujerre, I must take you to the new restaurant run by a very nice Irish lady and her French husband, who is a very good chef indeed, and he used to be the chief chef on Brittany Ferries, and they just do the most beautiful, beautiful steaks and lamb chops, and I know the farmer that supplies them, and oh, boy, are they good. He knows how to marinate them beautifully, and... No, it's a great place. They're also very, very nice people, and a pleasure to be around. We've kept sheep this past year. We don't have any sheep around. I'm very interested in them. Yeah, let's just... Can we get to the third one? Yes, please. I'm just going to stick to the beer, and actually, could I have... Oh, it's the one on the... at the right-hand end of the bar. Maybe I should go and I... I don't know. That's right, the sort of darkish... Yeah, the first one this end. Yeah, that's the one. That's right. That's right. Yeah, that's right. Same thing I had last night. It was very good. Well, it was the best I've tried in this neck of the woods. Well, if I quoted Homer Simpson, you know, fear is God's way of telling us he loves us and wants us to be happy. I think Homer Simpson has got some quite good philosophy. It must have been exactly what Grodendieck thought when he realized he hadn't got the sub-object classifier, he hadn't seen it first. I was on the point of, I was on the point of turning around and punching him a couple of times tonight, I was so pissed off.

1:05:00 I hadn't had that guy, you know, the Russian, Belarus guy, who's really interesting, really, really interesting guy, delightful guy. On my right, talking a lot of interesting math and most of all about continuum mechanics is Maxwell, a really nice, interesting guy to talk to, not just about his own work. He's a great friend of Jim Lambeck. He's organised a conference in memory of Raoul Bott in six months' time. And of course, because he and Jim Lambeck were pretty well contemporaries, he's been... I'm talking a lot to Jim, but he was just very interesting to talk to about a whole range of subjects. Well, he has very good memories. It's a very, very interesting story. And like Bill, he, this young, well, youngish Belarusian guy, you know, who's the one who asked the question immediately after Bill in the discussion, started, you know, kicked off his career as an electrical engineer. So they had interesting notes to compare about the cyclotron and what you do there. But if I, oh no, I don't want to go there again, but... It's bad enough having to hear how, you know, how all the Egyptians would, you know, be only so happy to have King Garut back again, because, you know, Arabs being primitive people can only be happy on the monarchy. Well, that's more or less what we came up with at lunch. There's probably something in that, but it's, when it comes out of his mouth, the fact that I have a crap attitude with... I didn't invite any of them. I mean, I don't want to shift the blame, but John Stachel invited them all. I hadn't even heard of any of them until, well, I had heard of Crane, because I'd read some of his papers. I'd read about it in Crane, because it was the first text that was used for the reading text for the Categories in Physics seminar in Paris when it started a year back. They seem to be a fairly smart guy, given the mindset of the people working in quantum gravity, but, oh, oh, oh, oh, as I say, I don't want to hear any more about, oh, and the Surge, of course, is working, you know, yeah, only 23 casualties in the last month have just proved that Bush and Cheney have got it right, you know, we're, you know, we're almost there, one more heave and we'll have beaten these bastards, not just as long as I'm about to go, of course, you know, they're going to have to speak for it.

1:07:30 Because I can serve my country much better in a hedge fund than I could in a... You'll have to expect the last I've never heard of will see this show. Oh, the AMS notices again. Finally, popular culture, of course. This guy bought time by knowing about numbers. He spun panels. He predicted them, and then wrote them, and then he scraped them. So, just to go on, rewind that time just to see. Oh, there's an awful lot of buzzwords and name-dropping. Oh, did he really? Wow. I remember when I saw A Beautiful Mind, and, in fact, Peter Fry wrote in, I think it was actually on Category's list, that there was this passage in A Beautiful Mind where he not... A student or a fellow talks about Galois theory and motivic cohomology when Nash is listening to things up and sort of asks him a question. Nash's recovery begins. Yes, that's right. The discussion about Grotendieck, yeah. Wish it could have worked the other way around. Well, Grotendieck was very important. He hoped that Grotendieck would rescue him. I didn't know that. I didn't know that. Well, I was going to say, because it never occurred to me that Nash...

1:10:00 I see, because I mean, looking at what Nash did, I mean, it's not very interesting work, but in a way it doesn't seem to have much connection with Grotenbeek's program. He may have just lowered the dimension by one. Everybody knew you could do it in 2n plus 1. He showed you could do it in 2n, allowing intersections to not be there. So, he showed about real algebraic varieties. Oh, okay, so it doesn't work in algebraic. Something astonishing like every real manifold is topologically isomorphic to some component of the real algebraic. I don't even know how you begin to prove it. It's sort of like a real version of the complex analytic manifolds. Well, but this was differentiable. Differentiable manifolds are all continuously isomorphic. And that, I don't know how you would know. Yeah, complex analytic, that's another thing. But that's what the deformation is about. This was this was already when he was saying this was actually when he was recovering. Well, yeah, but this wasn't during the recovery, this was going in. Oh, this was going in, this was when he was cracking up. But in the movie, there's that conversation. That's right, that's right. Thanks, we've already eaten, thank you. Very kind of you. Yes, that's clearly, well, the very theorem they're discussing couldn't have been around in the early 50s when his madness began.

1:12:30 Not just the notice, when the notices talked about three or four, there was a moving part. The moving part? Oh, proof, definitely, yeah, proof, yeah. The moving part was terrible. Well, with pi, it's not even clear that this guy's meant to be doing any math at all, as far as this. When I watched the movie, I thought, if possible, then he's just meant to be completely crazy. Oh, to me it's serious, but it's a serious look at this guy cracking up. What, he's one of these people who wants to talk about the different expansions and additional eight million places or whatever? Yes, yes, yes, it's based on the Chernowsky. I was going to say, like these guys in New York, thank you for reminding me of the name. And with this obsession, he just sees patterns everywhere, whether it's there or not. But they're full of other things. This guy's supposed to be a math professor. He's a brother of an FBI agent. He consults with the FBI. Oh, so national security issues. Yeah. But anyway, the thing is, my God, they're not called Arabic numerals. We're not. We're going to watch these like a hawk. So by statistical analysis, we figured out what I would say. One was that you have to think that a person not only has a place where he lives, but statistically he has various crimes he's done and where he's been spotted. You figure out, this appears completely bogus. And people wrote in saying, took to the notices, aha, that's the one of the episodes that was actually true.

1:15:00 The Montreal police helping out the New Orleans police, and they did use that method. I still haven't quite understood what the method is, other than noticing that people often commute from work to home. He always invents some kind of a mathematical model that implies a big computer. Sounds like you had that one with the diagram. This way they had settled, they had defeated all the doubters. There's one example. I think it was actually based on... Nobody dared to complain again. It might be true as well. Absolutely. A shadow of truth. Yes, yes. It sounds a little bit like the Planck scale. No, it's definitely an artistry. Oh, yeah, yeah, yeah. Well, exactly, my question. Do you know about Tocci? He's actually a string theorist. In fact, he edited one of his books. I've come across him. Green. Yeah, I've come across him. Anyway, he's, together with some other people, put together a four-volume book on popularized mathematics. And my friend, Renato Vetti, has recommended it. I bet he thought that there should be something about categories and such in Martacci's work. But Martacci describes the standards, the level of exposition, as being somewhere between the Scientific American and the notices of the AMS. I should shoehorn myself into this interval. An interesting question as to which of these he actually thought as the upper and lower bound respectively these days. Actually, I was thinking... And so they have an excuse for inviting somebody else to write about prophecies and capillaries.

1:17:30 Well, you did that very nice short but up to you in Figuri. Figuri in Space and Figures, that little exposition of... It was for that journal, but I'll go if you gave me a copy of it. The Letter of Pristin. Yes. That's not one of the articles. Oh, there's a book. It's got Gödel, Russell, Tarski, and me on the cover. That's right. That's right. Cool. Cool. I think it's as cool as it was. No, but it's the account of MacLean. I'm trying to think of a title. Oh, MacLean's obituary. No, I don't think it's his obituary. I think it came out before he died. It is an obituary. Yeah, you did. Saunders, MacLean, and the MacLeans. And there was a box. Oh, there was a box with the... Within it. Yes, which was showing the point about adequate and co-adequate books. Subcategories of a category. But I thought you'd actually written something earlier called... Well, at least the Italian title of which you might have written under a different title and not approved the translation, I'm quite sure, was called Spazio e Figure. And this is definitely a lot older. This is something that I saw in the 90s. So before...

1:20:00 Well, I'm really sorry if I've forgotten the title. I thought it was about C.O.I.P. Deleuze. Yeah, yeah. Alberto gave me a copy. Oh, Alberto helped me with this. Yeah, yeah. Yes, that's right. It's a nice, very nice article. But if they'd asked for a popular exposition in that level, it would be marvelous. That would be really, really good science. I thought that was a terrific exposition. I really enjoyed that. Well, it's an experiment that would be a waste of time because I'm sure no matter how hard I tried, I wouldn't quite be able to fit myself in. No, no, no. As soon as they don't know what they mean, they... Oh, right, right, right. I see what you're saying. Yes, I think there is at least, let's try and be generous, there is an honourable, although I think an outside chance that they genuinely did not know what they were saying. Didn't mean it as a... I'm trying to think, that was for Pristem, you wrote that, whatever it's called. I should be able to remember the title of it. Apart from anything else, it helped improve my Italian a good deal by studying it. I translated it back into English, actually. You must look at my translation back into English sometimes and decide whether it's any use as English. I'm not even sure where it is now, because it must be several years. It's in the archive, but knowing it's in the archive and knowing where it is are two different things, alas. No, it's definitely there. Oh, seriously? Now, I did. I translated it back into English. It was a very short article. It was only about four pages, I recall. Or maybe five.

1:22:30 In that case, we're thinking at cross-patterns, we're talking about two different things. The article that I translated back to English was, I mean, it might have been five or six pages, but it certainly wasn't more than that. It might have been an eight-down version. Anyway, I'll dig it out and send it to you, what it's worth, certainly. It definitely had that diagram on the third or fourth page of the article. Which is very similar to the one that our, in fact I think it actually may be the diagram that Umberto reproduced in his article in the Circolo di Matematico di Palermo volume, a monograph that contains his tribute to the anterior future. I think it is actually that very diagram reproduced from the article. But anyway, I do have a translation back to you. And then I have to find somebody, I was just saying to Bill, who can turn the CD or DVD that Bill's got of his Algarve's address, plus the thing he's got on his computer of the interview, into a copy that I can burn it on a CD burner. The interview is 19 pages. I thought I did pretty well, you know, I'm talking, just thinking up explanations for all kinds of things that I can never do sitting alone, but then it turns out their audience doesn't even know what I'm talking about. And they obviously don't do what I always do when I interview you or when I speak, you know, when we have an open, you know, recording, which is always to make damn sure, like I did with Pierre today, which is always to make damn sure that there are always two recorders, at least one digital and one audio, because the first rule of these things is whatever can go wrong will.

1:25:00 I always, always have a back-up recorder running for any serious scientific meeting. Well, you know, never mind. I'm mortified they lost it too. I would like to have it in the archive. More has corresponded to the questions that they had to ask you indeed, yeah. It's a terrible work, I don't know how people think, which people they could be. Well, I hope they were driven by such a sense of guilt and annoyance of themselves at having fucked up on the recording that you would... Yeah, yeah. Well, that's the problem. It's not like they were here preaching, you know, spending months interrupted by this three-month study. Yeah, with the boiler. Trying to turn a string of quotations, however well-chosen, into a text that sounds like a real conversation, a real country. Well, I'd certainly like to read it. I really, really would like to. Well, I'd even more like to listen to the original interview. Well, I thought I had to do this because that audience is a way of driving my attention. By the way, when Pierre was talking this afternoon about Boole, particularly about the notion of a domain, which is satisfied, and the connection with Boole's ideas about operators, I was talking in mind of your remarks in the Islander's Festschrift.

1:27:30 ...about the analysis of variation in general and the structure of domains of variation in terms of lack of homomorphism between parts of the domain of variation, quantity bearing over it being the more fundamental way of analyzing the structure of the domain of variation in the case of points as being a special instance and it naturally drops out of that as a restricted case. I was wondering whether that was actually at the back of his mind in what he was saying when he was talking about... Again, you know, the slanders of Boole and Schroder, of course, were just mere algebras, so they couldn't have had really deep ideas about logical constructions and the sources of... Yeah, exactly. Pierre, but... Greger. Greger. You and I, of course, are real philosophers, and we understand how logic is about everything. Boole and Schroder, those guys there... And Dedekind. And Dedekind, yes, I forgot to include it. Boole and Dedekind, these people are mere algebras. I couldn't understand what's really going on in logic tonight. Who? Sorry? Aristotle. Aristotle? Yes, I think it's much older than Bill. No, I think it is an Aristotle. What I put to you when we were describing it, you have a soup, and then you have animals, but you also have some chosen elements.

1:30:00 So the U is just a chosen element. When you operate on it, you're really just getting such things. But, you know, I mean, the chivalry about Euler's multiplication is really just a case of composition. But even the very basic examples, the composition of homothetic supplies, is also a composition of homothetic supplies. Because whenever you have a module or something, you don't always think that, but it's all important. It's not like another one these days, you can even have non-community things like big servers out of the... This actually connects, I think connects, in the back of my mind since listening to what you were saying yesterday about this. Notice I do call it by its right name now, a list or whatever you want to describe it as, of these various theories, a list of properties of rings, of ring classifiers. Crosswords on rings, yes, yeah, rings, that's an excellent word, yes, that's where I got the idea there was some kind of diagram, anyway, his, right, exactly, anyway, you were saying in the context of the film, Mark, about the understanding of the structure of limits and so on, that classifying rings was more fundamental than the notions that are naturally expressed in terms of sub-objects.

1:32:30 You said that you would always really dislike Russell's definition of a relation. Sorry, that's just a high school reaction. Yeah. Oh, I see. But tell me what it was that you disliked about it. What you thought was really the wrong question. Of course, you're right. He told the relation, but then... And where's the domain and co-domain of the map, which they should naturally be associated with? That's real-world relations. Well, you can think of it as a star, right? Yeah, yeah, yeah. In fact, that's a better way to think of it, even if that was a phenomenon in mathematics. Instead of reasons, it means problems like talking about sexual relations. The actual sexual relations, given one, that there's a partner member A and partner B, well, I mean, this is... that kind of explanation... Yeah, yeah. ...is more, more agreeable. Even if it turns out that it's a part of a moment, not merely some subset, something in itself, which I think was the intuition, which, dare I say, was the intuition that the idealist mathematicians like Bradley had, and why they rejected Russell's theory, that all relations must be inherently external, that Bradley's about internal acceleration, not completion. I think that was, I mean, obviously they didn't have the mathematical tool to express that. Thank you for your attention.