Discussions incl FW Lawvere & M Wright

0:00 Oh, don't tell me that they've stopped because they can't go any further than the road there where the ordinary people go. Yes, I was just thinking that. Well, this is a certain breeze. No, I have never read it. I've never read it. It's a seminar on philosophy and mathematics going for a while at Chicago. Uh-huh. Grouter was chairman at Chicago, and he was a bag man. The vice president in charge of getting grants. Well, I was going to ask you what his views in philosophy of mathematics were. I mean, I've read his book. Yes. You have to know at least this much mathematics, yeah. Yeah, in fact, somebody once said to me that... well, in fact, it was John Bell. John Bell said that Maclean had said to him that... This book contains all the mathematics that a philosopher of mathematics must know in order to have any right to open his mouth without looking extremely foolish. I've never quite understood what it is. I don't think he's completely blind because he doesn't know anything. If he didn't buy that piece of software, he wouldn't be able to do it.

2:30 He would be able to help slightly disguise versions of ideas. Well, yes, exactly, which usually disguise themselves as formal aspects of the world. We study formal aspects of the world. And this seems to me not even to label a problem, let alone describe a problem. Yeah, so I think Browder was rather... And these are multiple, these are multiple! Oh yes, indeed! When you think of all the great mathematicians this man's created. Very great indeed, mathematics. But it's difficult to to understand how he can come up with such trivialities in thinking about philosophically about... Well, one is sort of brought up to believe that philosophy is necessarily, or necessarily, the idea that In fact, it's not even serious. It's sort of, what do you call it, a coffee table discussion, a pub discussion place. It's not McLean, I'd say. That's the ones who aren't mystics. Yes, the ones who aren't place mystics. ...actually living in Princeton. William Hittbeck is now president of the American Maths Society. Really? It was described in all the newspapers. When, if you recall, Rejanev visited Nixon. Oh, yes, yes. Spirit of Camp David. Seek spirit of Tehran and copy.

5:00 In fact, he died the next day. Oh, that really is the irony of history. It's quite striking how mathematics is so intertwined. I wouldn't think so. Mathematics has nothing to do with politics. That's how I thought. It's an empirical fact that somehow it does. Mathematicians are more involved on both sides of the fence, you know, than other professors. And not only as applied mathematicians, obviously, in that role they are naturally very directly involved in physics. That's extraordinary. I mean, was there a background, a mathematical background, in physics back then? No, I don't think so. I found this, there's this journal called Contemporary Biography. So around this time... Probably Solzhenitsyn too. He might be. Yeah. Yeah. Rebellion. Small slavery. Your brother still runs the farm? And where is it?

7:30 I'd read the unreasonable effectiveness of mathematics and physical science and tried to... In fact, that was why I got so interested in philosophy and mathematics. Unfortunately, I never trained as a mathematician. Well, you know, I certainly regret that very deeply. And it has an enormous influence on people like Penrose, when Penrose comes to London. In fact, I must give you the tape of this. Penrose came to the Philosophy of Science seminar at the University of London. I can't really understand what his position is. It seems to be a blend of Blaine's position, and it really is a very interesting place. He really does believe that it's true.

10:00 There is structure in the world that's pre-adapted to the scene we're creating in our minds. I think this is why he's... Oh, he is doing that, isn't he? Yes, yes, it's completely... Yes, yes, because they think it's so trivial. It's not worth debating about. It's not as serious as much as you think. And of course I agree with what you've had with the rigour of a real man. In that sense, it is a real man. And I wonder, you see this strange work of Dirac, although Simon Sorbus is a great, who knows a great deal about Dirac, the creation of Philip F. Ogden Kelly, he says that this paper of Dirac that John is citing is a very unrepresentative one, taken very much out of his mind, just making a methodological point about how we create the kind of mathematics that's necessary for...

12:30 It's debatable. I haven't read the paper, there's no point in reading it. I disagree with the reading of the paper, but I think there is, you tell them, a Pythagorean, Pythagorean mysticism, I guess you know the director of the University of Florida, often from Cambridge, again, to make the investigation. Simon saw this in January, when he was a professor in January, for the book he was writing about the creation of, really the creation of, sea star arcturus, the work of Jordan and John von Neumann in the 1950s, which is a very interesting piece, he's written it since the 19th century, and he wrote a bit, he's got a piece of the book in the back, But anyway, he went through, and unfortunately he couldn't, he could remember, but he couldn't ask, he couldn't ask the question. Yes, he could, yes, he could remember the sequence of events between intersection when you have a free, yeah, yeah, yeah. And I'm not sure if there is a, is there a name for that? It's something you learn when you learn about scope, you know, how to, you know, how scope distinctions work, but I'm not sure it actually has a name. Do you know if it has?

20:00 Oh, sure, I mean, but I meant in elementary... I'm just trying to think what's the... Yeah. In the general case, it's sort of vibrations. I'm not sure they're driven by the keys you are. Yeah. In that special case. Yeah, it's a rule which covers, you know, what you can substitute. You could easily think of it as sort of bookkeeping rules. Oh, yes, it is. It really is logic. It is, essentially. Well, I'm sure I wouldn't say what he asked. Well, this is something I've tried to understand in when I read your remarks about this in the introduction to the about taking, not necessarily having to restrict, you know, with existential universal point of view, not necessarily having to think of So, maps along the projection only. I guess, perhaps we could talk about this when we get back, but I need to, I probably need to sit down with paper in front of me to go over the construction. Thinking about equations, you have some formula you want to quantify, but you can conjoin that with this equation, you get a property of x and y, not just of x, and then you put along the projection, and that turns out to be the same as the direction, but that's the blackest box in the category, it is again a case of dysregularity, but if you have dysregularity, you can reduce the general image of f2.

22:30 But this is only due to the fact that one is talking about sub-objects. You know, you always replace a map by its image. The map is a proof bundle and what it proves is the property which is its image. So your logical operations are applying to these sub-objects and eventually return to sub-objects. And all you need is pullback to get the projection to mark that Frobenius was a prophet. It's almost a tautology. Except that the only thing you have to care for is that the inputs and exits of products are different kinds of vibrations. One is one kind, one is another. I can explain. Yes, I really wanted to try to understand this. It seems to me to be such a wonderful deep insight. Even though it's not the most general case of a consensus of extents, and indeed an abstract quantity is sufficiently representative, when you sort of imagine that eventually every kind of quantity is somehow a part of the description of the size of the real object, it's not really a terrible loss of generality to take this concrete case where the quantities are just objects themselves.

25:00 It's strange how long it took for this kind of formulation to become formalized, because it's the sort of thing that anthropologists had in the back of their minds for 50 or more years. But the way it got formalized into algebra was algebra which was very far removed, in a way, from actual objects. And then the surprising theorems. We were debating as to whether you would have been able to see the coast of Ireland on a very clear day if you were a little higher up and Bill was saying that the Dunsink Observatory apparently claimed a hundred years ago that they could see the Welsh mountains from the Dunsink. There are also a number of different types of observatory on a clear day, but the President of Astronomer Royal says it's quite impossible he's trying to do anything even under ideal viewing conditions. You sometimes see that in eastern England too, that same pattern of lining it up into a fort, and I think that came from the old farming system before the enclosure, before the enclosure of the land, when, of course, the fields were farmed in common by the whole village, kind of primitive communism within feudalism.

27:30 Sure. Well, this is the thing you keep discussing, that primitive communism is different from the things that were formed by barbarians. So did my mother love me. Nothing sentimental about flowers. I don't know why my mother doesn't love wildflowers because of her experience in them. Nonetheless, the way she sees wildflowers is that they're child species, showing that a child is what they are. So then all their ideas are transmitted. That's very interesting, I think, but I think we can go even further back. Well, yes, I think there's a lot in that, and I think it obviously varies a great deal from society to society, and in England, because you had kind of rich peasants and young farmers, perhaps even some of the peasants in a country like Ireland, the peasants were very poor and marginalized and all united against the landlords, who were a different race, different religion, and particularly...

30:00 But it's here in England as well, perhaps only Wales, very much a tremendous radical socialist tradition, much more highly developed and in the industrial world than it ever has been in England as a whole. And you think all the great sociologists, admittedly, most of them, you know, are rather confused and sort of like an iron bevan, but still quite a great tradition. No, because you didn't have the division of the label. You didn't have it frozen in... Yes, we're coming, they're going to leave without us. Well, that's kind of fatal ignorance. Noble ignorance. So very dangerous to the society. ...rural life, particularly the old craft industries. Do we have to go down? Oh, that's okay, there is a path. Be careful. Do be careful, Bill. For God's sake, I don't want to be in hand when the position of R.A. is chosen.

35:00 Yes, this is something I love to write. It's a pity these things are all going on at the same time, because... And it's together, in this sense, the objects, and the objects are... The topology, yes. Here's your communication problem. See, I was very interested in that. So if we accept that at every good point, it's associated with trusting... So what... Here's my statement. Yeah, sure. If we take... If we take... If we take... If we take... What is the stack associated to a given group of points? I mean, I gave you an abstract description, but I don't think you can describe it. The answer is the torsos of the double group of points. Oh, that's very nice. So what's the relationship between those limits in these terms of the language? Yes, yes, yes, yes. Right, yes, I've seen that kind of statement in Xerox with groups. So I think that that's an issue. That the stack is eventually one-dimensional.

37:30 Is that interesting? Yeah, I mean, that's a perfect example. Well, I mean, the associate chief won't give you anything new if you just take associate chief. What about? How do people feel? I mean, what in fact is the lack there? No, but they think it's, I mean, for example, let me, what you said, I mean, we agree, I mean, I think it's important, but let's work in the case of tortures. Now, that's an acrobat, so it's not nice to move the sentences. Right. So, we take the stack associated to the category given, defined by the group, and let the associated group act towards it. Okay. And then all we'll have to do is not do anything. So, I'm not doing anything. So the caprice is still closed, can't it? Oh, it's, uh... Yeah. Would you close it? Close. Close. Well, I'm sorry, I'm not well enough. It's not necessary, but... Yeah. Well, it doesn't have to be. This is the definition of what a limit is and how it exists. If you have two canvases, it means that you can take the master class to make sense of the account. Recognize the local structure. So now let's work locally. We don't want it to be one in one. Local structures are a course of expression. How many torsions are captured in the first torsion range? Only one of them. And if you say it should be in the fourth torsion range... Categories are given by sections of the group, but you have all the other categories, graduations, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas, diplomas,

40:00 The problem is that there's probably only a few of these guys who know each other, and they don't have the same software that you want, I mean, because there's interest in the surface with all the different kinds of, but they're all instances of the same thing. Thank you very much for your time, and I hope to see you again in the future. Or, you do ask that the map to the base is more or less the correct part of the morning. So, for the case of a simple composition that we consider, say, for topology, we consider the spin spaces. Let me draw a picture of Bill's book, Produce, in which he talks about bicategorisms, and this is the stuff about these intensiv-incursive constants pushing forward to structure, which reduces intersexuality. I mean, that's how... The Galois theory of momentum is the way that it works, and I think it would be better if we talked about that. I mean, that's... Well, I can really give a good answer. It's just that I don't understand what he does. I have a good answer for this. In particular, why do we only consider what we have generated? Maybe that's not a very good answer, but let me make sure I understand what you're saying. You associate a topos to a topological or a locale or whatever blue void. Say topological. Or can we say to a topology already in a topos?

42:30 No, no. When you say topological group, why doesn't that mean that you consider it as a sort of sheet, so it represents a sheet on top? No, I don't know. You should all think of a topological group, typically even more effective, or for this application, something like a profile matrix, associated with a common value. That's why it's topological, for we don't think that is a topological group. He's just put so much into it. Then, of course, there comes the problem of space. That's on how to linearize what's on the page. I can't find it on the page. If you take a topological look, you walk into my room. It still says. It is Kelly, I'm sure. Of course, yeah. Ah, let me change your mind. I think I might have an orange juice as a nightcap. I see. I have another orange juice. If I have the money... What? No, no, no. Well, let me if you're sure. I'm actually going to go down and... Well, your nightcap is a coat. Oh, gosh, a big one. Thank you very much.

45:00 Why not? What a shanty should be. Disgusting modern invention of putting lemonade in shanty. Shanty always used to be made with ginger beer. Yes, quite right. I meant just as it were the addition of the beer at this stage. Well, at this stage in the evening, I have nothing to lose. It was a very pleasant walk this afternoon, by the way. Yes, wasn't it? Invigorating. Thank you. Thank you very much for your attention. Thank you very much. Thank you for your attention. Absolutely. This man will tell you that I am very good at keeping promises about providing... Yes, he's done very well in that. This is just Anders' little paper about Franklin's bar, which I'm very curious to see. Well, it was a fine book, mate. Did you hear it? Yes, I did. I liked it. It was the ideal there for which to end. That's right. Perfect. What is the idea of this lecture? Not that it is special for doing the CERL program.

47:30 No, no, I was going to say. I thought this might be okay for the show. Well, I've actually got the paper here. It's very straightforward. It's just that fractalism is a form of idealism. These people project... These people have a set theoretic view of the continuum, which is, well, for the most part, they have a kind of a purely arithmetic view of the continuum. Is that all right, I think? And then there's a lot of very sloppy philosophy about, you know, which goes under the name of the unreasonable effectiveness of mathematics. Which, I mean, he's attacking the proponents of fractalism as a, you know, not a philosophy, I'm not suggesting that this is not an important mathematical work, but... And it's the same sort of objection that I think people like Bill Laugier have made to the piano curve, to this, do you know this passage in Bill's 1976 paper about the space, yes, it's the same sort of objection, and his great point is, if these structures such as the west coast of Scotland, as an example, really are examples of practical geometry, well, You know, the practicalists owe it to us to show us those experiments, it's polemic, the experiments that they have conducted. Did they actually put their microscope in the sand? And did they confirm that in fact it does, just like the Mandelbrot set, continue to be frank right into the very small? Because if not, this is not a satisfactory claim. I think it's a plug for others ideas in synthetic differential geometry. We need a fundamentally different way of modeling the continuum. I mean fundamentally different from the reals and but there's a I think that Colin McClarty's

50:00 To work on the origin and the fact, you know, the intellectual efforts that led up to the modeling of the continuum as a set in the work of Dedican and Cantor was what was involved in suppressing what had before that been sort of set in aspects of the notion of function. In fact, it's really downgrading the notion of space and mapping in favor of making everything to find a potential set. And from the point of view of the topos of space and geometry, you can think of what is involved in the set, topos of sets, as involving imposition of additional structural assumptions, which are precisely the decidability of identity. So you have a well-pointed, which you don't have in a category of sets. The practice is that it's a kind of manifestation and dramatization of analysis. That's right. Is that a fair comment? Yes. He sees it as that. And this is in turn, for him, a variety of idealism. What was the phrase he used at the end? The continuum does not have to thank R or N for its existence. But over and above that specific position that he takes about SDV as a program, there's also a purely political aspect of the book saying, well, these people do say some very silly things about nature, about natural structures, and therefore nature has played a cruel trick on the mathematicians. I'm kind of interested because in science, it seems to me that people are crazy, totally crazy, they take the last station, today is Magdalene, yesterday is catastrophe, tomorrow is chaos, and so on and so on, and they, you know, they are starving for mathematical concepts, and they want to have mathematical concepts, and they don't necessarily need mathematical, quantitative, you know, to be honest. We are very happy to have heuristic descriptive models like these, so that they can be used.

52:30 Now, the thing is that if you want that, category theory is here, which can do a much better job than that. So why should we impose strange conditions on the reality? I mean, I'm talking about biological sciences, for instance, instead of using what we have. I mean, a bad structure like... Thank you for your attention. He's interested in a particular kind of phenomena, and he has in mind that it's a good thing, in inverted commas, for there to be something which he regards as a mathematical model of it. Now, I mean, what it is to be a mathematical model of something? Same ladies, pay no attention, there's no trouble, so just briefly. No, mi metto in guerrera. Dov'è che si apre la finestra o la porta? Quale porta? As long as they're not breaking any far-door glasses. No, possible. Tell them, tell them. What is? To open this window, because it's stuck completely. It's been painted in. All right, I suppose we'll have to try. You have to try just in any order to convince you that it's not possible. No, it's totally impossible. I'm not going to try and get up there, I'm sorry. It's them.

55:00 I'm sorry, I can't resist recording Meryl Carr, but both her daughters and her very own son said, leave these men alone. She said that just high spirited, like all Italians are. Both of them have a great deal more power than the older power. Anyway, you were saying. Sorry, you were saying, my friend. The good thing to have a mathematical model is that they have the steps. Now the question is, it's as if it's not the content of the notion to have a mathematical model. This is kind of clear, and there's nothing that really fits. What people want to take, and what scientists take, is exceedingly inappropriate for their purposes. Well, yes, I mean, the whole of mathematical physics relied on differential equations on the real line. And of that precise model they want to take into account is not, as it were, anything other than certain qualitative features of it. So it's not actually, as it were, the details of the model are doing anything. Now, you might say, well, there's still a completely different style of modeling, which is where you almost just write down the axioms of what you think is going on and kind of, so to say, find some categorical structure, which satisfies people in some branches of physics. I mean, I don't, I mean, I don't know anything about quantum theory, I'm not pretending that I do, but I know people who do, and I, in terms of, I mean, I've seen little bits of work on the kind of, the foundations of thermodynamics or something, which seems kind of... It's very interesting that nobody ever pushed them any further, and it clearly isn't the standard or traditional thing to do, and it's clear that people who do that sort of thing are sort of slightly nutty in some ways, and it's not so clear why they should be, or why the other practice is so very good.

57:30 Yes, and the people who do that kind of thing are usually regarded as, well, they're certainly sidelined. I mean, when Rob did it, special relativity, he tried to act, you know, I didn't tell him he doesn't want primitive causal relations. It's regarded, well, you know, this is not physics. I mean, why would I waste his time doing that? I mean, Kennedy Museum is a very good tool for doing something that's kind of an axiomatic, I mean, because it's something where almost that distinction between kind of an axiomatic and asemantic, so to speak, is not so very clear, in a bit. I suppose Stefano is thinking, as you were, I mean, I'm very uncertain about this, I mean, I think there might be good reasons. But they certainly don't describe it by just it. There's no sufficient explanation. Yeah, also, in the yawns, I haven't given it to you. I'm sorry. I should let you go. I can see that yawns should be given to you. No, no, I would rather come back and just hear you out, see if that's all right, Martin. I'm being a bad host. John, I'm sorry, I'm afraid I got so tired of talking to Martin, which I'm just going to go back and do. What did you think about this? It's quite not a sufficient explanation for the current practice in science to say in a very vague way that what you want is a mathematical fact and justify kind of choosing this sort of, I mean, it is heavily differential equation based, it's kind of, in some sense it's rather anti-axiomatic in the spirit.

1:00:00 I mean, I can see cases in the past where you could say, well, actually, you know, there are cases which you could imagine justifying by kind of historical precedent current practice. I mean, there's this very curious thing with... Well, the whole history of mathematical physics is new to me. In a sense, the precedent of modeling. Things this way, in terms of differential equations on the real line, has gone well, it has given us, and we have produced more, which have turned out to be very strong candidates for more, which in some cases survived without qualification for centuries, which is a very interesting kind of story, and it's difficult to break away from that, and it's one of the things which… And one of the interesting things about the sheath models is the fact that you do have a way of thinking of a structure on the real line without thinking in terms of real, sort of differential equations on the real line. And the fact that, I mean, there are people I understand who now do think directly about equations of mathematical physics in terms of sheath theory, particularly in Christopher. I'm very uncertain, but I think it kind of, I think it just presents a very interesting challenge to both the history and the philosophy of science. You can imagine a certain amount of quite a lot of... I mean, the exercises have been tried, don't they, which I think would be quite interesting to do in a really rigorous way, would be... I mean... I mean maybe this has been done because I know I mean I know there have been some attempts to do kind of axiomatic special and general relativity but it is quite a quite I don't know I must admit I don't know of any attempts to do axiomatic general relativity. Axiomatic special relativity has been quite a minor industry in philosophy and science for some years, to the point that it's really become a very sterile program.

1:02:30 There's one man, in fact, well, John Dawley, who could actually derive the whole of special relativity just from amending one axiom in Euclid. So you see that it works very well. The interesting thing is that you ought to derive something, you ought to have an aspect from which you just, what you derive is a classical special relativity with these definite presuppositions about, as it were, a real line of time and things like this. It's a very interesting thing that just before either 1905 or 1900 when Hilbert looked at this little book called The Foundations of Geometry. Do you know this? Well, it's not the thing he wrote with, um, well, I was about to leave there, and I'm thinking of this. It's not the thing with, um, what was his name? No, no, no, no, that's much more clear. This is a little book. No, I'm sorry, I don't know. I mean, it's very curious, because it's clear that Hilbert wrote it. From the point of view that if you are understanding the nature of space better, so there's a very heavy irony that we are understanding the nature of space better because it was suddenly a whole lot better by quite a different, for quite a different reason than this. And so it's sort of probably the first place in which... There's a lot that's written out here. It probably isn't the first place where the kind of the full axioms for Euclidian do the axioms that aren't there about between things like this, I've clearly said, but it's sort of, it's pretty often in kind of geometric algebra, so you get the axioms for space. You derive from them, as it were, the fact that you must really be talking about quantities which form a field with, because of certain things, as it were, roughly speaking, they must almost have the ability to take square roots. So, it's a very interesting character in which, as it were, the space of coefficients is... Some properties of the space of coefficients are determined by the axioms of the geometry, which become a kind of classical piece of this impression of the geometry now for a few years in this century.

1:05:00 An iconic theme is one of the problems with, I mean, the only bits of the axioms of social relativity, and they have the character of working through things a bit like this. Relatively, it's given to undergraduates where you say that actually, you know, you should be able to get quite a lot of this, what we are assuming here, from kind of some similarity kind of considerations and the consistency of the speeds of it. And that's enough to get you off the ground. Now, I mean, I think that what must be true is that those things, if you can, without prejudice, classical special relativity can never get you to the ground. Well, actually, this is part of John Norman's point in that paper. I don't know if you saw it. It circulated in the workshop. Yes, yes. It's quite an old paper. But my feeling is, sort of, I mean, there'd be, like, synthetic something. I mean, there ought to be something much clearer. I mean, my instinct is the right language to do anything. It ought to be a synthetic, well, not differential geometry, but sort of synthetic. God knows what. Algebraic, algebraic, space and time, so to speak. Sympathetic or mathematical algebraic geometry of a kind. Yes, I mean that's... Are you against that? No, no. Far from it. On the contrary. My main reasons for being interested in this are quite reasonable. No, I was just straining to think of a term for it. On the contrary, I think it is a reasonable thing to do if you've got... and in fact isn't it part of what Bill's idea is about intensive and extensive quantities and pulling forward things on the Earth that we're all about? I haven't understood. They can tell you a very special example of a corporation, which, it's a long story, again, but it turns out that it can give a rough description of the risks of speaking like that.

1:07:30 If you wish... Sorry, I'm not hearing by one. Through this meeting here, if you wish, at joint synonyms, whatever it is, another idea would be. So with this discussion of joint synonyms, with this work on proof, on graph, we are used to splitting by the form, but now we can interpret the same thing as the synonyms. And you've had a use for that in biology? Of course. What can happen? They look happy. I see. Is it anything to do with embryology? No, it has to do with the liver. With the liver? Yeah. Sorry, forgive me. I just pictured this kind of reaction. No, it wasn't a laugh. It wasn't a dismissive laugh. It was a kind of... It was just a laugh of sheer joy that such a wonderful... No, no, no, I'm sorry. Please don't take that for wrong work. It was a laugh of anybody who produces show-stopping live. Can't help but remind one of, as it were, Dick Digg, Freud's favourite joke. Yeah. Never heard of Freud's favourite joke? It's a joke which makes sense both in German and in English. And the joke is, and he doesn't say much of Freud's jokes. I was going to say, I bet he does. His favourite joke was, is life worth living? It isn't even Freud's joke, it's a very old punch card hoon joke about 1830s. It's apparently his favourite, as it were. I think it bears out Ken Dodd's remark about Freud, the problem with bloody Freud is he never had to play the Glasgow Empire on a Saturday night. I have an instruction. I was asked by John Maloney.

1:10:00 To give you his very best regards from a long time ago, should I see you. That's terribly nice. So I now do send. Well, I mentioned to him that I was going to come to this workshop because of Colin McClarty and he said, oh, will you see Martin Heiland? So I said, probably, and he asked me to switch it and say, sorry, he hadn't seen you for so many years. It's only a very long time. So I just do that. Oh, very good form. Yes, I see him quite a lot. He edits the journals on the history of economic thought and is pretty well embedded in women now. He lives in a little cottage, very large, very affectionate, very important. He's an English sheepdog. Oh, an English sheepdog. Right. And generally, no, last time I saw him he was in very good form. Well, I can give it to you. I can give it to his address with pleasure. So I have a brother who has lived somewhere near Poppins. He's really a very good Poppin. His mother's been very ill recently, which of course involves, well, I don't know too well, because he's the only living relative. And that's it for this book, but she had a sort of hip replacement operation which took a very long time to recover, but he's a really very good poet. He just came back from Madrid from a conference on history of economic thought back then. There was a time when he didn't seem to be very happy in Plymouth and finally wanted to get out of the place, but I think he's moved quite a lot, he's moved about four times in the last five years, so that was simply because we were kind of trading off places. I mean it's just being involved in something that kind of must sort of bring him in contact with lots and lots of people must be a kind of cheering. Yes, I think so, although he hasn't been in contact with that many people, I mean I mean I'd pop down to see him as often as I can because it's probably my own stress, but no, he's very important.

1:12:30 Thank you for your attention. I like it too much between the ages of 20 and 22. That's the problem. You should go on drinking. That can be the thing. Yeah. Nice. Nice. Well, that's what Bill told you in Cambridge, wasn't it? Oh, you mean stuff on the Hegelian factor? Yes, yes. Not even before. The unity and identity of all of those. Oh, that? Yes, yes, yes. I do remember the cylinder construction. Yes, actually, I'm sorry, he did talk about that. The two preferred sections. Yes, yes, yes. I remember this construction, the preferred sections. He spoke about so many things. He lectured for about eight to ten hours altogether, about two hours each lecture, and then we gave him another lecture at the end. So it was very interesting actually to compare his talks with the ones he gave in Milano. No, no, no, go ahead. No, no, no, go ahead. Just an information for him. A book for students? Thank you for your attention.