Discussions, incl. M Wright, G Khatcherian FW Lawvere, A Kock (contd.)

0:00 Right, let's see what this sounds like using the ear socket. We'll see whether this has any effect. Just switching from high to low.

2:30 Right, we're now testing with the Sennheiser microphone with a different Sennheiser HM33 electric condenser microphone. See whether that works a bit better. A new battery inside it and see whether the Sennheiser voice activated system. And it's very late in the evening, obviously, and I'm standing on the bed from a three-walk walk there. It was already getting difficult before. You've noticed better now. There are many people who've noticed better now. Do you have a recent picture? Yes, in fact, there was an awful lot of dead wood that was recruited at that time. There were an awful lot of people, really, who... There was the great expansion under Macmillan in the late 50s and early 60s, under Macmillan and Wilson. It was overdone. Yes, it was overdone. It was unsustainable, really. And a lot of people were recruited who, I can only speak really with philosophy, but a lot of people were recruited, probably because philosophy was very much in the doldrums in England then at any case. The people who came along rather later in the generations of 65 to 68 in Oxford actually included some very able people in the AI, Michael Dummett-Douglas and Christopher Wright and others, but an awful lot of David Wood was recruited in the late 60s and early 60s. I don't know if the same was true in mathematics, I'm not qualified to speak, but the... Then the cuts came and, of course, a lot of... In fact, just when standards, certainly particularly in analytical philosophy, were rising, I mean, standards of intellectual rigor, certainly the levels of confidence demanded of anybody who was going to do work in philosophy of science certainly rose very dramatically between, say, the late 60s and the 80s. I mean, it was...

5:00 It was possible for people in the late 50s or early 60s to have papers published in philosophy and science. People who are really not competent who have passed an undergraduate physics examination, now that would be quite impossible and the standards in philosophy of physics particularly are very rigorous indeed and I'd go so far as to say that some of the best people in that field are as able as the best people coming into mainstream physics, at least as able. But of course there aren't any jobs for them, so they all go to the United States, of course that's becoming difficult as well, and the standards in the United States have also risen very high in that area. I'm thinking particularly of my friend Simon Saunders and others, as I mentioned, Michael Redhead, Paul Telemann, but of Michael... Redhead's pupils, who have done PhDs under him since he was a professor at London, very, he was at London before he was at Cambridge, I don't think any of them have got jobs in England at all, not one of them has got jobs in England, and the same, I think, is true, quite the same is true of people doing work, particularly in the intersection between mathematics and physics, which is very much, very good work. Yeah, which is on applications of category theory to problems of, interpretive problems using particles, using the simplicial categories as a setting for solving the problem of identical particles, this sort of work, which, you know, ten years before, would certainly have got somebody a job at the time that it was done. There were simply no jobs left. There's sort of shrinking patterns in other countries, though. As far as I know, almost as badly in Germany. Yes. It's curious.

7:30 For similar reasons that they over-expanded and then all the positions were full. That's right. But I think it was much more acute in Britain. At least that's my impression. I mean, in the case of British universities, there has been a complete freeze on new appointments for something like 10 years now, in those 30s. There was hardly anybody coming in. So it's a torture. I mean, we really have lost an entire generation. And at the same time, the rhetoric, I'm not sure how important this really was, but the rhetoric of government became very... Hi, good to see you. You're looking well. So are you. You're looking summary. So are you. Great spot, isn't it? Wonderful. Who's speaking first tomorrow? Well, they're booking on her. I have an easy call. I get to speak the last one. Oh! I hadn't noticed that. The last one? Yeah. What time on Saturday is that? 12.30 or something like that. I'm sorry about that. You'll be gone. No, I will not be back. You're getting your time table informed. Yes, we are. I don't have to leave until about afternoon. That's good. So how have you been? Just fine. I'm finally clear of administrative jobs at Dalhousie. How did you manage that? Well, I served my term. So now I can say, fellows, somebody else do it for a while. That's good. It was a busy time, though. Oh, how many years were you at it? Well, I was the director of math for three years. Oh, they were good. Yeah, like, whatever it was. I like the stuff in the book. Yeah. When you get back, right? Okay. Because that's everything we're talking about. Yeah, yeah. The book is a logistic name. He died a few years ago. And he worked on automata and boolean algorithms and other related things.

10:00 I happened to be one of the editors of his collective papers, which we did unusually, not by just taking all the papers and trapping them together. We got people to write commentaries. Though it was a hell of a lot of work, I think he's much more useful than just a critic. Yes, particularly it's very interesting. That's the sort of thing that only normally gets done to, you know, with people like Turing and Godel. Well, he's not at that level. He's been a little bit isolated. I must confess, I never heard of him. Well, you couldn't. You didn't work on anything that was particularly close to what you said you wanted to talk about. Well, I was rather interested in automata, as a matter of fact, and particularly in control theory in the context of some ideas in quantum logic. Connections with logic, with automata, and later with some of the Ravens, and all those ideas. There are systems of many special functions, which should be one special function. Now, tell me a little more about A.J. Eyre. Oh, I couldn't, I can't tell you very much about him. No, no, I was a Cambridge man, as I say. And when I was at Cambridge, my own supervisor in that area was Ian Hackie, who is a Canadian philosopher. And I couldn't tell you anything about Eyre except... No, I think on the whole the people, the man who holds that chair now, Michael Dummett, is a much deeper and more careful thinker, although Eyre did have the one great advantage, at least in English eyes, of writing very clean, very accessible, fluent prose. He had an excellent Olympic prose style, rather like Russell, whereas Dummix's prose style, I'm afraid, is abominable. No, his prose style is really complicated. Atiyah was sort of more fun. So, and Atiyah became a public figure. He became a television personality.

12:30 He became a knockabout firm. He doesn't sit well with... He doesn't, on the whole, sit well with his philosophy. But look, there was a time when analytic philosophy was exceedingly strong. Yes, I don't think it's... That's true. I don't think it's... Well, it's just that an awful lot of the most talented people have gone abroad now. Particularly the people working on logic and metaphysics, the intersection between the two. People working on the sort of topics that interest Dummett and his pupils, people like Neil Tennant. Well, there were one or two early deaths, too, which were very tragic early deaths, which put them on the subject of an extremely able philosopher called Gareth Evans, who was an ox who would undoubtedly have become very eminent indeed, who died very young at about 34. And there were a couple of other very early deaths, too. There was a very talented generation though that came out of Oxford between about 65 and 68 with Crispin Wright, Andrews, Neil Tennant as I say at Stirling now, I think at Princeton, and at the same time the standards of rigour of philosophy of science were also rising very rapidly. The fact that all the, what did make the standards in philosophy and science rise, the standard of technical competence required, it really started rising in the United States first, I think because, possibly because of too many PhDs in physics and mathematics who have been graduating. There weren't enough jobs for them in the early 60s. Some of them started going into the transfer branch and started producing work at a wholly different level of rigor. Hmm, in that case the explanation is wrong, but it was noticeable if you look at the literature that the standards of rigor rose in the early 70s, well certainly by the late 60s and certainly by the early 70s in the United States, very dramatically, and they followed a few years later, I mean perhaps no more than five years later in England, to rise at the same time. Michael Redhead and the school we discovered at Chelsea had a lot to do with that.

15:00 Mojhi Makhova, who's a magician that you've come across, he and John Bell were very active in that department and John Bell has been interested in. This is John Bell, the logician, not the physicist. I know John Bell, the logician. Yes, he's at Toronto. He's a very good friend of mine at Sears and Jerry's. He was at London, but unfortunately, alas, he's so isolated. Because of the cuts, apart from Wilfred Hodges, he was the only logician in London, at the University of London. He was particularly isolated in that department at the London School of Economics. In fact, in seven years, I think he only had one PhD, and he felt that his subject wasn't valued, partly because of the dominance of the analysts in that department and the sort of people at Imperial who regard logic as a deeper subject. And in fact, there were attempts made to block his... In fact, there was an attempt made to block his being given a chair because the people of Imperial didn't want to see a chair in Logic. In the end, they created a readership for him, especially, because they weren't prepared to give him a chair. And that was because of the low esteem in which, unfortunately, Logic was held in. In London, which stems partly from the attitude in Cambridge, and he felt that he wasn't doing any good work there. He was publishing a lot of interesting papers on the borderline between mathematics, philosophy and mathematics. Well, he published a paper on infinitesimals. Speakers include synthetic differential geometry and a paper, a sort of semi-historical paper, about the relationship between the category of sets as a model of the toposaxons and the category of spaces of SDG and the fact that you recover the axis of the category of sets by imposing the... Condition of decidability of sub-objects, wider, weaker or stronger form of decidability of sub-objects, and suggesting that this allows you to see Cantor and Dedekind essentially did with how the historical development of the notion of function and mapping throughout the 19th century culminated in set theory, but looking back from the perspective provided by topos theory one could actually see this as

17:30 Having a geometrical side to it, as well as the, let us say, it was driven not only by the conceptual developments, but the standards. We've got a history of mathematics provided an account of in Cantor, but also by geometrical insights, which have been rather neglected. And he published a paper on that. He also published a paper on infinitesimals, which I like very much. But these were both actually in Philosophy of Science journals, these were in Synthase. And also a number of expository papers on... Oh, and a couple of papers on quantum logic, on... I'm trying to remember... There's a paper called OrthoFrames Attributes and Forcing, which is really the area that Gary is also interested in, taking the models for an ortho and showing that the condition that actually allows you to recover the Commentation relations in quantum physics is the condition that the covering, the covering of the coverings... The two types of coverings do not necessarily localize, sorry, the coverings don't localize, but the covering of a covering is not necessarily itself a covering, and therefore the second Grosvenor-Bakshi condition breaks down. I mean, I don't say it's particularly deep inside, but it connects to...

20:00 I don't think anybody had pointed out in the context of quantum logic the significance of this and he was trying to, he was working on what he called these ortho-logics or ortho-frames which were related to the forcing positions in conventional model theory and trying to do work. Model theory of quantum logic and see whether it might give one a key as to how to do quantum set theory if there is such a thing, inverted commas. Which is also an area which people who were interested in quantum logic and in quantum theory from a foundational viewpoint and who knew a little bit of category theory were also interested in at that time because you have this peculiar, you know, you appear to be in a category where there weren't necessarily equalizers and co-equalizers of pairs of maps and was there some intuitive insight? As to why this was so, in terms of the fact that objects don't retain their identity in interaction and stuff, there was a man in... There are a couple of Canadians, Hooker and Holsworth, who come to the survey paper, and Holsworth particularly tried for about five years to get, to find the axioms for what he called a quantum topos. It didn't really lead anywhere. It didn't lead anywhere. It might have done. I just came here from L.C.G. although people are doing things that you wouldn't do. At least half of them are doing large partners. I was on the plane with a guy. Sorry, I get mad if I come and sit here all day. Well, I mean, just take a set, actually, and look at the lattice and equivalent to some set. It would be nice if we could characterize these things, you know, in a categorical fashion.

22:30 If you dig around in old-fashioned lattice theory, what do you find characterizing? Okay, the relation between the partial order and the equivalence relation between the partial order and this is actually not clear. Sure, I mean, arbitrary intersection of equivalence relations is the end of equivalence relations. I think it's a good question because to know this would be sort of to know the jewel of our time, but moreover... There are some old questions in number theory. There are things called the Bell numbers, which look a bit ad hoc when you study some number theory or combinatorial part of it. But I think the right categorical structure of the lattice would be to know that everything is a natural state. It's hard to know what to look for. Have you started off with the finite sense? Then you might identify certain ones. How do we get on to the subject of equivalence relations on a set? I mean the lattice of equivalence relations on a set. Sorry, I just threw it out. What I want to get is a good categorical framework.

25:00 Recently I studied completely distributed mathematics, but constructively distributed mathematics, and this doesn't characterize our study, but it's fairly easy to characterize our study, starting with this nice bunch of mice. So, constructive complete distributivity is given by a string of adjoins. And as I say, that's a nice place to start to characterize the power system, or other nice ladders. The lattice of equivalence relations on a satellite is dual to the power system. It would be nice if one could get sort of a building basic structure of that order preserved in there. Sorry, I've taken your, I'm sorry, I took your seat. Well, I guess what triggered this is you mentioned modularity. You said also modularity, that's right. Well, that's right. That's why the society lacks it and the idea of modularity. I mean, these things are... Mathematics and equivalence relations, they're not distributive, they're not even modular. They have something called semi-modularity for a lattice. That's a word that you gave to the world, isn't it? I read somewhere that you introduced the concept, in fact.

27:30 I no longer remember. I did have to do with things, that's all. Sure you did. You know, of course, the famous anecdote about Hilbert going off to Von Neumann. Oh, yes, yes, yes. There's an anecdote about something, something in my scenario, whatever it was. There was once a puncher in my house, which I lectured on. That was not part of the road. It nevertheless had dimensions. I don't think I called it something like that. Before I was in the audience, I'd announced that there was no such thing, so there was a little controversy at the end of which we conceded that I would write it. Are you writing any other books? Can we look forward? We'll look forward. I have very vague ideas about how I'm going to do it. So there you go. It's smoothed that much. You were saying, though, you were just in the middle of making the point about the dual of the maths of equivalence classes. The context in which the remark about semi-modularity came up. I would like to try to get a categorical description of a class of lattices which contains the lattices of equivalence relations. Lattices of what? Lattices of equivalence relations, I would say. Because I think these things code up a lot of combinatorial and number theoretic problems. The nth bell number is the number of equivalence relations on an n-element set.

30:00 You know, you find all sorts of fascinating things in number theory books about these, but there's no coherent theory to tie it all together. And when I look at lattice theory books and see characterizations of lattices of equivalence relations, I can't at this point get my teeth into it categorically. They don't know about that one. It wasn't known then, was it? Oh, it wasn't known then. But even now they don't know. Oh, the lattice theory. The lattice, no. Well, we have to change that, don't we? I don't know how to change it. So the grand numbers are the numbers of the key students. I'm done. You mean they just won't listen to us? Well, I recently looked at the first writing of this book by Anthony McNulty and somebody else. Lattice, Juno, Rasmus, and Kant, which talks about clones and not about Le Verre theories, and he's finally got around to defining categories that had all been very clumsily done, not understanding what it was he was looking for. I wrote a letter to McKenzie saying, why didn't you do it better, and I guess it's out of your hands. Ralph McKenzie? Ralph McKenzie. He was otherwise a very good professor. Well, we found an interesting parallel example in the area that Gerry's working in, this category of projectiles, quantum logic. The... Well, no, but were those papers to list? I thought he was a mathematician. Oh, okay, I thought he was a bit more recent. I thought he was by 1977. It's not that long. All this stuff on resituated mappings, do you know the stuff on resituated mappings? They're just simply rediscovering adjoining factors under a different name, or in a very concrete...

32:30 I'm sorry, was it a long time before? Oh, there's great advances. So it was done on the model of the ideals in ring theory, where there were examples of that. So they couldn't have known then about it. But I think they just continued around. Well, the particular work we were thinking of was very much later than that. It was in the 70s. This is residuated mapping. Yes, sorry. There are these papers on residuated mappings in the context of ortho-lattices. No, you can answer. Your question is what is the origin of it. That's right. That's exactly what I wanted the answer to, although I was very confused about that. So the numbers, if the numbers are the same, then there ought to be something in it. Yeah. Yeah. So I just... If, by any chance, I get any idea, I write. I like combinatorial work. Oh, I do too. You can get stuck in with the minimum of class. But if the numbers coincide, then it's a good indication. Now, I drove him all the way from England and he's been nagging me about the origin of the word Residuated Mapping. The Residuated Mapping is basically one that has a residual and within it is... The mappings between partial orders and a resigrated mapping is the method by which the residuals arrive at each other. Now, this is what the theory was, and the textbook on resigrated mappings has appeared in 1972.

35:00 This is the special case of a year after your book, by Blitz and Janowicz. There are one or two diagrams, you know, but the word, if I'm not mistaken, I haven't read all the book out. The word category does not appear. This could be an all innocence. However, the question you had in mind is why do they call the left a joint, a restitution of the left? I just wondered if you could throw any light on that. The light is through the restitution of the left. Through the restitution of the left, as we've known already in the course. In the 1930s, when the motivation, as best I can remember, was all I needed to do in my life, it was a little more general than I thought it was going to be, and I think it was probably first Morgan Ward who said, you know, you're worth several acres of money, and you're going to be a peer in the work of this book, I guess. So there's all the theory of ideals, including the general range of left and right ideals, and the cross theorem. Well, it's very natural. I mean, the quantum logic stuff was originally worked out in the setting of lattice theory. It's very natural that it should now be redone in a more general setting of category theory. Maybe the professor will notice the quantum logic.

37:30 The closed subspace, the lattice, so that in the Boolean case you take a set and you look at all the subsets, modulate them, measure them, leave out the technicalities, it's a variable set, but you're hacking out the data. You now take subspaces and you get what they call an automodular or prolactin state. Well, what I did is I looked at this from more of the categorical point of view, meaning good for a job. And what happens is, if you take intersection by... We replace intersection by A. The axiom of automodularity, which comes in quantum logic, is precisely the statement that it has a right to change. So what's happening is something like moving from cartesian-based categories to closed categories. What I'm saying is, we know that it's open. We want him to start here. So let's grab another big board. We've got a week, we've got a week. Where is this water? Where is the famous said water? Already gone. Is that water? We'll have water everywhere, and not a drop of drink or other in this case. Is the lake from the water? Probably not from here,

40:00 not that that lake shore is anything to go by. I think... Who do you want to go into? Play the field, you've got a week, you've got a week. Thank you for your attention. Thank you very much for your attention and I hope to see you again soon. We use the Pantorian semantics to start. Okay. Oh, that's Bill, that's Bill, that's Bill. Uh, I don't know. This woman here is from Georgia. Yes, from Georgia. I just come especially as an Armenian. Thank you. Although I've never been to Armenia, I'm going to take you through that story as an example of course. It's good to see you again, well represented. How many of you here this time? This time we are eight. You are eight? Exponentially! This is indeed. Anyway, nice to meet you. Michael Wright. It was just over there, talking to the other, the spread friend, it's a nice man, as he stated, all the work on punctuals and that sort of thing.

42:30 Well, Bill, I think he's probably trying to escape from the Canadian. Well, that's interesting on the second film. The thing is, you have so much, what I'd really like to get out of it, the thing which interests me about, well, yes, that is a purely common problem. You mean in Italy, though? No, that doesn't interest me at all. Well, well, if you could find one, of course, it is. But you see, character is a sort of thing which could lend itself to a very elegant solution. You might actually connect up and characterise an awful lot of results in number theory tomorrow. But why do you have to have some? We're trying to get at him for the last time. I have a book by Henry Ray who is talking about a certain method of... The name Maslow was mentioned in work, and new methods were coming up with a sort of constant in some way. I was not expecting to come out here, which is how I then found that time is constant and things like that. Would you like to have a look at this book? I know it's well beyond me. It's a paper, by the way. It's a paper. It's just one or two papers. Recently. But he has a book on this. A book on this? He has a book on this which... I have, somewhere, a lot of them. And I think, uh, you know, Professor Thomas and you might make better use of it than I do. Yes, yes. Would you really like to? I'm interested in this, yeah. Yeah? Yeah, he had an article in the New York Times.

45:00 What's the need for Frank Constantine in mathematics? In mathematics? I don't know. The need for Frank Constantine in mathematics. I don't know. And where was this article? In the Bulletin of the American Math Society. Really? The need is a strange sighting. I know, yes, but this has... I'm sorry, this is totally ignorance, but this has nothing at all to do with the point you were making in your Cambridge lectures about the canonical-computational relations just being an instance of the relationship between... No. No, I can't... What will I get in exchange? Intensive and extensive quantities in a ring name. What was the ring that we... You christened it. You christened it, I remember, in your lectures, and now I've forgotten what the term was that you... This particular ring that we're in, in the, um, I can't, no, it'll come back to me, I don't know, the first dream, hmm, I thought so, you know. I think so. I think so. I think you, you, I will remember it before they, before they leave it. It doesn't matter now. But anyway, obviously Mr. Boyd has nothing whatever to do with that. See, yeah, I'll mail that to you by the time you find it. I think it's in time. See, my books are now scattered. He is the custodian of some of them. I'm the custodian of the Kajarian Nakhla. Some of them have gone in the garages. I'm keeping them intact in so far as I can in one place. I now have a proper life when you come and visit me again. What was this claim that he was making about? Well, I wish I knew. I didn't see it that way. I thought it was just some... The solution, method of solution, part of the French equation that we speak of in the morning is really I don't know if it's just some old man's language. I was surprised that you saw it in the open audience.

47:30 Thank you for watching. I have been telling him that Mussolini was executed by a partisan. Thank you for your attention. No, I'd rather not. We had an altercation with an Austrian customs official. I reminded him that Hitler's father had been an Austrian customs official. This was not the tactic. The German Austrian customs are really fascist, aren't they? They're ordering us back. I shouldn't have lost my temper. Thank you for watching. And here I am trying to pass myself off as a quiet-spoken, shy-recurring Englishman. After that I have to buy this piece to protect me. Yes, that's right. So the needs of the devils are not the same. I stole cases of experiments. I told you about my visit to Lodi.

50:00 I think you, yes you did, you were there a little bit, yes, yes, but tell me more, remind me. Actually, I'm not sure you did, though. I remember you telling me when we were in Cambridge of an earlier lecture. We sent you the menace speech. Now we've only been working a lot, but I've worked a lot. After Cambridge really when I came back here, I had a couple of dates with Haynes, and got into his office right now, and now I'm down to a couple of classes to look up to. In fact, he liked it so much he's going to take his vacation next week to that same area. The visit to Grotendieck was very disturbing. Well, he split. Well, you judge for yourself. He split. I'll describe what happened. So after two days of driving, we arrived at this little stone hut in the middle of a wine field far from the city. After a while, he came in a long white robe, hair cut, beard, long hair, and he made this sign, like this. Then he looked at me, and he recognized me, and he said, Well, I'm just glad to see you. This is the last word he said. The only word he said. Because, and this was a mistake, you see, because then he took us in the house and he started writing. He said, now I'm on a regime of silence for a period of three months. I can't speak. However he compromised, he would write. We could speak and he would write. So actually, I have everything in writing that he said, which I can actually show you, you see. I wouldn't believe it otherwise. And then, of course, the next thing he wrote was, no mathematics, of course.

52:30 I think when you're around those cars, people find it difficult. Where are those cars? Near Toulouse? Near Avignon. Near Avignon? In Provence. In Provence. Beautiful, beautiful cars. The main formal reason to go was to discuss with him this manuscript which Ronnie Brown suggests should be published, which is his So he said, yes, you are the best person to edit it, however, you must agree that nothing will be changed, even though there are many errors and false starts, this is good for the students, it should be as it is, however you, well, I can write an introduction. I've been complaining that maybe I'll do whatever extent I want, but I told him it might take a long time, but anyway, so we basically have this agreement, but he has this strange insistence that since it's his creative... The creative process should be displayed in view, plain view, all to see, like Shakespeare's manuscripts with all the crossings out. But then, very quickly, he turns to other questions. Oh yeah? And he sleeps. And these spirits have informed him that he has a revelation. In the very near future, the whole world is going to change dramatically. Science will no longer exist in the present form of science, either replaced by something totally unexpected or not. Science will develop upon cursing him.

55:00 He even knows the date, which is 1996, so we've got, I think they've got, he must be in touch with some guru, or just come, so he gave me two books. No, no, no, no, no. You gave me two books which I took home, they allow me to take them home and read them. But I do take some notes. Most of these books emanate from the Tintorn community in Scotland. That now I remember. You asked me about it. Well, that's why. There's a Trovarian involved in this who uses his house as an international meeting place for New Age themes. And they're very well funded. Again, one asks, you know, he's obviously... In both sense, materialist question. And they are very well-founded into all communities. I think they bought the island of Iona, not so long ago. You read these books and you came out. Oh, yeah. Because they could have done a lot of damage. Quite unbelievably. I have a son from my second marriage who is a commercial artist living in Greece, and he came to visit us. He hadn't come for many years, and his mother, who also lives in Greece, has finally written a book and has become, according to him, famous. She has paid to go speak about this book in many different places, including Fendhorn. Just as a stab in the dark, I said, by the way, do you know anything about Fendhorn? We have sex and she's gone there twice. The theme of her book is Gaia.

57:30 Oh, yes, Gaia, the Gaia hypothesis. Who is this guy? Ralph Abraham, the chaos man. Oh, yes, it all connects up with fractalism. He has begun to openly preach about Gaia also. Oh, it connects up with fractalism and non-equilibrium. I didn't know about Ralph Abraham to speak in New York City about Gaia. By the way, Ralph Abrahams. My brother used to be the lover of my ex-wife before I knew her, but that probably has nothing to do with it, but anyways, she went also to Guatemala paid by the UNESCO, but as part of this whole thing, so somehow there's UNESCO funding for this, which could be just some... ...curiosities about the utter degeneracy of human life, but it's a material problem. He has destroyed the leading mathematician of the century. It doesn't work. It's absolutely appalling because I've obviously grown dark. He must have felt very lonely at the time, or was he never mad? He wasn't mad, but he lived some time on his own, of course, for a certain amount of time, and he doesn't have any intellectual contact with other mathematicians. Thank you for watching. But he wanted to present these two books about the centaur and the unity, which is another spot, as being an indication of what was going to happen in 1996. You've heard this, have you, and it's about Grotendieck, who's apparently been... Captured is apparently, well obviously mentally very ill, in the grip of some weird cult and has announced that mathematics and science are going to completely cease in 1996 and give place to some kind of new age revelation.