Discussions, incl. FW Lawvere C McLarty, A MacIntyre (contd.)

0:00 The first thing about projected non-singular cases is that you push it into the singular cases and it's fantastic. People have followed it up. This was done by the Navy and finished. Japanese Fujiwara has gone a great way. It also seems to be an essential ingredient for the Langlands program. You get representations out of the telephoto homology. And, in addition, I mean, this is so precise, I mean, the information about the eigenvalues, I mean, they've been able to use it on the one hand in the theory of V-modules, and it's also been an application to differential algebra, to difference algebra, to make precise various conjectures that Jacobi made, claims that it was 160 meters or more. I mean, no, I think that... And in so many different dimensions, I mean, just as sheer combinatorics, and I'm told people in combinatorics need one result or another of it very often. Sorry, I missed the... The big point is that they conjecture. Right, okay, I missed the noun phrase, the sentence. For them to have given these conjectures, what a mind it took to imagine that anything like this could be true. And they... And then Derrick represented Hubble. Yeah. Well, maybe that's less surprising, isn't it? And then they had to believe that a cohomological proof could be given. I'm inclined to agree with Sarah that they didn't really think that. They did not really think there'd be a cohomological proof.

2:30 But Sarah did. Yeah. And Rotenbeek did. Certainly by the late 50s, they was was insulting cohomological strategies. But I think Sarah may be right that he never believed there would be a cohomology to have seen the left half fixed point theorem in those numbers. Yeah, this is pretty extraordinary. I mean, I guess others, I mean, others had seen some trace of the remnant before he saw it for the curves. All of a very different nature. But I think it's sort of mind-boggling to spot this possibility that there might be a phase formula. I think it was all for curves before Vey. All the different versions were for curves. Well, I mean, Vey proved, was the one who proved the Riemann hypothesis for a curve. Well, that's right. I mean, yeah. But, I mean, specific cases for elliptic curves are to be done by Doring and Witten and Massa and others. Yeah, yeah. And the curve case is old. In these cases, it's not easy, but the point of the curve case currently is that there are at least three or four proofs, of which some are elementary, in the sense that they are difficult, but they only use Galois theory and Riemann-Roller theory. The idea that there might be such a proof for a big conjecture. Also, you see, it's always by some kind of, maybe a week or less leading analysis, it always gives one some kind of inspiration from it. The original Riemann and Hobbes, I mean the stuff that Sarnak and Katz did, I mean, they took the, they took these, they took these observations, the people about the gaps between zeros and zillion functions, and they, they, I think, roughed up some of the matrices.

5:00 The things which, I mean, this analogy is a classic of Lehmann's, but you can play it back in taxisonic proof that also gives a tremendous amount of information. It would bring a probability theory into a theory of varieties of a finite number. Now, would that be why Sarnak kind of favors stretching from the Bay Conjecture to the classical Riemann Hypothesis? That he thinks may be a better... Yeah, I mean, the Dennison thing is a bit different. I mean, but it's certainly highly respectable. It's not flaky in any sense. But I've read three of the popular books now on the Riemann Hypothesis, two of them don't mention Denninger, and the other spends the whole entire book attacking him, H-286, yeah, and when it gets there he spends most of the time attacking him, as you were talking about earlier. Well, I mean, I mean, okay, so which books? I mean, Marcus de Soto I... He mentions. People mention he's selling a lot, right? No, no, no, no, no, no. And, uh, I guess there's... Connes, of course, is very structured. They're purely connected with what Paul Kohn has been trying for many years. I mean, Kohn's is certainly fantastically appealing. What is his strategy? His strategy is invariably to find a trace formula that will... I mean, this is the whole point in the post-Lillian theory. But it relates. I mean, the classical theories of Lefschetz things involve a trace formula and then fixed ones, okay? But this general Grotenbeek system is a formula.

7:30 This guy Fujiwara has been able to prove and something to identify these other things. He's working on the addels, relations on certain trace forms. It's how to use it, how to make sense of both sides of it that follows it, certainly. And discussions of Wiles' proof face it back to Langlands, and they don't mention who Langlands was talking to when he came up with this program. Barry Mazur has tried to put it in connection with Grotnik, because Mazur wants much more credit for Wiles than he gets. And I guess he's got a case for it, I would try to judge the case. There's that big volume on... And that volume is dedicated to the idea that it's based on Mazur's theorems, but when you look at the popularizations in like AMS publications, and so then this becomes a big thing for Friedman. Friedman has this conjecture. No chain of references starting with Wiles and leading through bibliographies ends in the growth geek school. I chose to check that. I chose to check that. And I'm not good at checking this, so I only got as far as the person that we are with.

10:00 Indivisible group schemes, I mean, this is an essential feature of the... But even the popular presentations of ours that make this fair, at least one does, I can imagine. What I remember on public TV in the US, maybe two or three different sessions. The formulas were clearly all-knowing functures invented by Grudenbeek. Even though the name Grudenbeek was never mentioned, Mazer was even interviewed. I mean, it's just complete nonsense. I mean, Coates, who was a strong influence on Wiles, he studied in the Groton League. He spent time in the Groton League, Simon Armitage. Well, the man who could put a stop to this nonsense and, you know, about to argue for him to shut him up is Wiles. Why doesn't he do so? Wiles doesn't read far. Okay, that's an answer. I got as far as checking the first entry in the bibliography. And the first entry, I've gone and forgotten it. It's two authors on the duality theorem. The book is typed up in the format of the SGAs. And so then I checked, what does he actually do with it in the article. He says that this is where he's... He became a rock at a certain moment, he had these two cohomology classes, and he realized he could do that using the growth of duality, you know. I mean, Harvey says this based solely on his will that growth of duality does not matter. Yeah, yeah, sure. I would certainly do that with one word. Yeah, yeah, sure. Yes, like one or two other of his political... Well, I hope you don't agree with Steve Simpson. They're not on speaking terms. Harvey's on speaking terms with Steve, but Steve is not with Harvey. Oh, wow. Did Harvey betray the faith or something? Harvey noted some inadequacies in Steve's defense of reverse mathematics. Steve felt this was completely unfair. It was done in a criminally public manner. It could only reveal hostility. Yeah, sure.

12:30 I've just severed my connection again. Not that I've ever contributed anything to it. For a while I got it, and then I stopped taking it, and then I saw Simpson for the first time in many years at a meeting in Connecticut, and he persuaded me to. Take it again, I took it again, but it was coming to my Edmund account, and recently I just, I closed my Edmund account a few days ago, and I said, stop reading for me. Well, it hasn't got any better since the 98, you know, the period when it did have lots of interesting people contributing to it. Well, it was fun in the days of constitutional law and finite injury methods in recursion theory. I missed that bit. I really just got the bit at the beginning with Fefferman and Hugh and Angus, you know, being talked over the... There's a section of you, I mean, Van Andries... Van Andries too, yes, yes, yes, yes. Van Andries, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes, yes. I mean, Dave Marko still reads it clearly and occasionally gives some information on quantification. It's a pity because it was a huge opportunity. Oh, and I think, I'm awfully glad I had that argument. My favorite is where he quotes Harvey Clinton. As far as I know, the first thing students are told to know about a set is extensionality. The two sets are identical if they have the same elements. And he quotes me writing back, yes, and that's also the first thing they're told to forget when they apply set theory. For example, the definition of different kinds of numbers. Simpson was reduced exactly to the position of Bogart in the witness box, McKay mutiny, clacking the ball. ...with me about what he meant in a certain paragraph written in French. He starts out by saying, I don't read French, but I'm pretty sure... But I know he meant this. I know he meant this. And I know MacLeod, he doesn't know anything about French. Clack, clack, he just did exactly that.

15:00 Well, that's interesting, isn't it? Yes, because he actually mentions that at some point. First of all, I wanted to say that I feel rather miffed that the rest of you guys are criminals. I'm a mere charlatan. You haven't discovered me, so I'm a mere charlatan. You're a mere charlatan. It's pretty out of town, Cambridge. Didn't they have to be in Cambridge to be in particular? At some point, I guess perhaps maybe someone raised some doubts. I did. I said some things about your guests. Whoever it was, Tarvey then intervened and said, well, I'm the only one of you guys who personally knows Le Verre and Sandow. Ah, exactly. But I know that they're charlatans. I'm the actual, if anybody, the actual adversary, taking any position against logic or any of this sort. It can be construed as. He challenged me. He's brought into it the personal experience that Harvey has. The funny thing about the personal experience from my end is this. When I arrived here, there was Harvey. Of course, he was a star. We were discussing, you know, thinking about Marxism, and he says, he says, my family has 20 million dollars. I'm part of the ruling class. So I shot back, sir, you have to have at least 20 billion to be part of the ruling class. I think that's a typical person of the sort who could easily be recruited into fascism, precisely because of this complete misconception of the true relation to the way things are run. I was absolutely offended by that first meeting. However, ever after that, it must have been two years at least that he was still there, my impression was that we were on wonderful terms. I would talk with his office, and we'd talk mathematics, and he would talk to me. It seemed to be on fine terms. Everybody else hated him. Everybody else hated him, but I thought we were getting along fine. So then there came up this question of the chair. There was a chair that was funded by one of the heirs of the...

17:30 It was called the Martin Chair, designated for mathematics. It had been established around 1930, but then people thought all the funds had disappeared during the Depression. It turned out they were still there, so they were finally in 1977 going to finally award somebody this chair. And this was one of those brief periods in America where there was a lot of enthusiasm for actual democracy. And so the math department actually voted on it. It wasn't decided just by the chairmen. So there were two candidates. Well, the person got all the votes except two. So the person soon left their actor. Clearly it was because they just couldn't stand the guy. It was the other person. The one who got the two votes. I did the best I could. It was quite a flexible and lucrative chair to have. I did manage to organize several conferences. He was on trips just for a five year period. I was the only one who was democratically elected, so to speak. Because after the five year period, they decided to use the same funds that they were automatically awarded to as an additional prize to whoever was chairman. To get somebody to accept the chairmanship, they were given this additional margin chair. The margin chair is held by the chairman since that time. Anyway, that was since 1982. The last meeting that we funded with it was the one, the joint meeting with Truesdell. The unity of continuum mechanics and category theory. It's been slower to develop, the unity between intuitionistic logic and topology theory, but it is developing. This young man from Rome, I think, is going to finally be able to do it. Yeah, he's really impressive, Bernardini.

20:00 Bernardini. Anyway, Harvey's personal, the fact that he was on the faculty at Buffalo intersects with his discourse on Homer in that way. I had said something about you and he fired back, were you his colleague for five years? I was. Well, you checked, you said it was three. But I didn't have time to write back and say no, you are. It's also true that he swept Chanuel into the condemnation as well. It's never been his colleague. Well, he was. There's no reason why he should attack Chanuel. Except that he associates you and Shannon together in the same mathematical program and the same correction of grades and the same general philosophical stuff. But a couple of years ago I stayed up until 4 in the morning at a meeting at Notre Dame talking with Harvey. And at 4 in the morning he said, you know, maybe I've got you category theorists wrong. I mean, I still don't agree with you, but you care about foundations. I was trying to get him to explain his strategy for blowing the lid off mathematics and revealing that they're all incompetence, which he's going to do someday soon if he doesn't start getting more credit. Because why haven't they given me the Fields Medal yet? He's obviously been around saying that, hasn't he? Well, he's upset that he didn't get it. That was reported to me, but I know it's not quite authoritative. Trace aside! It's pretty understandable, isn't it? They give the guy a chair at the age of 17 or whatever it was. He's in the Guinness Book of Records. He's obviously completely emotionally immature. He was on the cover of Time magazine. I don't know how you do that. It's exaggerated. Grotesquely, he's given the idea that he's the genius of his generation. He was an inspired person when he was young. If you get him to forget his ambition and just go ahead. ...marvelous imagination within a very limited range of foundations as he understood it, but within that realm, he had a fantastic touch, I mean, put ideas together that no one had put together before, he had insights that he had, but this is a huge angle, a whole way of understanding that it's a jungle out there, I mean, there were people who were older than him, say Tony Martin or someone, who were in the end going to make a much bigger difference in subject than Harvey ever did, because Harvey spent all...

22:30 I wrote for him for the Waterman Award. I didn't expect him to get it, but I certainly wrote my heart out about his work, as I understood it at the time. I thought it was totally limitless. I understood anything. Yeah, but it's emotional. It's just a complete failure of emotional intelligence. Exactly. But even job offers. And plenty of people would be... If he wasn't such an unpleasant person, he wouldn't still be at Ohio State. Oh, no, of course not. And he doesn't attribute it to being unpleasant people. Well, deeply unpleasant people almost uniform themselves from total lack of self-awareness. That's one of the characteristic features of them, you know, that they're quite unaware of the impression they make on other people. Well, to be honest, I mean, within this genre, he was very much a sort of universal man. I mean, he could do anything, you know, with theory and set theory and recursion theory at this moment. All of these have moments in life when they go and give him a nice touch, although he never ever did that when no one else had done, but, I mean, Jerold Hirschfeld was a Robinson student, but he had the following periods, he had just struggled and struggled and struggled, and he had finally, one weekend at Yale, managed to prove the proper initial segment of himself. He switched on the TV for relaxation to see Harvey announcing this was the Wilson show. That is a unique experience. You read Harvey's papers from the 70s, and you know why he wanted to solve this problem. There's a lot of logic papers and you can't tell. But with Harvey, you always know. I just regard that as a tremendous waste of time.

25:00 Yeah, yeah, yeah. That's right. I mean, it's strictly analogous to the situation that we're talking about. In that case, in this case, it's a state-sponsored endeavor to create geniuses, to create people with this aura of geniuses. The great tragedy is, the real big tragedy is, that some of them take it seriously, and that's our loss to science. Precisely, people who could have contributed the most to science are lost. That's because they're infantilized in this way. Public ideologues. I don't know if you've seen, David Gaubin wrote a dissertation about the IAGS, about life at the IAGS. And his main point is to prove that René-Tom actually understood the future of mathematics, and this guy Grotendieck did not, and there was this clash between them. And Tom had these much more important insights, much more comprehensible and more useful. The problem with them was they turned out to be false, but... Yeah, yeah, yeah, yeah. This was the most important for Harvey. I mean, it was, I think, most here. Like Simpson, for example. Simpson was disastrous for other people. I mean, people like Solovey or Schellach and so on. I mean, Harvey would call and bother them sometimes. They had great mathematical respect for Harvey, and they would listen to him. And that was the end of it. You know, Harvey was one of the small, ultra-gifted people on the subject. And that was that no fuss needed to be made because there were always new ones coming.

27:30 I'm wondering why we suddenly blasted country in Western. It's no way of letting us know. Gentlemen, please complete the premises, is it? It's a plan. No, it just looks to me like Steve is a rancho table rapper. I think Kreisel principally admired Harvey's work in proof theory, which was very imaginative, and how Kreisel was looking for some more imagination, and most of the people at that point in proof theory would go on the very predictable. Shall we make a move to the next door where we can talk more partly? I mean, Kreisel, of course, would mock Harvey quite a lot, but he... There's no more that he did with everybody else. He did with everybody, but I think he remains... Thank you very much for your attention. What he christened the Nelson-Barnacahan principle, you know, you know how much you're worth, you ain't worth much.

30:00 Excusez-moi mon petit. Ah, mon petit. Ok. Ok. Il parle pas anglais. Ah. Hi. Hi. Bonsoir. Hi. Charles. Nice to see you. Charles. Hi. Good to have you. Thanks. You didn't want to have Sarah's Blast of Country in Weston, did you? Haven't even opened up yet. There was a cartoon in New York recently. A couple in bed and a woman... She's got a guitar in her arm. She's not going to tell me I've got a heartache coming up. The New Yorker did think it was as good as that any longer. Shall we just stroll up here? That's a good one. I don't know if you know this book by heart. I think it's Patras. Patras. It is Patras. He gave a talk at Cartier Seminar at the École Normale Supérieure. In fact, I've actually got it on my... They have this excellent Diffusion de Savoie service, whereby you can download all the seminars on RealPlayer. Great. To me, the discussion of Grotendieck didn't go very far, but what I really liked in it, he really hits hard on this theme. There's been this technicization of mathematics, especially under Vakim, that we give proofs, we don't care if anybody understands them, we don't give philosophies, we don't give interpretations, we just give proofs, and he says, This has resulted in slashing math requirements, it's resulted in slashing math enrollments, it's resulted in engineering departments teaching their own mathematics. This has been, if mathematics wants to be a part of cultural life, you've got to claim that it's the highest exercise of reason.

32:30 It's not just giving proof that we don't care if you can understand them. You've got to claim real insight here and also be developing real insight. You've got to say this is a subject of understanding. This is blaming the victim. Not entirely. I mean, Weil was energetic in promoting that view. But Weil ended up being the publicist for that part of Bourbaki. But the claim about mathematics that you have to see this is that this is a cultural achievement. This isn't just something some people happen to do and most people shouldn't care about. Did Bill Markey promote the view that people shouldn't care about it? People should respect it without knowing any of it. I don't see that. But I think Patras is a very interesting guy, and he's actually one of the people I asked to come to the history and philosophy of category theory meeting in October. Yeah, yeah, yeah, yeah. But again, apart from the history, insisting that mathematics has to be this, I've been pushing this around the university the last two years, all the sciences. I mean, the science department used to say, oh, we matter more than humanities because we invent stuff. I don't know if the science department has made that stuff. We can talk about it. Because the engineering department is doing very good. The chemistry department. Except the chemistry departments have mostly already been closed down in England. No, it's just been, as it were, soft-out, like to the call centers in Bangalore. Well, but now how are you saying chemistry? That's something like, how many British universities are now closed?

35:00 And so they've started saying, yeah, right, the point of the biology department is we produce basic understanding. You've got to value basic understanding or you can close all the science departments. Of course. But they should have been saying that a long time ago. But the science department's in cases. I have to say, I think in the case of physics, People, Feynman had a lot to answer for, promoting that, thought out of the past, sign of, sign you have got no real talent if you go round, yeah, exactly, I mean, Powley started it, but Feynman was the one who really promoted it, and it's acted absolutely catastrophically, I think it was a really, that's, that's, that's it. Yes, all those renaissance humanists, as you can find, humanists. They did Joan of Arc at just the same time. They did Joan of Arc at exactly the same time, or the same year anyway. Interestingly, and she became almost overnight, having been a very, very obscure saint. I mean, nobody in France, well, even in France, there was no cult of Jeanne d'Arc in the 19th century in France, even amongst the most, you know, ultra-montane cooks. Suddenly, after 1929, she suddenly became, there was a huge cult of Jeanne d'Arc built up, which, of course, was immediately taken over by... It was actually promoted by Action Francaise in Monard and the clerical fascists, whose leaders were almost all atheists, but they just had this line that was one great instrument, effective instrument for social control, and that was therefore not likely to be abandoned, and of course reached its apogee under Vichy.

37:30 It's still very promoted on the extreme right in France by people like Le Pen now, but if you go back a hundred years, Joan of Arc was a very obscure figure in the Catholic canon, and not just because she hadn't been canonized, but she was just more or less a forgotten figure. So, kind of pre-fascist, but, you know, kind of proud. But, um... Now, how is, in your previous report, how does he relate to Catholicism? Well, I don't think anybody's going to try to make Giordano Bruno a saint. No, he's, uh, he relates, he's on the kind of science fiction wing of Catholicism. Yeah, ideologically, you know, there's always something of a split, I mean Goebbels, for instance, remained very openly sort of anti-religious, you know, right to the end, on the other hand, they were certainly quite happy to make use of the... Hitler did remark at one point in his table talk that the only politician that he had been seriously afraid of, who he thought seriously might outmaneuver him, I mean in German domestic politics, I'm talking about during his rise to power, was Brüning. And the Catholic Center Party. So the only people I seriously, seriously believe would destroy my strategy for retaining power if they had changed their own tactics and recognized in time were the Catholic Center Party. What did he want out of that? Was he trying to promote a certain conception of the Catholic Party?

40:00 No, this was a private pronouncement during his total talk. I don't think there was anything to it except whatever he was thinking at the time. I think he just thought that Bruning had been tactically very clever. A politician, if the slump hadn't come, might have consolidated a new kind of conservative consensus around the policies of the Catholic Centre Party with a lot of social being, might have kind of stolen the clothes of the non-communist, particularly the paternalist, you know, we're the party who can really look after the workers, manage capitalism. There's a big fuss now. Somebody in, oh, I forget which French paper or magazine, the King of Pettigrew. Oh, I know, I've got the book. I just wanted to think about Nazism and Philosophy. It just came out. It's the last book I bought, actually, the day before I arrived on my way down here. I haven't got around to reading it yet, obviously, but it looks quite interesting. Emmanuel... Sorry, I just can't think of the author's surname. But yeah, that looks quite interesting. I read a bunch of advice to him about how Heidegger in some way inspired Hitler. Well, he makes a case for Heidegger having, you know, for Heidegger's kind of explicitly Nazi writings, including all the ones he suppressed between 1935 and 1944, if you will, having had much more of an explicit influence on Strasser and Hitler. Not specifically so much on Hitler himself, but on some of the Nazis. Well, Heidegger's been disputed in the Nazi and far more of an active... Well, no, it has been disputed, but that's partly because Heidegger himself and his son, who controlled all access to his papers and his estate, were very careful to do everything they could to destroy all...

42:30 The evidence, other than the stuff like the rectorial address, the stuff between 1933 and 1935, that just couldn't be suppressed because it was just too widely known and had been translated, but the idea that Heidegger, as it were, had the scales from his eyes in 1935 and he retired effectively from the directorship of Freiburg and then went into kind of... In turn, he didn't really, he was really sort of seen through the Nazis by the mid-1930s, absolutely crazy, he was still writing the most explicitly Nazi apologetics right up until 1944, to the very last year of the war. He even gave lectures, and the thing is, we now have the seminar notes from pupils of his which were not known before. Defending, you know, the Nazi racial theory and Nazi eugenics programs and homology in 1939. In 1940 he gave a seminar in which he sort of waxed lyrically about the beauty of the scenes of the German army crossing the French and Belgian and Dutch borders. That's the line this guy takes. I mean, I've only obviously just read very, very briefly the book. I've only handed it to myself for a few days. The material he presents is fascinating. He spent almost 30 years writing and researching the book, and he dug up all of the seminar notes, lecture notes from Heidegger's surviving pupils, found out what Heidegger's son had done in the way of, as I say, of weeding his nachlass of all the really damning stuff, and also uncovered his correspondence with Carl Schmitt, who was the leading The philosopher of law was the leading jurist in the German universities before 1933 and became the theorist of the Nazi legal.

45:00 I don't know enough about jurisprudence, but he was the legal, he was the chief, as it were, official Nazi jurist, still regarded apparently by many people in the conservative philosophy of law departments in Germany as a very great and serious and important jurist, partly because he also managed to cover his tracks pretty effectively in 1945. Who have been taught by him, exactly. But he and Heidegger apparently gave a joint seminar in Eiburg in 1942, which this guy's managed to turn up the notes. I was curious what Derrida thought about this. Derrida has a book on Heidegger, and I don't remember if it's the title or just a leading slogan through it. I'm going to talk about fire and ghosts, and then just by the end of the 80 pages, not to mention any fires that people were in. In a book on the Nazis titled Fire and Ghosts, he doesn't mention any fires people were in. He doesn't mention any deaths. I mean, it's an amazing piece of cap dancing. That's ridiculous. It's not even impressive because he wasn't called on to do it. Yeah, why shouldn't he do that? Did you ever run across that? Paul Christeller was a student of Heidegger, trained by Heidegger, and because he was Jewish, he had to leave and went to Italy, where he was a student of Gen Filis. And then he moved to the States, where he published a book on the philosophy of Ciccino, Lawrence Platonic Academy. When Cheney's wife was the head of the National Endowment for the Humanities, she gave him an incredible grant, an incredible position, and was basically in charge of all the countries in the world, insofar as the U.S. imperialists had control of them.

47:30 I think, I think he's not negligible at all. And what's his name again? Krister. Krister. K-R-I-S-T-E-L-L-E-R? No, that's not it. The student of both Heidegger and Gentile, if you want to know. And of course the... Derrida with his... Now he's considered the leftist, I suppose. Of course the other guy who links the fascination with Gentile with a great respect for Heidegger and, of course, worship of Derrida, this protege he was, is our friend Charles Oluni. Charles Oluni, of course, yes. I'm sure he's nowhere near as influential as Kristaller, for example, though he believes himself to be. He thinks he's a great string performer. He thinks he has the authority to completely revise all the universities in Europe. I was explaining to Bill that I'm... The second thing to me is... Ah, right, right, right, yes. So much about Steve's way. Actually, it really would be a good idea to have a day on the moon. You know, if it were formulated in K-theor, this would already be a step toward, it might be for all I know. Yeah. I think people who know a lot more about it than I do say is very, it really is odd how many Riemann hypotheses have now been proved. Things that wouldn't, there was no reason to... I don't think they were even true, except that they've been proved and don't have an obvious relation to the classical one, except that there's so many and the family does seem to filter around it.

50:00 I mean, the Riemann hypothesis, you would almost want to say it's not just special to the integers, there's all these variants, except that they've all been proved without that delivery of proof of this one. There are quite a few things about Steve's work that I wanted to ask. So much so that some of them end up feeling that the geometry, the geometric objects don't have any real, don't have any reality at all, and it's one source of this kind of non-committal geometry program. And in fact that's one of the other questions I was going to ask you about, Steve's fascinating paper that you pointed me and Basil Hiley towards a couple of years back on the triangular matrices. Oh yeah. That is an astonishing. There's a huge amount of stuff I'm studying there, and quite a lot of the other things we can talk about. OK. Well, shall we stroll back and have something, a nice cool drink in the shade? And then, how are we doing on time? Oh, it's 3 o'clock. That's OK. We've still got another hour or so before we need to get back going for me. This material, this guy, as I say, I haven't read the book yet. He spent 30 years working on the material about Heidegger and the stuff that he's turned up in Heidegger's seminars with Schmitt and his seminars on the defense of Nazi biology and racial theory.

52:30 It is absolutely damning. Nobody can any longer possibly deny either that Heidegger was entirely committed or that he and his speaker, Count Fiora, his son, were in control of his papers. Engaged in a huge operation of distortions and fabric falsifications. Just as a piece of literary detective work, regardless of its value as philosophy, or its history as philosophy, it's a pretty convincing... Well, put it this way, certainly when you look through the documentation, I mean, I'm afraid I've never... I learnt the story about how he had Zamella dismissed from 1935 for refusing to give him a Nazi salute. Well, I have a crack in Guinness, it says in the paper on Schrödinger in the... Sorry, no, on Zamella, I'm sorry, I'm going to Lally. God knows why I was suddenly thinking of Schrödinger. It says in a paper in Zermelo, actually I think it's in his entry on Zermelo in his little historical dictionary of mathematicians, that this was what ended Zermelo's academic career, that he was dismissed from the University of Maybach at the instigation of the then rector, Heidegger, for having refused, you know, consistently refused to give an artsy salute.

55:00 Well, that's right. I agree with that. That's what you said. I'm not sure if it would be the thesis or the opposite of what you're trying to say. I mean, isn't that the portion? Yes, that's right. Or the opposite, right? It's the same way. It's the same way, you know, Kant's idea that the thing in itself is the source of our ideas, but we'll never ever know it. So absolutizing the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and saying the number of elements is the right thing to do, and relativizing it and Hi Janine, ça va? Très bien, merci. C'est possible un panaché? Oui. Excellent. Bonjour monsieur, ça va? Bonjour. Would you guys like a panaché? That's a shandy, it's a lemonade and it's fairly nice and cool. Yeah, straight through there. Quatre panachés? Merci. Where do you want to go? Certainly.

57:30 There's even a rather good line from Auden about the tactic. Teach men to associate truth with a lie and in truth's name. They treat Dave and Barthwater the same. What do you say also struck me, I can't remember whether it's Ben Rovers or David Deutsch, I mean, who deals with them quite gently. No, Deutsch is quite an enthusiast. Deutsch is popular, very bad popular, but the fabric of reality is he's got the last three chapters all cheerleading for two of them. I'm going to be there and partly over the point, together with the community of infinite minds, and it's all in Hegel, something, they actually claim the authority of Hegel for all this. Anyway, this is what Hegel meant when he talked about the absolutes. This is going to be the culmination of this. Yeah, I was going to say, we'd better make a move. Shh! Not 4.25. We'd better make a move then. I don't doubt now, but John and me have traveled a lot. Well, it's okay, we won't be. If we leave now, we'll be there with about half and twenty minutes left. Yeah, we better pay for these. Well, I need to use the loo, actually, before I do anything else.