Conversations incl M Wright, FW Lawvere et al on stasis & identity maps (contd.)

0:00 I was having dinner with Bob Speckens only two nights ago in Paris. He's just been at this Perspectives meeting down there. He's giving some... I don't know, does he know that he has a category named after him? Yes, he does. He does? Right. Oh, well, it's a nice, it's a very nice, yes, a very nice piece of work. It just shows how much, well, as I say, it just shows how much you can say about quantum mechanics without straying outside. I think it's a pity she didn't allow a bit of a question and answer session because I think we'd have had quite a few questions about that. Well, I guess so, yeah. No, seriously, it's very nicely set out. That was very interesting. Oh, cheers. I'm actually going to go and eat. Thank you very much for your time, and I hope to see you again soon.

5:00 ...every two years on foundations of space-time theories. Oh, really? Yeah. Yeah. Well, there should be. It'll all be on the Oxford site. All the sites. All the talks he recorded there. It's about a month's time. Foundations of philosophy and physics. Yeah. Should be. All the talks from that should be on the... As a matter of fact, we just recorded the talks at the meeting they had in Paris last week, Perspectives in Physics and Philosophy.

7:30 Which Bob Speckins was mentioning, was talking in, and those should all be on the Oxford site, too, in about a month's time. I have to make MP3 files of those and send them off to Dennis. The problem is that they're a bit long, and I need to get some software to allow me to break them up, because if you send anything more than about five or six megs, it... These are almost all, nine or above, but it just involves getting a bit of additional software. It's not going on, though, but I wish there was. It'd give me more time to actually try and catch up on the backlog of work I need to do on the bloody Argyll. As a matter of fact... That was a request for these things, so I will organise them. Yeah, that would be brilliant if you could. I really would be grateful. And not only that, but I think, oh, Bill said he's fine. But no, Bill has said to me he's fine about you sending it to me. Yeah, no, no, but he also asked him about if I sent it to somebody else. Yeah, yeah. No, no, no, he already told me. Oh, that's okay, yeah. It's just that I didn't get round to posting. No, no, it's perfectly reasonable for you. The problem is I don't get round to posting things. Well, you're like me. I mean, I know exactly how to feel it. There's so many other bloody things to think about. No, if I don't get in a month's time I'll chip you again and drive you up the wall, but what I was going to say is if your friend, the guy who's now the mayor of Udine, is thinking of, I don't know if there's any point in trying to happen for funds, but what I've been trying to do is to put together a website for... There's a great extension to Bill's website, but in addition to his writings, in addition to what he's got on there of his republished papers, I also wanted to try and get this. There's an archive of recordings on there, which I've been making since 1989, since the Cambridge conference in 1989, which is now pretty extensive, which now has something like, well, I'm in the middle of cataloguing them now, but certainly there's something like 200 recordings on it of various interviews, discussions, talks is given, or conferences taking part in other discussions. I went down to Frigere, where I got this archive, together with Pierre Cartier, Colin McLarty, a couple of other guys, and spent about, I was going to say a week, actually it was more like ten days.

10:00 We're doing a kind of intensive debrief where Carlton and other people have questioned him about the whole body of his work ever since his thesis. Well, of course, we didn't get anywhere near through all the agenda we had. As a matter of fact, that's one of the reasons I wanted to talk to you, because I had a long chat with Colin McLarty. And we thought we ought to do this again sometime soon, and Bill is up for it, and Colin suggested that you and Bob Roseborough are really the people I ought to talk to, that you would be the ideal people to be involved this time around as the interviewers, so think on, as they say. Well, the thing is, we need somebody to put up some money, obviously, for a website, because we'd have to pay for a server, and there's no way I'm going to have time to transcribe, you know, that, because there's stuff on there that, quite honestly, there'd be no point in putting the recordings on because they're so faint, you can't really hear what people say. I can hear, and of course I know people's voices, so I was going to use this. There's some video. There's a video of the Florence meeting in 2003. But the audio is not so exciting to put on. The video is... In terms of the capacity you need, yes, but the actual quality of the recordings is a bit of a concern as well. All the stuff I've recorded in the last five or six years has been digitally recorded, so that's fine. That can be put on as it stands, no problem with that. But the earlier stuff is all on audio cassette. In digital, you need some quite expensive software. There's a software called CEDA. It stands for Computer Enhanced Digital Audio Restoration. Plus, you're a computer, you know, you probably talk to the engineers who design this stuff. It's very good. I've seen it demonstrated. And it will clean up. It will cascade up to 32 tracks in real time through digital soundboards and re-record them. So that where the signal has been degraded or people are speaking over each other, then you have to use various tools which come as part of this software in order to sort out the signal. But very often the simplest way of doing it is actually just to, so somebody who was there originally and who knows the material, knows people's voices especially, Bill, to just sit there with a pair of headphones and just repeat what is being said into one of these automated transcription.

12:30 ... pieces of automated transcription software like they have now, like Dragon, because, I mean, if you did those straight from the raw recordings it would be hopeless, but if you had somebody just simply, if you had somebody with a clear voice listening and speaking, just speaking the words... And then obviously it would have to be edited, but that would be far, far quicker than trying to make a transcription, you know, the old-fashioned way from the original recording. And I think it's doable, but it's a big project. We're trying to get some funding for our archive generally to do a lot of things like this, but when it comes to Bill's stuff, of course, a lot of people have got their own ideological agenda and who are not keen on supporting. Things to do with history and category theory, unfortunately. So maybe it would be worth talking to your... Yeah, and how. I think we get a rather dusty answer. Actually, I'd be more worried if we didn't get a dusty answer, because I don't think Bill would take very kindly to the thought of being, you know, God knows what they'd try to do. Oh, yeah, I know, I know. It's not impossible, but you can also bet they'd probably have somebody there to edit down and twist the whole bloody thing around. I don't think Bill would be too happy about that idea, I have to say, so I don't think, don't go there. You might be more interested in a debriefing. Yeah, yeah. Who's that you're saying? This is the one from Wooden. Oh yes, yes. Yes, I think he could be. Would you be more interested in that? Well, what I could do, we've got a complete set of recordings of that, of course, as well. We've got a complete set of recordings of that as well. Yeah, but I'm saying he might be interested in another one. Well, I completely agree, because we need to, we literally got maybe a third of the way through the agenda that we drew up beforehand, and even that agenda was very incomplete, I now realise. Very incomplete in many respects. We actually ended up spending four days really talking more about Grotendieck than about Bill, which was very much with Bill's approval, but that's not unnatural considering how much of his work has been in the Grotendieck circle, they've got some stuff on there, it's pretty thin, it's very thin, because there isn't very much.

15:00 That's a project. Well, what's terrible is what happened, you know, what happened at Rotenbeek, you know, the fairies got them, you know. By the way, you shouldn't. Bill's got these little handwritten... Ah, you've taken the words right out of my mouth. Have you seen this famous note that he wrote in 73 that is... No, no, no. Oh, well, this is something different in that case. No, the interview is with Bill. No, I'm talking about something different. What's the... He told me that when Grotendieck was in Buffalo in 1973, Bill Womfatt wasn't there at the time, he was in Italy, but he gave a talk to the local in Buffalo, and afterwards they all went out to dinner, Jack Duskin and Grotendieck and some of the others, and Grotendieck was a Chinese restaurant, and Grotendieck spent the evening, they were just sitting at a table, a big table, about 12, and Grotendieck covered the entire... Our tablecloth with this, I've not seen it, but it's kind of, I've heard it called a chart, I've heard it called a diagram, I've just heard it called a list. It was a classification scheme which essentially was set out in a form of a circumference and then spokes running, I think about six spokes as it were, running through the wheel. And it was a general classification scheme. As I've understood it, I'm built on that to talk to, because he's seen it and later talked to Grotendieck about it some years later, for arranging every theory that Grotendieck could think of, starting with the obvious things like complete, ordered fields, things like that, according to the The underlying ring of the classifying space of that theory and the idea was that anything which deals with logical notions like relations, properties, quantifiers would just drop quite naturally out of this classification scheme as a fragment where you've got a sub-object structure in the theory. The idea is that you would completely bypass logic this way. In fact, Grotendieck actually, at least in one version of the story, but not the one I got from Bill, but from somebody else, Grotendieck actually labelled this diagram, how to bypass logic, or bypassing logic, but I'm not sure if that's true. I think that made somebody's subsequent kind of read.

17:30 I'm not going to be dishonest. I'm just going to go away. But is there any way that you can just buy a glass of wine or something like that? I'm sure they let you. I think you can buy it. Oh, okay. You can pay. But you have to pay. Oh, yeah, yeah, sure. We can get you out of the... Yeah, but I haven't got a ticket, so I'm not going to... Oh, hang on a second. Thank you for watching. Clarity is a challenge, a kind of thinking, always having to re-think. One or the other, I think I'm going to say that set theory. Somehow I never quite worked out, when you have very little time, what to do about the difference between a set of sets and an indexed family of sets.

20:00 This should be a pretty important difference. Yes, I was going to say, a rather important difference. Oh yes. They're one that the philosophers have yet to get their heads around, I feel, a bunch of... Another reason why I thought it would be very good to do something like the Portuguese guys did with that pamphlet, for the subject of, no, set theory, set theories of fragmented algebraic geometry, discuss, as they say in the scholarship examinations, when they... All right. Expound the discussion. There's a conscious organized conspiracy against parenting, which unfortunately Sir Michael Atiyah is one of the participants in his Wubaki bashing. He took the occasion to say that... It's possible to have too much national sovereignty, and since we accept that by analogy, it's possible to have too much clarity. I don't know, maybe you know of other statements on his part, but this one struck me. I think he's smart. I mean, for a clever person, his influence has been very negative in a lot of things. Yeah. He'll certainly face some difficulties when discussing... I don't know if there are things we're interested in promoting as we came here today. There's a lot of work which I dislike very much because it's not that in some sense I think that the theorem in the end is a true statement. It's just that you've got to it. With such a casual treatment of the combinatorial details, and you made no attempt to sort of organize the thoughts into something which then makes it clear and simple, sometimes people say to me, you know, you get your students to do that too much.

22:30 I get my students for doing too much. They're inhibited from doing certain kinds of things, because I won't accept it unless it's something. Excuse me, please. I'm so sorry. Sorry. Oh, excuse me. Oh, sure. Oh, not my fault, eh? The trouble is that that casualness is a very sort of Cambridge English amateur type thing. Yes, though not confined to Cambridge by any means. Let's talk to the organisers, perhaps. Organisation. Sorry. I do apologise, yes. It seems to me that you need some little assistance here. That's very kind of you, thanks. That's great, thanks very much. Yes, do you find yourself accused of pedantry from time to time? A little. This is usually a good sign that you're having trouble. But you're on the right line, so... I'm careful, I mean, I don't stress the fact that... Space needs to be non-empty before it's got a chance of having a fixable return. That's one of those academic verbs, isn't it? I am careful in my definition. He labours the obvious. I'm not quite sure what the you, the second person, would be.

25:00 I am surrounded by pygmies. Your work has not received its due recognition. He is an embittered plank. I have the other one because I have complete mastery of the sources. Your work is not very original, he is a plagiarist. Thank you for watching. So, all you will see... Unconvinced as I am that symmetric monoidal dagger categories hold the key to complete understanding of quantum theory, what is good for each category? I'm sure that anything is done with that which wouldn't have been obvious to Paul. I think there's a problem with that which is sort of clear. What is the mathematical payoff? What's the conceptual payoff because I can't really see that it makes any... the idea that this dissolves the problem surrounding the interpretation of quantum mechanics just strikes me as crazy. It simply sweeps them under a different piece of the carpet. What do you do in some sense by way of clarification is that you take certain things that are very confused, like discussions about so-called quantum teleportation.

27:30 Yes, yes, yes, yes, yes, yes. And since those things like the no-cloning theorem, as you say, are subjects of a great deal of mystery-mongering, then to have them clarified by using the right categorical tools is useful, but it doesn't seem... At one point I thought he was going to say something interesting about Frobenius in relation to the quantum formalism and to Mackey's approach, but it turned out that he wasn't. I think it would be a very good thing if somebody went back and redid Mackey's work using rigorous category theory. That would be... Subtitles by the Amara.org community McLean and I gave a course three-one years ago. Well, that must be on my list of topics for our next debrief. Which was the course that you and Saunders gave? The University of Chicago, a sort of joint course on Mackey's... On Mackey's theory, right. Ah, that I hadn't realized. Amazing book. Again, some less than careful historians claim that synthetic differential geometry came out of that course. But it's wrong, because I was giving another course. Yes, you were giving another course. My own course, which... Ah, yes, of course, 1967, so it was the time, yeah. Yes, well that's... That's typical sloveness because you're giving two talks at the same time.

30:00 Thank you for your attention. In a way, there isn't a very good way to say. I just want to see something more interesting, mathematical. I would get serious! You're right, something doesn't have to do with mathematics or mathematics and mathematics and mathematics and mathematics and mathematics and mathematics and mathematics I don't know if there's anything significant about the fact that a fair proportion of these people who are now trying to apply a smattering of category theory learning to problem-interpreting, quantum theory, seem to be coming out of computer science departments. Is that simply... I mean, I think the situation in physics is very different now. There's a world of... High-energy physics with predictions about the latest experiments based on a series of hopeful models of this and that and the other. That hasn't got any time for this particular kind of thing because it's got nothing to do with... Well, it's funny you should say that because I was just at a meeting in Paris on foundations of physics, which actually started with an imaginary dialogue between a physicist...

32:30 And the philosopher, which went something like the following, I work at Chern, your philosophers say something interesting. The measurement problem, no. Philosopher making huge effort. Quantum gravity, I work at 1 TeV, you know, it doesn't look as if quantum gravity is going to do anything very much for us on that scale. And anyway, continued in this vein, you'll make the point that there are many, many different physics communities and they all have their own, as it were, foundational perspectives. From a Cambridge point of view, you have the sense that the biggest thing in the world is cosmology. Of course, because... Of course, it is the whole world, so how could anything be more important than human beings? Ah, thank you. Merci. So, you know, there's all this theory of grains and how the universe has been doing this and so on, which, I mean, are hugely fanciful things, and the question about whether that's real physics in a sense, which, you know, there's a tradition of actual thinking about the physical world in some way that's productive for... Well, there are several issues there. In fact, there is the issue that the quantum gravity work is largely uncontrolled speculation because it's 20 orders of magnitude away from anything, any kind of energies that could be probed experimentally. But there, I think, seems to be, on top of that, there are even more. There's a massive conceptual confusion in any case apart from that to do with the speculation about the breakdown of continuous space-time at the Planck length, which is actually quite separate from the fact that there's no kind of empirical constraint on the speculation, and then on top of that there are also... As you say, cosmology, of course, has always been a field for pretty wild speculation, and so I'm sure it's a bit more constrained now than it used to be. Actually, I will say, and I don't think Bill will take kindly to these next words, but in fairness to Sir Roger Penrose, it is...

35:00 I see no reason to say that. Well, you thought you'd just say Bill, the trouble of saying that. No, but he does have his latest cosmological theory. Which is a conformally invariant cosmology, which comes out of his thinking about the vial curvature hypothesis. It does have a bounce mechanism, so it avoids the singularity in a way which is dependent on the conformal symmetry. And it has, which I find astonishing, a very... Intriguing. It has a very robust prediction, observational prediction, which is that they should find within the background radiation, relic radiation, the COBE data, what is interpreted as the COBE, as the background radiation, relic radiation data, when they search for it, a series of annular structures which are, in his prediction, he predicts... They will be found because he believes that these are actually the signature of the coalescence of the black holes in the final imploding phase, contraction phase, of the previous universe, pre-bounce. Predictions sufficiently robust that the people studying the COBE data have gone out and in the last two or three weeks have actually written the computer code to do the search and are going to be running it this month. So if it's there, and if there aren't fudge factors, but I've been told by the experts that it is a pretty robust and not... This is model-dependent prediction. Well, it's model-dependent in the sense that it's related to this. Conformal exactness. But if the signature of this radiation is there, and if it's detected, then there will be a huge brouhaha in the scientific press. I have no feeling at all for whether it's likely to be detected or not, but you can just imagine the headlines to which will be written. Not only have we seen back to the very dawn of time, we have seen back beyond the dawn of time. We've actually seen back into the week before the beginning of creation, yes.

37:30 This is the Vatican recently. Imagine what Teflon Foundation, what you said. It's fine if we use the headline, of course. The Vatican's chief astronomer. Ah, I see. Just the guy who's fronting for him on this one. Yeah, I mean, you can... And what's the Vatican's position on the souls of these extraterrestrials being here and their prospects for eternal life? They all could be here, could all be here. Well, I think there are pretty obvious theological problems with that one. My belief, you see, is that that's the purpose of extraterrestrial beings, as a concept, as a theory, is to lend some kind of... ...semi-material plausibility... ...to angelology, of course. It's absolutely explicitly clear if you read it. ...if they had faster than light... Right, right, right. Sure, sure. Those wings of theirs are really amazing. Well, it's like, I should actually claim that the, that the, that the, thank you very much indeed, Cetan was the actual pilot of the spaceship that was, that was powered by a black hole, the black hole, and that's all, that's why we have this idea about Cetan, all right, that's like, it's a folk memory about it, it's a folk memory, it's a folk memory about the spaceship. The latter-day reworking of people fell into the black hole. Very useful that Wheeler christened it the black hole. I think this is the whole right, I see. Star Trek and all that. It's really that you could sort of think, well, by stretching the idea of materialism, you can actually perp it, maybe. You can accommodate angelology. Accommodate it. But it's even more explicit than that, Bill.

40:00 That's the motivation, but they, I remember in Star Trek they actually had an episode, one of the early episodes, where they actually encounter all the gods of Olympus, all the ancient Greek and Roman, and they're real, of course they're real, yes, so that's the kind of thing that they used to have. And they toy with different societies as well, completely removed from any kind of material. Well, I don't know if I've mentioned it to you, but more than 50 years ago, I was a science fiction fan. So I attended a meeting that was held in the Morrison Hotel in Chicago of science fiction magazine editors, writers, and fans, two or three hundred people, including, for example, John W. Campbell, the editor of the astounding science fiction magazine, and several other great writers. See, this was in 1952. You were just a little kid, huh? Fifteen, I guess, yeah. Fourteen, fifteen, huh? The point is, you see, okay, that they actually had a board discussion on the floor. The premise was this. It was science fiction. Up until now, it has mainly been a matter of extrapolations of known technology. That's what I was interested in, why many people from MIT and so forth. This is how the MIT people were gradually, anyway, brought into talking about theology instead of engineering, you know. But it was a process of 50 years. The main criteria for accepting something to be published in a magazine, if you like, was for the writers' press. This was, you know, this, that, red and butter. And also, separately, there was something called fantasy that had to do with real world things like this, and this was considered as separate.

42:30 The two issues which were discussed, first of all, science fiction doesn't have to be about technology. It can be about sociology and even theology. And this was discussed. Well, as long as entertainment, as long as we're in the business of entertainment, as long as entertainment, that's okay. Other people objected, but we met by science fiction. And so it was all discussed, and sort of a consensus was reached about the S&P to now on, in 1952, henceforth. And it happened before, of course, but now it will be acceptable. And so they appeared shortly thereafter. There appeared books, a book about, I remember this, the author felt obliged to provide an introduction to not just the topic, and it said things like, what this book is about is fascism, which is a social system which has not yet been seriously tried. Seriously, right? Seriously, right. Amazing, you know. And the other issue was, well, we can mix up fantasy and science. Was that Heinlein? No, he wasn't. Well, that sounds like a sentiment that he might have entertained very easily. Thanks very much. After all, we can have werewolves and interstellar spaceships and so forth. And again, due to policing, some often said that it appeared in science and mathematics. The idea is that this was a conscious conspiracy, isn't it? I've basically done no real work of scientific quality whatsoever. And so I've gone out on a limb. I just think it's outrageous for us to do this. We should do this kind of thing. And so, I've now been asked, you know, who are we to believe, right? The Royal Society or you? Well, actually, you know, it's a Penrose protégé.

45:00 Am I sure that Penrose doesn't understand? No, no, no, I'm sure he doesn't. That's an extraordinary thing to have done. Except, of course, that in some sense it's an establishment. This is the guy who came up with so-called quantum computing? Yeah, he's the guy who originated the subject pretty well. Blasenberg. Is there more to it? I don't know. That is, no, and I find it absolutely stunning. That doesn't come as a surprise to me at all. The Royal Society, of course, is a very strange place. The only logicians they ever elected in the 20th century were, they never elected, did they ever elect Tarski? I don't think they did. They never elected Tarski. They elected Gödel and they elected Kreisel. Oh yeah. I'm going to tell you something about the criteria of the establishment. They didn't elect us. How are you going to get five degrees? That defies comment, really. Kreisel. Well, Kreisel was an old crony of Dyson. Oh, yeah, absolutely. Who was the other one? There was a trio. Dyson, Kreisel... Maybe it's just a bit too far away from a random state. Oh, I know which way to go. I think it's, oh, it's pretty easy. You go through that door and then turn left and just keep going until it brings you straight to the end, inside the building. I do, actually. You could have been a great geometer. I would probably have been a lousy geometer, but I was a reasonably competent tour guide, so that's where it comes from. Yes. No, you just turn left there and just keep going right to the end of the building. Oh, somebody was asking me. Oh, sorry, it's Bob Walters, in fact. Just now, we were chatting about the same things we were talking about, about this dagger categories and this attempt to try and tidy up, but without any great insight.

47:30 Formalism of this particular, very operationalist view of what quantum theory is supposed to be about. Yeah, we'll just go through there. Anyway, it came up in the course of the discussion. Bob was asking me a bit more of, if he could get some more information from you, so straight through here. Oh, yes, we've got half an hour, haven't we? We could. It's really rather nice, actually. Okay, in that case I won't. Yes, yes, that's, that's well, but this was something quite unrelated. This was about the... This document that, now I know I've asked you about it many times, but I'd really like to try and do something, I was talking to Colin about this, if possible in the near future because of... Jack Duskin's rather poor health. This list, document, whatever you want to call it, I know I've miscalled it, a chart, and I know it's not that, but in the past, but anyway, the document, we know which document you're talking about, that Grote indeed left with Jack in 1973, that contains this extraordinary scheme of classification of theories, according to the... The ground ring of their classifying space. I would really like to understand a bit about that and I mean you're the one man who I think you could write a commentary on that text. It should definitely be preserved because I have a little fear that when Jack's office is cleared out somebody might just chuck it away. Well, okay, I'm engaged in helping Jack clean up his files. There's a major possession of that, and so far we didn't find it. Oh dear, that doesn't sound too hopeful, does it? No, we may find it. It may still be there, yeah. Yeah, this was... There's something Grotendieck? I've often cited this. It's why we don't need logic. The bypassing logic paper. The narrow sense, you know, in other words. Memo. Because instead of using so-called topos language or whatever, Grotendieck simply uses the idea that focus preserves no limits and finite limits. I will need to talk to you actually about a little project that we've got. There's a sheet of paper where I guess Jack was just standing there, maybe other people. He wrote down, you know, integral domains.

50:00 Classes of rings, Japanese rings, and so on. They're very, more and more complicated. Wow, interesting. So, a whole list, you see, like this on a sheet. And then, interestingly enough, he still had more, so he turned this sheet and wrote a cross. And said, you know, like people used to do letters. Yes, yes. I knew it was— So, this crisp spokes of a wheel. With these names of classes of rings. Right. All of which are classifiable, you see, by topology. This is the point. These are classifiable. Right, I see. Well, there'll be a lot of cases that— I wouldn't know were classifiable probably on this. That's right or you know one would not but but the thing is that the the standard method that we have is when we first translate these things into logic i.e. in terms of sub-objects of products. So we use the narrow logic of sub-objects and then we say oh it has this form there where it must be whereas he went directly without going through the sub-object reinterpretation of the structure. Just limits and co-limits, and so... Right, right, I see. If you almost kind of, almost imagine you just saw visibly. Yeah, you sort of, in some sense, it's almost a pure use of the opposite thing, you see. A deduction of structures without bothering too much with the... Interpretation in terms of properties. Because in that context, you make statements, but these are just sort of side comments on the real constructions, you know. The balance is completely... Yes, different. And so the fact that he was able to dash these off, well, of course, he's grown deep, but at the same time, he knew no logic. Right, right. And so... But was effectively able to bypass it by means of this incredible... By probably more direct means. Which may, in fact, tell us something very interesting about the... Basic epistemology of logical notions of a kind that Balberto Peruzzi has often speculated about. I think this is conceptually very interesting, quite apart from its huge mathematical significance, which is why I really hope you do manage to find it. So the list itself doesn't mention this point, of course. It's a comment. It was because Pierre Cartier wrote something about...

52:30 All of those theories sound completely logic and different from what Godendieck did, and I pointed out to him, well, Godendieck didn't need logic. That doesn't mean he couldn't think logically. What a mind. It would be fantastic if you did. I think it would be a major work for the history of science if you did dig that up. So, yes, Cartier's sort of remark is really the kind of opposite error from the error, but this is much more... This is much more perverse of Locke Alusi in that extraordinary What is a Topos article, where, of course, he goes into great detail, well, not great detail, he's only about two pages long, but he spends all his time talking about the original Schrieff cohomology construction and mentions in about two or three lines at the end, oh, by the way, you know, since 1969, somebody called Lorvier has got into his head that this has got something to do with logic. Well, I'm hardly exaggerating. It is absolutely extraordinary and perverse. He was actually present at the meeting in Dalhousie where we... You know, this book, 274, you seem to remember his name. A summary of that, yes. Yeah, his name is on there, which makes that article all the more unforgivable. Right, that's right, that's right. I think he was deliberately setting out to provoke... Maybe he felt threatened then and hasn't gotten over it since then. Could be. He certainly went out of his way to be offensive in the way that he worded that article, I thought. Are you going to go and sit somewhere and doze quietly? I think I might. Yes, you can. I'm sure there's an entrance at the other end of the building. I don't think it comes in, sir. Touristic possibilities of Calais I explored a little bit last night on the way to your hotel and largely because Simon Cochin told me this fascinating story about what happened here to him in his boyhood and I discovered the centre of the town as he said was indeed pretty well completely destroyed in 1940 although there's still two or three old churches which were intact.

55:00 Quite a few memorials, but the centre of the town, as I say, apart from three or four old churches, there isn't really anything of great touristic interest. There's a hideous monument, a hideous stelae, which the local Gaullist Association has erected, which is about the size of this square that we're in, literally, to commemorate the fact that... Colonel and Madame de Gaulle got married in the church. I think not a fact of such historical significance that it merits a major public monument. This is France. And you get some rest, Bill. I may go back actually and see the art patrons about this. Bonne nuit. Have you got any plans for dinner, by the way? I'm supposed to have dinner with the scientific committee. OK. No problem. OK. Well, I'll pick... I'll baptise them for their bad choices. Yes, I'll keep quiet about that. Well, obviously, I'll be around tomorrow morning for your talk, but you may not see me again today, so get a good rest. Sorry I'm so tired. No, on the contrary. I'm sorry I'm in such bad shape. OK. Take care. See you later, Martin. Cheers.