Conversations

0:00 ...computative geometry, because, I mean, the geometry, the problem is that non-computative geometry... Happy 69 and a half, I guess. I said, happy 69 and a half. It's today, yeah? Yes, it is. That's why I thought we would raise a glass. Come on. Only one infinitesimal. One infinitesimal. Yes, infinitesimal, yes. All two, sorry. All right, all right. It's the second neighborhood. It's the second neighborhood. It's the second neighborhood, definitely. You don't realize this when you look at it. Yes, that's definitely. Oh, my God. Thanks. Cheers. Thanks, Richard, that's fine. Yes, I haven't got a problem with, you know, I'm quite happy to take, you know, the... Sorry, can you just run past me what you were saying again? You were saying that, obviously, in addition to possible generalizations of the metric. You know, whether a la Finlow or something perhaps mathematically rather more kind of conceptually motivated, you know, clearly motivated. Yeah, obviously in addition to this kind of... Investigation into the as yet unexplored richness of structure and differential geometry. We should also be looking at, well, just much more radical ideas about space. Yeah, sure, yeah, of course, I mean, I agree. And not just things like loop quantum gravity, but, you know, things like... Well, I mean, you know, this is what I have said some time ago. The problem of quantum gravity is actually not how to quantize gravity,

2:30 Later, in the context of Dimitris, I said, actually, what we want to say, and they say it. I mean, you know, the ordinary perspective of physicists, unfortunately, became application of some tools that we... The toolkit that they were equipped with 40 years before, or, you know, when they were doing... Application, you know, just in order to obtain the result of calculations very, very quickly, you know. I mean, you know, let's say, the geometry of space is very, very old, yes? And it really... It cannot give an expression to certain things. The same is the story with the linear topological spaces. And actually, Bob was given the sense not only by Ravel, but I think that his example is one of the most important. It's not true that in order to consider the problems of functional analysis we have to deal with linear spaces. The most striking thing is that in quantum field theory, all interactions between whatever we treat as quantum fields, yes, but, well, quantum fields are thought to be operating for power distributions of space, yes, but in any case, this is what we call an interaction and what we actually measure and what we, well, we need a quantity which we describe the results of experiments. All those interactions are non-linear, and he ordered to describe those linear interactions, and now he came back to you. And not to mention the conceptual difficulties we have in defining what is a particle, what is a particle number, and the whole business of Rindler-Quanta and the conceptual issues that they pose.

5:00 I mean, one of the reasons that this structuralism in the philosophy of physics bandwagon has become so huge is because the philosophy of physics people, you know, just kind of essentially given up on these conceptual problems and just said effectively, just let's sweep the arm of the carpet by saying that all we ever can deal with is the mathematics we have without, as it were, attempting to get any kind of conceptual understanding of how the mathematics we have. What they have might in itself yield... With the result they end up with this ridiculous, woozy, pan-structuralist account of mathematics, which in fact, of course, makes no use whatever of the one genuinely fruitful account of structure in mathematics we do have, which is namely category theory, which they refuse to learn. Well, it's striking. It's also scandalous. Again, what's your point about a non... How would, for instance, a synthetic SDG version of Cartan-Einstein help with the treatment of non-linear solutions? What do you mean about Cartan... I say Cartan in the sense of torsion... I mean, theory of torsion? You mean theory of non-symmetric matrix sensors? I meant both, but the second, taking account of the non-symmetric tensor, I mean, how does this help with the non-linear solutions? I think the interesting thing about the description of non-symmetricity, I mean, I was rather wondering about the description of this geometry in terms of... The original approach to physical geometry is, well, you know, they try, they using norms and they're using somehow more topological approach. And I think that, you know, that's why they don't have much machinery to create infinitesimals, correct? I agree. At the end of the day they obtain, you know, quite complicated structures because they have to, you know, they have to have like a projective tensor bundle and...

7:30 Again, you know, how the hell do you define direction, for instance, it's because it's the, it's because it's a nice object. Yeah, I agree, as I'm saying, I think it's precisely because they don't have the right, you know, mathematical conceptual tools to begin with. The program itself, you know, of enriching Riemannian geometry in this way is extremely interesting, but... They don't have the right machinery, I agree. It would be absolutely fascinating to see what SDG would give them. That's something I really hope you'll work on. It's a pity that Bill couldn't be here, listening to you and Richard. Right, but he has never been able, you know, I tried to get him interested in general relativity. He has actually said some, quite a few things to me about it. He had a very interesting discussion with him about the Christoffel symbols. Well, okay, that's just general, that's differential, general differential geometry. No, no, no, in general relativity he told me that there was, the first thing he told me... Why C appeared? This should appear, you know, something, a special discovery or a special structure that appeared in the development of... But then they put it at the beginning. But actually, it might be not true that... I mean, this is a problem of Lorentz group. Yeah, I know. This is quite a historically involved question. At the end of the day, the women's group... It was set up, the canonical interpretation of the Unico-Florence group, yes, in the context of Einstein and so on, but actually it might be not the case that it encodes the actual facts of relativity. Well, you know, in 1917 there were things like, were done by, I don't remember the name of this guy, you know, who studied this problem very generally, and then he said there are different kinds of...

10:00 You know the addition, you know. Yes. And according, you know the name of this guy. I don't remember, but I know. This isn't Kehler. It's not, you're talking about Kehler, right? No. No, no, no, no. Yes, but there was somebody. But at the end of the day, at the end of the day, I mean Tesla? No. No, no, no, no, no, no. But at the end of the day, what I want to say is, going through the line of this talk about possible additions of velocities. And general analysis of the, I mean of the, well, Einstein argument, well, Einstein reasoning and its further improvements, yes? Yes, yeah. And at the end of the day... It appears that the structure which really encodes this principle of relativity, in this sense, is a group of it. Ah, yes, he was saying this is because you're... It's a path, it's a path group of it, and it's... This is assuming, this is, he was saying, this is assuming that the Markian program goes through and that you can have a completely relative motion-based account of... I mean, people obtain it. Actually, you know, there's... It is quite, I mean, it is something like a seven years of development, yes, but the final results are something like five, last five years. And, well, the idea is that when you are trying to analyze, well, because, you know, the derivation of this Lorentz, the Lorentz transformation, I would say, yes, from just writing x equal to, you know, to a x plus b b and x prime, yes, this derivation does not work. It doesn't take care actually of the physical meaning of the symbols. That's what? This derivation. Here's his Einstein. It confuses the physical meaning of those symbols. And when you go inside of it, and the rule of addition of velocities, I mean, what actually, you know, when you analyze in details which objects are particular, you know, positions, times, and velocities are attributed,

12:30 And you gently analyze it, you obtain that this rule of additional velocity, I mean, there's something called the Lorentz b-vector, and I mean that one has to take care about the rules of additional velocity. I would just, I would send a reference to the paper. Okay, shall we go very pathetically from now on, I mean, driven downtown and climb a bit uphill and then return downtown and things like that, where we like stopping for a coffee somewhere else? Very good idea. Excellent idea, yes. Right. Yes, yeah. Demolition derby, trashing a few bars, you know, kicking a few... Sounds good to me. I'd better remember what I did with my... Oh god, I hope I haven't forgotten. Oh no, it's here. Good. I've just got to get my passport in the car or anything else. And right now, for instance, if this works with Anders, I will add that. Yes. And so then I, anyway, so there are a lot of things that I would like to to change. It sounds to me as if the, you know, the theory of the alternate differential equations is going to go through in this setting quite nicely. This is what you were looking at the other, yesterday afternoon, isn't it? Yeah, yeah, that's right. But you have the two, yes. Yes, that's right. You could actually have pairs of equations to make it, yeah. Right, with Anderson. There are no real... Well, we have to do the general for any great algebra, so that's more complicated. It should follow this pattern somehow.

15:00 So that you really reduce the problem to find the potential solution, uniqueness. Yes, yes, yes, it can be proved, yeah. Yes, existence is obviously easy enough, but uniqueness is, yeah, uniqueness is tough, I can see, and then, oh yes, this guy, very impressive young man, I have to say, isn't he, yeah, clearly, I think we'll hear a lot from him. Well, here, when I was in Athens, I prepared this talk, because you know that I was under the impression that I was going to give this talk today, and so fortunately I had prepared that, you know, and I look again at this note, and then I... It was a lovely talk, as I say, it was beautifully clear. Well, what I wanted to talk to you about a bit this evening was about this archive and the plans and where I need to go with it. But before I come onto that, because otherwise I've got a feeling we might not get round to talking about it, I really wanted you to run over for me this viewpoint that you put forward. In your paper back in, you know, 92 with McNamara, the one about, well... One about various topics, but essentially one about the constitutive role of kinds as domains of quantification, and the way particularly that you think in category-theoretic terms of this general notion of entity. Can you explain a little bit more about that viewpoint and what you were thinking about at the time? The impression I got is that you got everything. I think I probably did, but it's always nice to have it confirmed. Well, the thing is, I think I did get it at the time, and then when I looked again at the paper just a few days before coming out here. But I'd still love to hear you go over it again. I was rather hoping I might be able to steer you back into interesting yourself again in those topics and doing some more work on them, because it's desperately needed.

17:30 The correction is desperately needed to the viewpoint of philosophers, and it connects with one thing in Bill's work that I wanted to ask you about. Now, oh, shut up now, go on, go on. Thank you. So, this is, uh, I like this one, 110. 110? Thanks very much, yeah. In 1985, I don't remember which date, maybe it was, I invited John McNamara, whom I didn't know, I never heard of him, to give a talk, maybe it was around, I don't know, to give a talk in our group, you know, in the seminar at Rupert McGillis on logic in... ...in learning of children, because he was interested. You see, John McNamara, he was, well, as you know, he was a priest, but also he got a degree, I think, in education. He had not taken, like that, and so on. And then he got... The question of children learning two languages at the same time, things like that, because there were things like that. Big topics in linguistics at that time, and in cognitive science, more generally cognitive science. And in Ireland also, because you know, there were children that were learning Irish and then English at the same time. Yes, of course, yes, yes, because it was a bilingual, well, it set out to make a lot of people bilingual, yes, yes. That's right. So then, because of that, he was interested also in all these kind of ideas.

20:00 At that time, he was looking at the work that Piaget had done. And then Piaget had a theory, you know, how... And then there was, at the same time, there was somebody, if I'm not mistaken, that did something similar at the level of reasoning, and I think it was called Kohlberg, that I never heard about. And then John found all that completely crazy, and he looked at the, you see that crazy thing, Piaget, had this car, and then... Contrary to some critics of Piaget, he had no problem, but only he got the wrong result from there, you know, he drew the... Yes, well, he, you know, his theoretical framework was completely defective then, And then the wrong conclusions. And then you start to look at them. What was its main intellectual... And then he gave an example that I still remember in that seminar, you know, in 1985. This is an example that he took throughout all his career, more or less, and this is an example we discussed with Pierre, practically, you know, and that was Freddie Isidore.

22:30 Yes, yes, which I remember. Alberto also made great... And then he said... And that example, the way the math terms and count nouns and proper names are... Incredible difficulties there, because, for instance, you say Freddy is a log, a dog, okay? And then in the actual description, in the actual account that people give of that, people like PSA and other things, there are several things that really go wrong, because, for instance, how does a child know that Freddy... Yes, how do they know that it's the proper name of this individual dog? It's Quine's problem actually, this business of the so-called Gavagai problem. How do you know when the field linguist who, you know, the natives are sitting in a field and a rabbit jumps up and runs past and they... Just as they say, Gavagai, Gavagai. So the field linguist goes away and writes down his dictionary of the, you know, this is their word for rabbit, but how does he know that it does in fact mean rabbit and not, well, Quang is really very silly and straight examples, but how do you know that it means, that their conceptual system is not such that it means, you know, temporal phase of a rabbit or undetached part of a rabbit or... The platonic universal rabbit hood is instantiated here, or whatever other translation you could plausibly make for that word, yeah, and so, yes, this whole problem, yeah, yeah, sure. The question, I mean, even if you had more or less an infinite amount of time... And then he says this is due also to the fact that one of the troubles with that is that the notion of entity is not well formed.

25:00 We believe that we have a notion of entity that is going to refer to everything we want. And then he gave several examples, for instance, that... You could be talking about, you know, the sunset, the color of the trees, or making love in the corner of the room, or the color of the room. Thank you very much for your time, and I hope to see you again in the next lecture. Well, Frege's answer to that, of course, was simply that, you know, one had to have an inbuilt notion of division of reference for a member of that kind. I mean, Frege's solution to the problem was that you had to have an inbuilt notion of division of reference for members of that kind in order to say how many there were, so you could only point at... So, if you say, if you hold up that and say, how many is this, the question makes no sense until you specify, do you mean, how many... How many pens, or how many hearts, or how many fingers? Usually it's clear from context what the countdown involved is, but it's not always clear. More and Russell were the examiners and more never recovered. He said, well, I think there are three points. And then Russell said, there are four, there are three objects. And then he, in the universe, in the universe, I said, no. And then he was never able to get that. And finally, you will never understand me.

27:30 You also probably know, going off on a tangent, the famous report that Russell wrote on the examination for the university. You know the famous story? No, I don't. He just simply wrote on the script, this is a work of genius. This is a work of genius by perhaps the most important European philosopher for the last hundred years. Nevertheless, it satisfies. The qualifications for a doctorate of philosophy in the University of Cambridge. No, that's true. Nevertheless, it may be considered that it can satisfy the qualifications. It's the point about there being no trans-categorial notion of objecthood or entity that is the question. But my interest is in how is it where you express that in category-theoretic terms.

30:00 Because the idea of Hilbert space at that time, I still remember, was a completely trivial problem, many domains of logic, I mean this was crazy, anyway, so then nobody came, and I was sorry, anyway, so then...

32:30 I mean, he actually identifies the problem in saying that what Frege assumed, well, is that they, well, is that, okay, it is a kind of inclusion, but it's an inclusion that, well, he obviously thought the membership was more basic than inclusion, but he thought of the inclusion as kind of lattice theoretic inclusion, but there would always be a single global top element for the lattice, universal top element. Which I guess is really to say, is simply to repeat the claim that there is this absolutely universal stable notion of entity. And then we start to look at the obvious question of what is the relation between different kinds, and of course there is actually a hugely restrictive assumption. And then we start to look at things individually, you know, that they were not inclusion. An example that we found are things like passengers and so on and so forth. That was the main example. And it's very curious that people didn't understand that. I think that they never understood that. But it's even, even, I think, the way, you know, he told us, your way of doing it. You know, for me, passenger is just I have to think of a person at a given time and then a person at a given time and so on. So I said, look, I mean, we don't care, but maybe we can find this kind, another kind, whatever we are saying, is that there must be some kind. How would you obtain one from another? This seems to be a secondary problem, you see. And in some cases you may do it, in some cases maybe you cannot. Maybe it's very complicated. But the funny thing is that people said, you know, there are no kinds of facts. If you can't define one thing in terms of another, then this means that this is something that is a theoretical construct.

35:00 But anyway, and then once that we have that, then we have several things including, I don't know if you have seen that paper that we wrote with John, and he, John one time, you know, after discussing this, of course, he said, well, I hope he wasn't being too serious. Oh, he was. He was still... He was terrible serious, and not only that, but he wrote a paper, and then he said... Look, he says, I put your name because this is a question we have been discussing, but if you don't like it, you can take away your name. And then I said, well, I don't care because this is something that I believe that we have done. And Marie said also, so we kept our name, and then the question is where to publish that paper. And so we sent to, what is the name of it? So you've actually had a paper in a theology journal? Well, it's a paper. I was rejected. And the person who rejected was furious. He said, these people do not take into account the suffering of the Christ. Well, no. That this is like a game, an intellectual game, I don't know, you know, and then... Oh, yeah, well, well, well, well, well, what can you do with this? And then I... What was the... I mean, just a matter of interest, what was the argumentation? I mean, that... I mean, what was it? I mean, what was this? And how did it connect with this treatment of the notion of entity? And obviously, for Christians, the Trinity can't be a set of three gods, although somehow it is a set of three persons. Yes, I know, he had a modal version of the ontological argument, it was...

37:30 Yes, I don't think it was published in his lifetime, I think it was... Yes, why don't we send that to that journal? And then we sent that to that journal, and we received a very positive answer. A guy who really understood the paper said that it was very interesting, very important what we did, and then he recommended that we should publish, and it was published. Fascinating. What was the name of the journal? I must look it up. It was Faith and Logic. Which I've never heard of, but which I'm sure these days you can Google and find a reference to. You can find that. Well, I'd love to read it, just out of sheer intellectual curiosity. I don't think I'll become an orthodox Christian as a result, any more than the author did. But I'd still be fascinated by the argumentation, so tell me a bit. Well, the thing was very easy, you see? It was just the case of passengers and persons. Yeah, I was going to say, it obviously connects with the passenger-person example. So then, the question is that we have... Just, you know, there seemed to be a vibrational looking at the argument here. There are two elements here. So one is the kinds, you know, and the underlying objects, the underlying elements of the underlying kinds. And then the other thing... It was something that already Aristotle realized when he said, although a thief is a person, a good thief is not a good person. So this means that from our point of view, this means that it has a property of a kind or not. And then we have an underlying kind, right, like this person, then if we have a property, this property may not... By the way round, surely. Right, may not go, may not slide, I think, I don't remember, slide, I don't remember how we use it, right? Well, it may not transfer, or whatever. Right, it may not transfer, but it may transfer, or less in all cases, because if a person is a male, a person is a, well, it's a mammal, I think, it's a male mammal, and so on and so forth.

40:00 Well, anyway, so, then... With these two ingredients, we construct our model. You see, we take as an example the Athanasian Creed, and the Athanasian Creed had several axes. It did indeed! And so we took all the axes, you see, and then the idea was to put here, we have three divine... So here are the divine persons. So we have the kind of divine person, and here we have the kinds of God. And so in this kind of God, there is only one. And then underline each divine person, then there is the same God, exactly like the passenger. Sure, sure, sure. And then, for instance... So you are just looking at the conditions on the sections and fibres of maths. That's right. And then here the Sun, the Holy Spirit, and what is the other? The Father, the Son, and the Holy Spirit, or the Holy Ghost is sometimes termed that way. This doesn't transfer here, so the god is not generated by the god itself, and things like that, and so then we make a list of the property we shall transfer, the property we shall not transfer, and then we said, well, that was as simple as that. We have a model of the... Thank you for your attention. All of this was created. And the Holy Ghost is neither begotten nor created, but proceeds, you know, whatever that means, but it's whatever it means, isn't it? And you know that, what was it, Paul Simon, I think that he left because he believed that this was inconsistent. Yes, he couldn't honestly say the words of the Creed. I talked to Bill about that and he said it's very good that we are doing that because we have to be very clear about that and we are not rejecting it.

42:30 And then you saw this was published and then in the next issue it became a rejoinder to our rejection. And you see, the reaction was crazy, because they say, oh, they're using two notions of equality and so on, but the whole thing we're using is just this set of theoretical values with three elements and elements and so on. There was no kind of contextually relativized notion of equality, it was just purely as a... Yes, there would appear to be if you tried to force the thing into the mold of set theory. Because obviously if you would try to do everything, well in terms of epsilon, you know... The father is, you know, the son is a member of, and that he is but is not. So yes, you would have, you would have a, you would have a, kind of. Well, you might have told them to go away and read conceptual mathematics, just read the simple introductory notion that is there, this introduction notion of the section fiber of a map, and, you know, start giving examples of it. So, they obviously haven't grasped the notion of underlying kind at all. Well, it's the whole point about the kinds of constitutive domains for the quantifiers. They don't understand what you're meaning. There isn't some all-encompassing... No, sure. Hi, here you go. Hello, gentlemen. Hello, hi. You came to a very important moment, you know, we're discussing...

45:00 I was explaining a paper that I wrote in a theological journal connected with this idea. I never knew about that. No, Bill never mentioned that. I read the paper with McNamara, the one about, as I say, you know, kinds as constitutive domains of quantifiers, and that was what interested me because I thought this is something so important because it still hasn't been got across to the philosophers of logic how important this recognition of the, you know, that there is no stable global notion of entity to underpin the structure of the domain. Therefore, one must think of the structure of domains of variation in a different way. Rather than being composed of objects the same or different, absolutely there to be the values of the variables, and, you know, just the same or different, as I say, absolutely. We need a different way of thinking of the structure of domains of variation. Hill, of course, suggests in one of his papers, I think it's in the Eilenberg Festschrift, that the correct way of thinking of domains of variation in general, or their structure, is in terms of a lattice homomorphism from parts of the domain into parts of the domain. These are all parts of a quantity, which is either what he calls an intensive or extensive quantity, which means that it either transforms covariantly or contravariantly in terms of, you know, functorial constructions into other categories. But a lattice homomorphism from parts of a domain to parts of a quantity varying over it. Inclusion and membership. Inclusion is actually the deeper notion, and membership should be explained through inclusion, not the other way around, as Coe Blee, Fregren Piano Blee, Fregren Piano's mistake was to assume that there had to be a global top element, so the lattice of inclusions, and that it was absolutely fixed, whereas in fact, the whole point of the constitutive role of... The idea of the kinds of quantifiers, relative to ranges of quantifiers, is to show that... There is no such underlying notion, and therefore, and all of this can be expressed very nicely obviously in terms of categorical structure, in terms of limits and co-limits.

47:30 There is one further element called, and then this is what we call the nominal category. I don't know if you came across that. I'm not sure if I did, I don't think so, no, that doesn't ring a bell. The nominal category, that was suggested to me by Bill. Bill said, it's okay what you're doing, he said, but... You're forgetting an element. So the nominal categories are categories of names. Okay, I was going to say, this is just the way it is. And so then, of course, we didn't have that at the beginning. And then this clarifies a lot. So, you know, one has the nominal category, and the other part of... What we did was a unified, this probably you have seen, that it's called a unified semantics of math, now. Yes, in fact you gave me a copy of that paper when we were in Montreal, sorry when we were in London visiting John Bell, but I don't... I haven't looked at it for an awfully long time, so remind me. I ought to look at it. Because obviously this goes to the whole issue about mass nouns and count nouns and the Fregean semantics of the way the Fregeans insistence that one had to have, as it were, a background notion of object in order to do ontology at all. The only way in which one can... The only way in which one can provide any answer to the question, what is there, is in terms of an answer to the question, what objects are there, where the notion of object is obviously given against the background of predicate logic and standard semantics of quantification, which is crazy because if you think in terms of vibrations and categories, it's... Oh, you don't remember what you said in the paper? Well, you must remind me. What we did, you know, but very vaguely, I think that it was a nominal category of nouns. But you had a way of treating sortal terms particularly, didn't you? Right, I would have a category of nominal maths, right. Well, hang on, I mean nominal... Right, yes, because obviously names for, I mean, mass nouns are going to have a quite different semantics from things which are bearers of proper names. For instance, here you see, dog is an animal. So that was in this category, you see, because, so that in this category were things of this kind of an animal.

50:00 Oh, this is, yes, not animal. So this is the category of nominal, nominal category. So these are really words. So to speak, right? But these are words. Whereas here, for instance, we have things like dogs are animals. So that from here to here, we have which is a plural. Which is a? A plural. A pluralizer, yeah, a plural, yes. And this, in fact, is a factor because it has a left adjoint. And this left adjoint is something that could be, variously be described as... ...portions of, or sets of, or according to what it is, for instance... Well, yeah, because obviously you're not going to have, this is not going to be full and faithful because of this, of course. Because you can't pluralize mass now. I mean, you can't talk about many waters or many... Well, except implicitly when you're speaking, when the implication is that there is an inbuilt. Division of reference because you're talking about specific portions of water. Right, in case you take from dogs to animals, you go to dogs are animals. And then when you go from here, dogs are animals. And then, how was the thing? Ah, it was something like A. Yes, but you can't say... But you can only say gold is a metal, you can't say a gold is metal. That's right, that's right. You can say gold is a metal, but you cannot say a gold is metal. And then I remember that... So the way that it... The main thing was... So this would all be expressed in terms of conditions on the... Yes, on conditions on the east and then to the left and so on. Sorry. No, no, no, no, I just... I haven't been there, but okay. Okay, I'm sorry. Okay. I'm not trying to... And then... We have here, we have the now models, you see, and then at this level we have lattices. Yes. Yes. Two mathematicians. Yes. And at this level we have just objects, I mean sets and so on. I don't remember very well what... Yes. Yes. But the sets, the case where you had sets would really just be a kind of special instance in this construction, wouldn't it? It wouldn't be... Yes. It would be the case... You know, I don't... To tell you the truth, I mean, I don't remember very well. But this was more or less... Because Bill has this very interesting passage in that paper in the Isle of Westeros, which I can remember that it's...

52:30 It's been a long, long time since I looked at it, and it must be over 30 years since he wrote it now, but this business about the correct treatment of the correct way of analyzing the structure of domains in general, in logic, All of this would be based on this relationship, this lattice homomorphism between the parts of the domain and the parts of the quantity, bearing with respect to the domain, and he has some interesting things to say about how the case of sets, the case where the domain does consist of objects, which is really the case where... It's determined by its points, of course, naturally fits in as a special case of this lattice homomorphism, I guess the case where it's kind of trivial, where you do have a global top element, and I wish I could remember the details, because it seemed to be an incredibly interesting and deep idea, and one connected with his point about inclusion being the more fundamental relationship, the more fundamental relationship of the membership. This is a portion of water, and then you take the pluralization and then you say portions of water, and then you can say water are portions of water. Yes, but do you actually want to say that water is all the portions of water that there are? I mean, in some sense, you know, numerologically that's true, but it's the question... Let me see, what's a portion of water? It's water. Yes, ah, yes, whatever is a portion of water is water, that's perfectly, okay, yes, yes, yes, yes, yes, but now it seems to be more a category of adjectives than of nouns, now it seems to be more adjectival than a nominal construction, whatever is, whatever is a portion of water is water, seems to be more. yeah but you can say a portion of water is water and certainly yeah and this is something in the let's see a portion of water now my god well let's take a simple example example example whatever is a portion of gold is gold i mean well that's not um but what would be the conditions on the front

55:00 what would be the conditions on the on this front i remember that there was yes And you see I don't remember now... And what are the unit and co-unit of the adjunction? Well, that was plural, one, and the other was portional. Oh, right, yes, of course, portional. Now at this moment I don't remember really, because you said dog, for instance. So, dog, and then a mammal, and then I say a dog. I don't remember that. But it was on that kind of idea. And then there was something else that was interesting that I'm forgetting. Then, to test that theory, we discussed eight different syllogisms. For instance, to add it is liquid. I remember this. I think you gave the version of this talk in Cambridge, didn't you? Unfortunately, that recording didn't survive. It was one of the ones that was lost, deteriorated. I'm really annoyed about this. There's only one of that conference I don't still have. To remind me, so what was the syllogism? Claret is liquor. Liquor is liquid. Claret is a liquor, no, claret is burgundy, burgundy is a liquor, therefore claret is a liquor, but there was another, claret is burgundy, burgundy is a liquor, therefore claret is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, therefore claret is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burgundy is a liquor, but there was another, claret is burgundy, burg Yes, whether you used the indefinite article or omitted it, because obviously depending on whether it's a classifying mass noun or... Effectively membership, which of course goes to the same point about the relationship between inclusion and membership. So in fact this is getting at precisely that distinction between inclusion and membership, which Bill sees as being so important, the correct understanding of the structure of domains. And then the interesting thing is that everybody else that I saw that had studied these things,

57:30 It is more, how do you say, it looks more natural to say that. Okay? They didn't have a theory. No, no, no. They just had intuitions about what is... Right, and what I'm showing is that it was a theory, and this theory gives yes and no answer. Absolutely. Which the linguists, the kind of field linguists, will in fact confirm are the natural way that we express ourselves. There was only one difference with the guy who approached this, you know, that was also a game from... More or less we believe that and so on, but there wasn't only one difference with this guy, you know. However, they say, oh, no, no, I mean, it cannot be, I mean, it depends on what people believe and so on. I mean, it was this kind of a stupid thing, you know. Here there was a theory that was developed and gave an answer yes or no to all of these theories. And they cannot accept that. So I got... At that moment I got discouraged, because we had that, and this was a piece of work. Let me see if I can remember that. I mean, it's so trivial, I mean, the solution to that. Yes, of course, it is determined by people's beliefs, but these are not, as it were, inculcated beliefs. These are beliefs which are absolutely... This is the belief which goes with the categorical structure. I mean, categorical in the metaphysical sense, I don't mean in the technical mathematical sense, that's just programmed into our language, already programmed into the syntax. Yes, actually, I do mean into the syntax, because the correct use of particles and mass nouns is programmed into the language. Now, there are claims that have been made by some philosophers of language that there are alleged to be... Some natural languages, I think there are some North American Indian languages are claimed to be examples. The people I've all studied where they are supposed to work by just direct feature-placing languages. They don't have a category of So they really do say things equivalent to Quine's weird example of blow-it-rabbit-it, you know, like it is rabbiting here, but it's very much debated as to whether that is actually correct.

1:00:00 You have to fix that. For him, the main thing was to fix reference. Yes, well, of course. You know, can we go to the, maybe to the... Yes, sure. It's just in the... And then maybe we can find this... Yes, I'd love to. I'd be very interested indeed. But don't let me forget that I do need to talk to you a little bit about the archive. Okay. Yes, let's do that now. It's just in this room here. There are some people having a meeting here I'm so sorry we need to use the computer that's one of these there it's their computer but these ladies obviously having a bloody card game I'm so sorry, we need to use the computer. Yeah, thank you very much, I'm sorry. Well, maybe we should come back later, we can't really completely break up there, can't we? It's okay, we'll come back later, it's okay, we'll come back later. You silly bloody old trout, why can't you have your card game at a different table? Okay, let's go over there and have another coffee or something. Well, look, we can sit down here for five minutes. Let me get you another drink, and I just wanted to ask you about this. Were you thinking about something else that's coming to your mind about entities? Well, I'm trying to figure out some business, but maybe if we go afterwards... Yes, we'll just give them five minutes to finish their card game, and I'll get you... Would you like a beer? No, but I would like a Coke, please. A Coke, sure. Good idea. I'm waiting for them to finish their, excuse my language, their bloody blasted card game. So why with 20 other tables in there they have to use the one right next to the computer? No, well, I already told you a little bit about what it is that I'm attempting to do with this archive and the priority at the moment is to

1:02:30 Complete the catalogue and get it online to get a much improved website which really looks professionally, is professionally designed and which carries all the information about the project, about the archive and the catalogue. And then to complete the, I mean I've got the catalogue of all the recordings that I've made of... All the meetings in category theory and in particularly historical and philosophical aspects of questions connected with category theory since the Cambridge meeting, which is almost 20 years now. And I mean, I won't bore you by running through it now, but it starts with the Cambridge meeting and then the 1989 and 1990 international category meetings, which included a very long, a very interesting discussion between Bill and Eilenberg and McLean in Como in 1990, which was absolutely fascinating. It must have been one of the last things, I think that was in fact the last meeting Samuel Eilenberg attended before he had his stroke. So that's extremely interesting. Yeah, he had a stroke about two years after that, or three years after that. This is 1990, but I got several, oh, certainly maybe eight or nine hours of recordings of Eilenberg talking with Bill and McLean about the early years and about some of the motivation. Not just gossip and personalities, but really interesting. ...exposition of basic ideas and, you know, what he thought had been the crucial turning points in development. And then also with, in fact, with Benabou and Kelly and Peter Fry and other people. Then, 1993, the meeting where you were in London, Ontario. And then meetings with Bill in Florence in 1994 and 1995, and with Colin and other people, some very, very interesting talks he gave on the continuum hypothesis and on foundations of analysis. And, you know, his views about, in fact, his views about differentiation and integration, which were absolutely fascinating. Then all the stuff that we did in Bolzano in 1998, and then obviously various personal meetings, interviews, discussions, and the big meeting we had in 2005 in, well, no, in Florence in 2003, and then in my house in Brugera in 2005 for about 12 days, no, two weeks, when he was there with Cartier and Colin and all the other people.

1:05:00 And of course, you know, quite a lot of meetings in between like in Copenhagen in 2002 and Nancy and in Paris. So the total, we're talking about a total probably of something like, just in terms of interviews with Bill, conversations, I mean, you know, important scientific conversations he had with people like Eilenberg or Machanel about... No foundational questions. Probably about three or four hundred hours of recordings at least, just of that material alone. And then together with other category theory material, probably something like another six or seven hundred hours of that. Even that's only a very small proportion of the total archive. The total archive is something like 26,000 recordings, going back to 1973. About one-third mathematics, about one-third physics, about one-third philosophy, obviously noise-to-signal ratio, there's a lot of stuff in there which I wouldn't bother to re-record, but there is a solid core of at least 30 or 40% of material that I think is of serious scientific value, and perhaps 15 or 20% of material that I think contains stuff of really major scientific importance. The 10 days of conversations with Cartier, as you can imagine, were absolutely amazing. So what I want to do is, it's now been formed into a foundation, and it's now in fact a trust. In UK law and Chris Isham, I think I mentioned this, Chris Isham has agreed to be one of the trustees and so has Roger Penrose. I don't know how Bill is going to react to that but as I was explaining to Richard the other day, the point is that with somebody like Penrose's name on the letterhead as trustee you do have a lot... I did this funding proposal about a year ago. The total cost of digitizing the whole thing, putting it into hard drive, given that you're talking about 25,000 recordings, given that, you know, some of the material is quite deteriorated, so it needs restoration with the software. There's a very, very, there's an extremely It's a very powerful tool nowadays for the restoration and editing of...

1:07:30 Very large quantities of recorded material, spoken recorded material and video material called CEDA, which stands for Computer Enhanced Digital Audio Restoration Software, which was developed in fact at Cambridge in the 1980s for the National Sound Archives and has now been developed a lot more since. It can cascade up to 32 recorded tracks simultaneously in real time and has got incredibly sophisticated tools for writing the digital soundboards and taking out distortion, even isolating individual voices in conversation. There's a lot of conversations where you've got people speaking over each other and it's just incredible what it can do. But of course it needs a technician, it needs somebody to ride it, it doesn't run itself. I estimated that the whole thing would take at least three years. Well, to be on the safe side I've said four years, but I think it probably could be done in three, to digitize everything and get it in a couple of big... ...server hard drives and obviously we need a very large server and then you know to make it available as a public archive but that's a big project that would cost probably something like 150,000 euros but the key to it is to it seems to me is to I've done a fairly costed well costed funding proposal the key to it seems to me is to now that the archive has been established and it's got A website, although the website needs completely redesigning and needs a great, but still haven't even begun to get the catalogue in life, is to get some Seedcorn funds, I need some Seedcorn funding, sort of Seedcorn is the word I'm looking for, like start-up funding, enough to complete the catalogue, get a really good website on a large institutional server, and negotiate an agreement with, you know, a credible academic institution like... In return for the copyright, at least to get enough start-up funding to put a selection of the most important material, the first maybe 300-400 hours of the most important material online, so that people have some idea of its scientific value of the whole archive overall. Yeah, so 2,000, 3,000 euros here, 2,000, 3,000 euros there. I've already applied, I've already approached the British Society for the Philosophy of Science, and they're going to come up with 2,000 euros.

1:10:00 Oh, thanks. Yeah, sorry, Richard, do you want coke, whatever, or wine, or whatever? No, no, no, maybe juice. Juice, okay. I mean, my friends in Oxford and Cambridge suggested the obvious thing to do is just to write off to various bodies like the Oxford University Press, the British Society for Philosophy of Science, Blackwell's, asking, you know, showing them the proposal, giving them the copy of the catalogue, you know, backed obviously by people like Isham and Penrose now that he's the chair of the trust. And just asking literally for 500 or 1,000 pounds or 500,000 euros from each of them to get the initial phase of the thing completed in their life. So, is there any source in Montreal or any... I mean, given that Montreal is obviously just about the world center of category theory and... And particularly people who actually know the history and philosophy. In fact, I should have been out in Montreal doing interviews for probably the last three years. Do you think there's anybody there who might be able to support this or that, you know, we could turn to to get just a bit of Seekorn funding? I mean, Seekorn funding, you're talking maybe, you know, sort of three or four thousand Canadian dollars. So not a huge amount but it's it's difficult oh um no well i've actually checked out so i'll give you cash if that's okay um so five seven altogether thanks very much there you go thank you thank you it's very good so that was my question yes and the other part of it of course is that i really need to talk to you about what's in your heart Thank you very much for your time, and see if we could at least merge the task catalogue in this material, I'm making sure that it's an idea, I'd like to scan your stuff and get it online. Let me tell you some facts I know, you know. First of all, I've never been in a science field. Or finance, either at the university or anywhere, and so then all that I know is what I've seen, okay? For instance, let's say, Montréal University. There is nobody in category theory, I was the only one.

1:12:30 I came out, for instance, I... Michael Barr, there's Mike McKay, he's still there, and who else? Well, I don't remember. Nowadays, they decided not to bring any category theorists. So none of these people who retire will be replaced. Because they consider that category theory is a bad thing. Given that fact, my impression is that... No, this is a very bad place to start looking. Okay, fair enough. Well, it's better that I know that than that I waste time breaking my teeth sending applications to where they're not going to get... where they're going to get thrown straight into a little bit. So it's good that I know that. Especially, André, because whatever I did, I published. Yeah, but André never published stuff for a long, long time. I have a lot of things I wanted to ask you about Mike McKay and you know his program for bypassing identity but we'll come back to that okay so well this material of Andres that all these this material about Andres work and the notes you made that you're holding and the other stuff is is physically in your possession in your in your house okay so if it was if If we wanted to scan that so that it could be put, it could be digitized and put into a hard drive for conservation, it would just be a question of my arranging for somebody to come and scan it. Material wouldn't even have to leave your house, I mean, it would remain in your physical possession, but we just arranged for it to be scanned. I mean, roughly how many boxes of documents or pages are we talking about, would you say, to guess? What size of... Well, the paper of Marquis and Mead is not there, no? No, because it hasn't been published yet. No, no, no, but maybe, you know, the pre-print is there, you see. No, it's not even a pre-print, it just says it's forthcoming in the history and philosophy of... Because it seems to me that there's something like... 10 lectures by year, so that maybe from 69 to 70, maybe 10 years, so maybe they could...

1:15:00 It's about 100, about 100. Maybe less. Well, let's say on the side of caution, let's say about 100. Yes, but some of them are very long. For instance, I have something that... That Andre has dictated to me, that was something like a hundred pages on what is the name of these pro-objects in category. Yes, that would be fantastic. You've still got that. But even if every single one of these documents was a hundred pages long, you'd still only be looking at 10,000 pages. So, so, I mean, what's a safe upper estimate? I mean, scanning 10,000 pages is not good. This could be scanned very quickly indeed. This would be a very short, this might be two days work, you know. I was thinking we're looking at maybe a month or so's work. Well, in that case, as soon as you get back home, if I can email you and chat, we could arrange something for it to be scanned. If you think that we do that, that's okay with you. Obviously, I'll send you a catalogue of everything I've got, you know, in the, in the, well, already in the catalogue, the archive. As far as trying to get Seekorn funding is concerned, okay, so Montreal's not a good place to start looking. Um, okay. What about the, what about the American Mathematical Society or the American Society for the History of Mathematics? Well, Bill should know about that in the Mathematical Society. I became a member of the American Mathematical Society last year. There's a thing called the Canadian Society for the History and Philosophy of Mathematics who hold meetings. I think their last meeting was in Montreal. Jean-Pierre Marquis is a member. In fact, I'm not sure, they might have something. This is the university themselves, you know. Well, I get the message. There's nothing to be looked for from the university. But I mean, there are lots of other fish in the sea apart from the University of Montreal. But this is, I mean, you should ask people who know something about that. Well, who should I be asking? Like Marquis. Yeah, Marquis, okay. This seems to be the... I'll pester, I'll pester Jean-Pierre Marquis. Okay, I'll pester Marquis and... Just as I've pestered pestering people in England, I'm afraid you do have to pester people endlessly if you're looking for this kind of seacorn funding.

1:17:30 You make yourself a nuisance. In the end, it's more, unless you're talking about a very large sum of money, and frankly, in institutional terms, two or three thousand euros is complete, no, small change. It's a total pittance. You know, sooner or later, they'll just pay you to go away rather than, you know, just to stop bothering. Because you are in institutional terms talking about a very small amount of money but on the other hand it would be certainly enough to spend at least to do a year's work to complete the catalogue and get maybe eight or nine hundred at least of the most important items online. I think from that point onwards and if you had a foundation with Penrose's name on the letterhead they're getting the funding for the main... The main project, which, as I say, is a much bigger scale, longer term thing, would not be too difficult, but it's like threading the needle, it's getting the seacorn, it's getting started. Okay, well, I'll talk to Jean-Pierre Marcus, but about the archive that you're holding, I'll send you an email as soon as you're back and have a chance to recover a bit. When I looked for Thaisrie, when we were preparing this paper, No, I look at that, and it was not enormous. It was not enormous. No, the bibliography was not enormous. It covered a lot. I mean, it covered some, as I say, from 59 to more than that, you know. Did you ever see that? No, I did not. You don't put these papers on your website, Gonzalo. Is it? What's it called? It's not called that. It's called the early years. Really? No. Categories in Montreal in the 70s. I'm sorry, I must be going blind or mad because... Collection or something like that. I'm terribly sorry, when did you put it on your website? How long ago? I'm told that I'm not being bribed myself. Well, I hate to say it, but I don't think you did. Because if you did, I'm pretty sure I would have noticed it and would have read it by now. Especially a subject with a title like that. I don't think you did. Well, maybe you intended to do, like, you know, well, when those wretched women have finished their bloody bridge game, we can go in and look at the, we can actually go and look, and it won't take a few seconds to check. We want to use the internet, but there is a whole gaggle of women there playing a card game.

1:20:00 This is my contribution to the paper, my real contribution to the paper. With Marquis, yeah, with Marquis, yeah. And so, because I said to Marquis, look, this is what I have, and then I told him that Bill didn't like some part of it. Yeah, yeah. Some parts of history? Oh, yeah. Bill is very, very pernickety about the history. He really does insist on getting it right. I mean, this is one of the things he almost had the big... Which, of course, means... Which means getting his viewpoint. Of course, that's the problem with Bill. About that, and then I said, you know, the main section is about the ideology that was prevailing, you know, and then at that time, and then how we were working with Lenin, interpreted by Mao, interpreted by Lovin. Oh my god, I can imagine how you really would be walking through a minefield with Bill in that case, oh dear, no wonder you have the... The funny thing is that there was a girl who, I never met her, I mean I met her once, and I never seen her again, and she had organized that. I think it was in Montreal, there was something very strange, because I had never seen this girl before, and then she organized that, and it's about the history of category theory and so on. Oh, not Elaine Landry. Not Elaine Landry. Oh yes, she's at Calgary now, she's at Calgary. She's one of those two authors of this article in Chiropractic and Mathematics. Yes, yes. She's a philosopher of mathematics. She's now at Calgary. She's quite a bright girl, I mean, as philosophers of mathematics go. She's a good thing. Colin McLarty has a, you know, quite high opinion on that.

1:22:30 Absolutely, of course, how can I say, the climate, the ideological climate, and I wanted to connect that and to see that there were some problems that could not be solved because of this ideological problem, this ideological climate, and then to my great, unbelievable surprise, Bill LaVie appeared. What about the meeting? Oh, actually, I think Colin McClarty told me about this, yes. I think Colin must have told him about it, yeah. I don't know exactly what is written in it. And then Bill didn't like the things that I said, especially. You see, for instance, let me tell you some of the things that I think, I don't know whether I said that, but some of the things that I lived through. You know, this girl called... Oh, my God. Well, at this moment, I don't remember the name. Anyway, she's a... Welcome to the club. Barbara Feig. Barbara? Barbara Feig. V-O-I-G-T? V-E-I-T. Oh, yes, no, I have come across this. She's published in the JSL, I think. Yes, that's right. Yes, I have, yes, I have, I have come across it. She's published in the JSL. She did, like, when she was working, like, a thesis. Yeah, yeah, I know. She was one of your PhD students, wasn't she? Right, yeah, I remember. She was not a PhD student, that was informal. Anyway, she was one of your students, yeah.

1:25:00 Well, so, anyway, she used the techniques that I had used, you see, because up to that point, everybody was doing logic from the categorical point of view, so what category theory can, you know, can apply to logic, you know, and then I had the idea of using the opposite, you see, since we have categories, we have a way of... Passing from category theory to logic, from logic to category theory, then I said let's use techniques of logic to get results in category theory. And that's what we did with Mackay. And then on this, what is called, what is called that, the, I'm sorry, this book about, no, the modal logic, no, no, the first order, but then there is something which is small, there's a main theorem there, which is called conceptual completeness, okay, so conceptual completeness. Yeah, I don't know this work, I told him, I'm afraid, that's my ignorance. It's really a nice statement, purely categorical, and then... However, the proof that we found was a proof in model physics, and then this girl was impressed by that, and she tried to do the same thing and so on, you know, but then the Italian guys, she was in Italy, she was in Italy, she's not Italian, and then the Italian guys there, you know, there was Carbonio, the real hardliners, oh God. Subtitles by the Amara.org community Don't ever repeat this to Bill, but I do think Carboni has been a dreadful influence on everybody he's come into contact with. Have you come across this guy, Aurelio Carboni? Well, I only know this paper about, you know, extensive... Distributions. He did quite interesting work on the category of distributions. Now, how you should do the theory of distributions in, I mean, the Dirac. There are distributions as a category. I mean, I have to say, he's quite a smart guy. He was also one of the first people to really, I think, some interesting ideas about functional analysis from a purely, you know, category-theoretic viewpoint.

1:27:30 As I said, going back to that early work of Grothendieck, which obviously was not directly, you know, category-theoretic, but... Actually, if you look at it explicitly, it's got some very functorial ideas in it, but he's a bright guy, but politically he's even more hard-line in a Marxist-Leninist than Bill, if you can imagine such a thing, and unlike Bill, who is whatever. There may have been glitches in his personality. He's a genuinely very good-hearted person. Carboni is just a fanatic. You can't have a normal conversation with him. He'll only talk about politics or mathematics. He's just a complete automaton. Alberto Bruzzi, who is a very close personal friend of Bill's and one of the nicest people you can meet, he can't. Converse with Aurelio Carboni because you only have to say one thing, use one phrase that kind of has the wrong connotation, you'll be immediately denounced as a kind of Trotskyite or an imperialist running dog. I mean, the guy is really the most humorless fanatic I've ever come across. You just don't want to be in the same room with him. It's a pity because he's, you know, I've heard him give a couple of good talks. He's obviously a reasonably fine mathematician, but I would pity anybody who had him as a supervisor. It would just be... You know, nightmare. Well, I'm quite sure if anybody came along and said that you should use logic to investigate category theory, came along and was probably lucky to escape from the room alive if Carl Bernier was around. The other guy is a guy called Maloney, Giancarlo Maloney. The two of them are the most ultra-Stalinist category theorists in Italy. Yeah, I was going to say, I can imagine if she ran foul of Maloney and Carboni. You see, from my point of view, what's nice in category theory is that... If we can express things invariantly and so on, but at some point we have to compute, and then we can use, we can bring logic. I mean, why not? I mean, this is something that is there and so on. But then this was considered quite reactionary, and because of that, for instance, she was deprived of working on some real category theory and so on.

1:30:00 Yes, I know, I know. So this was one example. Very sad, I can imagine that. Another example, which is... But you mentioned this in your talk. I think I mentioned it. And the second example, that was something that I lived. How come that we knew perfectly well that first-order logic was interpretable in a category, that in some way was an invariant expression of logic and then we never used logical We would never use the internal language, which of course we knew before Benabu. Because we knew that the whole thing, I mean, that was the whole point, right? Now, how come that we never used that language that was this fossil at that time? And then, once again, I say because of ideological reasons. Because, you see, logic was supposed to be reactionary. You see, logic and geometry were dialectically related. Yes, sure, sure. And then, according to Mao... The principal contradiction, comrade, or please the phrase, your grandfather was a... Right. They were the main... they were the principal... Oh, the Russian acronyms for it were there, I can well believe. Because you grew up in a family that obviously, you know, knew all about this kind of thing. What was your grandfather's position, you were asking? He was just a kind of member. Oh, I see. He wasn't any... he wasn't a very senior party official or anybody like that. He wasn't kind of, you know, he wasn't Mikhail Suslov's, you know, kind of, PA or anything. However, till today he has a photo of Stalin in his room. Wow, that is unusual. That's pretty... You said lots of ultra-nationalists, because there are probably more than... For example, he denies nowadays the Communist Party or the Russian Federation. Oh yes, of course, they'd be total revisionists. Anyway, you say that. Well, he'd get on very well with Bill. And then my answer was precisely that. It was like a geological reason, because the logic was considered to be reactionary to the secondary in this...

1:32:30 Yes, the principle contradiction, Comrade. ...contradiction that was Mao and so on. And then, well, at that time, Bill had ceased to be a Maoist. Yes, because he was only a Maoist very briefly, I recall. My god, briefly, in 73 he arrived in Montreal for one year, for several months, and he would arrive with the... Oh, he was still a master in 73, was he? Oh, no, okay, I thought he kind of worked... I thought he swung back to being a... In 73 and 74, in 74, we had two meetings, you see, in 73 and 74, and he was a Maoist in 74. And suddenly he said he hasn't ever been a Maoist. Well, yes, I know. I knew he was a master in 69, I thought he was from about 69 to 71, 72, to the time that he was thrown out. He would say, well, it's very nice what you said and so on, but there are more important things to discuss and then he would take the book and bow and so on. Anyway, and then, you see, I tried to explain why this didn't come out, this language. Then he wrote me a letter, a long letter, saying, you know, that I was mistaken, because, and so on, and that was kind of hard. And yes, I don't agree, so I didn't change that, my paper. So I don't know, certainly he doesn't like it. And then I did several things on that level, you see, which I was trying to explain. Well, I'm sure it won't affect your friendship, I mean, it's a bit... Well, but it's very good because it didn't touch our friendship. No, no, no, which shows how much he's mellowed in the 30 years. But no, I knew he had gone through a very intense amount of space, but I didn't realize it had lasted as long as that. I thought by 1974, just really from the internal evidence of his papers, because whereas in 1969, whereas in 1970, Nice... He makes great play with quotations from Mount Seytoun, which you probably know as you've read the paper. Well, I'll send it to you. I've got that, of course, and everything else. Whereas in the 1970s, he's making great play with quotations from Mount Seytoun. By 1973, which is the Bristol Colloquium volume, which I think was published in 1974, it was written in 1973,

1:35:00 All Engels and Lenin and the section on the Eleatics from Hegel's Conspectus of Lenin's philosophical notebooks and his marginal notes on the section on the Eleatics School in Hegel's History of Philosophy. And this kind of thing. And it's all very orthodox Marxism-Leninism. And Mao has gone out the window. And I have the impression that by 1970... Before 1973, he was already, as it were, reverted to the kind of super-orthodox Marxist-Leninist Stalin's criticism of Mao, which was, of course, that Mao failed completely in his historical task of industrializing China, you see. They never had a proper collectivization in China. You know, in 74 we had a very important, I mean, 73 and 74 were very important in Montreal, because in 73 we had one Mao which we invited, you know, the middle of the year. In 1974, we had a seminar on category theory. This seminar was important. Practically, everybody who was there, and we did. How I wish to God people have been recording everything then. Incredible time to be here. Given anything could have been a fly on the wall there. How on earth did Peter Fryde of all people manage to survive in an ideological atmosphere like that? I mean, by growing a very thick skin, I imagine. Peter Fried is a banker. I mean, he's got a complete... Hardly a few people could be a more wholehearted supporter of the capitalist system. He never makes... He just never bothered to argue with them. He just got on with doing his maths, I guess, yeah. But the person who suffered the most was Benabou. Yes, of course. Because Benabou, you see, was a member of the Communist Party. Yes, yes, exactly. Of course, we're all running, rotten, you know, rotten running dog revisionist renegades, you know, exactly. And then he would say revisionist, you know.

1:37:30 Because as with all, as with all extreme, as with all people within the various sects of the Marxist Leninist Church. They spent far more time and energy attacking, you know, their nearest neighbouring sect than they ever did to attacking the capitalist system. Peter Fry just, you know, doesn't mind. Okay, he's a rich banker and a bourgeois, but no problem about him. I mean, you know, we don't mind sort of having dinner with him. I mean, we might disagree with him about, you know. But when it comes to the essentials, the most terrible word of abuse in Bill's vocabulary without... A possible comparison is Trotskyite. You can survive being a fascist reactionary, no problem at all with fascist reactionaries, he might snarl at you a couple of times, you know, ah, damn, fascist reactionary, but you know, go have a beer with you a couple of hours later. But if you once suspect that you're a Trotskyite, there is no hope. You are cast into utter outer darkness and will never be spoken to again. Do you know Max Dickmann? Of course I know Max Dickmann, friend of John Bell. Do you know what kind of... Well, of course I do. I do indeed. Yeah, but what do you... Because I heard all about him, both from Max... Yes, I did hear about him. Oh, I heard both Bill's version and, of course, Max's version, which is... I know Max Dickmann's version. And John Bell's version, which I suspect is to the truth of the three. Fantastic. You must tell Richard that. It's just out of the abuse, Richard. Max Dickmann is a topologist. Well, he does sound real. Was he at that time? He was a magician with me, I mean, we were together at Berkeley. Okay, I'm so sorry, but in the last 20 years he's done almost entirely... Well, maybe he's done something else, I don't know, but for instance, even the only book I know that he wrote was on on infinitary cards, on infinitary logic, on an infinitary card in 1992, something like that. Okay, well now he does, now he works almost entirely on what they call real... Real algebraic, real algebraic geometry, which means real, yeah, which means algebraic geometry over the reals. I mean, yeah, yeah, that's all, that's what he does now. Yeah, yeah, yeah, that's his field now. And he's done paper, working topology as well.

1:40:00 The work that we did with Machai and things like that and so on. And finally, these people have a good smell in real life of cataclysm theory in France, what's not very well. And then they switched to algebraic geometry and other areas. Actually, now you mention it, of course, I did know that Max Dickmann had been a logician because he, of course, worked with John Bell. That's right, he did work with John Bell. He is a person who had a lot of troubles, you know, because he had the... He was Trotskyist and in Argentina I think he had a lot of trouble and then he had to leave and then he went to Berkeley and then Berkeley also at one point, you know, his situation became precarious, I don't know. Yeah, political reasons. He took part into some march, I don't know, I don't know. He felt Halabtarski, I heard. Yeah, well, that was one of the reasons, but I think that maybe there was something else. And then, finally, he decided to go to Poland. And so, in Poland, you know, he believed that everybody there was Maui and was Trotsky. Well, simply because they must be anti-Stalinists because of what Russia has done. And he won't speak out. Yeah, surprise, surprise. I hate to say it, but his political judgment was a little naive. His wife was still with him, but his wife was even more aggressive, you know, politically than him. And then they didn't know... And at that point then Bill came and gathered them and gave them shelter in Halifax and then Bill discovered that was a Trotsky house. It's so typical of Bill. He was so kind-hearted and generous. He invited these people into his home as refugees, you know, and then discovers the guy is a Protskyite, which of course for him is the ultimate, you know. I mean, he just discovered he was a fascist, you know, an arsehole. It wouldn't have been a major problem. He could have lived with that.

1:42:30 I believe they did actually end up having a fight physically but I mean John Bell says he came and found them literally on the floor you know sort of grabbing yeah kicking the lights out of each other All the information, all the dossiers have been identified. This is fantastic. Have you seen that? No one has told me about it. I never had the gall to ask about it. I would be interested. On one condition, which is that you never ever tell Bill that you've given it to me or shown it to me. Well, I never told Bill. On that condition alone. But I can't pretend I wouldn't be very interested. I must imagine, it must be incredible. I mean, this is just the political stuff, you know, not his... I mean, does it contain records of his seminars and of his... No, no, it was just political stuff. It was just political stuff. This is the dossier that the university brought against him when they... This is the thing which contains the evidence that he, you know, this business about his election having pulled the gun on the professor of law and all that stuff. Well, of course, yeah. Well, he denies it, he denies it. It was much more interesting than that, you see. According to what I read there and what people told me after what we were there, you see, then Bill was of course the head in some way, although was not maybe the head of the Maoist party in Halifax. The Communist Party of Canada mocks us very much, to be exact. And he was also, of course, occupying the Killian Chair in Halifax. And he'd been given all this money by the Killian Foundation. The position, more or less, was in Canada at the time. And he'd been given all this money to assemble this research group and had about 11 people who were all basically, you know, tenured. ...professors who he, you know, was given the money to pay in order to assemble this amazing research group in category theory, which is probably the biggest and most fertile research group in creative research group in category theory there's ever been.

1:45:00 You know the notion of topos in this case? Topos was created for that in those years. Oh, so it was... Oh yeah, it was a really important... It was a fantastically fertile period. Fantastically, yeah. But then, at the same time that he had this... And Scroate, indeed, was visiting Merman. This was 69 to 70... To 71, I think. 71. It lasted for about two years. But at the same time that he had created this fantastic book, he had a group of... He started working, you know, in the group of... And somehow he became, you know, the head. I don't know, maybe he was not the head. He was never the head of the party or anything remotely like that. But he goes ahead in the sense that he had a lot of influence. Well, he was certainly the leader of that cell in Halifax, yes. Topos theory was a tool in the revolutionary struggle, and therefore that people should study topos theory. Should we make compulsory for all Marx and Leninists to study because it was a tool in the revolutionary struggle? He was a boxer. There was a big box, and she never understood, and she said, it's hard, it's difficult, this stuff. I mean, difficult. Difficult not to feel incredible sympathy for this guy. And Bill would have been deeply sympathetic. Oh, it's not so difficult, you'll have to get it, because Bill, of course, believes that all people have just gotten to his level. No, no, no. Did you get your slides back? No. I left them at reception with a label of your room number on them, so sorry, thank you. I have to talk to you, because we have to make some arrangements for tomorrow. So let's do it now maybe, or maybe in a moment. Come and join us for a drink. War measures, because what happened was the height of the Vietnam War, of course, and the Americans brought a lot of pressure on the Canadians because so many American protesters against the war.

1:47:30 Not just draft dodgers who wanted to avoid it, but people who were really much more politically active against it were in Canada. And then there was a series of very strange, still unexplained episodes. There were a series of bombings in Montreal in 1970, which are now widely believed to have actually been a provocateur, a d'argent provocateur by the CIA, but which were blamed at the time. There was a party, there was a particular force. He had a complete breakdown in paper time. Yes, yes, I know. No, Fatima saved his life, quite literally. He didn't, you know, that he would go for anything, this gas, you know. This was just after his son died, you know, so he was terrible. He had this, he was a member of the Communist Party. And then, we arrived in the morning, very happy. Cardinal Bain said, very good talk, you know, eight hours. And then he developed this theory, which we've never heard about, the bourgeois theory of time. Until all contradictions have been eradicated. Well, that doesn't sound very Marxist. The whole point is that contradictions are forever, you know. You just go to the next level of con... You know, every resolution of the contradiction is the preparation for the next stage of dialectical opposition, comrades. Are you sure that this Hardy Old Baines is not a running dog as a revisionist? Actually, it was the error of Stalin who said that the negation stopped. I don't know exactly where it's coming from, because, Javier, yes, it probably was. These are all very similar in physics, I mean, in terms of time. Yes, it's a bit similar to those ideas, of course, which Isham is very interested in at the moment, about this business of internal external time. But Lorville has been very interested in that for a long time. He's never published anything, but again, this is one reason why it's so useful to record his talks, because he's been thinking about that for at least the last eight or nine years. I've got, you know, hours and hours of him talking on that topic.

1:50:00 Good question. We wanted to look at the transfer principle. Ah, yes. I'll shut up because I've done all... In this country, there was already somebody who paid a lot for correcting Yang. Who are you talking to? Him or him? You mean he's trying to corrupt this young man or...? It depends what you mean by it. What form did the corruption take, or is it too unspeakable? Well, I mean, this is what you see here, or even worse. Oh, I see. Well, you'll be telling him he's got to sign the offender's register next. Actually, I found some typos, but if you are not going to make a second edition, I think those typos are... I will give you two minutes and I will just talk with Marek about tomorrow. Well, I couldn't have done this. Oh, here it is. There is always room here that there is a transfer principle. I forgot what the name of the book was.

1:52:30 Was there ever an edition that was published under a different title? It's very strange, I don't recognize the title, although I know the book. It's obviously far too tough for me, but I read Anders' book, which was, you know, most of the necessary feel for SDG, and then I remember tackling Laventhal, but it's very difficult. Well, this is, you know, this deals especially with the models, you know, because this is what became of the models. There's still, if I remember from what John Bell was telling me, there's still some unresolved problems with the, in SDG, to do with the... The strength, you know, the conditions in the topos, the base topos, the topos of departure that you need in order to develop some of the constructions. Is that right? Absolutely. I'm sorry, I have a vague recollection of a conversation with John Bell about two or three years ago. He came to give a very general expository talk about smooth infinitesimal analysis after his book. The talk was public in Paris and there was a discussion afterwards, is there not some still unresolved problem about the, you know, how strong the base topos, about the base topos over which you need to construct. Well, this is actually the essentiality of why this book is called Models. I mean, there's one question. I think that we still don't have a half of construction which are needed, and we don't know, I mean... What would you need to be allowed to have this construction? Yeah, okay, that's essentially what I'm getting at, yeah. By the way, I have to say that it took me quite a time to collect half of these things, which are in references, and I hope that you have the...

1:55:00 But it's very funny that I don't find the book by Mordechai. Maybe this is on the embedding of money and then paper. This is the one. On the embedding of money flows into the smooth Starinsky topos. Oh, I thought there was this one. So that is the one question. Oh, but I've seen this book once. In book 48. And this is Quaker Escobar. Oh, I see. There are several other papers there. I mean, there's also a paper of Marta Buhler, probably, as I remember. By the way, don't forget to email me with the list of the things that, you know, the articles that you wanted me to send. You gave me three or four already, I know, but I didn't write them down. What do you want, a piece of pencil? No, no, no, a pencil. I want your email. Oh, sorry, didn't I do that? That's awful. Is that kind of... Yes. You sure? Well, write it down on something where you... I always do this and I always lose them, but... So, I always collect it. Good. You're much more efficient then. I'll give you my home email rather than the archive email because it's more reliable for the moment. I've got the site up and it's... There we go. Thanks. Thank you. My pleasure and thanks for giving me... M for Michael, sorry, it's M for Michael, and it's PB, that's not a six, yes, but some people misread that as a six, God knows why. It's MPBW 1879. I had to add four digits because there was already an MPBW on Yahoo, so I chose the date of Einstein's birth, Maxwell's death, and Fergus Begrift's rift, because it should be pretty easy to remember that. Can we make some technical, I mean something like 15 or 20 minutes of technical discussion about some things here? Yes, but first of all I would like to see how Maria is doing. All right. Yeah, sure.

1:57:30 Yeah, well, we'll stay here. Okay. Sorry. Actually, I'll look in that room to see if the computer's free and see if I can go online and check that paper for you while you're talking to Richard. So you say that you have some of those old papers and new ones, like, for example, . Yeah. Yeah, I think I've got all of Lorvier's papers. What about those recordings? Yes, what about them? Yes, I've made transcripts of about all. I would say, in the case of Lorvier's talks and conversations, about maybe... 25% of everything that I've recorded. But of course that's a huge job and it's, you know, far too much for one person, especially if you've got, you know, other things to do. That's why I want to try, that's why I've launched this kind of archive project and made it into a trust, in the hope that I might be able to get funding to get it done, you know, because it would need at least a full-time assistant just in order to get the whole thing digitized. By the way, I think you might be interested in... In the thing which is very far related, but in any case, some time ago I was talking with several people, it could be John Barrett, or other people, Andreas Doering, and so on. Well, Andreas Doering, you know Andreas. Of course I know Andreas and Chris very well. So I was talking with, and others also, considering the world. I think building, setting up and releasing something for what would be the open quantum gravity journal, I mean, opening the sense that, you know... Wait a minute, I just remembered, I'm so sorry, I'm very, very happy of interrupting you, I apologise. But didn't we, just before the meeting in January at Imperial took place, you were... So I knew I'd met you before, that's right, and you started talking about this very project, and I said to you, this sounds very interesting, because it might connect with what I've been doing with this archive, I must get back to you, but of course I didn't get your email then, I've got it now. Yes, of course, that's... So, as you see, I'm still thinking about it. Yeah. You're coming to London for the MAID conference? Well, I'll be there, so we could talk about it further then. I think that it's not directly connected, so probably those things cannot be joined, but actually the only... we have two problems with this, I mean, because John Barrett is very open for this idea, and he's thinking about this.

2:00:00 To make this project bigger, I mean, the idea of John Barrett is running this journal, you know, without any money and using, you know, just making front-end and referee network for some people to be at archive, you know, I mean, the, you know, archive org, but... The problem is that in order to start with it, yes, there must be somehow, somebody has to pay and give his time. So, in other words, if I'm going to be doing something full-time just in order in terms of getting up a really decent website and doing other stuff like that, then it might be possible to piggyback what you want to do on what I'm doing. That makes sense. I mean, you will need a budget for that, whatever John may think. I mean, you don't ever get things done for free. The trouble is you know you've got. Somebody's got to give their time and quite a lot of time at the sound of it, quite a lot of time and also obviously you've got to have a server and stuff like that okay well you've got all that already probably but yeah I know I find that you whatever whatever John thinks you will need a budget The project in principle sounds sounds excellent. I mean having a kind of quantum gravity equivalent of time, mind you that they're all really a couple of, yes exactly what you're looking at, yes it's a very good idea and obviously there would be a lot of crossover between the two, no I'm all in favor of it. Well, I'll be talking to Chris about the, as I say, trying to get some Seacorn funding for the archive project when I'm in London. Well, let's talk there. In the meantime, have a very safe journey back. You're going back directly to Poland, to Warsaw? Right, okay. I think it was a pleasure. Oh, yeah, yeah, definitely. I've been, well, I don't want to embarrass you, but I've just been utterly, totally, you know, you're all... Awesome. I'm really, really, really impressed. I mean, I think we're going to be seeing a lot of you in the future in maths and physics. And it's been a real pleasure and actually an honour to meet you.

2:02:30 You take care, mate. Cheers. See you again soon, Richard. Thanks very much. Yeah, and you. Thank you for watching this video, please like, share and subscribe to our channel. Hello, Maya isn't it? Thank you for your attention. This I had to do once at 3 o'clock in the morning in Lille, trying to find... Oh, a nightmare. I had just a very good night's sleep.