Roundtable Discussion (contd.)

0:00 It contains a chapter about Kelvin, a history of knot theory, which has just come out, by David Hawthorne. I was hoping he'd eventually do something here in History of Maths for a while, and he just sent me a chapter. It's actually published everywhere. Well, and it looks very interesting. All about the wonderful party tricks with machines for producing smoke rings that he used to do in order to illustrate... Yes, he was. Yes, yes, David was. Yes, yes. In fact, it shows how far back I go. I can remember when... I can remember, in fact, when he... Donald told me about him shortly before he became his research student. He said, ah, I've found somebody who's interested in category theory and in what you, you know, you regard as the philosophy of real mathematics. So I met him there. At that time and anyway he's now got a position at the University of Kent in Canterbury well he had um he was he was in York for a time but he wasn't able to get a position in a philosophy department or to do philosophy of maths he was actually working in history of medicine and then for a time he was in Tübingen in Germany and he's just got a I'm in a position now at Kent in Canterbury. I won't, thanks very much, Michael. I'm trying to diet. I might take advantage of the offer of a cup of coffee later if you want to have one yourself. I can even go and make one for you if you like. Is Jenny not here at the moment? I'm sorry. I am sorry. Oh no! Oh gosh, everybody seems to be getting it now. Oh dear, I wouldn't have imposed on you if I'd known. Oh crikey, I don't call it. Look, in that case I won't. I'm afraid I'm going to have to skedaddle by about 12.30 at the latest or 12.45 because I've got a slight chance to catch the Eurostar from...

2:30 The news from Pankhurst Terminal to Brussels. And then I've got somehow, I don't know how I'm going to do it yet, to get myself over to Utrecht this evening because there's a conference in Utrecht starting tomorrow morning, which I want to record for the archive, which is organized. Well, that's actually almost my main reason for coming to talk to you. But what do you want first of all, the good news or the bad news? I'll give you the good news first. The always good news is always more cheerful to start with. Well, the good news is that I recorded a great deal of new material in the last year or so, and I think some of it has been the most important that I've recorded ever since starting to bring the thing into being 35 years ago now. We had an extremely interesting meeting in Boston in November, organized together, which was I was really focused on the 50th anniversary of Grotendieck's and a very interesting, a very nice survey talk by Lou Crane on, you know, is physics ready for category theory, is category theory ready for physics? And it was an extremely good survey talk. Bill gave two very interesting talks, which for once were fairly intelligible, fairly accessible, about these ideas of cohesive topos. He's been working on them for many, many years. Emphasizing that there were always really two very important and distinct aspects of the Grotendieck concept. Almost everybody has since him, Grotendieck's time, generalized spaces, categories of sheets over a site. But there was this other aspect which connected much more with Grotendieck's work in functional analysis, which has been largely neglected. And he wanted to develop that and have it connected with his own views about continuity. We had a very good survey talk and also a lecture to the Harvard philosophers the day before the meeting and I thought it was a great success and the University of Chicago, Lou Kaufman edits a series of texts for them, have said that they will produce a volume on the whole subject of the foundations of geometry and its importance for the philosophy of mathematics.

5:00 But it won't be a proceedings, it will be written up in extended versions of the talks there with an introductory essay which Bill has agreed to write in conjunction with Colin MacLeod. The exposition will be a little clearer. So that's all gone very well. And then on the administrative side, as I think you may know, because I can't remember now whether I sent a copy of it to you or not, but with a lot of help from Simon Saunders and Guido Bacciaglielupi about Six months ago now, I drew up this proposal for funding the thing for transfer, I sent that to you, okay. Well, I did a greatly revised version of that, which I think shortened it and simplified it, and the advice I got, which I think was actually very good advice, from several people, including, was that it would stand a much better chance, we haven't actually submitted it yet, I mean, it's still sort of kind of tweaking it and taking some of it. But the advice that I got was that it would stand a better chance of success if the archive was formed into a proper scientific trust, and we appointed some trustees. So I've approached several people, of whom Chris Isham spoke to him yesterday, so that's me and Imperial, which they had on campus. And he said that he would be happy to do it, he would be happy to be a trustee. I can't tell you how pleased that makes me because it doesn't involve anything onerous, it just simply involves certifying once a year in conjunction with the other trustees that the archive is being conducted for the purposes that it says in the deed, which is to say that it is conducting, it is recording this material and it is trying to place it online, but I think our chances of getting some funding for that would be hugely improved if…

7:30 We had three trustees of the calibre of yourself and Chris and Katya, so that's marvellous, that's three hours of speech. So I'm very happy. Oh, well, the bad news is that my own health hasn't been very good, unfortunately, the last six months. And I've been, well, I haven't been, you know, hardly complained, you know, after all we've been through. I've been diagnosed with very high blood pressure and I've got to take medication daily now to keep it down. And also I've got this problem with my esophagus which has remained very badly ulcerated and they think I may have to have an operation to sort that out. As I say, even in the last couple of months, it does seem to be coming more and more in the right direction. What happened in the day before yesterday? Oh, there was a meeting yesterday on categories in physics, which was a very good meeting indeed, which of course I recorded. Incidentally, I've got a CD, a DVD, a copy of the meeting in Boston to give to you if you're interested in it. Yes, it was a very good meeting indeed. Chris Isham gave a nice survey talk and then several of his research students and some of the people over from Ukraine who had actually come from the USA and a couple of the people in Holland, in fact, in Utrecht who are speaking at this meeting tomorrow. No, Jeremy wasn't, unfortunately. Jeremy couldn't make it, but I think he's doing something with the, you know, I think he had some commitments in Oxford which made it difficult for him.

10:00 Andreas Dohring, who is Chris Isham's new collaborator, was there and he gave one of the talks. I'm sorry not to see Jeremy there, but it was a very good gathering. In fact, everybody commented that far more people turned out than had actually been invited, and there must have been nearly 100 people there, so it really was a very good start for what we hope will become a series, a continuing series. I think the general opposition to category theory is gradually being worn down, dare I say it, although an awful lot of very eminent mathematicians do stand still. The problem is, until you can demonstrate to physicists what it's really useful for in terms of solving hard problems rather than just conceptual organisation of the material in suggestive new ways, I don't think you're not going to get people plunging into the field. Of course, people wave their hands and talk about it, being a very fruitful framework for working on quantum gravity, but everything is quantum gravity these days, it's just every possible brand of speculation, and I'm afraid there is quite a lot of juju that goes on under the name of quantum gravity! Sorry, I didn't pronounce the name. Oh, David Ruel. Sorry, is that how you pronounce his name? I'm so sorry. I always thought it was Ruel. No, I've seen it, but I haven't, I'm afraid, got around to studying it yet. Yes, yes, I had seen, I saw it. It's on my list of, you know, my list of reading I must do in the next year. It's somewhere around number three or number four. I have to say that, no, actually I do know the book you're talking about. It's on my list. There was one sort of minor funny footnote at this conference in Boston, which I have to tell you about. Daniel Kahn turned up to the conference. He's the man who discovered the adjoint functor theorem back in 1958.

12:30 Well, he hadn't discovered it in the mid-50s, about 1956, but he only published it in 1958. And that was probably one of the most important landmarks in the history of category theory because it was the development that really made people see that it might connect structure over the whole of mathematics and not really just be a tool for proving interesting Facts about sequences in thermology theory is really how Eilenberg and MacLean thought of it. They never thought of it at the beginning back in 1945 as a net foundational system or a framework for the whole of mathematics. And I think probably the biggest shift in perception that made people think of it as being that was probably Kahn's discovery. Anyway, Kahn has been retired for many years now. He's 80 years of age. But he's living in Boston. And Jean-Pierre Marquis, who was one of our speakers, contacted him and notified him about this meeting, so he turned up. And it was the first time that he and Bill Lorvier had ever met, so they had an extremely interesting two days of conversations, which was quite fascinating to be allowed to record. It was utterly, not both the history and of course the discussions between them, you know, from the foundational point of view. Karl is an extremely interesting man. He's not, as I had always thought, an American. He's actually Dutch by birth, and he was born in 1928, in fact the same year as Grogendy. So in fact he's not quite 80, he'll be 80 next year. And he was Jewish and he grew up as a child in Holland, of course, which meant that he had to hide during the occupation, but he survived. And then he went when he was still quite a young man, when he was in his mid-twenties, so he was about 23 or 24, he went to Israel to a kibbutz. He's very idealistic and he wanted to work on a kibbutz. And he's had a degree in electrical engineering, he didn't have a degree in mathematics at all, but he was very interested and obviously extremely bright and very interested in foundations of mathematics. And Eilenberg came to Jerusalem to give some lectures about three years later, I think in about 1955, and Kahn got permission from the, I don't know what you call them, the director or the committee of this kibbutz. There are a number of different ways in which you can use these terms to allow him to go to Jerusalem to attend these lectures, which he did, and he button-hulled Eilenberg afterwards, and Eilenberg was a little bit dismissive and brushed him off because he thought he was a crack, you know, he was an electrical engineer, he wasn't a trained mathematician. But to cut a long story short, it became apparent after Eilenberg had, I think just in order to get rid of him, had given him a

15:00 and go away and bring it back at the next lecture. He actually turned up on Eilenberg's hotel room the next morning with everything down. And Islandberg had really intended this to torpedo him because he didn't think anybody, even one of his best research students, would have been able to do this lot in a week. Kahn had done the whole lot in a night. So at that point, Islandberg definitely changed his tune and started showing a great deal more respect and interest in Kahn. And the end of the story was that at the end of his lecture, of course, he invited him to come back to Columbia and do a PhD under him, which he did. And from there on, of course, he went on within a very short space of time to do all this wonderful work, which for him was really just machinery and not a big theory, but which turned out to include, as I say, the actual quantum theory, which was really, I think, exceptionally one of the biggest turning points in Cassiopeia. Anyway, first time he'd ever met Lafayette, they had a very, very interesting two days of conversation. I then went back on the plane with Pierre Cartier to Paris. We got snowed in, in fact, in Boston. Our return flight on Air Canada was cancelled and we had to make our way from one side of Boston to the other to another airport in order to just catch a flight from Air France, which was one of the very few that was going out that hadn't been cancelled because they had a terrific snowstorm blanketing the whole of the north-east of the States that night. But anyway, we did get back. And the very day that I got back to Paris with Cartier, which was the before... In December, there was a meeting in Resice, which is this history and philosophy of mathematics unit which they have in the University of Paris, which often has very, very good conferences and meetings, and it was a conference about duality. It wasn't specifically about category theory, but there was a talk by a young man called Rolf Cromer, who has recently written a book on the history of category theory, which was published by Burkhauser last year. He's a young German scholar, very far and very... It's a very pernickety and massive scholarly apparatus, about 800 pages of footnotes.

17:30 Some, I do some rather sense that, you know, the proportion of theme to pudding in his study is a little bit lacking. I would like a little bit more of the sense of the, you know, controlled sense of direction of the big picture. And he's a bit of a pragmatist when it comes to his philosophy of maths, but he's a very careful scholar and a very well-informed guy. He's, I'm sure he's going to go on to do very good work. Anyway, he was giving a talk on, surprise, the adjoint functor theorem. and on the work of Kahn. So he came to ReSites and gave this talk in English and I had literally arrived from the airport from saying goodbye to Kahn about an hour before and hadn't slept for about two days and I sat there and he spent 20 minutes about exactly what Kahn and Lorvier must have said to each other in the three years after the Adjoint Fundamentale had been published in order for Lorvier to have produced his paper on a jointness in foundations. It is, he said in that very general way, it is of course inconceivable they could not have met and discussed this because it is evident. Well, I really bit my lip very hard because I didn't want to kind of show him up by saying, well, actually, I can assure you they didn't because I've just left their company and they just met for the first time ever. Because it would have just been a bit too, well, I wouldn't do that to somebody, especially somebody starting, but I did take him aside afterwards and had quite a... A bit of thought at his expense. But no, as I said, that was the first time they had ever met. Anyway, as I say, the work goes on, and I'm trying to record a lot of other stuff as well, including a lot of these history and philosophy. There's a good seminar on history and philosophy of physics now, as well as some very good stuff in history and philosophy of maths. Dennis Lemko very kindly records a lot of stuff in Oxford for me, and the faculty, the sub-faculty themselves are actually now starting to record stuff for themselves for their own website, so I think I had a hand in sort of gingering them up to do that, and so a lot of other people, so I think I seem to have started something quite useful. In the meantime, I'm just hoping and praying that I can survive, that I can hang on for long enough, you know, to...

20:00 To allow the thing to, you know, for us to get this funding grant and to start getting the thing digitized and put online because right now there are 26,000 recordings sitting there of which in the last 10 years most have been made digitally so there isn't a problem with their kind of permanent preservation. But all of the earlier stuff of course was made on audio tape and it does deteriorate and you've got to get it digitized within the next Certainly within the next five years, otherwise much of it will have deteriorated too far to be useful. One of the things I absolutely must do, and shoot myself for not having done it before. Your retirement conference in Cambridge in 1997, I think it was, must have been ten years ago now. We made a complete set of videotapes of that, as I'm sure you remember. Did I ever present those? Oh gosh, how awful. Well, in that case, one of the first things I must do is to get those videotapes, which are still sitting in the 1996 or 1997 section of the archive, I must get those turned into a DVD, which is quite easy to do now with videotapes, and send them to you, because they're still fine, they're perfect. I looked at them, in fact, about six months ago. I really wanted to get there for the launch party Simon was saying what a splendid occasion it was. I'm glad you were able to come down for this Yes, the son was saying that he gave a very nice talk and that you were there for it, of course. But we went to Oxford to do Cambridge and Peter Lipset... Terrible shock. Terrible shock. I heard... Yes, I know. It must have been only about a month afterwards. Yes, oh yes, we did talk that much. It was a terrible shock, yes, and he was in, he just collapsed and died, I know, I saw it about three or four days later in the French newspapers. In fact, Le Monde carried quite a lengthy obituary. It was a great shock. I never really knew him at all, but I mean, I've been to the department and heard him speak a few times, but I knew various colleagues of his. It was an awful shock, yes.

22:30 Do you have the launch party there on, I think it was about, it must have been around the beginning of November? Yes, it was, it was about that, yes. Yes, it must have been about a month after that. Yes, it was, it was. He was quite a lot younger than I am, I think he was about 53. Yes, he was. Which is a pretty sad thing. Incredibly sure, incredible shock. And he's got a young family, too. Yes, they're not very young. They're 19 or something. Oh, so not very young. I wasn't quite sure how old his children were. Well, this is splendid. As I say, I'm going to... Of course, I've got this on me, but I haven't yet. Well, as soon as I have a copy, I will devour it and let you know. It's certainly a book I've been looking forward to reading for a very long time. It's quite interesting the theme of the conventionality or perspectivality of invariance principles was one which was taken up in Luke Crane's talk yesterday at Imperial when he was arguing for the possible uses of He was making much of this point about, I mean, he's a relationalist about quantum gravity as we could please him very strongly in what we call the kind of Barber-Smolin program about

25:00 The importance of background independence, I've never been completely convinced of that position myself, but at any rate, it's a very interesting convergence between ideas in mathematics and physics, seems to be coming about through that. I certainly would love to read this. For a start, will it actually clarify the meaning of gauge principles for me? No, I don't deal with gauge theory. Ah, okay. Oh, you don't deal with gauge theory? Well, I don't deal with gauge theory. It still seems to me to be almost the mystery of mysteries. Yeah, it's a mystery. Well, that'll be for the next volume, won't you? Ah, yeah. Really? Oh, so he's got a tremendous, many, many strings to his bow. There's a chapter here, obviously, on localization in quantum physics. That's, again, I should be very interested in reading what you have to say about that. Did you, um, Matteo Morganti was a student of yours at a time, wasn't he? Yeah, he's done so, I hope. No, well, I saw him in Paris about nine months ago. He came to give a talk about individuality, actually attacking Simon's views, but it was a very interesting talk. You know, his view that she theory might provide the right background, the right scaffolding for a formalization of the theory of tropes and tropes and what was the splendid expression that you termed for the kind of basic entities of quantum field theory? Ephemerals. That's right, ephemeral.

27:30 I'm not quite sure whether ephemerals and tropes are really the same thing, I suspect. I can't argue. Well, his tropes seem to be very, very short-lived indeed, though, so I thought they might be, you know, virtually candidates for a friend. Like I said, all of that speculation rather tends to reinforce my kind of structuralist views about ontology. You're not really going to be able to produce, well, you could produce any number of more or less heuristically fruitful kind of positive characterizations of your ontology, but that's what they are. They're just more or less heuristically fruitful, isn't it? But this looks absolutely splendid, lots here that I want to read about, I'll carry on. Unfortunately at the moment I'm not in a happy position being able to afford to buy a book still often, but I hope, as I say, with a bit of luck that may change in a year or so. Well, that was why, of course, I got together with John Stagehall to bring about this conference in Boston. I'd like to use my place in Puget for some more conferences. I had one there in 2004, and then one in 2004 there with Basil Hiley and Fred van Oostein and Maurice de Nossen and various people on topological and geometrical methods in foundations of physics. And then I had the big one with Bill LaVere in Cartier in 2005. But I haven't, to be honest, I just haven't had the resources to do anything since and last year I've actually let out the Because you haven't actually seen my house, I know. I was really hoping that you and Jenny would be able to come there sometime. But the big room, the big, big room upstairs, which is the one that I have been using for these meetings, I've had to let that out. In fact, it's let out to the local Masonic Lodge, the Freemasons who chair at the moment,

30:00 because they wanted somewhere to have their bi-monthly lodge meetings. And it turns out, it's just a matter of interest, that... There are some historic mason's marks on this house where I live, and they believe that it may very well be the place where they held the original life meetings back in the 18th century. So for all sorts of reasons they were rather keen to rent it, and of course I, although it's not the solution to my problems, it's a very helpful little additional income. It brings in 300 euros a month, which is jolly useful at the moment, and certainly helps to keep me afloat. Um, no, the problem is that, that, that, um... The income from the travel business has just dried up completely, as I guessed it would do, I mean it had been going down and down ever since 9-11 and I did have this contract each year to do this, these Australian school children's groups, but that's now been ended unfortunately, they were very successful, I got an extremely nice letter, I got a very nice letter signed by the Prime Minister of Australia, Mr Howard, just before he... Lost the election but still a very nice personal letter saying how but apparently they've had this series of educational cutbacks and they're now not any longer going to be doing these annual trips for the school children to take them to Gallipoli and well they are they are going to still take them to Gallipoli but they're not any longer going to be doing these 10-day extensions of France and Belgium so that unfortunately is not that on the head. So at the moment I'm just going on what I can pick up in the way of working together and in between my recording stuff for the archive and working on a catalogue and doing all the other things administratively and being supported by a very... Very helpful and, in fact, we've got another completely indispensable grant of 1,600 euros a month from this foundation in Sweden, which Basil Hiley is involved with, this chap, George Wickman, who organises these annual conferences in Asklosta on the coast of Sweden each year, which I've been going to record for him, in fact. And he's been giving us a bit of support. To get up a website initially just with the intention of putting all the recordings of the meetings that they have sponsored, but then I'm hoping that you'll also let me start putting on some of the material from the archive as well.

32:30 So I have my fingers crossed, but it is very difficult, to be honest, because, well, we've just about survived, but the big problem I have is that... I had to take on a mortgage, as you know, last year, in order to pay off the tax man, which I did succeed in doing, almost all of it, unless it was small enough, but most of it, but most of that's now settled. But then, of course, I now have to pay off the mortgage in its turn, so, you know, just wondering, so, you know, it just goes on and on. I think I will probably have to downsize in the next year and find somewhere. I'd rather like to get the archives settled and digitized along the way before doing the report. I don't think so. I don't see how I could ever afford to be able to live in England again, to be honest. Not unless the housing market here absolutely collapses, which obviously is not something I would wish for all my friends. But I really can't see that happening. I seem to have settled quite well in France now. And to be honest also, things like the health side is so much better and more reliable. If I do have to go to hospital and have an operation, I think I'd rather have it in France right now than in an NHS hospital. There doesn't seem to be any problem with cross-infection and things in the hospitals in France. When I had to go and have these, I had to go and have this exploratory procedure for these ulcers and sclerosis. It was absolutely amazing. They did the hygroscopy, which is obviously a rather unpleasant procedure, but after I'd recovered from that, tea and a bun, you're not supposed to have anything to eat 24 hours before it, I went in. Now in England, I'm quite sure you'd be told that... You know, the photos would have to go off and you'd be told if you were lucky to come back three weeks or a month later to get the results. I was sitting 15 minutes after having had the procedure with the consultant with a complete set of photos and the dossier and a file,

35:00 saying, you know, here you are, this is what you've got, these are the lesions and so on, but it's alright, they're not cancerous, you know, you've basically just got a very severe case of ulceration and this is the drug I'm going to give you. And this was all 15 minutes after I'd had the procedure. No, I mean, you'd have to be paying, you know, you'd have to be going to Harley Street to have that sort of service in the UK. And here in France, it's just part of the normal health system. So, I have to say, I think there are all sorts of reasons I will probably remain in France, but I'll leave my days there. Which is not to say that I don't miss England, I do, very much. But it's not the other side of the moon. No, no, no. And of course the Eurostar is wonderful now. As I discovered yesterday morning, it now takes only two hours and ten minutes. Into St. Pancras it's just astonishing. It's just such a smooth journey. Ah, I was going to ask. Oh, I can recognize the face. I can see the family resemblance. Oh, I was going to ask which of the two little girls is your mother. Isn't she delightful. That's a very splendid portrait. It was a great society beauty. Who's the artist? Can I ask him? It's a magnificent dress, isn't it? That's a necklace, you know. The gentleman got the necklace. Oh, how wonderful! Oh, that's splendid. Oh, good. I bet that's the most treasured heirloom. Oh, yes. That is magnificent. So she was your grandmother on your, obviously on your mother's side, right, because you just said that's your mother in her arms, yes, yes.

37:30 Well, I think you've done an amazing job. This is the most beautiful plaque, it really is. This feels very, very comfortable. It feels like you've lived here for years. Well, if you would have said that, we'd be here, and we would have been here, and we would have hired up people. And that was done more or less than that. Well, it's in a far, far, far better shape than my place, and I've been there for four and a half years. Half of my books are still in boxes, I'm afraid. Well, that was partly because I did have them all in the big room in the front, and when I had to move it out to the Masons, I had to move my entire library into the back, into two rooms at the back. I still haven't managed to sort it all out yet. Simply getting through the... I have at last, however, sorted out the archive. All of the recordings are now perfectly sequenced in order and all labeled, so it's simply a question of... In fact, what I've been doing is just simply photocopying the labels and then hoping to scan the thing and put together the catalog that way, but cross-referencing it by speakers and topics will obviously take longer. But when that is done, and when we are able to say that the... Copyright of all this material has been placed in the Trust, and that the Trust has got you and, as I say, and Chris and the co-authors amongst the trustees, and I think our chances of being taken seriously as a project getting the whole thing online will certainly increase enormously. I was also going to approach Roger, and Chris was quite encouraging about that. He said that he would have a word with Roger and see whether he would be prepared to be a trustee as well. He might. He does, of course, get an awful lot of requests for these things like that, and, you know, it wasn't his time now that he's, as it were, such a great name, and, of course, he's probably not too good at saying no, but if it comes, if the request comes from Chris or indeed from you, I'm sure he would take it very seriously. I'm going to write him anyway with a kind of brief note and explain what it's about. I have to go and see him anyway next time I'm in England because the chap in Russia... Who organized these conferences on differential geometry, this Russian guy that I met in fact at Chris's 60th birthday conference at Imperial three years ago, which I remember very well because we had dinner together afterwards.

40:00 He has organized these three conferences in the last three years about differential geometry and has encouraged me to. And obviously I was hoping he might come up with some support for the archive. That hasn't happened, but I stay in touch with him. But one of the things he's been very, very keen to get me to try and persuade Roger to come to a meeting in Paris with Gromov. Gromov, the great Russian topologist who's now at the IAGS. But Karl Pavlov, that's this man in Russia. I should explain, Pavlov did a PhD in mathematics back in the 1980s. He's about 40. He did it in differential geometry, and he's really bitten by this bug about Finsler geometry, which I have to say I don't regard as a particularly great or noble subject from what I've understood. It seems to be a slightly empty generalization of Riemannian geometry. And then you have to see, because if it is monoid, for example, but they do this all the time, they have monoids and co-monoids in here. If this is a monoid, you instruct the task force.

42:30 Yeah. This is all, yeah, this is very, you know, idea. This is all a direction of the law of iceberg about quantities, about, you know, about the way one should think about the action of quantities on a space.

45:00 So the thing is, I think here is a structure in the morphism, and there is a lot of structure inside the morphism. Yes, yes, actually inside the morphism. It's very geometrical, but it's still, as it were, a geometric structure on, in some sense, some underlying spatial. That's why I was reading Goyalty and Robinson Perkins. By the way, I didn't understand Charles's point about the going to pre-sheets rather than pre-sheets gives you a much weaker structure than his. I didn't understand what Bruce was... I'm not sure that we can just compare things. But it would be helpful, I think it would be helpful if you could point out some... But what's, why, why, why, why does... Why do you think the one for non-analysis just gives you a much richer structure? The point is they're very hard to reason with. Yeah, I agree. I mean, which is why I think, which is why I think that the USAR suggests that the USAR is a good one. Yeah. Yes, okay, yes. It was a bit of a discussion, wasn't it? Well, yeah. Yeah, it was. Well, actually, the USAR's response was the hardest bit for me. But also quite the most interesting. The only other thing... Thank you for your attention. So that is the greatest, or the greatest failure of the period of the Constitution, is not to see the sum of the classifiers in the problems, because that is the greatest failure.

47:30 There is another one which goes by a number of directions, and it stops and stops and stops and stops and stops and stops and stops and stops and stops and stops and stops I don't understand why it's quite easy to have a sheet of paper in front of you, but it's weaker than me, so it's really unappreciative. Yeah, sure, that's fine, but I mean, are we going to go for some pizza? Are we going to go and have something to eat with all these guys? Oh, if you want to go straight home, that's fine. I think I don't want to get on it if you're feeling really tired. Oh no, but I've done all that. I mean, I just need to get hold of the number. The only reason I had to get hold of the computer was in order to find Fred's number, which I did, and I rang him, but he wasn't there. So, that's engineering. Oh, yes, of course, of course, yes, I was expecting that. Now or never. Um, but aren't you staying, but aren't you, um, can I come round tomorrow? I'm going home. Oh, you're going home to Africa? Yes, that's where I live. I knew, but I thought you were going to take me on a trip. I have an office here. Um, about the notion of empathy, from the point of view of... It's just a study of some sort of stuff. It's excellent. It's very, very good.

50:00 Not even the universe will ever be able to read. Well, it's in a really nice book by McNamara, which Gonzalo edited with the guidance of Dr. McNamara, called Studies in Logic and Cognition, which has got a beautiful essay by Aldo. Another book. Excellent, excellent. Yeah, you know, they're the best of enemies. The trouble is they're both my good friends, so I can't really put John in this picture. I didn't realize it had become as bad as that. I'm sorry for that. This is like now the most prominent, the largest, very third to the opposite of the state of politics, one of its many worlds. Oh, the Everettians, the bloody Everettians. That is annoying. I never understood why Simon became an Everettian. He was much more intelligent than that when I first knew him. When he was doing his PhD under Michael in Chelsea. I've never been suckered in by that stuff. Do you find David Wallis attractive? No. David Wallis is 100% heterosexual. Is he? No, he's not. Everybody thinks he is gay. No, not at all. I assumed he was. I agree this does come as a surprise to anybody who's met me. This guy is like a caricature transsexual Indian costume. You would expect to meet him coming home from a gay brothel in Bombay. He's just so effeminate, it's not true. Thank you for watching. It's true, once you get to know them, they may well live up to their service.

52:30 But he's a strange guy. But I, although he's certainly very, very bright, I think he has had a disastrous influence on science because he's been, a disastrous influence on science because he's been thinking about the physics of science because he's been kind of crazy about the physics of science because he's been thinking about the physics of science because he's been kind of crazy about the physics of science I'm trying to put a ready-made metaphysics on the piece of mathematics. I can see why you're not on speakers. I'm not repeating you when I say that he's a prick. Well, I know what you think, but I'm not going to talk against my friends behind their back, I'm sorry. I wouldn't do it with you and I'm not going to do it with scientists. But I think he could do with loosening up a bit. No, genuinely, I used to go to these philosophy, physics seminars in Europe, and before I even knew it, I thought, what sort of mathematics is this? You had smart, butter-filled, and I had sort of cautious, proud, hard-brained science. It's true, it's very, very... Well, Carvey is very cool, I mean, like, Butterfield's always very sharp, and very, very precise, and thinks things out extremely... No, Jeremy Butterfield's an absolutely brilliant guy, you know.

55:00 It's a lovely personality, isn't it? Excellent. On the other hand, Michael Redhead always considered that Sion was his smartest student in his PhD ever. I'm checking whether the next one is true. Have you ever changed Redhead's thesis on algebraic theory? Well, I'll strike you. Yeah, that's what he did his thesis on. You know, he's a very good man who got lost in metaphysics. And obviously the motivation for this meriotopological system is axiomatics. But first of all, can you... I'm in the very street where my hotel is. I thought I was miles away from it. I think it's number four, so it must be just around the corner. All the cheap joints in all the possible universes. In all the confessions, all the superpositions, you know, you have to look at this one, yeah. No, I was just going to ask about... Mario, I apologise, I was very impressed. Well, I probably won't be able to say it after a few beers, so I'll say it while I still can.

57:30 Thank you very much for your attention. Yes, it's number four, it's the first street where my... I think we'll probably need another water. Yeah, I think so, yeah, it's a good idea. Yeah, I will drink some more, but I don't want to guzzle it all away then. Well, you're going to drink some more anyway. I'm okay, but I'm fine. Yes, is there a way of reconstructing, effectively reconstructing the notion of point itself within the system? Because if there is... So, doing some of the things which people like Leshnetsky and other people who speculated back in the 20s would have actually been a kind of underlying theme in some of the work in, as I said, some of the things which have been in the background. Conceptually and cosmologically, topos theory as well, and finding a purely geometric surrogate set theory, or at any rate purely meriotopological surrogate set theory, or at least the parts of set theory, based on the part rather than on the membership relation. Are there any connections with those, really? I know there were various systems around at one time that novelists were interested in. I mean, of course, the first thing that people did was to try to reconstruct points in terms of... And how do you do it, in terms of... It's ultra-minimal. Yeah, exactly. I was going to say, I assume it would be, in terms of alphabets, which would be motivated intuitively in some kind of minimal... It's more complicated. This is similar to ultrafilters but more complicated because typically what you want to do is be able to take a topological space, take some myriad topology out of it.

1:00:00 And then reconstruct the original topological spaces in your lab. Now, if you use ultrafilters, you don't get the original topology back. You get lots of ghostly points, funny things. But with Whitehead's relation, what you can do is... You can have things which are like ultrafilters, but allow you to reconstruct the topology. There's a whole bunch of results like that. It's sort of a stone representation theorem type idea. Yes, I was going to say it sounds very much like stone. Yes, there's a lot of stuff like that. But intuitively it's motivated in terms of minimal discernible regions, I would assume. What, you mean the reconstruction of points? Well, yes, I mean, since you don't have the whole, the notion of regions is the fundamental one, and you say that the motivation of the calculus is to model our spatial intuition as it were. Calvacy originalising, I mean, yeah, that was originalising. At that level, it would be something like, you know, minimal discernible region, wouldn't it? Well, points come out as points, points come out as points. Well, yes, but what does that mean in this context? I mean, it means that if you start with the original topological space, take an area of topology over it, under certain conditions you get the original topology back. Yeah, but you're starting from something else. Hang on, but when you say starting from the original topological space, but you can't start from the notion of open sets of that space because that's already building in the notion quite to begin with. So I thought the whole point was that the period of topological relationships was supposed to be primitive. Indeed. Well, for Whitehead it was. Yeah. But that's not what Tarski did. No, no, no. And Tarski took this very differently. The problem with... Starting from scratch is that, well, you get the problem, what are the postulates which govern the theory, right? Sure, there's always the question, there's always the problem of starting from scratch. But the, it's certainly true that you can sort of build up topology purely from this region-based point of view, and you can prove that the standard point-based representations can be recovered using some ultrafilter construction. And in some sense, what I was talking about today was a geometrized partial map, so it's doing it for geometrical topology, not general topology.

1:02:30 Yeah, it's an extremely interesting idea. I mean, it connects with, I think, some very... Deep ideas about how one ought to think of the structures and the means of variation in topos theory. I don't need to run into that category. You're a physicist or a topos theorist? My background is in category theory and topos theory. I haven't done any... I've been out of it. I've been out of it for a long time. I've run this kind of archive for a number of sciences and philosophers. Oh, right. But you're a category theorist as well. I've studied category theory. I wouldn't be so arrogant as to describe myself as category theorist. I've only published a couple of my survey papers, and my thesis was more a history, a history of mathematics, but yeah, that's where my chief interests lie. And one of the things which I found very interesting was a very fascinating remark by Lord Mearing in one of his papers in the Islandberg Press Report about how... The various ways that one can think of the domains of variation and the way that Fregeans think of them is obviously in terms of this primitive notion of object theory which assumes decidability and identity whereas in fact you can actually think of points as the decidables of a topos and this is as a particular construction of the one that's in the case of... Topology is precisely what you do have, separately when you decide on the objects, because you've got behaviour which is very classical. But the more general notion is that of a kind of lattice hall matrix in between parts of a delay. ...which already, of course, suggests some meriological notion in the background, and parts of a variable quantity, where you don't think of a variable quantity in the way that one does in classical logic, as having... In the domain, things were so more different, absolutely sitting out there to be the values of the variables, to begin with. In other words, it really goes to the point which is the question that Dennis was raising in his talk about, you know, the very notion of... The identity of Indus Connors. Yeah, yes. I do find the programme which was around in the 1930s, certainly, for reconstructing set theory on the foundation of some kind of myriad of topological primitives, for philosophical reasons, essentially, phenomenally, but they went to the whole issue, as it were, which comes first.

1:05:00 Geometry, geometry or arithmetic, which is one of the oldest issues in the history of mathematics, and you know, what rises in one form or the other is usually very, very subtle, successful phases of the development of the subject. But I'm interested to learn that there is a way of the symbolism. I'm interested in the way that the ultrafilter construction would be motivated semantically in terms of this. Well, of course, the thing about ultrafields is that they are higher-order objects, and if you're interested in first-order theories, and there are reasons to be interested in first-order theories, because in some sense most of the fun from logic comes when you limit your expressive power, and then, of course, you get interesting sort of... Well, and there's also all the considerations about compactness and completeness and all of that stuff. The whole story about the relationship between the formal languages and the structures they describe is more interesting. Yes, yes. So, and then ultrafilters, of course, you can't, although they in some sense exist mathematically in these first order theories, you can't get out of them. So maybe there are other ways to represent points, and indeed there are other ways to represent points, but the standard way of doing it is to develop first order treatments a little bit later, but there have been some quite, recently there have been quite a few papers. In general topology, from a merit of a logical point of view, and it's pretty well been solved, pretty well. Really? If I sent you an email, could you send me some references to that work? I'd be very happy. Yes, so the people who did the nicest stuff really, I think, there's Ivo Dunch, who's in Canada at the moment, and there's Dimitri Vakarelov, who's in Sofia. And they've more or less done it. You can tell a semi-simple story and get some nice correspondence, but it's not difficult, it's quite approachable, it's not really difficult.

1:07:30 I've always been particularly interested in the way that choice and extensionality principles get expressed at the top, and of course there's a very intimate relationship which becomes clear at the top of the setting between choice and extensionality, and one sees just how much of the logical properties of the domain that you're dealing with. The topics I'm dealing with are actually coming from considerations about the topological and geometrical structures that we've talked about. So, for instance, the existence of the choice is equivalent in a topos to relative uniform separability. There are other conditions which have a very topological flavor. And it's quite natural when you think about it, because one of the things that choice implies is that there are no obstructions to the existence of inverses of maths, and the whole subject of algebraic topology these days and homology theory is to do with studying the conditions for the existence of obstructions. The inverse is a fact. It's essentially what the subject's about. Well, you've got no structure to inverse the math at all, because everything is, as it were, points are, well, you've got, you know, the Cantorian. The picture of the set as a bag of dots is just an absolutely pure, pure, Lauter-Heinsen as we call it, which are free to move around any way you want them to, so one point can become any other in a completely trivial way without any attention to the topological characteristics of the space or connectivity or considerations about the components of the space, because points just aren't the same things as components. You've essentially got the mathematical setting. You've just got the notion of a set. It's a set of points of space. Which is completely discreet and co-discreet. It doesn't have any kind of additional cohesion or topological structure imposed on top of it.

1:10:00 And that's one way of thinking, I think personally, a quite fruitful way of thinking about the axiom of chaos. It's certainly not the way that magicians and sceptics normally think about it. But when you ask why it is that weird things like the van Arkshalsky paradox, the paradox of the decomposition of the sphere, are obviously not true of the real world, although they go through as the truth. Then it's very got to do with the kind of collusion and connectivity that the real world bodies, that stuff and matter has as against a world which is really composed of pure points. So I think intuitively there's a military connection to that. Oh right, so that's the painless issue in some sense. It's connected with the same thing. It's connected with the same thing. It's like tame topology. I wish I knew more about tame topology. I got very interested in that stuff. I tried to read the book on tame topology and O-minimality that the guys had written. Yeah, Van der Beek said it. That's tough stuff, but it's obvious that the motivation is there. Yes, clearly, that's all connected. It's not tougher than homology theory. Well, maybe I learned homology theory when I was young, and now I'm old, and it's much more difficult for me to learn it. Well, maybe it's just I wasn't familiar with the subject. But, I mean, homology theory, I had real, real... Well, it's strange, because I actually took to... I took to homology in normal astrology, but I won't say I took to it like a drop of water. But I certainly find it... I find it in many ways the most interesting subject I've studied. And I found, but certainly I see the point about the motivation to do with technology and mathematics. Essentially you're trying to do everything in terms of components which, between which there are geometrically reasonable, there's a geometrically reasonable notion of mapping, and the notion of map space and things, so that you don't get all of the... You know, the topology is coming from, well, essentially coming from the theonic construction, coming from things like the space-filling curve and, you know, the various monsters in 19th century analysis, which are obviously generated by the assumption that, you know, that everything can be arithmetized.

1:12:30 It's very interesting, isn't it? The expression chain of topology is a trick to Grosvenor. Do you have any questions about that? Oh, no. No, not at all. Essentially, the program is... I mean, how would you characterize the program of topology, at least, or explain something about it? Reasonable mathematical simplification, but not a topology, it's not as good. How would you sell them on the conceptual significance of the program? Well, I'm not really the right person to ask about that. Not really. I mean, it seems to me to be very deep, but I'd like to understand more about it. Well, okay. So, I'll see if I can try to... There are certain properties which you may want to prove of systems. I would say about the components function of space, but then, of course, I think... Okay, so you want to be able to establish... There are certain things about, certain collections of sets, right, which account of regions, and the things you want to establish are things like the following. Topological, you're working in a topological space, you've got bunches of regions, you've got certain collections of sets which account as regions, and you want to be able to show that these have certain properties. For example, property number one. Curve selection lemma. Property number two, existence of finitely many components. Property number three would be, say, something like triangulability. These all come together and connect with a finite sub-analytic set that they use a great deal. Is that right?

1:15:00 I think FSA, isn't that the... Oh gosh, I know I'm getting out of my depth. No, it's just that when I tried to read the book by Van den Dries, this was one of the notions which is obviously central to the subject. FSA, which turns out to be... Well, not really. I'm sort of yes and no. It turns out that what Van den Dries did was that he showed how these properties follow from certain assumptions about the set of regions. So the idea is that you should have this thing called an o-minimal structure built on top of your field, which is basically a bunch of sets of two poles. Which satisfies certain graphics for example, closure under projection, so an interval can always be projected after an n-1, closure under unions, usual booleans. This is the reason that the subject connects with these investigations of Tarski way back to do with decidability, quantifier elimination, decidability of the reals, and that's where the connection comes from. Absolutely, intimately connected. So closure of the projection is exactly quantifier elimination because it's like existential quantifier, you're projecting out a dimension. So in an algebraic way, or I might even say in a geometrical way. It's a geometrical way of thinking. So you've got this collection which is a minimal structure. This is your collection of regions. Now, in the context of ordinary algebraic geometry, real algebraic geometry, the set of... Semi-algebraic sets are the key notion, because the semi-algebraic sets, the Tarski-Seidenberg principle is that the semi-algebraic sets are both going to project. So that means that anything you can define by an arbitrary first order formula, you can define by a quantifier.

1:17:30 So that shows that the semi-algebraic sets form a nominal structure. By the way, the polygons, they're the semi-linear sets. They do too. It's much simpler to do. But it's the same thing. But again, you've got an extremely intimate connection between the geometric figures and the properties of the logarithm. And all the interesting properties, triangulability, blah-de-blah-de-blah, it's going to follow out from this system. This works over ordered fields in general. I guess maybe you have to add some stuff. In fact, it's even more than that in some sense. What's his name? The way he organized it, he showed that for some of the properties... Finite decomposability, I can't remember which ones. You don't even need a lot of the field structure. There's some vaguer notions, more general notions. So it's all beautifully, beautifully... So that's the whole thing that's going on with taint of logic. Fascinating. I would love to learn more. No, no. The exact details are... I'm now beginning to struggle. I'm so sorry, but I didn't mind if you could argue it, as it were, by calling a logician or a mathematician. You don't need to apologize for the question. I'm not sure I can answer it, though. I originally... My PhD is in philosophy, but I may... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do... I mainly do I run this little kind of foundation down in France, near Rennes, which organises meetings on foundations on mathematics and physics about four times a year, and also maintains this archive, we go around recording interesting meetings and interviews with people, and we're trying at the moment to get the funding to put everything on the web, you know, to put the whole thing on.

1:20:00 We've got a website, but we don't have anything like the resources to digitize and put online the over 20,000 recordings of what Pat inherited this large archive of over 970. I've just been sitting there in the catalog starting to get a little online. But we do have about 400 years. We're overdue for a good philosophy of... Subtitles by the Amara.org community Sub-category, geometry, serious philosophy of geometry, which obviously has been a pretty neglected area of philosophy of mathematics, and mainstream philosophy of mathematics. I think we're well overdue for a good meeting on that, and I'd be wondering if you'd be interested in coming? Um, yeah. Yeah, okay, well, sure. I mean, in principle, yes. I mean, obviously... Well, I'll send you all the details. So you're actually at Manchester or at UMass? Well, they're the same now, but I was always at Manchester at UMass, you know. You don't, by any chance... No, it's a very long shot, because I didn't realise it was a big place. And he's a historian or a mathematician. You're in the maths department now, if you could all... I'm in computer science. In computer science. Well, you almost certainly don't know him. But a very old friend of mine, a very dear friend of mine, who's a reader in Near Eastern and Balkan studies there, Peruziazni, you don't know him? As I say, I wouldn't expect you to know all of your colleagues. You come from New York, are you? Yeah, I know, exactly. I worked as a tour guide for years, I always had that, you know. Gee, you're from London, Mike. Do you know my friend Ginny? No, I don't. Fucking friend Ginny, you moron. The six degrees of inter-interfinitive thing. You probably do know somebody who knows somebody who knows somebody who knows. But that's a matter, and so does she, but I don't want to discuss it with her. No, it is amazing. So you live in France? Yes, I lived in France for about five years. Oh right, you live there at the moment? No, I haven't lived there since 2003. In a little town in Britain, it's called Fiji, apart from REM.

1:22:30 It's a very nice place. About two hours from Paris, I think. Well, it's probably not as lively as Manchester. Yeah, I'm visiting Bolzano at the moment. Bolzano, how about you? I recorded it. We actually, it's funny you should mention Bolzano, because the last time I attended a meeting which was all about Mariology, it was in Bolzano in 1998. They had a conference at that centre there in the castle. They haven't shown me that yet. Well, they just stuck me in an office and started giving me a bunch of problems. Well, this is not the University of Bolzano. This is something called, I'm trying to remember what they're called now, as I shared with the Chinese this year, as we were involved in it. I wasn't one of the organizers, but I was involved in it second hand. It's a philosophical foundation. Which is financed by, don't laugh, financed by the, what was the then, the then grand duke of Liechtenstein, Rabe. And various people like Barry Swift, you must have come across Barry Swift, who is a very good politician. We're very much involved with this, and we've got lots of money out of it, and it all sounded a bit sinister and suspicious, you know, some kind of hamster, a restoration outfit, but they did give money to people doing analytic ontology, philosophical logic, and particularly to people who started, and they decided to have a meeting on the theme of holes and parts. Oh, I know, the Achilles, the Avasis, yeah, the Barry Smith, the Kierkegaard. Yeah, well, except that this one was very good, because... Various people were allowed to kind of keep control of it. So they had a thing on holes and parts in mathematics, which, dare I say, the Grinnell Foundation rather managed to take over. So we got lots of interesting people there, like John Bell and Colin Clarke, and there was holes and parts of physics, which was mainly... People like Maurice de Gossard, who does very interesting work on covering sort of phase space by the metaplex that grew at the top of the origins of France, France, and other ideas like that. Very interesting guy. And Romov, the Squeezing Theory. People interested in global and local structures, generally, and also some quite good biologists and system theorists.

1:25:00 We had a guy who was the big sparring partner of... Sorry, nominal phase of 15, brutally after your 55. The very well-known American, Stephen Jay Gould. Not Stephen Jay Gould, but the guy who was his chief sparring partner. He's the director of the National History Museum in Washington. Well, I'm afraid I don't know the chief sparring partner of Stephen Jay Gould. Thank you very much for your attention and we will certainly come across Eliot Gould. ... extremely enjoyable weeks spent in, as you say, in a beautiful place. That was in a castle near Bolzano. It's right in Bolzano. It's that thing on the hill in the clan, isn't it? So there are several castles dotted on hills around Bolzano. It's ten years since I was there, so I don't remember... I only remember it was pretty near the centre of the town. And it's actually owned by this foundation. They have about three or four conferences there every year. It's not Rumpelstein, is it? There is a parcel there that's kind of called Rumpelstein. Does it ring a bell? No, it doesn't ring a bell. I would just have to go away and look it up. I mean, I've got all of the recordings of the conference. They never do the proceedings for that one.