Discussions, incl. FW Lawvere

0:00 I repeated in a recent article that he, in the dialogue, it's on the morning when he gives that proof, and it took Miles Burney to point out to, I mean, you know, in an article of his, he points out or finally makes it, he still, the statement isn't there. He develops some definitions that might be used for such a statement, but it's only a page and a half, and all you have to do is read it and see he doesn't state a theorem, he won't prove it, he develops a definition that might help. And I even caught that myself, but I couldn't bring myself to say so. Because it's not that I was aware of this. We want to go left here, Bill, and straight on down here. Yeah, self-consciously I expressed it into the world that everybody could say anything. Right. Well, there's dual things that I pointed out in Cantor, where everybody read and nobody ever saw. Yeah, yeah, yeah. It would have bugged me that I even caught on this issue and I said I don't see it here, and yeah, I would have thought it was there, or close. Yeah, we know, now hang on, don't worry, don't panic, don't panic, well we have only one way to go, which is left. And that's great because you don't want to do a left here, you only want to do a right, and then in fact we, this is the very street we wanted to be on. No, no, it's not. It's straight on here. You just carry straight on along this key. Should the water on our left? That's exactly right. Yep, it should be the river. Actually, it's the canal, Saint-Martin. You just carry straight on here, and then it should be signed left for Saint-Marle and Dinard. And then it takes you straight on to the water. Do we know that Eudoxus knew that?

2:30 I'm not a guy. There's no good evidence about your doctors at all. It's not at all implausible. It's likely enough. Well, that's what I was asking. Yeah, straight on here. Actually, I made a boo-boo there. We should have taken notes from a director. Sorry, that was my mistake. We should have turned right there to stay on the water. I'm sorry, Bill. So, I think it's retrieval. Oh, it's okay. We can do it from here. No, it's okay. You just, all you're going to do is to, you're going to come onto exit 11 of the ring road. You just, in the direction, it will actually be signed, and it's only a very short distance. You come onto exit 13, so this will work fine. Yeah, just stay on these signs. Who's, who's, is this Bernice? No, this is, um... Dissertation advisor to a friend of mine, a German, a German guy, isn't it the, oh, no, don't mind, we'll come to that. But, yeah, he claims that there were some Pythagoreans who pursued mathematics around, around contemporaries of Plato, but even they didn't think Pythagoras had believed them.

5:00 But then later on, the Academy started saying that Pythagoras did it all, or that everybody did it. All of these stories you hear, you can't help but give up them. It certainly tears up the textbook and all kind of pre-Socratic scholarship, if that's right. Well, yeah. I'd say it's fanaticism. What is there to document? Well, that's the thing. There's so little evidence. Exactly. And he shows this, and he shows what evidence there is. He shows that the evidence there is... Hang on, sorry, can I help? Sorry, sorry. That's okay, we'll go straight ahead here, not the auto-rick here. It particularly does a great job of pointing out what, again, you only have to see the text, but people hadn't, that Aristotle doesn't say any of the same things that the Platonists do. Only just, it's okay, you'll tell when the little green man goes red that it's time for us to go. I can see it. Yeah, okay. Just watch the... ...the figure of the man when it's red and the other lights. Yeah, it's okay. It's red. Well, it's still red. Oh, okay. Yeah, because it always changes just before. Surely it must be green by now. Yeah, he does. He does. Which is better than if he was green. Yeah, the private facie objection to that, obviously, is Aristotle is even further from the sources than Plato.

7:30 Well, yeah, but on his reading, and he's very precise about this, Plato didn't claim any of these things. We want to turn on the signs for St. Marlow and Cairn, Bill. We want to turn on the signs for St. Marlow and Cairn, which I think are this. Not this one, but the next one. Well, that's not where we want to go. We want to turn right here, Phil. We want to turn right here. Sorry. I'm sorry. That's Final L'Oréal. That's very, very confusingly signed because that first sign, okay, right, stick on this and I'll tell you how to retrieve it, don't worry, yeah, but we are on the right order, so don't worry, I'll get you there, don't worry, yeah, I'm on the way, don't worry, let me concentrate on the, getting us onto the right turn, okay, it's okay, I've seen how to do it, don't worry. Well, Cartier was very pleased when I told him the aircraft was going to be there, although, fortunately, it's only going to overlap by one day, because, yeah, he also thinks very highly of it. I was perfectly happy with that attitude, bumping to it, you know.

10:00 It was a really nasty shock. ...response by trying to read some... ...a little newer response by coming up with very learned reasons why you shouldn't learn any... Well, he didn't come up with those with me. He didn't give me one even, completely unlearned reason. Okay, he's just made it apparent that he's happy he's learnt any. Well, yeah, yeah, yeah. But then he'll mention Hilbert. Yeah? Well, Hilbert's an important figure, so if you can mention him as a reason not to learn category theory, then why shouldn't you? And what reason does Hilbert give you not to learn category theory? Well, that's the problem. That's the weak point in all of this. Yeah, yeah. I mean, he's almost as crazy as that. This is scarcely even... It is almost, it is pretty well as bad as that. I've been to the conversations in bars, you know, late in the evening in Lille. I'm not authoritative for what he's, you know, what he's going to say in print, but I haven't seen anything he's said in print that suggests he's got any deeper or more serious reasons. I'm not on the camera at the moment, I agree. And these are the, you know, pan-structuralist-like. French and Lederman have also got no excuse at all. Like Stephen French and James Lederman have got no excuse either, to the extent that they don't hold themselves after doing philosophy of math, when they're doing philosophy of physics. I mean, there's even less excuse. And you can point to Stewart's books and say, well, there's no dimensions category here. That's the one thing Stewart has done is he's written a long, long and accomplished book.

12:30 I don't know, but there's something in the plane. I mean, when I was applying to the I wrote to Chicago, I wrote from the Isle of Mull, from where it came into existence, and my mother was in McLean, but not the same spelling, and there were two tribes on the island, but it didn't really get on all that well, but it probably charmed me, it utterly charmed me, it let me know to go to Chicago, but I'd given it my influence, but for now, I kept it for a long time, I told it all the time. The family got down to the, I mean, on this island, and now there's a lot of buoy that on the planes, Hizmet planes, comes up as a castle, and so it's a big island, and the roads are not so easy, so I've never actually been down there until about five, five or six years ago, and I went down there on a day, and maybe you could not see ten years upon the best for rain, but there was a post office there, and no one said hey. It has the highest rainfall of any place in the British Isles, I believe, Martin, over 140 inches a year, and I even know the castle you're talking about because many, many, many years ago I had to take a group of ladies, probably wealthy ladies, through the National Trust of New South Wales. There were all these grand Australian ladies of Scottish ancestry who wanted to go around looking at places in the Highlands, particularly the Isle of Mull because Macquarie, the first Governor General of New South Wales, was buried up on Mull.

15:00 And they are just paid to have his memorial and his tomb renovated. The then Lord Maclean, who I think was then the Lord Chamberlain. Yes, that's right. Yes, he'd taken over from Cobbold, he was then the Lord Chamberlain. He was at Dewar Castle. That's Dewar, that's right, but that's not the castle, that's not Dewar. Yeah, but there's also the castle down at Bowie. I mean, the Macleans of Dewar were I remember he organized a ceilidh. His son, or his son-in-law, I think, who was an interesting character, who published a biography of a state from, actually been known as a state from, during war, a state from a German prisoner of war candidate, who I got chatting to. And all these Australian ladies did these rather dreadful songs, one of which I can still remember. It was so embarrassing, all Kupferbauer sings in the old oak tree, and I remember sitting in the back, literally biting my lip and praying that I wouldn't burst out laughing. I learned that as a grade. Yeah, I mean, this candle is typically dead. It's still doing a pen and a mixture, you know, something quite beautiful occasionally sometimes, you know, something exclusive. It was one of the most excruciating events of my life, I have to say. I always remember Jewett Castle for that reason. But he was a very delightful old boy, all right. Yes, yes. A very delightful old boy. So terrible. He didn't have a son, so I think when he died, the title passed on to him. I don't know. A cousin or something. A second cousin. That's the small one over there, where Chateaubriand is buried.

17:30 Yeah, coming in on the ferry, there's all these islands reaching out, and I thought... No wonder any kid growing up here would want to get to the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island, and then the next island.

20:00 It's like non-standard roots of unity. Now he's shown that basically something like a Chagnot conjecture has been proved that something, an algebraic relation can happen if and only if there was a multiplicative relation down in the original source. And in fact, this has in fact now become a very common thing. Zoltan has detected a very general pattern for which Chagnot's conjecture is only one, and it's led to some very strange conjecture. Now, Chagnot's name is quite often mentioned at the Newton, isn't it?

22:30 I was going to suggest before we go in and eat here, oh, no, they're closed, so we have to go straight in. I was going to say we'd like to have a drink first in the Reckon bar, but that's fine. They normally open on Wednesdays. Wednesdays? Wednesdays through Sundays. Did you get my air net text? I think it's with some problem with the phone. Yes, yes, yes. Anyway, it's quite beautiful. It's incredibly beautiful. I'll give you the address if you want to try to send it to me. I'll give you my e-mail address. No, but I cannot support it. Of course you can. There it is, exactly. B-R-U-T-E-I-L-L-E-R. That's what we say. And then three-five. Go away. What's Cote de Cochon? Well, that's... Here we are. Cote de Cochon? Okay. Oh, you have an assignment. I'm sorry. Cote de Cochon. The striking thing is that you don't have to assume anything except that there is a system. Ah, and Bill? There exists a totally unique, top-mighty, all-top-mighty, in a totally rigid way. Ah, totally different. You can imagine there's a total natural. This is just your problem. But I'd like to point this to you.

25:00 Well, I wouldn't... What about Bill's math? Well, if you... You'll get that they have a map from the ring onto the ring, which doesn't have a ring section, but it has a, what do you say, a space lesson to it. The earlier concept from which this, the map, the distinction, you can stop losing them.

30:00 I don't even know the perfection of saying there aren't negative questions about it. This would be the thing to do with the guy since I don't want to see this person's blue chair.

37:30 And, you know, eventually Nagai. I'm not going to get any peace until I go down and see this place, so, yeah, it's great. It sounds an interesting old town, so I'm just going to spend a couple of hours, half a day there looking at it, but I'm not going to be interested in the house. Of course, the moment I saw the house's location on the side, especially the courtyard rooms at the back, and saw what kind of a library would make it that cheap, although the house needed a lot of doing to it, I mean, which has now been done, but it was, you know, where you're sleeping was just a sort of... I think with bare debris lying around, I thought, yeah, this is the one. I'll go for this. It'll take a year's work. In fact, it'll take more like two. And this place. Also, I just had a good feel about the town from the people I met here. They seemed very friendly and very open and friendly. It was a bit further from places I liked to be nearer to, but I discovered that you can get to Paris in two hours on the train from Rennes, an hour and a half from Laval. I thought, well, once I've learned to drive. But even so, I think I made the right decision, and now I've been very happy here. Do you drink water? Yes, of course. They never did bring me any fizzy water, but I'm not worried about that. After a meal as good as that, the wine was very good as well. But mainly it just seemed a place which would be big enough to have meetings like this and to be able to use it properly. A tranquil place.

40:00 Hang on. Anyway, they've decided in this part of the world, if they do, then I'm hoping that John might, because he obviously adores Kate and wouldn't want to be parted by a long way from her, that he might make his way around down here as well, which would give me a lot of companionship and stimulation. That's the one thing I'd rather miss being there.

42:30 Do you like the box, though? Yeah, so do I, but okay, but there's some very nice little places. Wait until you go down into the... No, they're not pubs. I like pubs too, but I, you know, could actually live if I... Actually, there are two. There's an Irish pub and an English pub. That's why Dr. Johnson always went out of his way to say Scotch. He did a very good job, particularly good, actually. I hardly ever go near the places, but I think that will probably only be enough to keep John going. He'd like to go very far from here. That's the thing which might bring him here, but I... To be honest, I never... I don't know if anybody's ever ordered the clover Joe. At the time it was pretty.

47:30 C'était dans les menus? Oui, c'était dans les menus. No, no, no. I'm really sorry I wasn't able to come down here. You know, students were, many of them graduate students, but others post-docs, and others young assistant professors. There isn't all of them. Bernardini is actually a professor of engineering at Rome. He was already a professor. 32, assistant professor. Assistant professor, yeah. He's only 32. I think he just turned 35 actually, so he's not terribly young, but he's incredibly energetic and enthusiastic.

50:00 Wish for rigorous foundations of continuum mechanics. And I must say, I've learned over the last 30 years to be quite cynical. I'm really quite enthusiastic that that regression is reversed. I mean, there's still some of those people there, I suppose. How was your model theory session at the Newton? It was still running, and I've really been very encouraged by it. I mean, all sorts of great young people on the way up there. I mean, a completely different kind of training. Of course, certain things they may be ought to know, they no longer know. I mean, certain things are the same. On the other hand, they are people who understand things like, you know, serious complex geometry and so on, There's a young guy, Ibrahim Moussa, he's now at Waterloo. He's doing logic, but a lot of it's been stripped away, you know, a lot of the nonsense. He's just so mature, he's a family therapist.

52:30 I mean, they've got complex geometers who now are trying to go back to classifications that people like Kadira and so on have done and understand them better in terms of things that come out of order here. It's really going very well. I mean, a lot of young people are not all sensationally good, but there are five or six people who are really... Many of them have been in the Midwest, you know, they've been at Urbana, from Ash and Branagh, and Scanlon. No, it's, I hadn't quite expected to see, you know, people just, I mean, it's like they hadn't quite learned those great geologists, but these people are absolutely secure. Six or seven of them are very significant outsiders who've come in and, and you've got some certain natural connections to what he's doing. He came and did something like this, you know, something pretty small.

55:00 They will go to the, but they will kind of go to the common theme one, that's the thing about it, I don't know who will be there, I don't know who's to blame for that, and that's certainly been out there for years and years, you know, back there and really do things in a way that people like that don't do, you know, two people who know, know well, but too many of them still do, and I guess it comes down to the shower, you know, anything you do with sheaves you can do, I mean, nothing could be more absurd. I think it's been a big influence. He may have been slightly overwhelmed. Quantum tori and geometry and stuff. I don't think he really sees, he doesn't really understand the connection. But still, it helps. You know, he has holes with new insights. And he's had a tremendous influence. And for Schatz's work, it would not really be possible. But just lately, he's tended to be a bit more coercive in a sense, imposing about physics, and he has no complaining about the call.

57:30 The language is slightly dangerous. Nevertheless, he has made a very good point. We have an excellent group. He likes coming back from the States. He's going to Leeds to have three chairs. I think it's fantastic that I've lost 10 or 15 years. Who's that? Anand Pillai. I tried to hide him. It's always purely and simply that one very general feeling that the great work has barely been scratched.

1:00:00 So there's this huge effort to get it all on the web. There's all these people trying to read it. Well, it's very useful when the circle is done.

1:02:30 You have all these things out there. ...circled it for most of the SGA and EGA that was providing URL. Somebody would have them scanned. Thousands of them. Yeah, yeah, yeah. No, no. What's the situation in the geometric Galois theory? Is that a thing? Yes, certainly. It's not there all night yet, but there will be coming up. And Polk is coming out there, and then it's kind of... Well, I mean, the only thing from directly within logic is that there's a guy, Koenigsman, a German. I'm not going to go into too much detail here, but I'm going to talk about some of the things that I've learned over the course of my career. I was involved in this about 25 years ago with Vanden Rees and Chern, and we developed what we called a co-logic for Galois theory, so the idea was to get a model theory where the Galois, you wouldn't look at the model theory of the Galois group of a field as directly as a group where you quantified over the elements, what was important was the profinite structure of the, some many-sorted motion of finite groups, and many of the main theorems in... Here we showed the things that Iwasawa had done with just the exact dual of cantos, back and forth, at the time it was just a technology, but he has begun to use this to give alternative axioms, sometimes alternative axioms, but you can axiomatize many things in terms entirely of the gauntlet. And he has recently come up with, well he hasn't approved it, but, and it's not, the thing is, what he goes to is not just me getting the field with Gallatin, but he uses this co-logic of ours where it's, you've got to have more than just the group, you've got to have the restriction map onto the absolute Gallatin, the prime field, and he has a very, very plausible projection of maximizing...

1:05:00 There are several power series over the finite field, which has never been done, one doesn't know. Things are quite healthy in this direction as well. I mean, there will be a few talks at the final meeting in July on this. But Pop is one of the main, he's done a number of papers on analytics. And they have really done a lot, I mean, this is typically one of those very heavy government papers. I mean, I talk of Marlow in New York as... I mean, these people have come very close to proving what we expect them to be true, and that isn't part of the logic. We can certainly take things from that into account. The Newton Archive, everything at these meetings, don't they? They're extremely good. This guy, Jody Bobring, yeah. Extraordinary, doing a good job. That's one of the reasons I wanted to stay in touch with him. I think most stuff that's been done so far is on the book. Well, I wanted to show some of this archive that I've been maintaining all these years onto the web, including that, well, some of it needs to be edited first, for instance, you know, the transcripts of your talks in, well, they're sitting there for the last 15 years now, 16 years, I would imagine, Cambridge, well, not just those, but others since, you know, some of, well, many of which, of course, have been written up, but not all, there have been quite a few that haven't. And, um, you know, there's... Yeah, it always bugs the hell out of me when people ask me, you know, well, have you bothered to record all this stuff? Because, I mean, anything that's of significance is always bound to get into print soon. It's patently not true! It has to go through a definite process. Exactly, it has to actually go through a process. I mean, look at Groton. It's easy to say that. Well, absolutely pointless exercise. Anything of significance will have obviously been written up as a result, so, you know, why is this? It can't be anything more than gossip, no, not at all. It would be a very valuable source, but because, as they say, anything from heuristic conjectures that didn't, at the time, lead anywhere because there wasn't necessary machinery available, or things got laid aside, or just things because people fell out into other different personal trajectories, or, you know.

1:07:30 Yeah, the long version, which I copied, in fact, while I was in Haute Bordeaux. Well, I was telling him 30 years ago when I was trying to learn this stuff, I was reading lots of his papers, among others, and just trying to get a grip anywhere, you know, and as I would read each one, I'd think, you know, I've got to come back to this someday and really get a cold. Well, that paper, I went back and got cold because I checked it. Every sentence, I knew what that sentence meant. We're TechTable's Phenomenology of Spirit. ...serious dedication. On the subject of that kind of scholarship, I'm going, sorry, off topic, what you've been saying, but your project of producing this new translation, and I think the intention was to have a critical commentary as well of the Ars Danings Lira, how far did it get? I mean, on the, you know, the papers that were available in, that your students, the translation, the new translation of the Ars Danings Lira? No, it didn't go further. There was a... The first one was published by an open court. Ah, yes, you did, of course, think what you're actually writing.

1:10:00 Think what you're giving a story about. I refused to write an introduction because I thought the translation was so bad. Yeah. You know, Steve Alden was actually a copy boy for an open court at that time, and he claims that he actually improved the translation by the time this was published. All right, I didn't study it in that way, but, you know, Hingenburg also did it, which was published in the AMS, in the, um, that's not the AMS, and so I, I, yeah, yeah, that's very much the story. I wanted to look that up in four weeks, just letting us know that we'd like that. No? Eight, nine, that's very good. Okay, now take it from there, Karen. I'm sure by the end of this week we will all have squared up with, you know, people buying. Thanks very much. Merci, Karen, merci à vous. And there's the French translation as well, which I think is rather good. We just go down that way and it takes us straight back.