Time (brief extract) / conversation Dan Kurth et al — Foundations of math, Saussure & Leibniz

22:30 Which is why I was saying to you the other day that there is, I think, this fundamental tension in category theory between the algebraists and the geometers, between the founders of the subject, MacLean, who were definitely a melange of something, but actually coming out of very concrete and specific problems in algebraic topology to do with the definition, for instance, of Solomai. I mean, there was some very, very concrete problems.

30:00 A fixed number of people involved and they have to wait for somebody to die or get kicked out. And it certainly doesn't have the kind of kudos that it had in the previous generation. They still have to retire at 50. I was going to say this is the Algebras.

32:30 And the second generation, was Cartier in the third generation? No, Cartier. Pierre Cartier. No, no, Cartier. He's in his late 70s now. Even the younger Cartier, I think, was a little old to be in the first. You see, he was right about in the 50s, wasn't he? Maybe he was in the first generation or even the second generation. Eilenberg was in in 1948. So it is a self-renewing thing, but at the same time it's been a self-renewing thing that's really pretty distinct. Probably Erisman was for a while. Erisman was, you know, being the source of that. And then in the most recent generation, Korn, Poncevich, I'm not sure apart from Korn. Oh, and Bourguignon, who's now the director at the... IHES. But they will no longer be in it because they're well over 50. Absolutely iron rule in Bovati, which was known. Nobody can tell you the name of a single member of the present-day Bovati movement. But it does... Contrary to a lot of people, there was a rumour which was circulated. It had been wound up in 1968. And I think, in fact, Grothendieck did attempt to wind it up in 1968. I think this was actually one of the reasons that he... One of the many reasons. But he did attempt to add Bovati. He... ...in the middle of the événement in May 1968. He exceeded his authority. The irony is that, although he was an anarchist, he was actually extremely authoritative.

35:00 You have to be a card-carrying Frenchman to belong. No, because the disprover of that is Eilenberg, who was the great American, well actually Polish-Jewish, but man of the age of America, algebraicist of his generation, who was a member of it, and I think... Chris, just as well we don't have the Retire at 50 age limit in ANPHA, right? Otherwise it would be quite a few people, not a few. It's very sad actually the way that ANPHA hasn't... I mean, there are all sorts of understandable reasons for this. I'm not holding anybody to account for it because I think that because of the way that the combinatorial hierarchy program went it. I know that Clive and some people did try to bring in new blood in the first ten years. The problem is that it is sad because the founders have grown old along with it, and there's now this division between the original members, again, outside, who have all sorts, a wide range of interests, and then there's this third side, which is, if you know the, if you appreciate the reference, if you know the district line, those are the last stops beyond Barking. Yeah, I'm trying Barking mad here, where I'm trying Barking as a physical place. Well, no, I'm afraid I wasn't right.

37:30 The three components don't really matter, do they? I think it's the same. I don't harm me. I don't harm them. Let's try and conjugate this. I am not afraid of gold in radical space. You are. You are flake. There might be various regulations. Unfortunately, no, I'm afraid I've been absolutely lured up and chock-full of antibiotics and painkillers at the moment, and I only got the... What did you... Well, there's some tablets left on the floor. They might have been, I don't know. Gel? Gel?

40:00 Were they blue? Blue tablets? There were three different types. Oh, they might have... Well, it's okay, I've got a big surprise. I might have left them in there yesterday because I was so woozy. Now, I've got a... I mean, you know what, this is boring, but I've got an abscess in my jaw which I saw the doctor... They're really kicking in now, the infection's going down rapidly, but this morning I just, I didn't hear the phones unfortunately, all the talk on time, the only thing I heard was, and in fact I slept through the whole of Luke Halfman's talk, which was not because it was very interesting, because it was, I like Luke Halfman's work very much indeed, but it was just the effect of these bloody things. One is the pills, in case they're yours. Yeah, well I'll go in and check, they're probably on. No, they're not there now because the people are worried. Oh, well don't worry, I'll check tomorrow. Well, it's alright, I've got them to fly anyway. The other thing which is why we're running out of time is that... It's all the stuff about angular momentum. Yeah, I remember you talked about it, I asked you. It was seriously interesting. Yeah, I'm sorry, I missed that. I would not have expected this. Exactly. I would never have expected this. I have heard Viv for the last god knows how many years. And when Viv started with us, I thought, my, we're more of the same. More of the same. And then we saw the two guys. I mean, it was as if they were speaking from different hymn sheets. I was feeling lousy, but that's one reason I didn't go to it. I'm really perfectly off there. I'm really sorry I missed that. Fortunately, it's all on video. So if you capture... You're going to be here for the next couple of days. Yeah, because I gave an undertaking to tape the whole meeting, not Monday and Tuesday. There's a guy here, his name is John. I don't think he's going to be here tomorrow, but he is coming back before the end of the meeting. And he videoed the whole thing. Oh, I must have missed that. You get a copy from him. Yeah, I agree with that. Because the whole issue of angular momentum and classical mechanics, I think, is very intricate.

42:30 Where's Luciano? Luciano, he's very bright, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, There are thousands of people. If they think they say something deeply original, then they start varying gravity or at least general relativity. And the only one which you can say is, yeah, yeah, it's fine. Now I must leave. I'm sorry. But this was very interesting. They did good examples, even with, in principle, possible experiments. I'm sorry, I'm at sea, but in what sense do they mean? Is this, is this, is this, is this, is this, is this, is this, is this, is this, is this, is this, is this, is this,

45:00 In this moment I thought, okay, now comes a lot of rubbish. But I had an answer. It is, it was interesting. You jumped in, catching them by a semantic weakness, not even inconsistent. You standing on a, what you need, another. You find then he and he also then said this object is trying, is trying his natural orbit to, to, to, yeah, not, not, no, no, I'm not, I'm not, I'm not sort of, I'm not sort of scowling with the back of the tree because it sounds like a term to get back to Aristotelian. It is, it is, it is not a natural, and I often say, no, this is the, this is the, this is the, this is the, this is the, this is the, this is the, this is the, Do you even think what a natural locator is? I mean, rather more sort of scenery and background. Have they got some account of inertia that derives from, you know, treating the Lorentz transformations as a kind of... There is no linear motion. There is no linear motion. As radical as that, there is somehow...

47:30 Sorry, indeed, I missed it in that case. I'm afraid, I'm afraid... Well, I was feeling lousy and I didn't want to...

50:00 What was so encouraging was the other two guys. We're much more humble and much more answering questions and making much more modest claims and saying, look, you know, if we, no, no, it's an artist and a politician about, and they walk around sitting there until they finish their PhDs and they're sort of sent out into the world.

1:05:00 And like I read it last year, of course, I'm glad it was probably, you know, slatted on his feet. As far as I'm aware, unless something has happened that I'm unaware of in the last three months, I don't think there's any change. There hasn't been any, as it were, further meeting. It would be really excellent if you could get there, Dan, because your interests are so, and it would be, if I say it myself, we have actually got some quite impressive people coming. Dana Scott is speaking there. It's mostly, as you can imagine, it's mostly, so it's actually slightly skewed towards. But on the other hand, there will be plenty of grist to the mill. John Mabry is going to be there, John Bell, the logician, Colin McLarty, and Alberto Peruzzi, both Italian philosophers, historians of mathematics, you might have come across them.

1:07:30 I have read the original, I have read the book, which if you have understood, you have understood Topos, I cannot pretend to have understood the whole of that book. I wish I could say, I wish I could say, I have it, I have it on my shelf, I have, I have, I have, who was it who was saying this morning, Lou Kaplan, wasn't it, who said, well, you never read a book. I have gone into the index. I read the passages on the Ricoh equivalents, which I was particularly interested in, in the context of understanding Lafayette's reasons for being so hostile towards non-commutative geometry, and I think I've probably read about 10 or 15% of it, and I will make the effort in the next year to go through it from cover to cover, but how much I will get, that's a little bit like going through the Bible from cover to cover. I don't think I'm going to get a great deal out of it. I have not elapsed the mathematical maturity. Thank you for your attention. Yes, I'm sorry, it's B-O-U. My U's always look like these, I'm afraid. It's Boutier, literally the bottler, the road of the bottler. It's currentburner.com.

1:10:00 Yes, it's the old cheap and cheerful currentburner.com. Actually, it's a bit of a nuisance because I believe they're going to be closing that server down before long, so I'll have to get a new address. Right, and you can register online. I can say who has to pay the registration fee and who hasn't. And the conference hotel is called the Hotel Alinari, which is a three-star hotel near to the, and the actual lectures are going to be, the first two or three days are going to be in the Galileo, where Galileo actually went. So watch it. Don't say anything contentious. It's written...