Discussions, incl. FW Lawvere, C McLarty, A MacIntyre

0:00 Oh, in that case, that's interesting. Well, in that case, I'm very flattered that he actually listened to my accounts, or he was. He seemed to be a very genuine, you know, nice guy who was very eager to learn things. Somebody, I heard somebody, it might have been John Bell, told me a year ago or so that, you would know about this, that a comprehensive, sort of annotated edition of Clifford Truesdell's... The expected writings were being prepared. Is that right? Do you know what we've heard about this? I don't know. What? Yes. I talked with the widow. I remember when you spoke at his memorial meeting. Yes, I did. I like him really pretty irreplaceable. I met you and you were actually asked to come here. No, I wasn't at the memorial, but I met you shortly after. I met you almost immediately after you'd spoken. No, you came to Florence just after, well, shortly after speaking there. That's right. I mean, the widow Charlotte was there too.

2:30 And then again, you know, there are two major memorials. Part of a huge, huge meeting. Some of the same thought. In fact, many of the same. People from Italy. Does the young, very fine young note-taker and all-round good man, Davide Bernardini, he was already aware of Truesdell's work when he came to you, was he? Yeah, yeah. The inspiration for wanting to get in touch with you. Del Piero. Del Piero. I'd like to have got Davide Bernardini to come down and spend a few days in Fougere. I asked him, he said he had to go back to Rome. He really impresses me and I'd like to get to know him better. He never, I'm sorry, it's a very personal question, you say mind your own damn business, you should probably understand the answer, but he never, nothing ever went any further between him and Sylvana. He would have made a wonderful son-in-law, I think. ...entrepreneurship, to nightclub, yes, to being a nightclub. But he took it in stride. No, but they were, you know, they were together in Halifax. Oh, they were? Oh, yes, good, he came to the Halifax meeting. With us, I mean, the four of us, a lot of us. We went to Peggy's Cove, the famous, uh, weird, acclaimed lighthouse.

5:00 Ah, we did the sticky seat. Oh, yeah, there's someone, weird, there's someone doing it. The baggage code has now never changed in fame. It's the place where the twistor went down. Oh, I'd forgotten about that. And they gathered all the survivors. Well, not the survivors. The bodies, the remains. The bodies and the surviving pieces. The debris. Until they finally figured out, by the way, that the cause of the television was the individual screens. Which they, you know, the things at the back of the seats. No, I don't, and I don't recall you telling me. You might well have told me, but I forgot. I found it fascinating. Well, the Germans had long telephone lines in outer space, as it were, and they whistled dark high and go down, successively longer. This has outer space, but it has a hemisphere. Yes, I do know that name. Who worked out and studied this phenomenon and published it in Nature. It's fascinating. The thing is that the, uh, okay, you have, I mean, the lightning, it just crashed with frequencies mixed into each other.

7:30 I wish my father was still alive to listen to you explain that, because he loved studying this kind of thing.

10:00 He was just so fascinated. Radio and sound waves were one of his great delights and interests in life. Incredibly fascinating. And the fact that, you know, even what I just said, the fact that you could really wave audio to my mind. Normal, you think, well, one has to be used to modulate the other, and then you detect and demodulate and all this stuff. I actually built an audio amplifier for the purpose. One problem with this is that it's hard to hear it in the city because of the interference precisely from the 50 or 60 cycle power lines, which also produce plenty of waves of audio, low audio frequency. I'm sure you can do it nowadays. Totally suppressed power line signal in the air. So the thing to do is to go out into the wilderness somewhere far from electric power lines. So I did this in a state park near Wilmington. I found a fire tower. I went up in the fire tower in the middle of the night with a long antenna. I hung this antenna on the top of the fire tower down in the wilderness, in the forest. In the car radio, I had unplugged one tube and plugged in another one somehow so that I could directly use the audio part of the car radio. This is the sort of thing my father would have spent. I love it. I still love it. No, no, of course. If I had time, I'd build one again. But this is exactly the sort of thing my father used to do. He used to build antennae and go out and I don't know if he was ever aware of this phenomenon. I think probably not. But listening to you so often reminds me of him. Well, his enthusiasm is tremendous, of course, he never has.

12:30 Well, a miracle of physics is that a crash can be turned into a whistle. Into a whistle, yeah. So, I did this in 1955, and I did this exactly 50 years ago. Oh, my God. 50 years ago. Yeah. Well, you were a very young man. 50 years ago. Oh, my God. Anyway, so I knew the literature up to that time, and then slightly thereafter. Seattle, Washington. Washington. You know, listen to these things for a long period of time and try to quote them. There was no correlation whatsoever at that distance because these are too far apart. So that sort of verifies the general geography of the things I was telling you. And by contrast, there were simultaneous observations in Alaska and New Zealand. Both the odd and even things, but the number of signals is almost completely coinciding. Thus confirming stories, I can't do it. Not that you're magnetically counting a sign. What story, I have, I do recall reading a little bit about the story. Was he, was he a student of Heaviside? Was he a student of Heaviside? Heaviside? I don't know, but I have a... Heaviside had students too. I was just going to mention that beside the next breath because it's obviously a continuation of the spirit. Well, that's why, of course, I asked the question. Well, and even the connection with long-distance telephone lines. Well, that, of course, was precisely why I asked the question, as you very well knew. I had also a recollection of, I think I've only ever read about the story in one place, and I could be wrong. What he might have said was just that, you know, his work naturally, you know.

15:00 And I looked into this again about maybe ten years ago just to see what was further advances that had been made. And what I found was it was used for measuring all kinds of things. They go on up in the upper atmosphere. Oh, you know, electrical engineering is so advanced. All sorts of imaginable and inimaginable measurements based on Aristotle are studied with the help of this phenomenon. You see, I mean, you could consider it part of electrical engineering, part of geology, or part of atmospheric physics, which of course is real physics. Real-world physics. Oh, that's absolutely fascinating. You haven't told me about the whistling, the whistles. I would have remembered that. I would have remembered that. That definitely has to go into my autobiography. That definitely would have stuck in my mind. I would have had to do it. I have a summer job with the chemistry department which involves certain ways of measuring undergoing chemical reactions. ...which involved audio frequency. I had this amplifier typed in the chemistry lab sometimes. I borrowed some huge batteries from the physics lab.

17:30 This was before you were working as an assistant on the cyclotron? No, just after. Oh, just after? So you were even younger then. No, come to think of it, I wasn't. So it was 1956, hmm. That's very interesting. Do they still use that technique of kind of sound... There are sound waves to probe reagents, the behaviour of particular reagents. The reason was that the... That was my father's other great love, was chemistry. He got all the school prizes. I never pursued it. He, and so did he in fact, was the great of his life because he got a scholarship to go to St. John's Cambridge to read... He had decided he would study chemistry and he got the top scholarship in chemistry in his year but was never able to go because the scholarship was still a very small amount and his father, who a year or so before had been easily able to afford it, was wiped out in the crash, in the 29 crash. ...because his idiot son, my father's elder brother, gave him terrible advice and got him to invest all his money with this crook, Akron, lost everything, and as a result of that, my father was told, you know, having spent two years, you know... ...study and getting school prizes in maths and in chemistry and science, and wanting to devote his life to this, that he was suddenly told that he was not going to go to Cambridge as a student after all, because there was no money and the family needed him to go and work as a clerk in the city because they needed the income, whilst his darling older brother, of course, never did a hand's turn of work in his life, so I'm not surprised that he was a bit embittered.

20:00 Does Peter Johnstone know about this? I've never talked to him. St. John's? No, it was my father's non-connection with St. John's. I've never got into a conversation with Peter Johnstone about my family history. I like Peter Johnstone enormously. In fact, I've really warmed to him in the last ten years. The first time I met him, I thought him very forbidding and rather scary, He doesn't mean to be far from being arrogant. It's just the opposite, really. He's just a very shy person. You know, he invited Peter Pride to stay at St. John's College. Well, this is Peter Pride. He's more Joni-ish. Yes, the new Peter Jon- I'm sorry. You can be indifferent to this sort of thing. You can be pretty indifferent to it if you want to be. I can imagine him entering into that kind of Oxbridge High Fable game rather readily. Still, it's the college that had Dirac as one of its... It's a great college. No, no, you certainly hadn't told me that before. It's very, very interesting. I'd like to... What did story do? I'm trying to remember. I'm trying to place story on my... I'm a sentimental man, because I'm sure I've read a couple of short articles about him. EY. I think it is.

22:30 He died very young, didn't he? Oh, relatively young. Well, again, it was obviously Google. I'm just wondering whether I've got him... And this work, explaining what the Whistlers were and where they came from, was done actually during or just after the First World War? I think in the 20s. In the 20s, yeah. And the British would have been quite happy to let them believe that, of course. Yes, because obviously one of the disadvantages that the Allies labored under in the First World War, by comparison with the Second, was that because the war in the West was, for most of its duration, except at the very end, at the very end and the very beginning, Almost entirely static and attritional behind the front and on both sides was affected by landline because radio is it yes that's that's it oui merci the opportunity for eavesdropping on enemy radio communications and gaining signals intelligence that way which was hugely greater in the second world war because of the um this is absolutely fascinating i really want to learn more about this No, that name also. That name also rings several bells. E-C-K-E-R-S-L-E-Y. Yes, yes, this definitely rings several bells. I'll get onto the Google when we get back, unless you want to just take a short siesta. The Germans themselves... Yes, it's curious considering how good their physics was at that period. They didn't realise themselves. Of course, their country had been introduced. They had to pay...

25:00 Well, of course, the fact is they never did have to pay it because the whole plan of reparations was so insane that they had to pay for the ammunition, the license, was it Vickers? It was Armstrong. It was Vickers Armstrong. It was Vickers Armstrong. It was Vickers Armstrong. But of course, that also operated the art. In fact, it's very strange that you should mention that. Almost uncanny that you wrote that. We talked this morning about that topic. The British during the First World War, not all the way through, but until I think until 19... Alexander the Great. Maybe that's where this one world stuff is coming from. Of course it was the Hellenistic, it was the 4th, 3rd century B.C. equivalent, wasn't it? Have you seen this movie that Oliver Stone made about Alexander the Great? It's not very good. It just came out, right? It came out about six months ago. Yeah, it came out a little bit longer ago. Yeah, it came out six, nine months ago. There are several of these movies. Yeah. You haven't missed a great deal, but it's... There was one about Troy, I saw that. That was awful, that was so heroically awful that the Alexander the Great one looked quite good by comparison, but only by comparison. But it had the usual, it had the great and good British knighted actors like Sir Anthony Hopkins and people like that. And it had a relatively unknown Irish actor called Colin Farrell playing the part of Alexander the Great. The woman who played his mother, Philip of Macedon's wife, in real life was about three years younger than he was, the guy who played her. It was badly cast and badly acted, but the special effects were spectacular because they used all the graphics to create the battle scenes like the Battle of Issus and the spectacular scene from the Bird's Eye View.

27:30 But the line that was peddled was exactly this line. Here is this visionary guy who has this agenda of creating one world for all the peoples. Well then, he's a really good, no he doesn't, at the beginning he's got this, he's got this teaching, he's got this, by Aristotle, teaching to him about the superiority of the Hellenes, and also played by Sir Christopher Plummer, scenes of the young Alexander with Aristotle, which were hilarious, which were mainly geography lessons. The suggestion is that, which I think is correct, that Aristotle's geography was... And this is one area where you don't really want to always question are you on the way from or to first principles, there's one subject matter about which it's not always a very good idea to ask that, that's the really fact-rubbing stuff, and because Aristotle really thought he did have first principles in geography, he was convinced that the Okeanos, the old ocean, must surround all the land of the earth, and this, it's alleged, was the reason why Alexander was so determined to keep going. You know he wouldn't give up when he got to the Hindu Kush, he wouldn't give up when he got to India, he was quite certain that when he got to the top of the next mountain range he would see the Okeanos, he would see the world ocean, he would have come to the end of the entire earth and he would have copied everything and then he would then he could begin making the one world, the one complete political of all human beings I was wondering about that the other day. Was this primarily motivated by exploitation of these colonies? Was this the main goal? Was it really just what you're saying? No, I don't believe for a second it was that. I just think the guy who wrote the script has just decided that's his theory. It's total speculation. There's nothing whatever as far as I know to base it on. But he's just decided since they told him that this has got to be a kind of prestigious movie and it's got to have a few. ...serious planes to... ...collecting tribute from all those places. Yes, although, of course, the Persians had already established an incredibly efficient system of communications and of posts,

30:00 and a kind of postal system of astonishing efficiency. It's a matter of kind of stealing that. He was just basically taking it over. Which is why he did, of course, soft-pedal the Hellenization and insist on his generals and commanders all marrying Persian wives and trying to create a new cosmopolitan elite. No, it's a very flawed movie. It's pretty crummy. It's not as bad as the Troy thing. It did very badly, apparently, in the U.S. because it was a CD, allegedly. Christian Wright didn't like it because it made, well they didn't go into any actual heavy bed seats, but it made it pretty obvious that Aristotle, sorry not Aristotle, Alexander, like all creeps of his, you know, was homosexual, or bisexual, emotionally homosexual, was in love with Hephaestion, you know, big deal, I mean, a lot of tedious, smouldering glances and, you know, whole lives between them and, you know, a lot of kind of heavy, but nothing... Nothing too, nothing too, but just enough to upset the kind of people in the Christian right who get set up about these things as promoting a gay agenda, so that didn't do good for it in the box office. It's funny because I remember hearing that somebody was going to come out and say what they were saying about this. And maybe it never actually came to Buffalo for any sort of reason. No, that's right. It never got a general release in the US precisely because they didn't like what they saw as the hemigay theme in it. I have to say, you didn't miss much. But there is the scene at the beginning where Ptolemy played by Anthony Hopkins in his old age. This is looking back from about 40 years after Alexander's death. I was sitting on the balcony of this palace in Alexandria watching, looking at the Phaeros, talking to his librarian, the guy who's sponsoring all the learning of the world at this library, and saying this tremendous vision of universal learning and one world, this is all made possible by Alexander. But of course we had to kill him, you understand, we had to poison the guy, because he'd gone completely crazy and he wasn't going to stop, and we realized that we had to do something about it, so we got together and poisoned him, I'd say.

32:30 Speaking of power, when Bernard Heaney and Solaner, Autumn and I, went to Peggy's Cove. Yeah, yeah. So, Peggy's Cove has always been a place where there's practically nothing there, and it's just some of the math. How did one pass from one to the other? While most of them are effective, the fundamentalists in this regard can also comment on everything completely unprincipled and they are expected to be accepted. As Tom unfortunately did, undoubtedly. So George was certainly like that, apparently. I didn't know that. I didn't know that that had happened to Laurent Schwarz at all. It was quite clear it happened to René Tom. There's quite an industry erected around his pronouncements. I know that Cartier has a dim view of Laurent Schwarz for various reasons. One reason you have to do it without hearing him more than just personally. More privately, in fact, the writers to the support. Something like that, I mean, this was Cartier told a long story. You've heard Cartier's account of how Sayre summoned him to his apartment whilst he was fighting in the army in Algeria to meet Sartre and de Beauvoir and to argue with them about the Algerians. Has he told you this, sir? No, I didn't. Oh, no, he told me this about the first time I ever met him, which was, in fact... At the meeting where you spoke, just after the talk in Nancy, you gave a talk at the École Normale Supérieure, you probably remember about a couple of weeks later, just before we went around Paris to look at the places connected with the commune.

35:00 Well, that evening, Cartier sat next to me and was very, very... I was the only non-mathematician in the world, and he could easily have just ignored me, but he got chatting, and one of the stories he told me was how when he had, having delayed his military service for several years, he decided he couldn't delay it any longer, and he did his national service at the period of the Algerian War, and could have done it in the engineering branch, but decided he would do it instead of... There were many, you know, debates, intense debates within the party at that time about the Arcturian War, was it, was it? Yeah. It wasn't simply a, you know, a simple open, oh yes, I don't want to give anyone time anyway, what is it? Who was there again? Oh, shoot, that means you're up to date with siesta, I'm sorry. Half an hour maybe. Okay, let's go and do that. Actually, I find ten minutes. Yeah, yeah. You probably could just sit in the chair for ten minutes and close your eyes, you'd benefit from it. Well, you prefer to lie down. Okay, we'd better get going. I'll tell you the rest of the Cartier story later, there isn't really much to tell except that Serre comes out of it very well because Serre was so angry at what he saw as the total pursuership of actually de Beauvoir more than of Sartre on that occasion that he ordered her out of his apartment, just literally kicked them both out of the door. Because they had started abusing Cartier, and in de Beauvoir's case, allegedly, had actually started making directly anti-Semitic remarks. ...to Cartier. And so, just, you know, wouldn't stay anything longer, so he just kicked them out, even though he, of course, was an opponent of the Algerian War. But, anyway, Cartier probably told you the story himself at some time. Oh, I didn't hear that story. No, no, he did tell me that. He told I had to tell several stories, but I forgot how to deliver that story. Well, it'll come to you, because you're concentrating on driving, that's why.

37:30 Yeah, we're okay. Let's go straight ahead and... And does she have an interest in foundational machines at all? Oh, possibly. I mean, I'd love to get in touch with her and see whether we couldn't... I couldn't get something going together with the University of Rennes. I'd certainly like to get in touch with her. I mean, one of the things I had seriously... One or two other people around her. I had certainly known that there was a small group of category theorists in Rennes and that there were people who worked on real algebraic geometry, but my lack of confidence in French prevented me from approaching them and saying that you'd be interested in what I'm trying to do here. Very, very kind. She was still in Paris at the time, but she moved shortly after that to Rennes, where she had a permanent position and her husband too. He's called Rochelle, and she's called Francoise. Well, while you're having your forty winks, I could quickly Google on University of Rennes categories. With a bit of luck, I could probably find out for you. Oh, that's where you can find stories as well. Yeah, that's exactly what I was going to do. So if you just take a very quick twenty minute lie down. We should probably, yeah, because we're going through the center of Rome, we should probably still aim for leaving in half an hour if that's what we're going to do.

40:00 Can you, ah, damn, he's taken our parking space. No, you won't be able to squeeze in there, will you? I don't think so. No, I think we'll have to go. Hmm. You don't have a very clear estimate of the length of this car. Ah, hmm, it looks like one of those stations. Yes, that's the damn news. To be sure, it's much easier to clear up all this stuff and take care of it. Yes, that's the other news. Well, I know I can take care of that. Well, I can't go here either. Yes, you can. In the garage. Yeah, but hang on. We're only going to be here half an hour. No, if you pull up in front of... No, you can leave. No, pull right up behind this guy. You'll still have the garage. Yeah, it's a very short car. And if you pull in right in front of this guy's front door, you'll still leave the garage. And just go straight in the house and take your 40 wings off. Get all the stuff inside. No, no, no, you won't. Look, you need a little bit of brass belt. All right, give me the key. I'll do this. And you just go and have a lie down, and I'll call you in half an hour.

42:30 The menu of the season for me, please. First, marinated salmon. I know, it's a problem and you have it?

45:00 No, no, it's fine. Ah yes, it's good, yes, yes, I chose it. It's good because this is the one I like, grilled pork, well grilled. And the choice of dessert afterwards. Is it possible? Yes, it's necessary for dessert afterwards. Okay. Okay. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Do you want to have the entree as well? If you're ordering if you're ordering from the set menu then you know you're doing yourself out of the because it's a set price or if you wanted to order out of cart then if you order from the set menu then the entree is you know included so. Here is It's a wonderfully strong set of semi-soft cheese, and with the local ham, Bandian being the name for this region a little bit further south. It's very nice, it's very interesting. Well, I think we can either go for this deal where they give you a selection of three different wines for an additional eight or... We can just order a bottle, it's up to you. Well, you, hang on, you guys are having, you're having the coquille? Oh, sorry. No, the Tuscan custom, the red goes with the blue. Okay, and you're having, okay, we'll go for the red then? Red, yeah. Red will be okay, I don't know about that. I'll have a bottle of, the wine, this here is very good, too. No, no, it's okay, no, no, I don't know. I'm going to get the house ready if you don't mind, sorry guys. I have to budget his spirit is willing. Yes, the red of the house, is it the first or the second?

47:30 Do you have a good proposition for a good talk? Chez Berni, very well. Otherwise, we have a name too. Sorry, excuse me, I can't hear you. Chez Berni. Ah, Chez Berni, Chez Berni. No, no, no. A Bourgueuil. Ah, where, the Bordeaux? Bourgueuil, Bourgueuil. Ah, the Bourgueuil, OK. Cuvée Marguerite. But not... He's 22. The Bourgueuil, he's 22. He's going to have a spirit there. OK, we'll choose the Bourgueuil. Do you have a burger? Yes, of course. And for me, a gas burner, please. A big gas burner, please. Still water or would you like more? Still. And no gas burner. A carafe? A carafe, no gas burner. This burger is the bottle. Did you order? A burger? Yes, a bottle. No, I thought you might have got the idea we wanted to talk about this. Thank you all for your dessert. No, no, we can do it. So on the Amazon, did you notice, I think it was on the first page, an exposition of the Church for the United Nations? Yeah, I didn't see a way for the Miss Patricia to use it in the Ohio school board fight, but certainly... And from which church was he? From the Presbyterian? Congregationalist. Oh, Congregationalist church. In the United States? I wasn't sure how many generations of his ancestors have lived in the United States. I was going to say, on the biograph, well, there is, I'm sure you know it, quite a longish paper by Max Kelly in the Selected Papers, a little sort of Selected Papers, an essay by Max Kelly, sort of a category theory, which is...

50:00 Well, it was published in 1979, but it only really deals with, it doesn't touch on topos theory. Well, this paper I wrote is, it's about philosophy. Now, I can't watch it, but it's probably somehow for us. Yeah, I mean, anything you write. Yeah, which is true. But, that's what I wrote. I'm trying to convey this novel story. Well, I found the Max Kelly paper very, very helpful. It's one of those things I thought we might hear whether you think it actually gives up. This is the first overview of the history of the Bussamy Island book. It's just literally two pages long. It's called Saunders, MacLean and Geometry. You can see the title in the book. And the opening, it's just... I agree that we never talk about... And we never talk, you know, about... I did very good work in geometry, you know. I scarcely exaggerate. No, you have it. No, it's... It's interesting. I kind of suspect there's nothing to know about which one did which, except to tell the whole detail of the story. I expect they were so interlaced. In fact, he does say one interesting thing in that paper, which is, when it came to doing calculations, I could do a prior calculation and so on and so forth. You know, I was never any good at that at all, yeah, but I did, I did, that's the correct kind of concept, yeah, but, you know, Samir, he doesn't really say much, he doesn't say quite a lot, except I'm interested in it.

52:30 Considering collaboration, I think my collaborators are unjustly neglected. ...containing one article on Brodendieck, explaining the history of Brodendieck, because this article mentioned topos, but indeed, he notices, has this thing called, what is, what is a topo. So this was recently, then, yeah? Oh yeah, last year. So this was only in fall, after he said it. I'm asking myself now, did I see such a thing? But I'm not saying it's about you, I'm saying it's about you. Yeah, most of it. There are four descriptions of what topos theory was 40 years ago, and then there's the last paragraph, which dismisses everything that happened after that, the mere logic, the usual sort of disdain of the anti-physicians. No mention of tyranny here, it really happened. Yeah, I'm going to try to figure that out again, I want to know. No, I understand your point, yeah. Well, it's inexcusable, but at the same time, do you think it might reflect, to some extent, what you were talking to him about last night? No, I mean, he didn't say that.

55:00 I'm saying, do you think it might reflect the influence of that? It might. I think it was more the influence of the lead test. Grounding several NSP reports several times calls for people to work out some point of categorical logic, but in kind of a page 90 way, he says, you should go do this because I don't want to. Sorts of interesting things are not being investigated, particularly the boundary operators. There are really huge holes in what has been investigated. Well, the boundary operator is what gluing is about, though, isn't it? Am I, am I not that right, or am I not the one? You move along a boundary. No, no, but the open and close is a very, very special case. Okay, right, yeah, yeah, yeah, yeah, yeah. No, I mean, I said, as I said, I think this would have many ramifications. One is, one is for, again, you know, for model theory, because one can more or less identify gluing with the model theory. So, therefore, subtopos, as you see, are model classes, represent model classes, and so these model classes, so, in theory, if you take the theory of...

57:30 The theory of abelian groups should have a boundary, probably in many cases advantages, but in principle there is a theory, among positive theories, by the fact that that's a restricted class, you get an interesting population, so there's a co-hiding complement of every subject, whatever it is, for a group to be non-abelian in a strong sense. And then you intersect that with the abelian groups and you might get something. You surely do get something in some cases. In that particular case, I don't know, but... Again, this has never been investigated. I don't even want to... Well, I thought of an example the other day that might be. I've been worrying about this for years. I've been advocating and others should be looked at. The point is that when I gave this talk, here were all the professors. Some of them were totally shocked. They never realized this fact. They were contented with the fact, well, it's a hiding out. It turned upside down, wasn't it? But if you look at it, not just formally in the sense that it turned upside down, but sort of materially in an actual subject, that's where they go. No, an example I had was, it is related to tropical geometry and probably this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this. Thank you for your attention.

1:00:00 Of course, we are advocating in general the study of algebraic geometry over rigs, not just rigs. Absolutely. Sometimes the most interesting thing to use as a base rig is one where one plus one equals one. Actually, as Samuel showed, it's not entirely trivial here. If you look at the category of all rigs, that's what are the simple ones. Well, of course, there are all the fields, and all of them are simple. The rings are the main simple rigs. There's only one other example, namely this two we call two. But, of course, there are lots of two rigs that aren't distributive lattices. In general, for, you know, k rigs, We were talking about the monoid rig, you can take an arbitrary community of monoid as the multiplicative, you know, the gradient for a multiplicative and take the k-linear combination as an example of a free k-rig, for example, for that. It's not so a priori finite, although within it you can obviously... There are varieties among that, or much, much better, they're what I call a core variety, meaning that not only does the inclusion have a left adjoint, as is always true, but also a right adjoint, but it happens to be an intersection, the distributive lattice is an intersection, so you, when we say, when I say less than or equal, this is the definition of additively less than in terms of any rig. It could reduce the triviality of the ring, x less than or equal to y, if there exists an a, such as x plus a, so if you put x less than or equal to 1, there's an axiom. That obviously gives you another variety within two rigs, but it's a core variety because if you just calculate, you can see that if you take any rig, any two rigs, then a set of elements would satisfy that equation, closed under the operations equation right at the end of the equation. One of the important things about core varieties is that it means that the...

1:02:30 The tensor product continues to act as the co-product, so that the inclusion preserves both limits and codes, so that you have some chance of understanding it. Okay, so the lesson is equal to one. If you start, well, that sort of looks like an interval. So algebraic geometry over this means that, well, basically you have an interval and have cubes, products of cubes, and then you define subvarieties by means of equations involving supes and multiplication, the ordinary multiplication and the interval, and supes. So you came at this quite independently. Yeah, we came at this, you know, just out of the interest of the subcase of the program. That's something like a topical. It's not exactly what they do. What they do is another instance, just slightly. It uses reals instead of pure twos. But this was a sub-case of the program of objective number theory. Yeah. It includes algebraic geometry with a rig. Okay, so now, but on the other hand... Well, x greater than or equal to 1 is not going to be a poor variety, but if you throw in 0, intuitively, it would be 0 or greater than or equal to 1. It means that... It means that x is less than or equal to x squared. Take a rig where we're all in the rig, x is less than or equal to x squared, so there's nothing in the open unit interval. There's zero in all the positives. The integers are an example, I mean the natural numbers are an example. So again, the part of any two-rig that satisfies this is closed under conditional properties. You have a core variety. To be a distributive lattice turns out to be equivalent to all elements are closed under conditional properties.

1:05:00 And so, it's an intersection of two things that sound quite complementary. So, indeed, it's an example of a boundary. All we have to show is rigorously that these things are x greater than 1. In fact, we call that a complement. Which could well be true, that is. But there have to be loads of examples of boundaries, because if the boundaries are ungifted, you've got to prove the boundaries, and stuff like that, you know. For one country, we were basically... I noticed I was being chronicled. People like to say, they already said he wanted an algebraic geometry over the integers, but in fact he wanted it over the natural numbers. It's actually about rigs. Again, I don't mean just amount of numbers. You take any ring even, actually any rig, for example, an algebraic integer of some kind. The very idea that ideals are ideal elements. It means that, you know, taking principal ideals, it is a multiplicative, preserved multiplication. It's sort of what you were saying before about the group structure, that thing with the ring structure. There seems to be a lot of examples of that in particular. Let's say, for example, the principal ideal domain. The associated two-rig of ideals, and it's always a two-rig, but when you add ideals, it's an idympo, which is, the addition is an idympo, that's what it means to be a two-rig. The fact that it is principal just means that the principal elements of this larger two-rig of ideals are closed under addition.

1:07:30 Now what's this addition? Greatest common divisor. So the fact that you have an operation called greatest common divisor means that this two-rig structure, but you can make it explicit, that's what it is, it's a two-rig. So in some sense from the beginning, it's been about not just about... I've just been trying to write up something about monochrist divisors and philosophers. You know, we're trying to set and think, okay, I mean, the GCD is the sum. How do I make that mean something then, you know? But, you know, let's put it in that context. The dots have lost us, unfortunately. And they'll stop reading, but... I think in 1921 Bertrand Russell announced that you couldn't possibly be a philosopher in the 20th century unless you read Wittgenstein. Well, we need something far more radical than that. You can't be a philosopher unless you know some mathematics. Especially philosophy or mathematics. Now there's this incredible belief that if you write about the philosophy of mathematics and mathematics, you're going to be good at it. Yeah, the chair of geology at KSY mentioned what I did. He said, to do philosophy of math, do you have to know a lot of math? I said, well, it's a debated question. Is it David Kornfield or something? Kornfield, Kornfield. Philosophy of Real Mathematics. To what extent did you influence him? He certainly gives you quite lavish... Well, I made him co-investigator on an age grant, so...

1:10:00 Plus, I mean, I'll talk to him about his stuff. If he goes to both philosophies and mathematics, I'll just... I'll just blank out, but... What do you think of this so far? I've only read the introduction of the beginning of the first chapter. It seems to me pretty sensible so far. He is overtly contemptuous when he talks to philosophers. I see. This is related to having no job, aren't they? Yeah. The other thing which is related to him having no job is that he has to say it really understandable. He wouldn't have been conned into believing that n categories are the great things. His heart's in the right place, but I just wondered if he was going to do it. He's way ahead of the market on that, but no, he doesn't know as much as I would. He wrote this big book on operational quantum logic, which I think was, you know, mathematically... I didn't find anything in it that was not fairly trivial, but he did give a bomb talk behind the crowd, which Chris Johnston listened to, and you might have asked him about it, because obviously he's several orders of magnitude better qualified to judge than I am, and Martin Heiland was there as well. He gave a talk. Which was, in some ways, quite a philosophy of math talk about... No, no, he gave a talk comparing the program of, what do you call it, the Lorvier perspective on the direction that category theory should take in correct generality, Cartesian closed categories, with enriched category, the enriched categories program, Kelly, and the Benabu.

1:12:30 There are five categories, contrasting those three approaches, offering his observations on the philosophical motivation and overall conceptual picture underlying each of them. And I did not unfortunately hear the talk, I only heard about it afterwards. And I was told by, not by Peter Johnston, I didn't speak to Peter Johnston, but I did speak to Martin Ireland, who said he thought it was a very good talk indeed. I always wanted to get him to repeat it, but every time I pressed him on the subject, he's always evaded it and retrofitted, so no, I don't think I want to give that talk again, and I've given this a pity, because I think it sounded like the sort of thing that technically competent philosophers in maths should be discussing. Would you say that a leg, an arm, and an ear are approaches to the human body? No. I was simply reporting his use of them. No, I wasn't blaming you. I assumed you were faced up with faith. Hmm. You're very bad in that, in that form. But, I'm sorry, you'll have to, you'll have to... Vibrations, topos, and rich categories are necessarily organic parts of the categorical approach. They call each one of them an approach, which strikes me as... Yes, that's a good one. Well, he clearly thought he had something to say about the different ways in which one might envisage them all fitting together, and I, as I say, I wasn't there to hear it, I mean...

1:15:00 So the best way to envisage that would be to study some mathematics. I'm trying very hard to understand why Plato gives so much attention to mathematics. Why Plato gives so much attention to mathematics. Assuming there may be something to it, and something that will be found by thinking very hard about it. And assuming that you did know a little bit of mathematics, but yeah, this idea that you should learn some math, you've got to weigh it off against, you know, other curveballs. Physics is a pretty shovel. Mathematics is the most stable and enduring system of human concepts. Well, this is actually a problem to Plato. He calls mathematics fixed, which I looked into this word fixed. Mathematicians use fixed hypotheses which prevent them from seeing reality. And the only other place he uses that word fixed in the Republic is for the prisoners in the cave whose heads are fixed in place, staring at the shadows. Now then, what I want to say is, OK, but Plato also knows, perhaps, the aetetus of the Existence, probably Eudoxus. Plato knows that mathematicians' hypotheses aren't quite fixed. But to the extent that they're fixed, fixity actually keeps you from seeing what is. And so it becomes very important that they aren't really fixed. That one mathematical proof depends on one set of assumptions that will, in fact, change during the course of it, but that the assumptions do change over the history of mathematics.

1:17:30 Sometimes into contradictory assumptions, other times into better enunciated, but I mean, they do change. One crude question. Given what Plato says about the intermediates, Do you think that he had the view that there were general identity conditions, conditions of identity, non-identity, for mathematical objects in general? No, I think he means intermediate real seriously. They aren't one thing or another. Exactly. They really aren't one thing or another. In which case, did he have some kind of theory of relative identity for them? No, no, they just aren't one thing or another. They just aren't, no. And what dialectic does is it treats hypotheses as genuine hypotheses, which means as stepping stones and launching pads. I mean, the Greek is untranslatable, but launching pads is as good as anything. It's the root of the word hormone. I mean, stepping stones and hormones, if you want to translate it that way. Yeah, real hypotheses are stepping stones. They're not something that you leave fixed and just draw conclusions from. But if we suppose he knew these people, he knew that mathematics does that too. But not in the course of one proof. That's the stable part of it. In other words, the whole method of changing the axioms. I certainly remember the first time hearing you use it in college. I went back to James Clark Maxwell and read where he says it is. It's wonderful. No, but the intermediaries, isn't it sort of like Giordano?

1:20:00 They help us by bringing it within, in some fashion, within the realm of appearances. It's the boundary between. Plato calls them summoners. They call us to think. They call us to raise our minds. Namely to believe in heaven. Mahill said they need our help. These intermediate things are qualitatively more powerful than us, so we cannot question, absolutely, determining what God himself is supposed to be. But since they need our help, we have to organize and build churches. I mean, if everything were determined by God, this activity would be pointless, right? We need the intermediaries for that sort of thing. Well, of course, it leads back to the old theological speculations as to why should no perfect being create a universe, as it were, different from himself. Well, this makes me think of the sort of Feuerbachian meaning. Not obviously lacking, yeah. With Kronecker, and I've got some encouragement on this, Kronecker apparently did say, it's reported by Weber with a date, that God made the natural numbers, the rest is the work of man. But from a Feuerbachian point of view, what that means is, the natural numbers are uninteresting, the work of man is these other things. Yeah, I think that's a rather heroic reading. Oh, yes, that's right. The use of the word natural for that. I mean, a chronicler actually used it, I think. Actually, I'm not dead sure now. That's a paraphrase of it. I think it must have been introduced just shortly before that. It's not used in the 18th century at all. I don't think so. It's never used by Euler or by Kant.

1:22:30 It couldn't be used by anyone who was uncomfortable with the irrationals and negatives because they wouldn't be another kind of number. There's got to be someone who does, who is used to other kinds of numbers. Yes, and who has got that sort of take on systems of numbers. Right. So we're not trying to... There's a lot of work to squeeze into the mathematical numbers. Yeah, that's right. It's kind of like a big lie, you see, you keep repeating it, so that sort of thing, you know, without having defined it, that might mean you certainly never have improved it, you know. I actually had a philosophy math class, one of my students very knowingly said, of course, we can't picture things in four dimensions. And I said, you have never seen anything in less. They got the point. You have to do something to wake them from their dogmatic slumber. That's very good. You have never seen. They did get the point straight away. Well, they were reasonably bright students then. And this idea that you can't picture the complex numbers, and Gauss already says you can, and Feynman in his little QED calls it a clock face. Well, he's talking about the unit complex numbers. He calls it a clock face. It's not a hard picture. Right. That's amazing. That's amazing, you know, what one can picture. Well, actually, the example that you gave this morning of the Coxeter's illustration of the, you know, the space grips, just in terms of the, it's full of mirrors, two of them, one mirror and the other mirror, so that's the reverse, and so you do this, you have exactly the right angle between them. Any intelligent child can see that this would be exactly how it would go up here, exactly how it would go up here.

1:25:00 That's sea salt. You shake it off. Or you dip your... No, you just shake it onto the food. You start with a rig, and suppose it contains at least one top element. The top element is one of everything else. Since the glass less than or equal is not definite, there are lots of these two. They have these top elements, and then among the top elements... We have what I call, I should call top zeroes, top ones, something which, a top element multiplies by any top element itself, so I think things are within, quantifying doesn't really seem to be the answer, so. Oh, you're having the same ones. How are you doing, Jacques? The striking thing is that you don't have to do anything except... It's very hot. The top zero, the top one. The top minus one. Oh, really? So there's all the top elements. You can imagine the so-called natural numbers are outside of that. You have zero lines on that side, and you come to these infinite things, but they have rings of a ring, and this is just a problem with real-time mathematics, but I like the point is to focus on it.

1:27:30 That's the last thing I think of putting it on. If you ringify, in other words, you force the ring to be a ring, then that's the ring that you'll get. So you have a map from the rig onto a ring, which doesn't have a ring section, because it has what we call an Euler section, because it preserves plus and times, but not zero and one. Not only that, any range can arise that way, including algebraic number fields and all that sort of stuff. It's a completely different sort of... We've never seen anything quite like this, even though it's utterly trivial, which is in common. An anticipation of some of the ideas of objective number theory and the grassroots field of numbers.

1:30:00 He cites him as the source of this idea of abstracting using isomorphism. The first occurrence of the term whole, sorry, of natural numbers occurs. What's the, what's the earlier concept on which this, the Marxist, didn't?

1:32:30 Yeah, I was going to say, is it not whole numbers? When do people stop using them? This is not, I don't even know who first talked about imaginary numbers, it's not an imaginary number, it's about a sphere. They're far real, aren't they? Yeah, yeah, so that's the contrast. I mean, it's a silly name, but... See the nice perniciousness of that? Mm-hmm. Go back to the whole idea of what does arrhythmos mean in different mathematicians. If an arrhythmos is a collection of horses, you can see the attraction of saying there aren't negative collections of horses. Yeah. Thank you for your attention. You were saying to me that the builder, Steve Chaniel, now considered that his construction should be called the Eudoxus.

1:35:00 Not the real Eudoxus. The real Eudoxus. Interesting. I'm sure he told you that, didn't he? Yes, I think I will. Yes, I think it's much proof. Well, I said you go into the decompression chamber gently. After that, we'll do it. Thank you very much. The red line on that field is on the other side of it.

1:37:30 I thought it was safely below it when I left. No, no, it's the one that's traveling, it's the one that's passing. I'm certainly not suggesting we should eat here every night. It was open and it is now. It's a very nice place. How did you find your way here? Did you have some family connection? No, not at all. It was just extraordinary. I'm so obsessed with that. No, excellence is serendipity. I had to move out of the place where I was living in Epsom, because I was renting there and the landlord wanted the place back. We have these three small plants in Camberwell, which I was renting out, and thought that the London property market was obviously insane, and it was a good time to get out of it. So I sold them. Unfortunately, rather badly advised, I sold them all in the same taxi, and so I wasn't able to stagger the relief in the capital gains tax, but that's another story. I looked for somewhere in France where I knew I could find something obviously much cheaper. I'd always wanted a house big enough for all. So I stretched myself and I went to look for a place. I was originally going to buy in Normandy, much nearer to the coast, somewhere near Cairn, where there's also good air service to England. Channel crossing which is an area I know well. I didn't know this part of Brittany. I went over, I looked at a couple of places. I was on the point two years ago today of buying a place near Motard, which is about 40 kilometers north from here, that goes near Ovard, just north of Ovard. We were actually on the point of exchanging contracts. One of the agents, three agents that I'd used when I was looking for places rang me up and said, oh, you must come and look at this place. Thanks very much, I've seen the place I'm going to buy, and this guy, I didn't have a particular, I hadn't had a very happy experience with the places he'd shown me, I thought of all the three people I'd dealt with, he was the one I was by a long way least likely to be buying through, so I just ignored, but I happened to be here with a guy I sometimes don't drive, an old friend of mine from way back, who wanted to come out and see this part of the world, and I was driving and said, oh come on, let's go down and see this place in Boucher.

1:40:00 And, you know, eventually nagged, and I thought, 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'll just go and 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, its location, the size, especially the courtyard rooms at the back, and saw what kind of a library it would make, and that room upstairs, the meeting room, I was asking which was ludicrously cheap. I really needed a lot doing this, every line around. I thought, yeah, yes, this is what I'm talking. And this is this place. Also, I just had a good time. It's a bit further from places I like to be here, but once I've learned to drive, but even so, now I've been very happy. Yes, of course. They never did bring me any fizzy water, but I'm not worried about that. The wine is very good as well. Did you want one? Yes, please. But mainly just seeing the place which would be big enough to have meetings like this and to be able to use it properly.

1:42:30 Well, an intermediate level text, I mean, on a couple of countries that doesn't, as it were, Yeah, and it starts out looking like that. It starts out like it's going to be a really simple introduction, and then it immediately jumps to the geometric definition, the Giraud definition, and... Well, without giving enough intermediate steps on the way from the beginning. Yeah, it doesn't lead up to it steadily. It jumps to it. Oh, okay. You said you'd seen this book on this? Yeah, yeah. I just don't know who I would recommend it to. Yeah. Well, I mean, it presents itself as a series of examples. Yeah, but I just didn't think the... I thought the series of examples was too short, and I jumped up too quickly. I think that kind of approach could be great, I mean... Well, as I said, the only thing I've read is the publisher's blurb, which made it sound like it was exactly what had been needed for a long time, which is something, obviously, going beyond Bill and Steve's introductory text, but not... Yes, yeah, exactly. We're there with the... And Harvey Shorman likes web publishing. Could be, could be. He makes his living doing web publishing of biological research. No, I only know that they've got this publishing house, the Dolph Gambay, who edits the logic books, and that they publish a lot of very accessible, I mean, very, very price, very, you know, reasonably priced.

1:45:00 Look, I mean, just a fraction of things, they're 15 to 20 pounds or less. In other words, a fifth. Are these works of historic value or history? Some of them are conference proceedings, some of them are new textbooks, some of them are re-publications. Certainly somebody used to cut the ground out of these outrageous price gouges like Cloward. Well, yeah, Gordon and Briggs, I think they want $600 for their book on electrical functions. Well, is there any, do they assume the only people are going to bite off? Obviously, institutions with a big, big budget. There's a very entertaining comparison of phenomenology to Marxism written in France in the 1930s for $350. This I wouldn't pay $350 for, my boy. If I had a lot more of this, I wouldn't pay. For the conica I might want to pay, if I had $600, if I had $300. Does somebody want some of this fizzy water? I will show you some. OK, you don't do the fizzy, do you? And this is Gorton and Breach. Actually, one time I remember their books seemed to be quite, like Wiley's, to be, well, more reasonable than most scientific, most academic publishers. The people who are outrageous are the people like OUP and CUP whose standards of book production, actual physical book production, are binding and whose proofreading has just gone completely to pot. It's absolutely outrageous. Well, SUNY Press, they avoided that. They never really did proofreading.

1:47:30 Obviously, in some cases, the authors are diligent enough to do their own brief reading very carefully, but, you know, why the hell... They've gone downhill terribly, don't you think, since they published your book ten, twelve years ago? Some of their recent studies, too. Well, and I've just typed those on every page. I've just had this tremendous problem. I got an article on Plato. It's got some Greek words, and I mean, I'm talking about exactly what he says, so it's got some Greek words. The typesetters in India had never heard of the Greek alphabet. They had not heard of the fable. It's a standard LaTeX application. It's the way you type Greek in LaTeX. They've never heard of it. After two months, we finally got them to print most of the letters. But, any letter that's got a pre-remark and an accent on it, which is unusual but happens, is simply deleted. You've got complete... Yeah, I don't blame the people in India, but why the... And this is... Who publishes Philosophia Mathematica now? Oxford, that's what it's called. Yes, of course, it is OUPS. It used to be. Oh, well, that's absolutely outrageous. All the campers appear disguised. Now, it's true Babel-Poletonico has this Byzantine kappa, this kind of, I don't know, but still, it doesn't go below the line. It's a quixotic eye. They turn them all into things. Yeah, and I thought, this is what I need. I need an article on Plato coming out. Oxford University Press with the Greek misspelled. Well, I'd say that's absolutely true. So even the classics people can't prove three things. Or if they do, it doesn't make any difference because it was subbed out to some poor... Thank you for watching.

1:50:00 This is a completely separate issue. Angus will correct me if I'm wrong, but I was told that Greek, Latin, GCSE is no longer a requirement to read any arts. You couldn't even... I'm not sure I understand what you're talking about. Now you can go up to read classics without having to read the classics without a password, for example, or email address. Oh, schools teach that. I can see the argument for that. This amazed me at Notre Dame. Essentially, everybody I talk to in philosophy could read Greek. Well, I went to Catholic high schools and mostly went to Catholic universities, but... At Case, you mentioned you read something in Greek and people are, oh yeah, I recently trained a pony to jump through hoops, you know. Oh yeah, which I'm very busy with. Don't lie, I wouldn't know, I've never read the translation.

1:52:30 On all levels. You have to, yeah, I mean... You need to have an all GCSE. Well, you didn't have to have A-level to do an arts degree. You did have to have O-level in Greek. The Greek requirement was abolished around the very last year. They did, of course... It certainly applied to the maths drive, because, of course, maths was unspecified, and it still is an arts subject in the paper. Maths has always officially been an arts class. So it is at Harvard. At Harvard, a math degree, you take five math courses. And they come out knowing an ungodly amount. Because they hang around to the formal requirements. I think they were always flexible. I mean, if they had overseas students who obviously on interview were clearly wanting to read classics because that was what they were determined to read and they were obviously keen as mustard. And they just hadn't. I was amazed. They're redoing Plato's works in Greek. It's a nice new edition. As everybody said, there's essentially no new sources. It's just a better editorial job, a better comparison.

1:55:00 The answer is saying, unless there are major new papyrus finds or the study of Greek revives, we are unlikely to see a better edition of Plato in our lifetimes. And they're selling the book by mentioning that nobody cares? Well, that seems a bit... I don't think that's a particularly objectionable statement. Oh, okay, sorry, I hadn't paid enough attention to what you were saying, yeah, yeah, yeah. Yes, if you just left the first half of the sentence, lest there are many more. Yes, that's rather... ...weary, you know. On the subject of major papyrus finds, I'm not... Do you know, from talking to your colleagues in the classics department who know about apirology, ...deciphering some of the papyri, which have been completely indecipherable because they were carbonized. I couldn't understand. Oh, no, they're really carbonized. Well, I understood that there was a kind of headline story in the independent, obviously written from the sands of a quite good British broadsheet, but still without any of the technical details which would allow you to judge how much there was, which suggested that there had been a huge break. And of course, the actual time required to reconstruct, but they claim they got a fragment of an exact 40 lines, which is constantly, I mean, remember when I was a kid at school, the classics master telling us great excitement about 1966, that they were on the point of being able to read the books in the Great Library of Pompeii, about 10,000 manuscripts that were... Basically, carbon was used when they were found by the Italians for about two centuries. They thought they were logs of wood, and they actually chucked them on fires.

1:57:30 It was only a hundred years later they realized that they were in fact these. Nobody's said much out of Pompeii. Well, actually, it's Herculaneum, it's Herculaneum. There's one villain in Herculaneum which had a very large private library, and about half of which survives. But I think there's a feeling it's all perfectly well-known. Well, how can they tell? Well, but that's the feeling, you know. Well, that's what I'm saying. They're always hoping some new jar will be found in Egypt. They don't care what will be found in Herculaneum's library. Well, that's not what's being told. ...almost 40 years ago now by my classics master, and several times since it's like cropped up again, that there's some new development. There's a lot to do with spectrogrammary analysis that would allow them to read this stuff, and that might be all the lost works of Aeschylus and so on and so forth. Not to mention, obviously... Well, Reviel-Netz is going over all the Archimedes manuscripts with ultraviolet and infrared, because they were last read carefully in 1905 or so by Heath, who was a brilliant man, but he just did it with a magnifying glass, and he's doing that. Right now, he's publishing that in English. He is not publishing it all. Yeah, of course he will, but I have a friend who's terribly excited because he's a Callimachus scholar, and he found a whole new poem by Callimachus on a mummy from Egypt. He says that's a terrible frustration to him. There's lots of mummies, and the archaeologists don't want no touch. It's so costly by hand. That's right, you might have the whole of Heraclitus wrapping around in your grave. This was a 3rd century poem, that's the thing. You know, you get stuff from the 3rd century, but not earlier. But it's a whole new 3rd century poem, that's nice. Well, I guess because they weren't wrapping Greek mummies in Greek, yeah, until a lot later, until the Ptolemaic era. I was just saying to Bill, I went to see in January, I went to see this... Pretty dreadful, but not, it could have been worse, you know, Oliver Stone film about Alexander the Great with Christopher Plummer as Aristotle, it's quite, it has this wonderful scene at the beginning with Christopher, Sir Christopher Plummer, they have all these kind of great names, you know, knight in red jackets to play, like Sir Anthony Hopkins plays Tolliver, Sir Christopher Plummer plays Aristotle, and this kind of, you know, really kind of pushy, you know, he speaks with a really cool...

2:00:00 ...sexy Dublin accent, which is the accent that, you know, Hollywood produces more these days. So, um, the only thing is he can't act like that guy who plays... He's a Macedonian. Yeah, yeah, yeah, that's right. Well, that's precisely the point, you see. He speaks like a really cool, sexy Dublin accent. Make it clear that he's, like, you know, they're the new kids on the block. They're the Macedonians, whereas the Greeks always speak this really plummet-voiced word. British establishment voice. The people watching, he got the point. I did read a review that said Angelina Jolie's accent was just unidentifiable. It was totally unidentifiable. Her acting was unidentifiable as well. Plus, she looks 23, and Colin Farrell looks about 35. He's supposed to be her son in the movie. Completely ludicrous. Yeah, it's crazy. I mean, the guy is... I mean, he's meant to be her son, and he looks old enough to be her father. It's completely crazy. But there's this very funny scene at the beginning where it's all blamed on Aristotle, because Aristotle is teaching Alexander the Jogger. And explains that, as in any subject matter, we almost always ask oneself whether we're on the way from or to first principles. This may not... Geography may be the one exception where this isn't a good question to ask. Oh no, Aristotle already says of rhetoric, the science is one of which we never know first. Yes, well, he deduces that, of course, all the land mass of the Earth must be surrounded by oceanos. Uh-huh. And so when Alexander's depicted kind of pushing on over the Hindu Kush, and then with the Macedonians getting ready to revolt behind him... ...just refusing to go any further. And he's just obsessed because he knows that if he gets to the top of the next mountain range for free, he's finally going to reach, you know, the Okeanas. He's going to sail them all back round the rim of the world and back up the Nile, which obviously flows from the world ocean, to the Mediterranean, and they'll get home that way.

2:02:30 I don't know if there's any source for this. And then, of course, he will have reached the boundaries of the world and will have conquered it all and be able to start putting it all in. In order, I saw the movie Troy, and what I really like about that movie is what makes Achilles an invincible fighter is that he goes straight for what he wants, no false movements, no hesitation, nothing. That I thought they got right. It's not that he can jump 12 feet in the air and do a somersault. And this is based on some passages of Homer. They mention the whole thing though with no gods or goddesses. No, but you would never, you don't know what this special feature has to do with the movie because they...