Discussions

0:00 Of course, I know a bit about all of that. In fact, there's a seminar in Paris right now on category and the application of category theory in physics, and the very, yeah, it's just been going for about a year and a half. It's organized by a guy called Marc Lachier-Duray, who is a French cosmologist. He's also published a lot of info on applications of fiber bundle theory to general relativity. He's more in general relativity than I can. And then there's about four or five other guys who... But what I was going to say is the very first reading text that we had proposed to you was actually you and Crane and Ravelli. So we do know your work. Yeah, if I hadn't been born either English or French, the Americans would absolutely tongue-deaf everything I did. But one thing, you're not supposed to be a mathematician and a physicist. And you're not supposed to worry about foundations. Well, there's always been, you know, there's always been in American society, and certainly in the intellectual tradition, pragmatism, of which there's no coincidence that we're in the slipper that gave birth to pragmatism. And, after all, this is the most important. Yeah, no, no, I mean, I feel like in my, I feel certainly inspired in my whole life. Yeah, yeah. I feel like it ended life anyhow. Well, you're in good company, because I think Bill O'Beir, who is not in America at the moment, Our staff speaker tomorrow's session has also, would regard him also as having struggled against pragmatism in philosophy and foundations of mathematics in his entire life. Oh, yeah. Well, we tried to design it with that in mind, to bring together some people who were very interested in foundational issues, and particularly in philosophy and geometry, together with people who are working in...

2:30 I thought it had a lot of context. That we will find out, explore, in the next couple of days, I think. I wouldn't... I'm not sure myself yet. It's always terribly difficult to tell this bill because... Occasionally I see points of contact between his program and what some people are doing in quantum gravity and applications, but then he himself is actually is really very prejudiced against it, although I think there are certain aspects of quantum gravity particularly. It's this very strong... I'm not defending him for giving a brief explanation, and he's therefore very prejudiced against non-conversative geometry. Well, actually, I'm not prejudiced against non-conversative geometry. I am, but he's a gimmick, as the preacher said. What I would say is that the directions go, rather than imagining it as algebra, categorical stuff, and then communicativity becomes a more systematic identity than it is. I think he'd be much more sympathetic to that point of view. He's also rather unsympathetic to the n-categories program as well, because he's got this idea that in theory everything should fall out of the equation, purely equational semantics at the level of two categories. But listen, he can speak for himself. He can speak for himself. Ah, well, in that case, you may have been absolutely right from to begin with, and I'm talking through my own. In fact, you do have a lot of confidence in that. No, no, I'm just writing the introduction to Pierre Carter I've got to introduce this afternoon. No, I've finished it. I've literally finished it. I just wanted to time it and start cutting it out.

5:00 There's something very wrong about the idea that mathematics and physics are really separate domains. I absolutely agree. I always felt that Hermann Weyl got it absolutely right. You know, the first principles of mathematics and physics come as a package. How conceptually unified is for us to figure out... Well, you know, the Hilbert program failed a long time ago. We don't know what we mean when we say they're real numbers. I absolutely agree, you're singing for the choir. I'd go further, I'd say we don't even know what we mean on this paper, and who actually decided to use the definite answer for that. But that's another story we'll get to later. Okay, no, but that's going a bit harder. I know in topos theory there's something... Yeah, yeah, yeah, that's what I thought I had in mind. I mean, I would say topos doesn't even imply sastral. Well, actually, Bill has written some very interesting papers on the reals in the drop-off setting, and in fact, one of his most interesting talks that I remember recording when he put the first one to archive, it's as if I could record talks of foundational interest. About four years ago, in Nancy, there was a very interesting meeting, and he gave a fascinating talk called, The key problem of quantum gravity is that there is only a finite amount of information transcripted. There are theorems and classical relativities. An observer is observing something, and if any information will restrict it, then yes, and then it censors itself. And that's for all the observers. Any more information than that can have no effect on an external observer and therefore cannot play a role in quantum theory because quantum theory is about what observers observe. I grasped the argument. Okay. So, my feeling is that... I've questioned a couple of these premises, but we'll leave that for now. ...experiments that we saw when we looked at...

7:30 No, I see what you mean. That's a very interesting idea. I think you're onto something very deep there. There's a separate, completely conceptual piece. This is the chap who I didn't know. Oh, great, good. Yes, because John mentioned that you were bringing the student with you and I didn't. Hi, John. Nice to meet you. Did you get my phone message? Yeah, please come in. Do you want a coffee? Unless you want to walk. By the way, can I tell you, I did speak to the hotel after, you know, ringing you in your room, and it's definitely confirmed the rooms are taken care of by Boston University. It's just that there must have been some kind of snafu when you checked in. I think there's something really wrong with the administration of this hotel. They told me last night that they just... Not the first hotel I would have come across that... They just changed plans. Ah, well that probably explains a lot. Yeah, so they've changed plans. But I promise you I'll check with the lady. Thank you very much. Well, except you will have to pay your extras. The rooms are paid for by the university. Are you sure they didn't just swipe your credit card? No, they actually told me I have a receipt. Okay, right, we'll get that sorted out. No, no, I'm sure. I'll have to talk to John. I'm not quite sure. Don't quote me, but I'm not quite sure what the arrangement was to be at the East Shore. Oh, okay, right. That's what I was going to say. But in your case, your room should be covered completely. Okay, that's fine. So, and John said that Boston will pay the difference. Okay, that's great. That's pretty well what I understood, so, um, but we'll, we'll, we'll get it at the, but I did actually speak to them and they definitely have you in the, and not only will you not only have to pay the difference, but, um, the rate, for example, will be much better than the rate they showed you at the desk because that's their rack rate for people who come in off the street, i.e. for all of the chairs, the university, because they use...

10:00 Thank you for your attention. Oh, I wish. Unfortunately, my back balance is in the same position as yours. Otherwise, I wouldn't have done it. I know now these people from the UK come to America and they take a vacation and they shop. They shop, shop, shop till they get home. They pay for the vacation. They pay for the vacation. I think you can quit worrying about Bush. Have you seen Huckabee? He used to be a Baptist preacher. I turned on the TV this morning, and there on the Christian Broadcast Network was Huckabee, and the local religion that was saying, I want to make it very clear, this is not a temptation, I'm not endorsing him, he's just coming into the picture. And then the whole thing is Christian. Oh, yeah, sure, sure. Yeah, yeah, yeah. It wasn't much of a disguise. No, no. They're not too smart. No, no. He's a great Christian. Sure, sure. And I really wish I could have shown you Moustache of Pentagon, you know, it's just like, because the axioms of category theory turn into... Absolutely, I agree, which of course is how I got interested in this whole thing, because I was also very interested in that incredible, that pregnant remark of Einstein about, you know, we really don't need to go to... Right. And I got interested in Groten's work actually through an earlier interest... See, what I believe is that the critical problem is, if I know how to connect...

12:30 These are incredibly deep ideas. There may be some ideas coming from the simplicial category that we're looking at. The thing is that there are mathematical tools around that really look rather like the right sort. I mean, you know, if you tell your physicist it sounds extremely crazy, but in math it doesn't sound so crazy. It improves the making of connections. Absolutely not at all. It sounds very plausible. Yeah, I mean, people study simplicial categories all the time. Curiously, Bill was talking about simplicial categories right here in that chair just last night. The main subject of the conversation is that. Well, so the point is that you simply have to cobble the right stuff and then we'll have it. That's what I think. The problem is the notion of quantum mechanics. Well, there is a definition. Yeah, but there are several, but I must say they're not the ones I've seen that work very well. It doesn't have any sense. ...amongst other things. Oh no, but that's all I've got. The analogies... It's not only that. It's very important to realize that it's not just a generalized space. Because there's many different kinds of toposes. There are what you might call toposes of pure variation, which are like those, which machines are precise. But there are other examples... Just take a quantuloid. The category exceeds the quantuloid itself. It's a quantum logic. Yeah, no, I've seen that. And I've seen some of the other stuff that we worked on. ...this kind of generalised Sasaki book construction. I mean, I wish I knew more about this stuff, but my own impressions were rather messy and ad hoc construction. I could be wrong, I don't think. No, you're right. There should be an intrinsic... And a topos is still really a very classical structure. But on the other hand, there are deeper connections with homotopy that I think might indicate the route to go.

15:00 No, no, I agree with you there. I think this is largely what I got from listening to Bill, taking in what he said, and the spirit of naïve discipleship, because I think you really, the whole N-category program seems to be, I mean, we can do everything we need. Okay, I felt like when I proposed the categorical ladder, if you try to get higher dimensions, you won't get anything very interesting anyhow. And that's probably why four dimensions is needed. Unfortunately, when I said that, almost everyone else in the field is interested in string theory. Why don't you do this in eleven dimensions? I said, you can't. There are 11 categories. There's no adequate definition. Well, there's an n equals 11 category, but it's completely backless. Yes, right. The generalization doesn't do anything for you. But there's a really interesting thought. The interesting topology is important. It's a two-dimensional knot. The interesting category theory is two categories that are exactly the same. Which, of course, as you say, you've got the connection with knot theory, which is what's really important. That's right. By the way, I'm sure you know Luke Halfman. So, in fact, Lou, he wants me, we're going to record everything, and then the idea is we're going to... That's what he's offered to do, and that would be great if we could do it. I'm sorry you couldn't get here, but unfortunately this can happen.

17:30 No, no, I'm not. I'm sorry. We just got into this council, Tom, that I was supposed to go to Portugal and be on somebody's meeting, and after I bought the airplane ticket, they decided they couldn't have it for another six months. Oh, that's clever. Don't tell me it was a non-refundable ticket. You know that they're having a Categories in Physics London in January? I'm speaking. Remind me, is it the 9th? First time I've been able to actually go to a conference in the area somewhere else, but I'll be there. Well, I'll be there the whole day. If I come all the way over from France, I will install myself. That's brilliant. It's at Imperial, isn't it? Actually, you might meet my wife that time. Oh, I'd love to meet her. She wants to do a presentation on a library in Britain. She's also an architect. And the library service in Britain is absolutely falling apart. Why doesn't she want to do it at the TGB in Paris or somewhere like that? Okay, because I'm going to take my sabbatical next year and I'm going to be in the UK for the year. So she wants to stay the same place I am. But also, there's a brand new library in some town in the Midlands. I forgot which. And she's interested in new libraries because... Yeah, and of course, I don't, I mean, I'm sure there are new libraries in the UK, it's just that, you know, the overall impression we have is that our public libraries have been falling to pieces for years.

20:00 Unless, unless, unless some arsehole in a modern library, no, no, has deaccessioned it because they're just trying to get rid of all our, you know, decaying print media and install a whole load of interactive video games, which is what's happening in half of our public libraries. I mean, they were literally the University of London library just sent each entire range of philosophy journals to be pulped. Can you believe that? Oh, about four years ago. Well, they scanned them. They put them on microfiche. But they sent all of the original... Well, they didn't do a very good... No. No, that's a problem. That's really stupid. And two, not really. I agree, it's a little bit silly to want to hang onto. But no, they did a terrible job of it. The scanning, you know, they were using this, well, part of the thing else, you know, the OCR software, at the time they did it, was the old joke about A and I, you know, getting them to recognize A and recognize I. That's the problem. So, anyway, but don't get me onto that. I've never had to work in a Portuguese library. On the other hand, I like Lisbon, I like Portugal, the country. It's a wonderful place to be, but you don't actually have to be involved with what they do. No, no, true. If you were trying to do research in quantum gravity, it would probably not be the idea. It's just to get on a committee. There's just some things they can do and some things they can't. Anything with organization you can always be. There's a beautiful family full of libraries with no modern books in them. With no books in them either. No, I just think there's nothing in the universe. He told me, he went to the library one day, he wanted to see if he could get some research into it, and there were no new books, and he said to the librarian, there are no new books, where are the new books? And he said, don't be silly, the old books are in the old library, and the new books are in the new library.

22:30 Oh, they use the same principle with art galleries, I suppose, because it works well for libraries as well. I take your point. No, I wouldn't want to be working at a Portuguese university. No, I mean, I'm not sure I could eventually. I mean, sometimes it has to send out to another. You can't get this. And there's no international interlibrary loan at all. No. There used to be. Oh, there was? There was. There used to be. Well, certainly it was between France and Germany and the U.K. But, of course, I suppose they're all hanging on now. I'm hoping that with the next wave of money, if there was a bit of luck, the input from any library will be able to expand it. I'm going to send this to you as a file. That should happen within the next 20 years. I mean, technically, it could probably happen now, but given the administration and the time. I mean, one site somewhere needs to do it, and then you can just... French Library has a project for doing it, and Microsoft is supposed to still get it, so to give them a... The only problem is the sheer, you know, what it will involve in man hours in real time, scanning all the books in the TGV of the library. The trouble is, can you trust them to operate the OCR scanner? And also, can you trust the OCR software even now? I think the answer is no, because the error rate is still quite unacceptably high. And, I mean, even if the error rate is only 0.2%, that still means that somebody has got real time. Well, that's absolutely impossible. That's asking somebody to read all... I think that's what they're seriously proposing to do. I think that's what they're proposing. They actually have the technology to do that, and then you would get the error rate. Yeah, no, I'm sure you're right. It'll come about. It may come about a lot sooner.

25:00 Anyway, Knights of Canberra, Imperial, Wanda, I'll put that in there. I was going to bring John. I'm sorry. No, no, no, no, no. It just depended on you. No, great. You did. Why don't you, even if you don't like coffee, put that in there? Why don't you do that, and I will ring and see what time he wants us to go out there. Oh, I'll do it anyway, so you think I should stay right here? Well, yeah, because I think we'll be going off within the next ten minutes or so. Oh, no, sorry, Tony, I'm sorry. I'm looking at my... Sorry, I can't even read my damn watch. It's 11, I was thinking it was 12. No, no, no, you're right, we do have another hour. But I'll go and ring him now and find out what time he wants us to go out there. Okay. And also with a bill as well. I haven't even got a mobile on me. I was in such a rush to leave Puget. I hate them, but they are absolutely indispensable. The only reason I haven't got one is because I was in such a rush to leave Puget to get to Paris, because there was a seminar in Paris the day before I flew and I wanted to record. Yeah, I think that might be an idea. If you'd only take me a moment, I'll ring him up. In fact, wait a minute, I may actually have his number here. Would that be okay? See, there may be a local call. Let's have a very quick look and see if John's... Yeah, I've got it here anyway. Yeah, his office phone is, which is in his office, I know, is 353-9248-617. Did you bring a laptop too? Yeah. Oh good, you didn't wait in the kitchen. So we'll all know. Hello John? Do I have to print something? I'm not sure. I'm just getting... Oh, it's on hold. I don't know how... It ran. Do you want to try again?

27:30 Yeah. He said he'd be in his office, so... You've got the right number? 617-353-9248. I'll try him at home. I'll try him at home on his cell phone tonight. Thank you for watching. His wife died only at the beginning of last week, so they've been together for a long time, they were absolutely inseparable, so it's absolutely amazing that you've decided you really wanted to come to this meeting anywhere, and I've had to admire you so much in the last four years. That whole generation of French optometrists. I wish I could have ended up with a job in France. I think I would have fit in. An intellect into the society that we live in. You know, Fletcher and Chapman. I mean, they have this power fight as well. No, I know. To be insanely accommodative and aggressive. And I'm telling you, Fletcher is a thousand times nicer than the average French mathematician at his level. Well, the French can have a real edge to them anyhow. True. But on top of that, there's also this insane analytical taking order and competitiveness with the mathematical establishment.

30:00 He's quite exceptional. Yes, but leaving all that aside... Not lacking in any kind of self-promotion. I felt that a link between the kind of mathematics they're doing and physics would have been something, you know... No, the system is superb. I think I would have been okay in Britain too. If you would have been at a department where you were around people like Chris Isham and Roger Penrose, not all departments are as lucky as that. But we don't really have people like that in that. The exposed nail gets hammered. Yeah, yeah, the rolling, yes, I was going to tell you. The head-exposed nail. They're so conformist. They just want everybody to work on the same thing. And if it's all boring and your paper is trivial, that's fine. That's what they want, yes. I have to say, I think this is more of a problem in physics. I think the physics is worse than the math. I think physics is much worse at that point. Well, they just got through producing this magnificence. I mean, I was there right at the beginning. I was there in 85 at the... I got interested in it and about every six months I then realized that nothing really worked and there was no foundation for it and I said I'm going to do something else. You're singing to the choir again. Well you should have heard songs from the choir. Not the wind instruments. We don't need radio. Intuition is a genius. I think it's going to work in terms of its overall confidence.

32:30 Oh yeah, I agree. It's been very bad for mathematics. Of course, for physics, it's been... I mean, there hardly is theoretical physics in America anymore, but, you know, the experimental physicists have nobody to talk to because these people are all out of their heads. Yeah, yeah, that's right. And the worst thing, I think, is what it's done to philosophy of science. I couldn't agree more. Oh, these people who think that they can... because the string theory must be the theory, and therefore there's only... Which is more or less how it's supposed to be. It's just really terrible. And the conclusion, in the end of believing in God, you believe in string theory. It's worse than that. God and the devil. Well, you know, you'll be singing to the choir when you speak to Bill, because this is exactly how he feels. But in his case, it goes even further back. In his case, he's flying. Well, I could make an argument for that. Yeah, exactly. It would be interesting to hear. Listen, can I have another bad shirt? Shall we try again? Just try again. Yeah. It rang last time. It just did. It's still kind of a little bit busy. He must have a lot of people. Why doesn't he call himself? Okay, yeah, but the call is still in that case. He may have left it off. He did ask me to call him. Well, actually at 11 it's already nearly. So we should go ahead. Hello, John. Hi. Sorry, hi. Yeah, I was just trying to reach you on your office number, but it was engaged. Yeah, no problem. In fact, I'm actually on Sean Westmoreland's mobile. We're sitting in the coffee shop at the hotel. Right, just let me know what time you'd like us to come out. Oh, crikey. Shoot, I should have asked him, but obviously he's had so much on his mind in the last week. I don't think he's using any audiovisuals this afternoon. Yeah, he'll need a blackboard, yes. Blackboard or whiteboard. And I'm pretty sure that's all he'll need tomorrow as well, but I'll double-check that when I see him.

35:00 At 1? Okay, that's early enough, is it? We won't be in any rush for the talk? So we'll come round to your office at 1. Oh, okay, the only problem is we're trying to get hold of Daniel Kahn, and we wanted to give him a rendezvous point. Well, we're not sure. I'm waiting to hear from Bill as to whether he's been able to get hold of Daniel Kahn, and if so, whether he is going to come. Um, it would be good if you could. Oh, very... Well, that's why we thought we'd probably be best if we rendezvoused at your office. Why don't we rendezvous at your office just a little bit earlier? Perfect. Shall we say at your office at 12.30? Which means we should walk over here at about 12? How long does it take to walk from the hotel to your office? Perfect, so if we leave here at 12 we should be fine. Yeah, I've got your map. Yeah, turn left onto Beacon from the hotel and walk down in the direction of the decreasing numbers. St Mary's, right. Yes, I've got that, too. Yeah, I've got it on the map. I'm looking at it. Yeah. It's really easy. You've actually drawn it on the map, and then they walk along Commonwealth Avenue to 775. He's 745. Yeah, that's it. Got it. Can I ask him his office number? Yeah, it's okay. We can see it on the map from here. Don't worry. But when we actually get to Boston U, 745. Yeah. Give me his office number, will you? We've got it. Okay. Sixth floor, fifth, got that, excuse me, 505, got it, okay, we'll see you there, it'll probably be just a little bit after 12.30. Okay, take care. Well, it's going to be, who's going to be coming? Myself, Bill Cartier, Lou, who's sitting with me now, Colin McLarty, oh yes, Colin came in last night.

37:30 Yes, he did, yes. No, I thought he was coming tomorrow too, but he actually came in very late last night. Yeah, absolutely fine, no problem. Jean-Pierre, I haven't heard from yet. I'm not sure if he's here or not. And lastly, Marquis, don't make any, I think Marquis is fine. Marquis is fine. Yes, if he gets here in time and if he gets the message. Uh, yeah, if not, we'll just have to count on meeting him at the meeting, he'll come. Uh, Gonzalo raises an... Yeah, but he knows, he's got the address and the time of the meeting. Yes, I sent it to him. He knows, he knows, he will be at the photonics, uh, not the photonics lab, the place where, um, where Pierre is speaking, yeah, exactly. He'll be at Terrace Lounge this afternoon at 3, whatever happens. So will Gonzalo raise. But I don't think either Gonzalo... well, Gonzalo's definitely not coming to lunch. No, no. But he is coming to the meeting, exactly, exactly. And I just don't know about Jean-Pierre, but everybody, that accounts for everybody, exactly. See, you can relax. Take care, coverage. Very relaxing, which is what I needed. Okay, see you in a little while, John. Take care, cheers. I just mentioned his story one more, and eventually Laplace talked to the video of it, and it seems like you can't do it in a closed forum, so he had to write up perturbations in the audience. I'm still not going to yield on the question of the definite article.

40:00 Okay, okay, okay. Whatever structures we eventually decide correspond to our present intuition about real numbers. The next mathematical. Yeah, yeah, the next phase. Right. So in other words, you had to go forward to go back. Yeah, yeah, yeah. I mean, I completely agree. Ressule pour nous sauter, as the French say. Thank you for your attention. If you've been up against the polio for 25 years, you might just agree that all of us are in the same region. No, we do not. I have to say, it's quite English. It's in American, it's just from World War II. Yeah, and it's also, forgive my saying this earlier, don't get me wrong. I'm not going to be offended because I'm an Englishman living in France, so I'm pretty darned even for World War V. Because of France in 1914, even in 1940, actually. The French couldn't possibly pick off the terms on their own anyway. After all, in the First World War, they had taken the whole of the rest of the world together to meet. In 1940, the French were left, for all intents and purposes, complete dogs of five to two to start with, against an enemy that was qualitatively, tactically, in every other respect, better, better organized. They had just, they were still only 20 years away from a war in which they had lost 2 million people out of population, excuse me, but in the United States in 1941. In 1941, Roosevelt came to start a declaration of war out of Congress. We have the 17th largest army after Portugal. That was actually in 1940. By 1941, they'd actually done quite a lot rather rapidly to fix that. I did have another kind of, wearing another hat of a military historian on.

42:30 In fact, they had really done pretty well. Yeah, but can I just finish very quickly the point I wanted to make. The United States would have lost 10 million men in the First World War if it had given the size of its population, if it had suffered proportionately. I mean, the idea that the United States would have been ready 20 years later, you know, culturally and emotionally capable of fighting another war after losing 10 million people, I don't think so. I don't think any society... Yeah, yeah, yeah, yeah, all those guys. I mean, but I mean, the thing is that French had just been, they had been bled white so completely in the Second, in the First World War that I don't think any other nation, any nation in there psychologically prepared. But yeah, they were, they were morally ready to collapse. On the other hand, the Germans read De Gaulle and the French didn't. Yeah. And de Gaulle himself, of course, had an interesting experience, because do you know where he spent most of the First World War after he was taken prisoner at Verdun? In a German prisoner war camp in Ingolstadt, sharing a cell with Tukhachevsky, who later became the greatest expert on tanks the Red Army ever had before Stalin went and shot him. He and de Gaulle actually spent two years sharing a barrack room in Ingolstadt, because he was an officer in the Tsarist army when he was taken prisoner. Very interesting. Now, I really know about De Gaulle. I've just been reading about his superb biography of him. Very interesting. Three-volume biography, if I'm not mistaken. He was an absolutely amazing, interesting man. If you go to a book store and you look for World War II, about half of the books are biographies of De Gaulle. Which is a distortion, I agree. But no more of a distortion than the kind of British... I think the reason the Americans and the French get a little bit, you know, thin-skinned about the we save your ass, you know, twice, is that actually...

45:00 They didn't. In 1941, the United States had just sat on the sidelines and been neutral for three years. The only reason it came into the water was because the Japanese decided to attack them. They weren't exactly left with any option in the matter, and Hitler then declared war on them. So it wasn't as if, gratuitously and insanely and stupidly, but nonetheless, they didn't take the initiative. They didn't exercise any kind of option in the matter. They were drawn in anyway. And so they landed in France to liberate it. Only because that happened to be where the bulk of the German army in the West was, and if you're going to go and fight them, beat them, you know, that's where you go to fight them and beat them. It just happened that the French were in the West. You know, it was not, although obviously propaganda at the time presented it as being, you know, untouchable, it was not actually, you know, some glorious crusade in order to liberate something. That just happened to be an incidental thing, because that's what everybody likes to tell themselves. But at the time, it was simply the fact that, one, you can attack them anyway, too. Whether you like it or not, you're in the war. Three, that was where the enemy was. But on the other hand, the statement that France liberated itself without any help is also... Well, it's absolutely ludicrous, and I'm not going to emphasize that it's ludicrous, and I don't know any Frenchman outside a lunatic asylum who would assert that. In his speech, when he said, we liberated Paris on our own, you know. Well, he liberated Paris. That's perfectly reasonable to claim they liberated Paris on their own. But that was actually after the American army had run around it and the Germans had run out. Well, they hadn't run out. There were still German troops in Paris, which is the reason there were six days of street fighting. It was perfectly reasonable claim to say that the FFI liberated Paris. Although, in fact, even that wasn't perfect because they did use the 4th Infantry Division as well, the Ivy Division. But they were ordered to hang back and not... But if you'd been occupied for four years and you were liberating your own capital, you wouldn't rather want to take the credit for it, wouldn't you, as a matter of self-respect? Anyway, I'm going to stick up for the French. Have you read Turtledove? No, tell me about Turtledove. Okay, Turtledove is an author and a historian, and he has a degree in history. And he's just gotten some good writing. There's eleven volumes, fifty-five hundred pages in the novel. Eleven volumes? My God. And it's an alternate history in which the South wins the Civil War, and then you go through a second Civil War, and then World War I, and then World War II.

47:30 And America becomes completely different. And what happens is that England and France intervene on the side of the South. Well, that nearly did happen, as you know. That very nearly did happen. That came with a hair-spread. The convention of the genre would have happened if Seward had had his way, and actually also if the Prince Consort had literally used his dying breath to water down the telegram which Palmerston wanted to send in reply to Seward, which probably would have provoked... The convention of the genres, there has to be one quantum event that changes it. Yeah, that's right. This is many worlds, right? Yeah, that's right. We didn't talk about that very much, but it's fascinating. Oh, no, no. Say that again. Pierre is coming down, should be down any minute. Oh, okay. In fact, that's really good. I just finished this. I just sent out this 19-picture word. Which is, which one are we talking about? I've been working on them since the last day of February. I met them in Prague, in Prague. I went to a computer science meeting. I came to do this interview. We spent the whole day. It was a very nice day and so forth and so on. But it turned out that the audio equipment they had was ineffective, and most of what I said that day was lost. Ah, you should leave that to the professionals, Bill, dare I say it. No, but then they, with enormous energy and intelligence, discovered all my papers, wherever I made any statements, and reconstructed an interview.

50:00 I reacted to that by saying, well, this doesn't really sound like an interview. No, no, exactly, that would be the problem. It sounds like Bill LeVere preaching. So we went back and, as it were, reconstructed what it would have been in the actual interview. Fascinating. Yeah, so I went back and I just finished. Oh, well, I really want to look at that. By the way, don't let me forget. Oh, that's a hell of a good interview. Well, I want to look at them. I want to look at them. But I also want to remind you, as speaking of Portugal, when you get a chance, you will do a copy of that. Could you do it? Yes, I could. Yeah, I do. I do. Oh, here's Pierre. Hi. Hi, Pierre. Could I do that? Well, you don't have to get it now, but when we get back, it will be a good idea if you have it. Yeah, sorry. Harder to carry. Well, harder to lose, certainly. Sorry, Pierre, may I introduce you, please? This is Lou Crane, this is Pierre Cartier from the IHS, and this is Sean Westmoreland. I think we're waiting for Colin. Everybody else is here. Jean-Pierre can't join us for lunch. He's got to finish this dinner on Monday. He's got to finish it. And we know that Devin can't come, so that's everybody now except Colin, who I think is already out because he wasn't in his room when I called. It might be an idea to start walking over and just leave a note for Colin to meet us there. No, this is back home when he gets back to Canada. He's in Montreal. He has to give a lecture on Monday afternoon, and so he needs to repair it now. And he only got in 15 minutes ago. But he's going to be at Pierre's talk.

52:30 Right. Just give me a moment, Pierre. I just want to leave a note for Colin, because I think he's out there somewhere. I have a dream. Oh, yes. In a book published by the Norris Military Academy, because the French and the Russians were underlying themselves preparing for the First World War in 1912, there's a big volume, several volumes, military school in Petersburg that contains the latest stuff, relativity. In this Tuesday, I'll tell you about this. These books have been discarded by the American physicists, at least the universities, because they're old stuff. But I found them in the library in Milan, actually. It's fascinating to read this. But anyway, it reminds one immediately that, well, after all, algebra and geometry are these objects that are not regular in the sense that their tangent space and their underlying topological space have the same dimension. It seems a better way to model these things than a non-standard analysis, because it's really just the first few infinitesimal features. As I say, when these things are treated by an engineer, it's usually the extra-director vectors that are just tacked on as extra, like a 17-tupler of data.

55:00 Whereas if you look at it systematically, the category of algebraic spaces, these are usually what comes out, the natural tangents that are involved in it. But you've never heard of this being done in the number of many... No, not that I know of. ...circle grains, excuse the expression. Not that I know of. Not that I know of. But I think that's the... We were held up, actually, about two hours from taking off, so we got into Montreal a bit late and we had a bit of a rush to make our connection, but we got here. We flew from Paris to Montreal and then from Montreal down to Boston. It happened to me. They told me for five hours. Yeah. I mean, so close. But the airline was... The hold up wasn't so much. It was Air Canada. We flew in with Air Canada. No, no, no. No, no, the airline. No complaints with the airline. We'll take the next one. There were no problems with the airline at all, it was just the delays on the ground. But then, after him, after him, I mean, it's all quite natural. And I think one of the most promising humanities will be to follow what Sir Edward Nelson Keating using mathematics for his foily area. This is a very deep one. And it's, of course, it's a subject. And it takes seriously, I mean, that's what every physicist knows, that in the boolean motion, delta x to the square is delta t. But it can be taken literally, which means that I like to see non-standard analysis as a way of freezing limits, that means eventually we will go out of limits, but at the moment we keep the limits, because suppose there are many paradigms, so I mean if you just go to the limits...

57:30 I'm bothered to be alive. Thanks, John. No, no, it is. You know, in a sense, it's a thing that we do. Well, after all, if I say it's a little small. No, I didn't mind myself. It's a good story, but, you know. Is that where we wanted to be? All right. Oh, we just got out to make sure we didn't get... Yeah, sure, all right. All right, let's see. It's important, however, in a language firm, or maybe in a university, to take the sum of all the large numbers of infinities in a value, each one leaving a small value. The large number will come in a small value. It means that you have a sum of the number of terms that eventually go through. And with standard methods, it's quite a work to treat this. And once I have to devise a sub-examination plan, and I use my standard half-hexameter to do a very difficult test, and that's to detect the readings. And in that case, I use all my knowledge. I was in a course with you and I knew very well and I knew you were taking exam and when I got the paper... Is this one gone? No, next one.

1:00:00 I did not have to... Well, of course, people were not able to... You just had to look. You did it! This is fun! Do we read it? Do we laugh? What a good idea, okay, so thank you. Is this the one that Lou's talking about? Yeah. Great, okay. This is the one? Yeah. Okay, fine. Okay. Here we go, Bill. There are a large number of matrices, each one of which goes to one component of a unit. I mean, if you do it binaurally, that's a very typical example of a non-standard artist doing this. But, by a standard method, it's quite easy. I knew only one student could do it, and one student did it. I knew the number one competition, but I wanted to test the capacity. Do we think it's growing now? Yeah, it's growing by me. By doing what? Do we serve ourselves, or? Okay, right. Maybe I'll do it. Two more tests. I think two more tests. We have to serve ourselves. It's a self-service deal. We can leave these here. I believe that's what I was told.

1:02:30 You deal with an actual population, an actual set of properties, and a map from one to the other, so one can work with this kind of data directly without turning into, and so to a certain extent you don't have to worry about infinity because infinity is a problem because you've ignored the fact that it's connected by a map. Well, there are a number of things that have become more transparent in this day and age. These, of course, are just the objects in some category in the compact stage that we're in. I don't know if I can formally define the equivalence of objects in those days. Thank you for your attention. There are soups, there are salads, everything you have is good. Yes, this is great. Thanks very much, John. The ratio between the work of the students and the work of the students is the ratio between the work of the students and the work of the students. I don't know the answer.

1:05:00 Some of that work we were talking about from that period of 1910-1912, continuum mechanics, I think is absolutely extraordinary. I'd love to learn more about it, as you say. John is very well worth talking to about that because, of course, he has very detailed encyclopaedic knowledge. The background in classical physics in the period just before, where all the relativity... Uh, just behind you, here. Oh, hang on a minute. Oh, they all seem to have gone. Since the last one seems to have gone, I'm sure they'll bring some more. Now, I'll just go and... So, yeah. So, um, is it the Riverview Room we should be going into? The little room through the exit well. Okay, got it. Thanks very much. Well, I'll come back to that. And he said, making the direct point, I don't think this was any factor, but theoretically, you didn't have that when you were coming to it. If you are a convention, you define it as a combination. You could say, well, the absolute time. Yes, that's the natural definition, but it's still a definition. The point that I'm sending out is that nothing physical can you do. Nothing, no physical results can depend on the invention you've got.

1:07:30 Or even if you've got nothing to do with it, I don't know if any of you are going to find any take-outs in that. Oh, yes. The radar time. Yes, the radar time. You don't have to have it. By the way, can I mention the bond I introduced in the radar time? For a series of popular television lectures on general relativity that he gave on the BBC in the 1950s, can you imagine a public, that Bondi introduced the K calculus and the radar time for a series of popular lectures, Herman Bondi, for a series of popular lectures that he gave on the BBC on the subject of general relativity in the, He introduced the K-calculus and the radar time for those lectures. Can you imagine a public broadcasting system anywhere in the world today which would give three months of broadcasting time to somebody upon his statue to give popular lectures about general relativity? It was a very different world. The BBC is simply an arm of Murdoch now. It's an absolute joke beyond belief. Corrie's deteriorated now. It's so great, isn't it? I mean, it's still probably a little bit better than Fox News, but, you know... Not much more than a little bit. Seriously, I don't think anybody in this country, you know, in the United States, begins to appreciate just how dreadful it is that the BBC has deteriorated. It's the same dreadful, trashy, you know, reality-select shows, relieved by the occasional bit of... Infotainment of the, you know, did Hitler like Jell-O or the witches on Uranus? I've just completed all this. It's awful. It was for a long time. And there are bits of radio, there are bits of BBC radio that's still on. There are one or two serious programmes of analysis, both economics and science, on BBC radio.

1:10:00 But the television has just been a complete joke now for a long time. But in the time that Bondi was giving these lectures, there was, it was a very high standard indeed, which is good. Yes, that's very good. Yes, that's extremely high standard. How could I imagine that it would be a good idea to draw it from Slam Dunk TV channel? And then when I take the new bus train to Germany, I mean there is an announcement to the French and Germans that the staff of the French and German trains are going to arrive. And it would be good for training staff to inspire them. Well, in fact, of course, there's a completely open border now. There is no border. No, there's no border. There's no border. No, but the point is that there was a border. Oh, yes. I'm sorry. I was just thinking about what you said. I'm sorry I interrupted you talking about bonding. You were talking about relativity and simultaneity. So if you were in Newtonian physics, the speed of the ray of light would depend on the frame that you were observing. It wouldn't have a uniform speed. In Newtonian physics, yeah. I mean, if you were moving alongside it, it would go faster, it would go slower. You mean, the speed depends on convention? No, no, I mean, it wouldn't be like any other particle in the time of physics. It would have a velocity, and then if you moved relative to it, that would be subtracted. And that wouldn't be anything? No, light, no, light is, I mean, light is a planet. Oh, I mean, if you traveled in the, if you traveled in the mass of the place in the one time you were.

1:12:30 But I think you wouldn't find out that two events were simultaneous in one frame and not simultaneous in another. I don't think. I'm not sure. I haven't done the calculations. No, no, you're actually, I mean, you're, you're, I mean, I just realized that I'm No, no, it doesn't. But Maxwell's equations would be a big problem. So actually, if the guy you're talking about was using Maxwell's equations, he already sort of had one foot in relativity without knowing it. In fact, that was...