Conversations incl M Wright & FW Lawvere on etendues

0:00 I'm going to go into the middle first. It's surprising, getting a lot out of listening to Anders, talking to Jerry about the models that he's been looking for, for his quantal structure, and a lot of things. And Rosenthal, the publisher of the JPAA journal, very shortly gave her with the awful title, Quantaloids. It shows the non-standard nature of things that will not exist in a big movie. The sequence preceded is just simply mistaken. Yeah, you talked to me a little bit about this. I remember very clearly. I still retain some of it. That which I said has been written and much more. I mean, he has many more applications. The point is basically that they shouldn't all be monois. Some of them are categories of one and one object. Even the category with two objects, which is perfectly transparent. Distorted by a certain operation gave rise to the mistaken idea that the identity was almost one-sided. Have you seen the newspapers today? No, I haven't. I only saw... I'm ashamed to say. I only saw very briefly, but Havel has now gone to Austria to meet Waldheim and von Weizsäcker and gave a speech about how to accept our past, i.e. our Nazi past, I presume.

2:30 We all, we all have to accept our past. I'm talking about the obliteration of distinction, you know, the obliteration, the seriousness of distinction. I begin to think they are developing ideas. Well, no, actually they're not, of course. They wouldn't have chosen that role if he had been. I forgot about von Weizsacker. Von Weizsacker is, well, he is, of course, the brother of the Seattle von Weizsacker, the physicist, who worked with Heisenberg and was one of the people who worked on the atomic bomb project of analysis, and who was, in fact, which has been kept very far, the son-in-law of Ribbentrop. I think, I don't think many people know that not, not Isaac of the president, but his father, one of the physicists, actually married Rivencourt's daughter. I think their marriage was dissolved after the war, possibly, but, but, but, but, but, but, but, but, but, No, I should be very interested to see this. And it's coming out in the JPAA. Is there any chance you could send me out a preprint or will it be coming out very soon? It's already been contributed. I'd like to, because this is a whole area where I was very deeply confused for a long, long time. And now, thanks largely to you, I see much more clearly what's really going on. One question I wanted to ask you before we went. Jerry and I are going to have to get off very early tomorrow. We have to get to Paris to see his mother and I have to get back to England to meet these people who arrived the following day. Which is a pity because I really wanted to stay till the end. This is not the question, but would it be possible to really analyze it? I think that and Anders talks were two of the ones I most wanted to see, but apparently there's no way we can get to Paris in time otherwise. Subtitles by the Amara.org community

5:00 Would there be any chance of Jerry and I coming to visit you in Buffalo perhaps later in the year, if you've got perhaps around the end of the year? I know you did and I wanted to do it in advance, but I was just wondering whether the invitation was still on the way? Because I think we'd probably get an awful lot more out of listening one-on-one. The question I did want to ask you is, I don't know if it's, I mean, it's about a tom-do. I have particularly bad, I mean, I want to understand everything, my problem, and I have to submit, I have to go, I have to go, I have to find the time, somehow, I have to get in the situation where I can find the time to do. Several years of really serious, organized reading and learning, but one particular area that I want to understand, étendu. You made your point about étendu. I probably wouldn't be able to follow the relation to foliations because I don't have the concepts yet, but... I don't have the tools. Well, I'd like to read that. But just at the barest introductory level, the point about the way one thinks of the two topological characters of the domain, there's the flip, rather like Squidberry, which gives you, I guess... What I want to get at, the point you made, is that the mergers band is a good quotient in the sense that the quotient in topological basis is the same as the quotient in...

7:30 All of these are topologies, and I argue they are topologies. Right. It doesn't preserve all co-equalities, but it does, of course, preserve some. Right. And what you have to have to have an etendue, isn't it? I mean, so to speak, a genuine etendue as opposed to one that's merely an ordinary space. In other words, etendue is locally a space. So if it's globally a space, then it's, in that sense, trivially multi-modal. Armstrong, which is in broad italics. So what you have to have is basically a bad action of a group, perhaps, or more generally a monoid with only a monomorphic pattern. The action doesn't have to be invertible. But a bad action in the sense that stuff gets more mixed up when it gets moved around, as in ergodic theory. Yeah, I remember you drawing the analogy, the connection with ergodic theory, which could be an example, actually. I mean, my question is more... Some of the mysteries surrounding ergodic theory are due to the fact that it's sort of forced into, not a topological space, but a Borel space, instead of seeing it spread out as an A-kind theory, which it more naturally is. Unfortunately, I don't know anything about the Galic theory, so... You know the idea that the dynamics mixes everything up, so to speak. In other words, the good quotients, quote-unquote good, the ones that give an actual space, even when you take the topo-stereotic quotient, are those from which every point has a neighborhood which is completely moved away from itself by... Well, for each act or g, small g, group elements, and for each point, there should exist a neighborhood which g moves to. g is not the identity. No, no. For any g which is not the identity, and for each point, there should be a small neighborhood such that g moves that neighborhood completely to a disjoint neighborhood. So things are nicely kept separate by the action.

10:00 So it's another case where you have more mixing up of the original space than of the action, then you will get, so to speak, a genuine atonement where you really have twisting going on. I see. And in fact, what you said there, by relating it to the physical case of the garlic theory, actually answers the question, which is a much more naive question, which I was going to ask, which is, in what sense does this cross-site on the way that we think of the domain topological? In the case of the classical set, you make the point that these are a good example of a domain of variation which is too big to be a set. In a very physical sense, it's an enlarged domain of variation and assertion. You see, I think that a philosopher is what's been kind of exposing stuff in philosophy. It's that point about the very... We now have to think about domains of variation as against the way that the classical set theorist thinks of them. That's what I wanted to get at. So the point about the topological character of the... Well, you've got a kind of two topological character because of the switch in the case of the 8-0-0. Whereas in the case of the classical set, I'm trying to put the contrast, I'm trying to get my mind firmly around the contrast between the way one thinks about it. Is the fact that the... You didn't take one for yourself? No, I did, I took one for you actually, so you're okay. The sense in which the set, classical set, is not, as it were, the beyond and end all like Mabry thinks, the foundation of everything, you know, collections of extension, there is no more primitive notion in terms of which we can define this, it turns out that in fact it can be related to very materialist ideas of which we grasp with geometrical and topological insight. And that's wonderful to me.

12:30 It's a wonderful revelation that mathematics is not the... You don't have to be a religious believer to understand mathematical structure in the way that mystifiers have said. It's just a particularly beautiful example. I want to be sure I had understood it. Is the way one thinks topologically about the structure in the case of the classical set... Sorry. Is that... Is the point about the extensionality being equivalent to some relative uniform separability, the kind of the identity is the separator of any pair of arrows, does that change when you go over to an 18-year-old? Well, the way you think of the separator of any pair of arrows, you know. Well, the thing that kind of keeps track of where the arrows go, so keep track of when you've got equalizers and co-equalizers, the, I'm sorry if that's not the right term I'm using for it. Equalizer, co-equalizer, do you actually mean equalizer? Um, I, you know, in the sort of elementary books that I've read, it's usually referred to as the separator of a pair of arrows, but that's obviously not a standard piece of terminology, maybe that's something I've got. The word separator is usually used for a class of small objects, just in the sense that there exists a map from one of the separating objects. Oh, so you're asking what are the generators or separators in the A to Z? Yeah. Ah, okay. Yeah, I'm sorry. I'm very bad at expressing questions. No, no, that's good. I haven't learned the complex. So those are, yeah, so those are... I mean, it's a kind of tree. This is all explained in great detail in Rosenthal. Okay, I'll go and read Rosenthal.

15:00 No, no, thank you. So the objects which play this role in the category of set value achieved on an ordinary space... These are just the open sets of underlying space viewed as very special sheaves with just one layer that only extends over that open set, whereas the general sheave has many layers that may cross each other, but they're an upper layer. So in the case of the Etan-Do, yeah, there is something similar, but so these open sets are... I'm sorry, I can't get it very... Remember the etendue has this covering, it's the quotient of an ordinary space, which has these opens. So basically each of these opens gives rise to another piece, but then you have... So imagine little pieces of the original space, the little arrows, according to the action, which sort of go partly between them, as extra information. As extra information, which of course in the case of the quotient space with an ordinary... It's got to be the domain of variations of the classical set. You don't have to... No, because they're again just little pieces of the quotient space. Of the quotient space, yeah. Here you have little pieces with some trace of the... Of the variation that is precisely why one has to think of it as a domain of variation. It is enlarged relative to its way within the variation. It is really moving within itself, instead of being static. I mean, as opposed to the fact that the sets vary over any place. Yeah, sure. So that reflects itself in the generators as you correct me to it. No, no, I mean, it's wonderful to have it. It's so clear. But that's precisely what I was trying to get a hold of, that it is in a way that the motion is actually built into the domain itself, the variation is built into the domain itself. You don't have to think in terms of objects sitting there, the same or different, absolutely. These values are the variables that are piled up into the conic heaven. That's the only question I suppose that's been given in advance, hence the way the cardinal... I think this is a very important insight for a materialist who's faced with some of the uses of mathematics.

17:30 They're enlarged in a way. There's variation going on in them, which prevents them from moving back to the ultimate being, because people immediately think in terms of the class at the stage of growth. Well, that's cleared things up for me enormously. I mean, the intuitive way I'd grasped it was right, although I don't have the exact tools now. Well, I must go away and understand all about the action of the group and explain the twist and then the general. Oh, well, thanks very much for explaining that. Yeah, sure. We'll see you before we go, anyway. I've just had to explain simply in the way that Lumskull, you know, conceptual thinking like this doesn't sound so necessary to at least that level, and I understand the point about the connection between extensionality and probability and what's going on, the way that the kind of domain itself has got this involved, which is actually a very beautiful example of inter-involvement, because she's relating it all back to her body. The way one thinks of points, I mean, they point in regard to theory, and that is absolutely true, but it's also philosophical in the idea of mathematics and the way that one, the way that all these false, the choice of false starting points will be.

20:00 The way that they build up, their axioms, they give rise to this anti-transposition, it's a beautiful idea to know, but it really does deserve to be written off as an integral for law. For instance, it absolutely clarifies for me where John Mabry, good man though he is, is wrong in his understanding of... Absolutely, you really have explained to me, just in the space of 4 or 5 minutes. Absolutely good. Well, it's... I did ask this friend about this project School of Mathematics. They have no money, but they have a woman who runs out of money in September. It's pretty bad. It's a very nice guy. He's a very, very nice guy. He's a very, very nice guy. Very, very nice guy. They're running out of money too, aren't they? There's a thesis by a student, in fact he did his thesis ten years ago, on École du, which he is recommending to me, although I suspect I haven't read it. I think it would be a long time before I could actually read it with any kind of mathematical understanding. And he's just published a paper in J.P. Oh, he's in this present issue of the Journal of Theology, right now, but it's just coming out. Maybe Shannon can do it. Yeah, sorry, Professor Shannon, do you happen to know, I was just, Bill Norton was just telling me about this thesis by a student of his ten years ago, a guy about a tendu. Oh, Kimmel Rosenthal. Rosenthal, yeah. That's the paper. It's just coming out, apparently, in this issue of the JPA.

22:30 He says it's true for people. Absolutely. And his paper is all about math. It's not about math. It's a demolition job on the whole of this math. It's called quantalig... quantalipoids. It's quantaloids. It makes fun of... it makes fun of... But he says it's an idea, that you had a one-sided identity, a road, just a class working in the wrong category. Thank you for watching. There's an article in the JPAA on this issue, which is a demolition of the whole thing. But again, it's much more detailed than Bill went into, but the idea is that he's just working on it. He's got the he's the guy that the thesis is making, but anyway, it all sounds very interesting. It has domains of variation, the way one thinks about it. To that point that I was making when we were talking about the roots of the classical secularist who thinks of his domain, the way that the axiom of sectionality has the concept of an absolute identity in terms of objects there, the same or different absolute, to be the values of the variables, and hence you think of variation as something which can only be understood in terms of successive... All these issues are stages in themselves that one has to grasp the notion of the mental transmission of time to grasp what appears to be, in other words, basically the analysis of what does not, because in order to close out, where is the higher space in which the objects that describe motions, the morphisms, that give you the morphisms that we need.

25:00 There is something very materialist, very physical about this issue, with a spatial aspect of the way one thinks about sculpture. Where does this additional subject of space live? Well, obviously, in your view, in our view, this is not enough. And hence, as long as you're thinking of this purely logical, what Noamite calls a purely logical notion of all things, But if they're purely logical in the sense that the cosmological really has this space because of the conception of it, then you will have, of course, the right to say that there is expansion in one of those spaces. That's how, that's impetus. The only way that you can see it is by providing a kind of closure of the space in an additional way, which starts with this ontological conception of the sense of full objects. But that is the way, as I say, that Cantorian, sort of, metaphysics arises, and this, what, the point I hate to undo, I think, is a particularly useful one, because there you understand that it is by grasping a material phenomena, the way in which variation is conditioned in a domain, geometrical, topological notions allow us to grasp that variation is in fact conditioned in a domain. But it's a perfectly material ocean. It doesn't involve going outside. It doesn't involve trying to get outside. It gives you a hold on what is the case of this little flip operation incident that we're going to have.

27:30 Of course, the action of the group in that case is not, well, it's not exactly the action of the group, but it has to have certain, it has to, the action of the group on the motion space has to be sort of, he's explaining the cycle. I told him we'd have to go off first thing in the morning. ...rather than as a sort of permutation satisfying a certain range. No, I've just got some beer, thank you. Are you starting to want beer? You will start off with it. I'll start off with it. You know, you were starting to change a bit. It's all right. It's all right. You were saying to me, had I seen the paper... There was something in the basement. What I'm... I mean, my main... What was it? It's in John's description. He's playing around with multiple values. Oh, that's right. Yeah, yeah. Anthony Gollum told them all that we must learn to rehabilitate Valheim. We must learn to bear the guilt of our past. Oh, God. Yeah, yes, I remember. Yeah, yeah, yeah. Yeah, Anthony Gollum, yeah, that's right. What he was saying about his having been driven from his soul. Well, no, that's not him, his brother, his brother, yeah. Yeah, I, I, yes, that's...

30:00 Well, anybody with that, well, yes, because his father, their father was the permanent head of the... Oh, his father. ...farm office, the Nazi farm. When I say he was the head, he wasn't a, he wasn't a... He was a senior civil servant, he was the equivalent of... I'm not sure what the equivalent would have been in America, but... The first is probably someone like this, Claude L. Howe, or, I don't know, yeah, that's right. Thank you for your attention. On the left we have the words of the rectangular plot, and we have to look at that from a point of view of science, and we have to look at that from a point of view of science. Thank you for your attention. In fact, you might come to Buffalo after he finishes his class. Well, I met them at the building. The last young girl who was at the desk most of the time. Oh, yes, she was the one you were... She lived with him last month. Oh, no, that's a long time ago. That's a long time ago. That's a long time ago. She was the one who taught you. She was the one who taught you. She was the one who taught you. She was the one who taught you.

32:30 So, maybe mathematics is arising from the study of diagrams. Right, which you get distributed, or one version of which you get distributed, which I've been studying myself. In fact, Jerry's been teaching me the basics of graphs, I don't know. Well, I was brought down like that. The exposition. This is very interesting, I'd like to talk about it. He apparently actually originally wanted to be very profound in his ideas, and that's why he asked Martin Alvarez, but his father himself had explained the fundamentals in a more comprehensive way. There's a biographical article in the Dictionary of Scientific Biography about how important his father was in teaching both him and his brother, his father as well, but I hadn't learned how much of the work, how many of the ideas that he subsequently took up and developed did come from his father. There's work in linguistics or in chronology as well, including the first grammar of Sanskrit, which I understand from people who know something about it. Yes, it was a prodigious introduction too. In that really nothing was known about the classical language before in Europe. Jerry's actually been teaching me a little Grossman algebra. No, I haven't even begun to learn. But I do enjoy learning about graphs and algebra very much.

35:00 Are you pursuing... No, I didn't. Oh, no, I didn't use that. There's an article about the electromagnetism, which I've been talking about for 30 years now, as well, and there was my other daughter, and she's always been talking about the energy of the Earth, and she's always been talking about the complex of the Earth, and the problems and the current. I'm supposed to be staring at the desk this way. And did he just never publish this idea at the time? No, he published it in 1880. The British had a habit of ignoring him. Not only the British. I haven't looked at it. It could be the case of those. The same as Maths, we already have a different proposal we haven't been able to find out how to test it. That is absolutely extraordinary. So that would have been in the 1840s. Have you carried any further your project with your students in Buffalo translating the Astellas Lear? We haven't done further.

37:30 It would be marvelous if a new translation could be prepared with a foreword by you. No, I'm serious. I think preferably a fairly lengthy board, maybe, you know, really explaining why Garspin is of such fundamental significance. It would be very, very interesting. A group of ten students may have more or less resolved in the moment, and that was when we made really a pile of pieces, as well as consequences of any work that was done. Thank you for your attention. Let me say, it's astonishing that I never knew that Gaussman had done work in electromagnetic theory. Thank you for your attention. Thank you for your attention. In the 1840s, it would be proposed that the comfort of art should be modified so that it could be used as a form of science. What kind of terms? I'll tell you some more, to be modified. What kind of terms? Values of many terms. Values of many terms. Values of many terms. Values of many terms. Thank you for your attention.

40:00 It's interesting, you mentioned the Poynting vector in the context of when we were talking about Heaviside. It really was his discovery rather than Poynting's. I happen to know, a few years ago, ten years ago now, Poynting's great-granddaughter. She knew her very well. She was engaged to a very close friend of mine for about four years. In fact, they were living together for four years. They didn't even get married. That guy called Peruzi Azmi. She still has many of her great-grandfather's papers unpublished, yes. Well, not his papers, but his correspondence. When I say his papers, I mean in the sense of his correspondence and photograph albums, mostly just family, mostly of a private nature. But there are some letters that she showed me which do contain... Mathematical formula and letters from him to, I can't say now, it's 10 or 12 years since I saw them. I only saw them one evening when I was visiting them. But it seemed to me that, you know, I said to her that she really ought to try and, she ought to have them catalogued and looked at carefully by scholars, because there was obviously material in there, although it was very static, that was of major, I don't know, major, but certainly of scientific importance. I mean, there was at least one letter there, which I think was to Stokes. I mean, I'm talking about something I only saw for... A period of 20 minutes one evening 12 years ago, so we can't remember now exactly what the correspondence was, but it was obvious that there were about eight volumes, mostly of family photographs, but with it there were letters, perhaps about 40 letters or so, some of which were, you know, letters to other scientists, and it looked like quite an interesting line-up of archives. But she unfortunately was one of these people that had been got at by exercises of a new age idea, didn't believe that great-great-grandfather's work was of any value and couldn't make her understand why it was of great importance for people like her.

42:30 Thank you for your attention. One of them went so long there. The other published it under his name. This is about 1740. I don't think it was Lobital. I think it was a little bit later than Lobital. Lobital is the end of the, right at the end of the beginning of the 18th century. I think this was a little bit later, about 1740. I can't remember the names now. I think that's right. One of them was paying somebody else and just basically to steal his results. The problem is you've got a rectangle at the top, so you've got to find it there. Actually, that seems to make a lot of sense, but you know, it's a little simple out there. It's a little worse, isn't it? It's a little worse, isn't it? It's a little worse, isn't it? It is standard, the standard histories of mathematics all make the claim that British, actually British mathematics, because Maclaurin is obviously the principal experiment of calculus, were left completely behind because they were fixated with foundational methods, because they were so concerned with trying to analyze conceptually the foundational subject, whereas the real big boys like Euler continue to pile up solid results.

45:00 And, uh, develop the actual techniques. I agree. That's why I say it. The idea that if you bother about fundamentals you just get held back and don't press. It's all to do with the division of labour. Let the division of labour remain frozen until such time as either God in his heaven or the ruling class decree that now is the moment that you are permitted to unfreeze the division of labour. You may think, yeah, I agree it stinks and it has no flavour. Thank you for watching. Did you hear the speaker that... I'm sorry, your colleague that we had had the dinner with on the boat, Tom Butler, the guy who does all the work in the model there, was telling us he had spent several, about two or three hours talking to them. And they have told him about this giant, you've heard about the giant dinosaur? Yeah, yeah, yeah. Yeah, but the really significant thing is that the dinosaur is the size of a mangrove. The dinosaur is much bigger than Mount Ararat. And I thought I was doing very well. And this was one of the guys who had, you know, 8 plus on every exam. Oh, God. The laws of physics, the laws of physics, they're caused clearly, the thing we're playing through, it's not. There is this dinosaur the size of a mountain range over the physical sky, urging the laws of physics and order. I'm not sure why the laws of physics have order. I mean, I don't understand why they couldn't just get away with changing the fine structure constantly. But I may be confused about that. I'm not sure what claim it is being made, but it's...

47:30 He was saying that he'd been speaking to us about the provenance we shouldn't know about studying the laws of physics. That's right, because they're not eternal. Because they're not eternal. That's right, exactly. Because unlike Catholicism, they're not eternal. Exactly, exactly. You've got that ahead of you. I think there's a few more that you've got ahead of you. You know, theologic. Theologic, yeah. Actually, say what you like about Chuck Dorling. Theologic is a good... Yeah, because the horrible thing is, I haven't been to Japan, anything would probably jump at you, I would say. This is what we've been waiting for. Now let's try and read, let's try and embed this in the right category. Do we have a final proof of the nature of geography? I'm still thinking about what you're doing, Marlon. Well, that was my line. I'm sorry I used that. Thank you very much for your time, and I hope to see you again soon. If you've got only mathematics, then everything goes fine. I was just trying to put this in the room to remember our name. So I don't have to listen to it. I think it's the only sound. Yes, I think that is the only sound. The only problem is it probably makes it even worse when he gets back to Jordan. He'll probably make up for lost time. But I was doing small Georgian Jews. Oh, of course. I'm going to do it. That's the only day for us to be able to do it. Well, since they're obviously doing very good work. I'll have a look at every new kit that is out today. No, that's the law. And not just, as I say, not, as I, and this, on this point, um, was quite good. Um, not simple, a la, you know, Dirac, not simply a question of the values of physical constants, really. Not a question of gravitational constants, of fine-structure constants, all being, they're so beautifully correlated in such a ratio that, you know, that has to be preserved, that therefore there has to be a change over cosmological time. Nothing was...

50:00 No, no, the actual laws have to have changed, because otherwise a dinosaur as big as that wouldn't have been able to come up. Because you see what I told people getting these names. Somewhere in the corpus, did you remember where he was saying it had been found? Well, I was getting this from, I'm so sorry to keep on forgetting his name, but you're... I was getting all of this from... Yes, that's right, I was getting all of this from Duskin. But you see, because when we were having dinner on the boat, he was asking me what I was doing here, so I was telling him a little bit about... We got on to talking about the Georgians, so I told him about the Georgians. And he, you know, his eyes just got bigger and bigger and bigger and bigger, and he obviously didn't believe a damn word I was telling him, so I said, well look, I'm not going to say any more, just go and talk to him, and the next day, the next day, literally, he came up to me, literally grabbed my arm and said, I apologize, everything you said is true, in fact it doesn't even begin. And he told me this new story that he'd heard about the giant dinosaur at the size of a mountain range. Also apparently a line on you, which is that you're really a Christian. It's just that you really are a Christian. But for reasons either subjectively known to yourself or objectively known to the name of God, the Holy Ghost, you just keep it very, very well conceived. But one day, presumably in the fullness of time, when the fifth angel blows the trumpet on the right page of the book, you will reveal yourself as your true color, cast aside your... and reveal yourself as what ought to be true. Thank you for watching.

52:30 Well, that brings us down to earth. I'm surprised that they don't have the British monarchy. We've had enough kings called George and Arthur. I mean, you'd think they would have... ...themselves have the intuitive idea that... A topological space equipped with a foliation is itself again a space. It is a single spatial object. It's just that we didn't have, it had to be considered as a pair rather than a single thing and it wasn't quite so sharp because it didn't have sufficient machinery. The conception of it as, in itself, a kind of space, so that really the concept of space is apparently more general than pathological space, I think they must have had it, at least in terms of intuition, in a lot of ways. I think there really is a very good explanatory article for, I don't like the expression lay audience because it's a pedant term, but a very good article for a general audience to be written on that particular topic because after all so much... Metaphysical obfuscation is loaded onto set theory, and is loaded onto the set theory, the way the set theorist thinks of his domain, it's loaded onto the set theorist's notion of object, and the way that it gives rise to the primitive hierarchy of this Platonist view will end up with just thinking of the whole physical universe as a little bit of blob of structure at the bottom tip of the orbital cone. The contrast with the way that one should think about the variance of variation with the paratopological, geometrical structure in the case of Etendure is something which you can explain almost. I say almost. I mean, I know there's an awful lot of machinery that you can't bring in if you're explaining it to a non-mathematical audience, but you can just about convey the essential idea, almost in pictorial terms, when you discuss the notion of, say, a domain which is intrinsically developing.

55:00 And contrast that with the secularist picture of static objects there, separating them to be the values and variables and the piling up of them in the hierarchy and the formation of them so that you go outside physical space and you have to suddenly have this metaphysical revelation, the cantor, the infinite plenitude of God, all of that. You can get, you can, sorry. No, it's just that when you have understood clearly the order of, the direction of fit of the ideas, as between the set theoretical case and the domain of variation in the et en deux case, you see something, I think, about the world for the first time. This is of enormous importance to materialist understanding of it. Maybe I'm making much too heavy weather of this, but I think it's something that's an insight which could be put across almost in pictorial terms to people who are not mathematicians, and it would safeguard them against these arguments for mysticism and metaphysics and religion from the authority of mathematics, which are all too prevalent. And I just think a good pamphlet is to be written about this, so I'd like to try and do it, and obviously I have to send it to you for your approval. I want still to write a book in the office 24 months. Yeah, two years, you see. And then you have to write the book. You do have to write a book sometimes. You simply do. I'm only laughing because I hear this so often this year. The trouble is you're so busy having ideas, new ideas every day. It's something that has to be said, otherwise the people try to rewrite it. That is the problem. I will. But they're very industrious. Why don't you write yourself a note? I have to. You have to write a note. Well, have means if you want to obviously. We would like you to write a note. That's what we're saying. But the trouble is there are always these new beautiful deep connections being seen. New papers pouring out. He confessed that even if he regained in two years he might not write it.

57:30 I was saying something before about the bizarre nature of Czech culture, I mean the way that it sort of turns on itself and escapes into fantasy. Well, you see, they've been doing this thing now for years based on Mopenka's principle. Mopenka, by the way, is now, since three weeks, the education minister of Czechoslovakia. This was announced during the lecture also. Vera told me last night, too. The education minister. More or less at the same time that Schwarzenberg came in. I don't know if there's any relation between the two. I only met this perpetual once long, long ago. He's kind of their guru, in a sense. It's interesting to see, I mean, these people feel the need of some philosophical inspiration. They feel that they're working on a certain level. And they need something a little bit higher because he's it for them. Because he speaks philosophically and, you know, he knows a lot, of course, too, and he's very intelligent. So they frequently, over the years, they've frequently told me that he's their philosopher. But, well, Frank is a principal, yes. So he, by the way, he... He told them, which they take as just gospel truth, that the category theory is a continuation of scholastic philosophy. You know, he points out various analogies between St. Thomas and so on and so forth. International transformations. Well, does that mean he approves of that? Given his position, I would have thought that meant he approved of it. Well, who knows? I'm not saying the man has a reaction to that, I don't know. Yeah, but who knows what he's approving of? Yeah, who knows what the statement means?

1:00:00 It's certainly true that scholastic philosophy contains more substance than is often believed. He could have been pointing out something like that, or he could have been trying to say that category theory should continue to work in the inquisition and all this, you know, as George. I have no idea. Anyway, mathematically, but I always, but this was, again, this was announced explicitly today, and this is kind of a typically checked thing to do. Proposal of a large cardinal axiom made by someone who believed that you should try to have big cardinals, all right, and it is much stronger than the measurable cardinals that, you know, I'm not sure John Bell was all about this, but first of all, they said that actually Volpenka's principle was intended as a joke. This was seriously said. Frankl's present was intended by Bopenka as a joke. What he intended to do was publish two articles. In successive journals, the first of which would announce this principle and deduce some of its amazing consequences, the second of which would demonstrate its inconsistency, but there was a mistake in the second proof, and so he was stuck with having proposed this principle, and now they deduce all kinds of things from it. It blatantly contradicts results of this bell, which were based on non-existence of measurable cardinals. The point is, these results, I mean, they're not really results, they're consequences of actions. We don't know which is true, so to speak. So, it's partly a question of what seems to be reasonable from a mathematical point of view, and I think that, you know, there's kind of things that are reasonable from a... Mathematical point of view and things that are reasonable from an objective point of view and things that are reasonable from a subjective point of view.

1:02:30 I tried reading some of the Penker's papers on semi-sets, and I think the deviations in the sketch were the actual mathematics, but just to point out that it was intended as a joke, which is, as you say, something very Czech about that. I don't know whether to believe, you know, wheels within wheels. Do you think that's true, or do you think that was itself a further joke? My impression from listening to John Bell, the guy from whom I'd heard about the Fekir's Principle for the first time, he explained it to me. I don't think I fully grasped it when I first heard it. It seemed to be in the line with all this, the way that these people use reflection principles to build up stronger and stronger past cardinal axioms. Once, you know, you refuse to take variation seriously, or you think that all variation has to be analyzed in terms of, you know, static. If I can give you my, uh, interpretation, I mean, I don't know what's going on here. The consequences are the same. Well, also the consequences of measurable cardinals. All of these very large cardinals. The consequences can be attractive. They are in the nature of idealism. I mean, in the nature of saying that you could theoretically have a super language which would decide everything, if not more subtly. This is the nature of it, that there could be a small language which could totally control the whole universe. It's subjective in that sense.

1:05:00 Oh yes, the power of language to control reality. Language controls reality. I mean, that seems to me absolutely the large-scale axioms. The small sets which are supposed to exist are always about, I mean, that's the role that they play in the future. They play the role of themselves being idealized languages. By contrast, by contrast, John Iskell first formulated the symptoms and made the consequences. It's basically, you know, there are hundreds of different examples in mathematics of the duality between space and quantity. Which you've also written about yourself, as in many places. Duality of space and quantity, which is a pair of agile assumptions and so on, depending on the content of a certain type of pair of agile. So in this case, the simple community result is that these are actually inverse equivalences, where things are properly defined. And these statements are equivalent to the non-existence of measurable facts. Non-existence. Mathematics and algebra. I would like to understand this principle of Isbell's because it seems to be a very important materialist principle. Yes, but certainly the whole idea of language is the beat game in which you control realities. It's a profoundly active materialist and certainly applies to the face of the beat. Geometrically, of course, the whole understanding of the whole delay structure. Maybe you can come in and let yourself out. I don't know, does he actually lock the door? I'm not sure. We never actually see what happens, have we? I think... Maybe it's all a bluff. But that's very interesting. Where can I read about this principle of John Ismael's and the use of a jointness in this?

1:07:30 I think we are actually being told if we're just coming okay yeah sorry okay I think we have to go it's been good seeing you again I'll give you a ring when you go back to Buffalo. Okay. Thanks for everything. Thanks for teaching me so much. Thank you. I'll learn much, much more than I had to learn. God bless you. It was very nice meeting you. Okay. God bless you. Be happy. Oh, I am. Pleasure meeting you. Oh, enormous pleasure. Okay. I hope to see you in London. Yeah, I hope so. I really do. Either or both. Bye-bye, Bill. Cheers. All right, is that mine? Is that yours? What happened to mine? Ah, gotcha. Ah, more like it. One solo? One of you? No, solo. One. One man? Do a camera. Do a camera. No, do it for solo. Yeah, yeah, see, see. Come back. Now, what do you want me to do? Thank you very much for your time.

1:10:00 Now, what time do you want us to end up? Can you do me one great favor? Can you spread, can you spread another needle? Yes. Right. And then I can finish off. Right. Early. Yes. I mean, I'm not, it's just whatever is convenient. Well, I thought we'd be. My, my. My view is if we start fairly early in the morning, then it's a more comfortable drive. Well, I agree entirely. So I leave it to you, as long as you may agree roughly what's going to happen. Okay, we'll do it. Understood. We're safe and understood. So basically, if you want to shower, just set the other... No, I won't need to shower, because I showered this morning and I could shower in Paris. I won't have the years for that.