Discussions FW Lawvere & others / talks (parts)

0:00 Well, you're right, of course. You are. Yes, I know exactly what you're saying. No, well, it's entirely... Age is very, very largely a state of mind. Sometimes I run screaming from the show. Yes. Well, I'd make an exception, you know, for Bosseux, but certainly they can be very old fartish at times. A really massive historical turning point and the complete bankruptcy in every sense of political and moral as well as virtual as well as actual and arithmetical of the entire the whole system of finance capital in the scale of... But what staggers me, oh they were extremely interesting and I can't wait to get more once you've finished with the more pressing business of geometry and analysis tomorrow. I want to get the whole of Sunday with you to get a better handle on this. I think it's very striking. So there may be a very strong degree of convergence between the things which have fundamentally gone wrong methodologically and in other ways in mathematical physics and the kind of intellectual errors which even within the terms of their own, you know, suppositions led to this meltdown of the financial system. I didn't tell you this. No, no, no. He said he can't believe this. It's all due to Blackshaw. He didn't mention it. The idea that everybody had faith in these magical equations. Nobody understood them. Nobody understood them, exactly. Which is no excuse, you know, in a certain sense to bank employees. Implacable hostility towards ignorance, but in this case it was the other way around.

2:30 It's incredible. It's quite incredible. That's what I've been saying for years. Such a sort of theoretical possibility, you know, that there's going to be this complete triumph of ignorance due to the slow erosion of, you know, according to... Of understanding and rigor, yeah. Yeah. And then I take it up. That is exactly that, or at least, you know, in other words, exactly this is a major component of it. Yes, yes. Of course there is, there is evangelical religion as well. Yes, and there's obviously... There's physics, religion... And old-fashioned monomaniacal greed, of course. But for literate people, another thing that I saw, somebody says, the main thing that people are concerned about. What is the main concern of the American public? I think this was a theory or two before the crash. But anyway, what is the relationship between science and religion? Any instance where the people themselves have come up with this question as being central, you see? But the herd of journalists, as I said, the journalists beat on this all the time, you know, whenever there's something to remember that. I got the reference to the Mars slurper, as you put it. The Mars slurper is a magnificent term for it. Not to mention the Large Hadron Collider, and the top quark, and the Higgs boson, and all the rest of it. It's exactly the kind of thing that the religious people came up with in the 19th century, of course, when non-Euclidean geometry came along. Oh, gosh, you know, we've got all these extra dimensions. Ha-ha! That must be where heaven is, you know. It's incredible. But there's something not so different from that going on in the form of fideism that you have in branches of... Mathematical physics today, and certainly the people who want to use it as, you know, religious propaganda or religious ideology, it was a cover for religious ideology or a prop for religious ideology.

5:00 Leaving aside the question of whether string theory might have some spigot of truth to it, that's irrelevant in the present judgment. Sure, sure. Yes, no, its main function is clearly an ideological one. But in the banks themselves, don't you see? This guy looked like a relatively serious Wall Street analyst. Oh, he has his own journal and everything. That's it. There were these equations. He called them Nobel track physicists. Came over to Wall Street. Well, they obviously are referring to Black and Scholes because that's exactly who they were. Yeah, yeah, yeah. Nobel track physicists designed these equations. And again, you see, I've got all sorts of awards for them, even though it was clear that, well, I might as well cut across here. Well, again, it's not so much, I had no idea, you see, they might have been super serious people, I doubt it, in the sense of the hypotheses, the well-tied jarons, and so on and so forth. Again, in the application, that all goes by the board, because... Since nobody knows what they're about, nobody can explain them, nobody knows the precise definition, therefore infinite phase. Certainly, as far as the application is concerned. I mean, I don't know enough about the Black-Scholes work, but as I understand it, one of them, I think it was Black. Who was the, not the physicist, but the mathematician of the pair was, I mean his expertise was precisely in partial differential equations, so I mean these were all to do originally just with boundary conditions on PDEs. Then it was the it was Choles who saw how or thought he saw how they could you'd be used to model these algorithms in financial economics which determined when you should place what they call put and call options on various kinds of complex derivatives and here we are with the consequences. As I say that was extremely interesting very interesting talk by this Lebanese A woman historian of mathematics in Paris about a year ago, which I recorded, which I wish I'd stayed in touch with her, actually, because she had very interesting things to say about some of the cultural and social backgrounds of the whole thing. But there was a claim, and I would like to have had it developed more rigorously.

7:30 That there was a fundamental methodological flaw which led to this systemic underpricing of risk, which was subsequently identified at home, and then they tweaked it, so they thought they'd kind of got rid of that problem, but how far, I mean how far this whole collapse was triggered simply by their fault in modelling is anybody's guess, it seems to have been much more a... One thing, there can be very few figures in history whose reputation, even in the eyes of his own class, the people he served, perhaps didn't serve so well actually, can have melted down as completely and as suddenly as Mr. Greenspan. Only a month ago, he was still held up as the man whom we should all look up in awe and reverence as the greatest banker of all time. Yes, well, absolutely. I believe he was actually briefly her boyfriend, her dotage. But yes, he was indeed a great, still is as far as I know, like our friends at Penn State. I was hearing a little bit about the people at Penn State because of this Beyond Einstein conference that I was at. You know the Penn State Audition has moved into Templeton, of course. Of course, of course, of course. Together with his mentor, Friedman. You were telling me about this. Together with Schofield, all three of them. Well, David Caulfield, he doesn't surprise me because he has nothing to say, but Friedman, yeah, but Friedman does have something to say. It's pernicious, but he does have something to say. I am surprised to learn that. I don't think Caulfield is, well, I don't think Caulfield is frankly worth bothering about, but the other, well, and North for that matter is Simpson, but Friedman certainly is, and, oh, hang on, I think maybe we should wait for a moment. Except there are no lights here. Oh, I don't know. Yes, yeah, I was heading down to the Grand Place. Because, you know, there's loads of places around there where we could get something to eat. The only thing is, well, OK, let's take a risk. And I've got something here I want to give you. But wait till we're sitting down. Yeah, I'll have to skirt around this way.

10:00 But it struck me when you told me that, that there must have been, it could just be pure mercenary opportunism on their part, but normally the Ayn Rand people were pretty anti-conventional orthodox religion, they were fairly anti-Christian, at least as far as the official ideology ran. I call kind of sub, you know, semi-serious brand of teenage Nietzscheanism that they like to dwell on about the virtues of selfishness, which was a little bit difficult to square with the, or in practice, of course, not at all difficult to square, but at least in theory a little bit difficult to square with conventional Christian teaching. They proudly protest about principles that are unprincipled. Of course, absolutely. And the most unprincipled of the lot. I was thinking about them, and of course about the perniciousness of religion, on the way here, on the way up to your hotel, because from where I'm staying, there is, well, it's quite an interesting little quarter of the city around the south station. You come up past this vile statue of... Leopold, Leopold II, the man who probably, certainly one of the most, the vastest genocides in the whole of recorded history, and certainly, almost certainly killed more people than Hitler in fact, and they still have statues of him up all over the place, and then just after the statue of him there is this, there is this charity hospital with all of these plaques on the walls, these You know, virtuous worker priests and charitable ladies who donated presumably a very small part of the super profits that Leopold had raped out of the Congo and murdering millions of people in order to do it, and redistributed a tiny percentage of them to the poor of Brussels, so we're supposed to go down on our knees and thank these people for having seen that. The line between good and evil runs through the human heart and not, of course, between ideologies or classes. I'm not wearing all this, you know, pernicious, sanctimonious claptrap that I'm sure we're going to hear a lot more of in a few months' time.

12:30 Keep your... Ears open. It won't come right away, because obviously right now is hardly the opportune moment for it, but I guarantee you within three months we shall start seeing the editorials appearing about how the finger-pointing must cease and... We must be very careful with, of course, all the admittedly so needed regulation for the new environment in which finance capital will henceforth have to operate, not to kill the goose that lays the golden eggs, and very important to remember that incentives are needed, and there may have been excesses in the past, of course, but... I think it's already started. Yes, well, it's certainly... I don't think it will be long before... Well, I think they're going to be muted at least for a month or two, because they've got a little bit more tactical sense than to run that line right now, but they'll be out of the woodwork and peddling that poison very soon, very soon indeed. The same guy, by the way, this was an interview for 60 minutes. He made a second point. It's beyond the ideological role of the pseudo-physics. It's very interesting. I'm scared that they probably have it on YouTube. They often have those. In fact, it's on CBS. On the website, yeah, I can probably... 60 Minutes, the last one. I actually looked at it again there, but I only caught part of it. I thought, my God, is he saying what I think he's saying? I guess he was. Very interesting. They just come together for me the day before, that's what happened. Which is what you were telling me about, yeah. I thought you were in such a hurry. Yes, I wasn't quite sure what you... In fact, now I understand you were referring to science and religion, because I wasn't quite certain what the abbreviations were that you were employed. Yeah, I'm sorry, it was extremely... I think I guessed that that was what you were talking about. Extremely fast, yeah. But that is what, until yesterday, was supposed to be the main concern of the electorate, was it? The relationship between... Uh, yeah, well, I don't remember exactly. Within the last week or so, I saw this. Oh. Well, a very sensible subject for concern once you realize that their relationship should be one of unyielding antagonism. Right. It just reminded, it's an example of the, uh...

15:00 Uniform, lackey nature of journalism, you see. I have never seen anybody questioning this. Why are they always talking about the relation between science and religion? Is there something wrong with that? Even in the vaguest way. Incredible. I never saw this in the mainstream. At the same time I sell you insurance saying if it should go bad. I will, you know, pay you as an insurance thing, right? Except that, and of course there's a premium with that and everything, but it's not called insurance, therefore it's totally unregulated. There's no requirement for the risk to be small or for there to be capital to back it up. Exactly. The whole thing became a shogun, which is why... It was claimed that there was actually $60 trillion involved just in this swap, so-called swap, i.e. insurance. No, that certainly seems to have been a very major... And that Lehman Brothers and AIG and, you know, the first ones, Barron Stearns, they were all heavily into selling these things. And so, therefore, we, the taxpayers, just give them back all this money. Give them this huge amount of money, which is trillions, literally, so they can continue the... that's completely unbelievable. But what does... In some sense, that's just a detail. It shows... Yeah, because, in fact, the amount at stake is far... Well, what's happened, you probably saw it yesterday, the British government effectively nationalized... But to accept the context of deregulation is already a kind of reckless faith. Of course, of course. It's a faith, again, it's a reckless faith. It's the same reckless faith which led Bush to seriously propose privatizing the entire social insurance system. Yeah, yeah, yeah, right. Because after all, we all know that markets, you know, can do these things so much better than... No, just that it is depressing, though, the extent to which finance capital seems to have done such a very thorough job of lobotomizing the press and just turning them into eunuchs, because I haven't seen anywhere outside, you know, serious Marxist commentators, you know, revolutionary educators, certainly nowhere in the mass media. Questioning of this assumption that the crisis can only be addressed, you know, let alone sort of resolved on terms dictated by the very people who created it. And it's just seemed to be a no-brainer that you wouldn't have to be a Marxist to think that this is a very, very dubious assumption.

17:30 Crazy. And to start feeling some moral revulsion of the system that can find trillions to give to the people who caused the crisis. Lame remarks about, well, we'll have to rein in, we'll have to rein in some of these oversized bonuses in future. I mean, why isn't there a mass left movement out there saying, why don't we just expropriate these people? Why not call for a capital levy? I mean, if you're going to try and pay for the crisis and recapitalize the banks, wouldn't the idea of a capital levy be a good idea? Just simply take, you know, 50% of these people's assets away from them, considering how they would gain. A Marxist to think that this is a serious, I mean, 40 years ago, I mean, most social democrats would have thought that was a pretty obvious solution. The Labour government in Britain in the 1940s proposed a capital levy. But now this would be regarded as beyond the kind of craziest fringe of Maoism by most of the commentators today. One of his heroes, surprise, surprise, together with Gentile, I mean, why am I surprised, of course, yes, why am I surprised, why am I surprised by these people, you know, it's scaring me in the face, Kierkegaard also, I seem to recall, came into it as another point of reference, another kind of, you know, great good guy who should be there in the pantheon, you know, so I'm not.

20:00 Yes, to use that precisely as a kind of ski ramp to promote anti-scientific projects. There's a very interesting, I would hesitate before condemning it outright, because they do occasionally have a series on BBC Radio 4 called In Our Time. You can listen to the archive of all their programs. And they have, it's chaired by a guy called Melvin Bragg, who is a friend of Tony Blair, a very irritating... A fashionable member of the kind of new labor cultural establishment, posing as the kind of voice of the educated plain man who wants to discover all of these things important that we live at such an exciting time. There are all these wonderful, very clever people out there with great ideas. So let's get them all into the studio and get them to talk about them. And sometimes it's occasionally quite. Depending on who they have talking about which topic. Today's topic, Thursday the 10th of October 2008, which I did not listen to because I had to get the bus to come up here, but I will listen to it on the podcast, was Gödel's incompleteness theorems. It should be very interesting indeed. I'm quite certain there'll be a great deal of Phineas-ism in the background. They do occasionally have interesting contributors though. They had one about a month ago about Maizenko. And it was the usual, as you imagine, kind of anti-Stalinist rant, you know, terrible, wicked man, the destruction of Soviet genetics, complete, you know, threw Soviet science back into the dark ages. And then, towards the end of it, about three-quarters of the way through, one of the speakers, the professor of genetics at the University College London, just did let slip, actually, now that... We've got this increasing body of work in proteomics and understanding, beginning, we're just beginning to understand how genes... How the idea, how it's too crude to speak about genes coding for protein expression, because there are so many complex levels of structure involved in protein expression that one can't think of the thing as being determined in this essentialist way by, simply by, the genes.

22:30 Did I hear somebody mention dialectics? But there is of course this... There's an extremely complex structure which involves many levels of the structure of matter in motion involved. And it turns out there's such a very, very striking... Yes, exactly. And it turns out that there is this astonishing body of results which the classical geneticists are really too embarrassed to mention at the moment because all they can say is, well, neo-Lamarckianism reappears in every generation and, of course, has to be killed again in every generation. But it just turns out that there is now this incredible body of data which does appear to be robust because the size of the samples is just impossible to argue away statistically. The people who pass through the hunger winter, the winter in Holland at the end of the war in 1944-45, In condition of extreme semi-starvation, of very near starvation, because many did starve, there was in the cities, there was mass starvation and many people died of hunger in that winter because there was a complete breakdown of distribution in Holland. The Nazis stopped the railways from operating as to retaliate against the Dutch civilian population for the... The fact that they come out to help the Allies when they try to land to liberate the Holland when they did the big airborne drop in September 1944 and for various reasons the humanitarian crisis in fact became so terrible that in the last months of the war, the Nazi A Reich commissar in Holland, Seisingart, who was hanged later as a war criminal, did actually negotiate effectively a separate surrender, a truce with the British, which allowed them to, allied planes, to overfly Holland without the Germans firing on them to drop supplies to the... And perhaps half a million people would have died of starvation if this hadn't been done. As it was, something like 100 or 150,000 people did die of starvation. Now, so these people were... ...passed through as children, through obviously horrific experience of extreme starvation, and clearly it did very significant things to their metabolism, to resetting their metabolism.

25:00 Nothing at all out of the ordinary in their children, but their grandchildren... There is now massive statistical evidence that the grandchildren of that generation in Holland have a significantly lowered metabolic rate, and the statistical evidence is just overwhelming. And they are able to cope with deprivation of food much, much better than the average person. It does seem to be that there was something that did actually happen to modify the genetic transmission. Not in the immediate generation... But in the following generation after that. Which of course is exactly what Lysenko's vernalization theory purported. Very embarrassed silence by everybody around the table at this point in the discussion. Well, Stephen, of course Professor Jones is not suggesting that there was anything in Lysenko's theory, is he? No, no, no, of course, of course he wouldn't. Is he? I mean, I must send you the podcast. You can actually listen to it on the website. It's a very, very interesting discussion. Very interesting discussion. Those little things crop up from time to time. I rather like the talk about the cosmologist at the observatoire about a year ago that I remember talking to you about when you were last in Paris, that I'd just been to listen to, about all this work that was done on the so-called cosmic microwave back-road radiation was actually detected back in 1932, not by Penzias and Wilson. And was then interpreted as a kind of mixed master effect from Starlight. Anyway, the Lysenko stuff was completely new to me and I was very intrigued by it since this guy is a very respectable geneticist. It's become, to classical genetics, this data about the Dutch, the grandchildren of the survivors of the Dutch hunger winter, has become as much of a kind of embarrassing anomaly for classical genetics as, as I said, it's kind of the pioneer anomaly, it may turn out to be. Actually, I suspect it's probably much more of a genuine anomaly.

27:30 How does one get to be president of the Royal Society? Presumably one first is a member and then... Well, I think you have to be a member. I think you're elected by the membership. You're not appointed by Prince Philip. No, no, it's not a royal appointment. You do get elected by the members. I think the Queen probably has to certify, you know... It gives you some bit of vellum, you know, to say that, you know, she of her own mere will and volition or whatever it is, mere motion, is happy that you should be the president. But no, it is, they are elected by the fellows. Were you thinking of Atiyah? No, the present one. Who, I've forgotten. Oh, that, the present one, it's Rees, Martin Rees, isn't he? Yes, yes, yes, the cosmologist. He was the official of the Templeton family. God, him too now. He is a great proponent of the multiverse these days. The multiverse, you know, the great proponent of the multiverse and of Everett's interpretation, kind of crazed interpretation of quantum theory. You know, people think that I overemphasize the role of Templeton. No, I don't. I did for a time, I have to be honest, but not any longer, not any longer. They have just enough money to actually do have a global influence. Global reach. Vatican universities. No, I'll be absolutely honest, about three years ago when I first, or three or four years, but probably longer ago than that, but when when Templeton first really started registering on my radar screen because of what you... You said, I will admit, for the first three months or so, I thought, Bill does bang on about the Templeton Foundation. That wasn't too bad, was it? Bill does bang on about the Templeton Foundation, doesn't he? It's a bit of an e-day fix with him. Don't you think he's prone to get these, you know, these... And then when I began to dig into it, the more that I looked, the more I became convinced that what you said, if anything, was an understatement. No, no, I'm entirely convinced now that you'll spot on as so often.

30:00 One of the many here. Now I saw Reese again on the web. There's another Templeton official who is a professor at Princeton with a Czech name. He has the same name actually as the chief of the secret police at Prague, which I don't know if that means anything, so I'm going to ask the other man. In any case, so the two of them, you see, at the Royal Society in 1975 when he was their president. Which was the subject of a seminar which Caulfield, our friend, Caulfield for a time ran a seminar in Cambridge in the history and philosophy science department after Michael had retired and they brought in this new guy to run it and for about two years Caulfield had a seminar there on so-called new philosophy of mathematics which was supposed to be philosophy of mathematics done by people who have actually ...not actually gone out and studied some real math or talked to some real mathematicians, but who of course have gone out and talked to the mathematicians who are ready to give them the buzzwords that can enable them to parade around pretending that they know about all these subjects which they have not really studied any serious scientific depth at all and hence of course his ...lionization of Bayer's and of M-categories and the very non-competitive geometry and all the rest of them. One series of this, I mean, an entire term of this seminar, which I did, I confess, I did actually go up to record them for the archive. I gave up after the first term because I saw that there were not any readers. Although occasionally they had one or two good people turning up to them. But they soon lost interest when they saw that, you know, there was not going to be a really serious discussion. For one term he gave a series, I think it was about six, on the subject of this Royal Society lecture which Atiyah gave in 1975. Which I still have the text, which I must show to you, which is very much in the line of Jaffe and Quinn and...

32:30 You know, beauty, heuristics, much more. Anti-Bourbaki, you know, very, very terrible. I mean, the Bourbaki project, you know, basically a very bad thing because it wanted to kind of freeze mathematics into some kind of congealed structuralism and, you know, put a cap on imagination and... This is 75, yes, yes, this is 75, which is already 15 years or so before Jaffee and Quinn, yeah, oh, yes, interesting, so just from the point of view of the ideological record, interesting, even though the content of the lecture itself may not have been, of course, the content of Atiyah's mathematical ideas is very interesting, he's indisputably a great mathematician, that's the tragedy, I mean, look at the, Atiyah said that, I mean, there was one, there was one talk when somebody, a topologist, a very, Good topologists from the math department just came along and gave a purely expository talk about Atiyah's work as a topologist and about the Atiyah-Singer index theorem, explaining it for philosophers. And that was well worth going to. But that was straightforward education. It wasn't all this speculative stuff. Caulfield, as I say, doesn't ever seem to have anything serious to say at all. It's astonishing. Caulfield just doesn't seem to have anything at all serious to say. I mean, Colin, for a time, I know, was trying to encourage him to come to meetings, and there was this thing at the Open University in about 2002 that he, Colin, and the guy, Jeremy Gray, at the Open University organized a summer school where Colin and Jeremy and a number of other people gave courses, and some of them were quite good courses, but... I had him, I was going to say here, but I actually mean in Paris in 2005 for this meeting that we had in honor of Saunders-McClain, which where Colin spoke about your work, and we had one or two, there were one or two good talks at the meeting, there was a very uneven quality, I have to say there were some very bad talks, but there were perhaps four or so. Ah, you do! Sorry, I thought for a moment you meant during as in Engel's sparring partner, the other during. Yes, also a misguided me. Followers in Germany. I didn't mean that one.

35:00 He was actually proposing that we should have some meetings at the Perimeter Institute. Yes, well, I mean, I think there are some good things at the Perimeter Institute. I wouldn't write them off completely. It's a very mixed bag. There are some weird people there, but there are some ideologically motivated people. But they're not like Templeton. I mean, they do seem to have some... Well, they are literally a Templeton, several of them. Some, some, some, but... Not all. Not all, not all, certainly. I mean, I've met some of the people there, including some of the people working in this loop quantum gravity program, who do strike me as being, even though I can see conceptually there are some very serious problems with that program, but they do seem to me to be perfectly serious, mathematically serious people. And I wouldn't write them all off by any means. There are some very interesting people there, but it would be good. I think we seem to remember talking to you about this when we were chatting on the phone a couple of months back. I think you should definitely take them up on the invitation to go there, which Smolin keeps telling me that he, you know, has issued. Smolin, you know, Smolin? Yeah, this is the devil can tell. Yes, I know, he is, he is. I'm sorry, this is... Well, no, no, you're right, I'm not questioning your judgment. If I see that as a person's first credential, if he has that credential, as a... Do you have an approximation as a basis for investigating your first connection? Sure, sure, sure. As a first approximation, the assumption has to be that, you know... Are you obsessed? No, I don't. I don't any longer. As I say, when I first registered this about three or four years ago, I was a bit inclined to think you were, but not any longer. I really am not. But I do think it would be good to go there and talk to them a bit about, well, for instance, about Steve's work on... Analysis and on, yes I say, and on, and on, and on. Triangulated categories and on the source and the connections with Mackey theory and the origins of the canonical commutation relations because that's, I mean, the more I look at what Mackey did, this is one subject which came up, there's a very good expository talk on Mackey theory at this Beyond Einstein meeting by a guy, a Swiss guy from ETR, in fact, I can't think of his name now, but a youngish, well, maybe mid-thirties...

37:30 I'm a researcher from the E.T. Han, explaining essentially how Mackey's work related to what Wigner had done, you know, on representations of the Poincare group, but putting it all on a really rigorous mathematical basis, and it did seem to me to, well... I was left with a hugely increased respect for Mackie's, the depth of Mackie's achievement as a mathematician, but also more and more of a sense that conceptually this really is the way to go to arrive at a deeper understanding of where these features in the formalism of quantum theory are coming from, that the deeper meaning of, and possible deeper meaning in the hidden variables theory... I take, but I give to you after. You give me back my card? Yeah! He's a good man, an honest man. Very honest. Will you let me put something in, Bill? All right. Okay. Well, in that case, you let me do it on Sunday when we go out. Can we ask you one favor? Is it possible that we could order a taxi? Yes, sure. Do that. Oh, you can go across the road, can't you? Oh, there's a stop. Well, it's okay. I'm walking, but my friend here has to get back to the Hotel Chambord, which is Avenue Namur. Avenue? Rue de Namur. The other side of the palace. Rue de Namur. Rue de Namur, yeah. That's very kind of you. Oh, what a nice, helpful young man. Oh, he's going to do it for you. That's good of him. Oh, really nice of him. He's going to have to do it himself. Well, he'll certainly do it. Yeah, that's all right. I'm sure of that. Oh, okay. By the way, I didn't tell you my proposal for Sunday. Oh, go ahead. Do you remember my failed attempt to take you to the, uh... I would be surprised if you had already done tours. I ask it's 10 euro, no more. Very good. Thank you very much. Thank you very much indeed.

40:00 In our third evening, I want to wish the 15th day and the very long list to our guests, on 6th and 28th, and the 6th day in a row to the very important and very recent age, the young men who are here today. Well, as I said, time, left, west, move yourself, since you are already left with your marks, so I hope you will have, in many long years, to be able to do future research and so on. All that has been put to me, and I'd like to leave the third lecture, perhaps this can be justified by the fact that I am known for a few hundred years, since beginning the research, more than 30,000 years ago. In reality, the seven students working on this day, and as both of them, Dominique was a member of our research team, Theory and Applications of Technologies, and so we had long discussions in the office of Charles in Paris before and after the seminar we organized in Paris, and Francis and Tadai have sent us... These are the first research words, and we are delighted to give a talk in that seminar, and I remember that I was very surprised to see how it seemed after that we went to the restaurant, and I was very surprised to see how thankful it seemed to be for CSLT.

42:30 Very good recollectional concepts. So, today I want to say a little on the words of both of them, essentially. The title of the talk, Egoism, System and Mathematics, does not mean that I am going to give mathematical... But one day, that I want to try to give in a rough manner the philosophy to adapt to this underlying philosophy which was the reason for which we have developed. For mathematics, I hope that you recognize what I have learned and what I will say from there. The first is here are two. Two photos of them. As I remember then, for me, there are still two days like this. It was taken just not long after I had been there in 1973. This was during the work we had done in San Valery, a little resort station near France, during the first conference on the category. The theory we organize with Charles in Amiens is a two-year paper, if you count the season, it's not too deep, so we're going to do a second follow-up, we're going to organize in Amiens.

45:00 This one paper is going to be on the last day of the course and we are going to have six days here. And after that, both participated to the other, particularly, conference I organized after the death of Charles in M.D. I have no photo of this project yet, but at that time, what has been made, what we think has been made, so what we just observed, that's the article, two days at a time, and the last six days at the end of the conference, we had a very moving and thankful speech, and I've been very moved by it. The lecture consists also at the origin of the conference that I organized in 2005 from the address I did yesterday of Charles since he is the first who spoke to me to organize something that all of us in health and that was very important since he was able to find I have been training for several long-distance travels, and I am very happy to be part of it. So, just a few more minutes before we go into the server. Conxys have essentially done most of the study in Malabar, where we organized a very important category center. We have made many invitations and we have helped to the discussion of category theory, as well as by conferences, invitations, and also by comprehensive groups we have created. Dominique has been for a long time, for a long time, my colleague in Agnes, and after that, he is our professor in Paris, and where he is still working, the center, where we have had the opportunity to have a very interesting international conference.

47:30 Philosophies underlying the memory evolution system. So, I must give a very short idea about it. An evolution system... What she suggests to the latter of the ninth scale, which is the finite exponential part of the positive real, and for each type of category, which the idea is that it corresponds with models, the components of the system at that time, and also interactions that have around that time. And if D5 is more or less big, there is a transition from DOR, not from the whole of the category of HP, but from a sub-category of HP, from SQ of HP to SQ5. And the only condition being that the idea being that the H is not combination. Next, state and define, and the only condition being that if a key has a state and it defines, then it has a state and it is wrong. If a domain is a key defined, it has a state, a key state and it is wrong. But now, if I want to define the... I want to consider not only mathematics, but also the groups of researchers, the larger researchers, the university and so on. And also there are mathematics.

50:00 For that, I need three articles in each step. So after what you need, after that, the categories are the objects partitioned in different levels, context-level, and the variability between the objects of level n-1 is the probability of at least one diagram of levels of other levels. And the transition often corresponds to what we call a complexification process for a strategy. What does it mean? It means in mathematical terms that we leave a sketch on the entity, for instance, and on the third category of entity, and the transition proceeds. The prototype, what we call the prototype of the sketch, the sketch in fact, that is, in other way, we have also pressed some limits of polymix. This is a quantification process. So, in the last, the PRR, in fact, the research center, is the polymix of the developed world. Now, the memory system is an evolutionary system on the continuous of an enterprise of R, but in which we have also single downs. This is because we don't have one time, and each time, so we are, we are, so there are different systems, which is the memory. And also the family of self-evolutive systems called quantum networks, which model self-improvement of the system.

52:30 There are many other topics. For instance, there can be at the lower level just an individual. At the higher level, there can be, for instance, the research group, the research team, and so on. And each trigger has its time scale which is distinct. So what we have is the dynamics is modulated by the interaction between the different CRs. So at each step of the CR, so one step, first the CR constructs... For instance, for the research field, we will gather information that was quantified and so on. Then, in the second phase, we will strategy on the second phase. The second phase is defined as objects. The components of the polar category of LFP based on the system But only those which can be seen in the landscape. This is one of the important points in the memory evolution system. It is that the idea is that the sky has not the objective view of all. It can only have the view of the things which are already soon enough in the landscape and which are long enough to be seen in the landscape. This is important for it to explain why there is only something which can be conceptual between the different CRs, since each CR has its own mindset, its own view on education. The second aspect of the research team has been to plan, to planify the conference. So, the idea was that if it was possible to package it successfully, the new landscape after its realization should be the complexification of the natural landscape for its packaging.

55:00 But it is not already done. So, at the beginning of the next step, there will be a comparison. The actual landscape, at that time, had the antithesis of the science. They are not comparable, are very different. Then there will be the functional consciousness. For instance, for the research, he has very well... he is not very capable to find such a philosophy across the countries. And what is... Because the differential are competitive and so the little program, all their strategies cannot always be realized on the system. So the operative strategy is really realized on the system with your place. The result of the interface is with the different strategies. So now, I will try to give the view in my own own scale, so perhaps it is certainly not objective, and perhaps some of you will try to complete it all, because my experience is in my own scale, and I cannot give another thing that I hold nothing. So first, I want to... I would like to say some words about the situation when Francis and Dominique arrived at the University. So what was the situation and category at the University? So this is the evolutive system of categories in France. Tellurians were invented in the early 40s, but at that time, they were old, and the communication between France and the States were completely one. So, that proposal could work, except for those who were in the States at that time, for instance, on renaissance or on shamanism.

57:30 Now, after that, Schrodinger is up to 57. There was almost nobody who knows categories in France, except there was, naturally, Henri Carton, who has written a book with Heidenberg on the world's colors in art. I have been, I have looked at the index, the date of contents, to find the ontorial algebra, but particularly not good. In 1957, if you look at the different seminars in Paris, at that time practically all the research was centralized in Paris, not that there were not people who were doing research in other places, but anyway there were not so many mathematicians and we all gathered for... For the meetings of Société Mathématique de France, for the team of mathematicians. So we knew each other very well. So at that time, the categories were began. I can give a testimony of this. I was then a student of Schocke, who was a very open-minded mathematician, and at the time, in 1957, he asked me if I knew what was category, because he had heard some terms and would have more ideas about something. So Key was a very open-minded person in his group, a tradition who has made possible the small development of probabilistic theory and the possibility of both at some time in France.

1:00:00 So, and in fact, it has had many consequences. People decided to try to find things, and in particular to look at the book of Sacha and Agnès Baer, and I read some of the times in the library, and... He was charred one day, saw that I was looking at the book of Alexander A. Cartan, and asked and said to me that it could land me, and so I went for the first time in his office. And I was present from then on. So it has some consequences, as we always have all the consequences in life. So, at that time, there began to be people who began to seek knowledge, which we categorized and defined the seminar as the seminar of Carton, Chevalet, at that time, and also Cormier, and very frankly, during the years of... From 1758 up to 1665, there was a large discussion of categories. It was very up-to-date to do category studies, at least a little less in 1665, but up to 1675-1664, at least in my landscape. This is what I think. And then, no question being, why? So that in 1972 when Dominique and I, our research team, the opposition was already strong enough and he was much stronger in the following year and he was very welcome to us and he was definitely discovered for a very long time. Now, what was Charles' whole methodology? He was not so much aware of categories before he did it, but what he had used very much is compolites, is the length of these, and the form of geometry, differential geometry.

1:02:30 And so, at that time, he had no idea that compolites are subject to numerous categories, functional categories. Bobadet heard that it existed, but he did not know it. And it's during one of his courses in Brazil that one of his students, Constantino Barros, asked him if the multiplication defined on the infinitesimal space had got something to do with it. So, he went at that time to study the paper of the Mendeleev party and he realized that the cohomists were categorists at that time and that categorists were asked to do something interesting. He thought that categories were interesting, but he had some reservations. In fact, he thought that And so then we get to use Krokash categories, which are not from human-child categories, but were still sponsored by the theory of Krokash culture, and were still widely asked about that. I wrote the book, the paper on the type transfer, which is a kind of formalization of mobility, structure, theory, with frame categories, with the introduction of other categories. And after we give this time, we want to define topological categories, differential categories. And the fact is...

1:05:00 So this is the gathering of all the pieces of topology, for example, several local categories, then to define, more generally, the notion of internal categories, like in a concrete category, categories called structural categories, and after that, by the set of categories. After that, the steps to the Hitchhiker's. And so, from the Hitchhiker's, still more after 63, all his work was really done in technical research. Our research team's task, the orientation of the category, was formally recognized in the It was a research team, Amiens, Paris-Amiens, and in fact, there were the opposition that soon after that, in the 70s, so that it was strong in 72. However, if the opposition was strong in Paris, I must recognize that in Amiens, though there was some opposition, I always managed to have... The funding I wanted, I tried so much I can't understand, but really there was an opposition from my point of view and in fact in the end before I entrusted the research team to the week, but at that time I was not doing so. So now, for our focus, first of all, I have got something to say to find a job today, that's right! So, what I've got is a list of applications.

1:07:30 To try to see for each education at a different time about the domain on which the mathematics education was done, and then, which was much more difficult, to try to find this mechanism, the equation, to make them in a model of, in my own case, So, what you see, there are two very particular, I will give a lot later, two threads for translation. One thread is on Enric's structures, really here, and also a second thread on Schiff's algebraic structures. Here, there are some of the most numerous. So, which is here, first, we have like, let's say, a paper chart on this memoir. After that, the panellist, then the white brother with the algebraic features. After that, then the panellist, and after the... Thank you so much for this talk that we had with Mr. Kodakshwan. He came back to research on the issue of seniority and automobile, automobile and so on. Before going further in this class, I would like to thank you all for your attention. Thank you. And the brainwritter is a space actor. There are not many arguments to this. Here is a space. It begins by studying categories and monads, monads, monad-monads.

1:10:00 Then it takes place in notions of that meaning. So the first thread is this thread of cohomology with Aspoult and Oukouïs, their categories and Oukouïs. And there's a second thread which began with the production of homo-bubular categories in Yann Tzoua and the release of organism sanctuaries. That was the first part of non-Abelian cohomology. In 1964, Charles had defined and tried to adapt the categories, the homology as it was developed in the book of Magdalene on cohomology. That is, he took, he conformed from categories to cohomologies. And he tried to define the cross-homomorphism and in this way he identified the H0 which was just the set of components of the unit F and the H1, the cross-homomorphism, as a function of a tensor. The other terms, the set of components of the last years. So when Dominique Comart began his research on the last years, at that time it was about catalysis and analysis. The world has not been taken, and I think we have hoped to recall this world, but it has not been taken. And so I recalled him this paper, and he was able to define the answer. We have always thought this would be done somehow. So, in 3D, we were able to define the H2, in the case C, the boundary, and the H, the H2 values. And that, we defined the H2 as what we called at that time the tetra-limit.

1:12:30 But the set of components of the tetra-limit of F were different. So this, he realized that essentially what he's doing is that when you have an abelian book, you can always look at it as an end book with, in their life, to an abelian book with. An abelian book is not an abelian book. So he developed the notion of internals and categories and then first he defined the power of a category and then he did other works with that and later he came back with the power of exactuation between internals and categories. With definitions, instead of taking usual and rich definitions of hand movement, you can say he took the internal definitions of hand movement, so as if there exists a tower of hand movement, a tower, he is a bar, a car, a car, a tower of exact situations, from form to form, hand to square. In this lecture, we will talk about the generalization of the old plan of Chiorenne, the generalization of the old plan of Chiorenne, the generalization of the old plan of Chiorenne, the generalization of the old plan of Chiorenne, the generalization of the old plan of Chiorenne, And indeed, the category of Christopher and Euclid's theory is equivalent to the category of positive concepts of abstract.

1:15:00 And this equivalence is very important because not only it is good on the objects, but also on the world. And there, if you find the non-homological equivalence, in the case Euclid was written. Then this object group can be considered also as a common group in the fiber of L1, as the expression here, as an end group with an alien object in this fiber. This X is an end group. With global support, you can take university grades of this academic group by conflict of this class and ordain an academic group so that you have the possibility to define by iteration and in fact all the... Many of the works of Gordon, at least at that time, were based on iteration, which find a good iteration process, which is very interesting time, and so the cohomology hoop, as we find, for the algebraic hoop, is just the hoop of the variance of k, and for h, n is 1. It was then that the phonemes on all the X, on all the X4, on the H1, in the fiber of the X, are these adhesions. In fact, the pop-up, which will be an essential tool, is following what we have got on the protocol we have and so on and so forth.

1:17:30 That is, the integration of concepts, artifacts, and theory objects are an important part of mathematics and geometry. And mathematics is the interest of the square. And the if is very clear, then the category of homogeneity is monaic, other, other, and this is for comprehension and reach of, and this is very important in some of the projects. He finds, in some way, the power of a new point, which I have indicated before, by the power of normalize. And he tries to find an induction to the notion of normalize the point, xn, if the invariant of xn by the equation depends on the minus point of the point of the context. This is already not applied. And if you consider the Moffitt-Wattenside to finalism in the fiber, and this is this tower. And this guy, the chanteur, is a connexion. And of course, the connexion category of Paris-Rouge is the French-Rouge-Rouge. And then he finds the chanteur there, the connexion there, the connexion there, connects Paris-Rouge from this tower with the tower of the street and future of Paris-Rouge.

1:20:00 I have also noticed that I have never seen... There are two more movements in the Kupanar and Tsai, with Pellon, where they define the categorification process for structure, defined by Cartesian closed monads. We learn from Thor always using the detection process, and coming from Thor and a monad, a Cartesian monad on his domain, they define. When it is applied to the centers of set 1 and the identity monad, they define two different terms of knowledge and categories, with units in comparison, which stands for genetic code. So for the moment I will not say the second thread is the fourth one, because I will talk about it later, because both Dominic and Francis have worked together in this last thread, but I will go to the first thread of Francis. So the first thread of Francis is an average algebra, in the degree of physics. In this thesis, which was done with Lavendor, we developed a generic algebra and tried to define the social benefits and the benefits of eigencomponents and so on. And in particular, probably one of the most important concepts was the theorem, which is generally referred to as the first paper. Seventy-five is a notion of indexing of two sub-dots, dashed from A to Z, one where Z is the symmetrical polynomial of A, and Z from A to Z, and G from A to Z, and the vertex of Z is...

1:22:30 There are a lot of different types of physics, but the one that exists, the physics objects of mathematics, mathematical physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, physics, Then, in the following papers, in the following words of Francis, I had some problems, because while the papers of Dominique were translated and written by him alone, and the papers were written with the loan of Australia and China, most of the papers of Francis are written for the Westerns. He is a very collaborative mathematician, and not only with one person, but with many, many persons. So what to do? So I have put some words, some names, but at this time I have just used the name of the particular paper on which I have counted the abstract. Probably some people will find that I am completely forgotten then, and I cannot do more because I would have to write so many words, names, that it would have to be forgotten. So, as I said, we have first done exo-category, and then, and then, and after, it is the pen drive. He defined many enriched notions. So, in a locally, fanatically, preventable, and valuable application, it is very good that there are reflections between the notion of very enriched cheese, so that it penetrates the notion of very rich cheese, so that it corresponds to the localization of the category of very rich cheese.

1:25:00 We have discovered how the universal closure of the total organization of the aesthetic economy and how it is possible to reproduce it as a reproductive topology. However, the model with which Penrose came to the question of accessible categories, enriched accessible categories. What are enriched accessible categories? What is an enriched sketch? And is it possible to apply for an enriched case, for example, between the accessible and the sketch? And effectively, they rotate this theorem so that the accessibility generally developed by Cardinal is replaced by the consideration of some kinds of codes. When we find, we generalize the theory of regular rules by defining the notion of trigonometric terms, categories without rules and regular equations. In fact, in almost all the papers of the Francis, there are many applications of the ways of Algebras and also the analysis. Then, in the way that now is defined, it is an option of Adam-Muller, as in my academic categories. As you may have seen, the category, category A, category A, which was censored in A, is Morita equivalent with the category A, and Morita equivalent with Atiyah is equivalent with the category A transformation.

1:27:30 That's exactly the case of Barnard-Wood. This is not a thread, this is an algebraic theory. So, first of all, we start with the event on the gosh, and this is our book. On the day of the sheath of her locale, a ship of T-algebras, a ship of T-algebras, a ship of T-algebras, a ship of T-algebras, a ship of T-algebras, a ship of T-algebras, In science, there are a few platforms of theory, such as the spectrum of things, and there is a very interesting innovation to add. There is a TRG-1, an item of TRG-2, and a TRG-1, a global section, by the science, which follows the two spectrum machines. And these are developed in the group of three chapters of the application of these. In page A, you can find out the representation of Hohen by categorical method. The representation of Hohen of mathematics. Then, start presentation of Hohen. I think it's interesting, which they did show, saying that the categories of the separator objects for a Lauban-Pierre-Dernier topology on a set of topos can be completely characterized as a category, a locally presentable, locally conditioned category in which... Then we have a whole series of papers on quantiles. Quantiles are mutually deductible quantiles with the addition of each of the other points,

1:30:00 and so it generalizes the notion of the properties of the world's ideals. So I throw ideas of an algorithm that is challenging. The lab has written many papers on this, on quantiles, which many people, I am going to thank these people, made up of two co-authors of the paper, one of the papers traditionally presented. And there, they define the notion of shifts on the frontal and the side, or that there are three equivalent notions, equivalent sets, shifts on the frontal, or pointales, déparées, on the left or the right. Then, more recently, and somewhat mixed with the last 12 or 15 years. The structure is one of the stem of the node on the strength side to the algebras from a randomized theory, but now when the category of model is standardized, and this is where the category of topological model is homologized. In fact, more recently, I have seen that there is a lot of paper looking at the day prior to the 13th historical year and extending the 15th century. And the final day, in the second half of the day, with Clementino, Adams, Strauss, Cantonelli, Strauss, etc. They read the definition of the notion of photoreflection. And now, the last one, the 12th, on photovoltaic capabilities. So, in the 66th chapter 5...

1:32:30 To generalize the notion of weather, the notion of exact winds, in the day of the very high technical research that we can do. But now, it's another way that has been done. It's to try to take back mutual results on the field. This was just one example, and I tried to find the best example of this for a category, and among these categories, one of the best models seems to be the photomodular categories, which don't have any problems in any way. And the homology of the topic is defined with the help of the PPP. I have defined the situation of qualified objects. I have defined them. And it also proves that there are many other possibilities to classify the degree to several options, All by classifying students and the notion of cohomology as a category, as I said, we have heard in the non-political days, this is why I'm going to show you, I'm not out of it. All of this can be found in the book, in the done book, and also in books and papers, in the done books of physics and geometry. And I did not say more about this because I don't know much about it and I hope to learn more in the future and so I will just stop by saying that I wish that Francis and I will go back and find many new results and so have many years of fruitful work. Thank you very much.

1:35:00 Thank you very much for your attention and we look forward to seeing you again soon. Yes, I should have written also the words, but it was on the book, so that's it. And we thank the speaker there for this beautiful lecture. I think we've heard so many interesting things. I think we have three hours for questions and comments from all over the place. We've heard so many interesting things. We need three hours for comments and questions. It was a very enriched talk. So, thank you.