Evening Talk

0:00 This is not an equalizer, but this is. This is the image of it. And yet this is an isomorphism over there. Being closed there means joining to the syntax, the symbol which is going to be the inverse. Because if you say x itself or also the line, look at where it's convertible, you have to deal with these. If it's just one place, that picture is too complicated.

2:30 In the space x cross r, there is this subspace of pairs where x times y equals 1. That's clearly a clue. The subspace of the plane, but not of the line. But if you project back down onto the axis, it precisely leaves out this point, and so it captures this more complicated picture. You could classify topos for objects. If you wanted, for example, to insist that a certain sub-object 1 becomes 1, I'm sorry, you'd have to figure out the actual formula. I'm sure the same idea can sometimes be, in the geometrical world, you can enlarge the topos. One point of view that I would like to draw your attention to is the semantic divide of classifying purposes.

5:00 Because we have seen before the syntactic approach, so for a geometric theory you can obtain a syntactic size that describes the classifying.

7:30 But the fact is that since mathematicians are often much more interested in the semantics, in the structures, rather than in the syntax, of course. Of course, mathematicians have thought about presenting classified purposes in semantic ways, and one very natural approach is to view theories as portions of theories classified by pre-shaped purposes. I will call such a theory a theory of pre-shaped type. So, let's see if that works. Of course, all the theories here are geometric, because otherwise we can't even start finishing. This is a quite important notion, especially because the class of theories of each type includes important classes of theories, for example all the planetary algebraic theories are of each type, and also one can case by case also sometimes prove that other theories are of each type, for example the theory of linear orders. So, this is an important notion, especially because the idea is we can obtain every golden bit topos, we can present it as a sub-topos of a pre-shift topos. So, the idea is, and in a very natural way, so it's natural, plus if some...

10:00 It actually worked. I wonder if it's the same thing as mine. It was nearly gone and worked. I tried it in Montpellier. Yes. Well, you were fantastic in the evenings in Montpellier, I have to say. But the crucial point is when you have to stay awake for a third lecture, you can already see that it's just a recurring condition in my life. It seems to be the solution that's out there. I'm going to use it sparingly. Yeah, of course. Well, I'm sure it's not a deck deck. You might just get hit. Maybe. I'm afraid of that, yeah. Well, it's a herbal. I think it's just very strong coffee. Okay. Warm. Well, the Swedish Foundation... It's good to have you somewhat in Guadalamo. Guadalamo? Okay, that's interesting. Actually, it would be interesting to talk a bit more about that because this chap, the guy who runs this Swedish foundation that funds the army... He's my only supporter. He's the only guy in the picture right now. This is how he made his fortune. He has run the biggest supply of herbal medicines to most people. But they have some which they swear by, which they didn't try. It wasn't really good, I have to say. It was absolutely great. It sounds a lot like a rocket.

12:30 It takes about two days, though. You have to think of it as two days before it really kicks in. It's completely legal, it's not that, but it was actually Rodea, Rodea, Root, and then it was Soviet Union when they did these methods. Sure, yeah, you've already looked at it, haven't you? As it is, in fact, a rocket is a really good course. They've been testing in the U.S., they've been testing in wonders for their metabolism. She is, she is, she's likely to come in touch with them. They're very, they're very likeable people, actually. They know thee. Oh, well, if she's ever, if she ever has any interest in talking to them, just ask her. You might have me announced. Kiki, George's chief. What, in spite of thee?

15:00 I mean, obviously, some of them. The mask, the elephant. There's a great deal about specific cohomoses. But I think I get something out of it. And I particularly like today the fact that it's about this grass on the first day. And I thought that having you and John there would be talking about the whole ramifications of it. So I'm going to go in there for a quick one before dinner. Is that the plan? If you want to eat dinner in here, I'll just have a drink before dinner. They do do dinner, I think. What do you say? Okay, well, shall we go in and just see what they have? Okay, well, let's go see that.

17:30 I didn't know how he did get this much paper involved, so I think he just was clever. I'm very happy to be here. Hello, I think what we have is, well I'll have a pint of tribute, definitely, and are you still serving food? We are just starting to serve food. Thank you for your attention. Thank you very much for your time. Yes, there is more at the top. There you go.

20:00 Thank you. You may have been more aftershifts yesterday. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. Two minutes and a half ago. That's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better, that's better. Yes, a very honourable profession. At the time of her first marriage. I bet she was good too. I'm sure she was good at it. And very popular. Very popular. Now why aren't mermaids paid off the same way? It seems that in terms of what they do, in terms of the added value, they seem to me to become more deserving of it from bankers. Exactly, which they make a very great difference.

22:30 It's far more worthy of being paid on a percentage of your turnover than the financiers. Oh well. No, what I was going to ask, the characterisation of the subject matter of narrow sense logic, Roots and extensors in the supports of intensive and quantitative learning, which I think is just a fascinating topic and one which, of course, connects with the general discussion of the role of intensive and extensive quantity and the way that, in connection with it, one should think about domains of variation. In a way which is fundamentally more general than the traditional logician's way of counting up and weighing, I think those would be very useful topics for a little exposition for the philosophers one way or the other. Only after... You've got a boycott. No, no, no, we've got a boycott, but I didn't dream of... I'm not suggesting for a moment... Oh, no, no, no, I'm not suggesting this should in any way take the place of what... On the contrary, I'm saying after you've had a chance to develop your points too. It's just that when the philosophy was there, I think it was the only reason for us to have it, in some respects, or unless you want to reserve it for the final session, I think. John is a mathematician or is he a philosopher? John has been in the philosophy department for this whole career, but he's now retired. And he's now a member of the philosophy department because he had a bit of a run in, as he was explaining last night. He explained that, yes. I'm sorry, I meant to say he has been a member of the mathematics department in his whole life. I'm sorry if I take philosophy as a separate department. No, he's a member of the mathematics department. There's still a mathematician, but he now happens, for the last, since his retirement, he's actually in a philosophy of science.

25:00 He's essentially a model theorist. Most of his publications have been in model theory as well. He wrote a book about foundations. Atiyah has done arithmetic and mathematics which is equivalent to some new systems. There is no isomorphism in the natural numbers theory. There are just simple infinite systems that are dedicated in a different way. He's interested in trying to establish and develop the system. It's great for the system and also for other systems and seeing what runs it good. He's also interested in terms of rescuing the citizens. Once it's good, everyone will be, by the rest of the time, given a symbol. He also connects with other interests of his, which go back to his interest in the Greeks. Richard did his first degree of mathematics in Edinburgh, then did another degree of mathematics in Oxford, but then came here to do a PhD under John, actually still in the maths department, on the several Euclideans that are in the mathematics department, and has become more interested in it. Have you seen in the corridor that goes to your room there's a picture of Richard with a heart around him?

27:30 Ah, an arrow crossing. So, he's not just doing philosophy. No, I think, you know, without being heavy about it, it's obvious that a lot of teenage girls will find him very different. Think about it, it's just a simple example, it's very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, This year they averaged off. This year they averaged philosophy. I'm sure I noticed that, so I'm sure that's the explanation. I'm trying to get lots and lots of valentines from the students, it's probably a bit of an embarrassment for them. It has to be, it has to be. Can you just change angle now? Yeah, it's a very serious problem. Reacher. Yeah, so it needs to be... I was very gratified about the needs of which we accepted this whole seminar. I can leave that to you. No, you have to respect what we have to do. We have to respect what we haven't been able to take, particularly the Beattie's talk about international analysis. That's not very cool. Thank you for watching this video, I hope you enjoyed it, and I'll see you in the next one. I've never heard of it. It's an actual unit of complex analysis. Primarily. The card is this way. The place will pass. And then we have the experiences.

30:00 I've never heard of it. I've never heard of it. I've never heard of it. I've never heard of it. I've never heard of it. I've never heard of it. Thank you very much for your attention and we look forward to seeing you again soon. Sorry, did I hear right? Picard himself was working on complex analysis. Yeah, okay, sorry. So, he didn't set out to develop the notion of Picard's direct contribution to any analysis of the natural development. Okay. Oh, I see, he's quite good. There are a lot of hotels in that city. Many, many, many, many, many. Oh, many? Okay, well, that's impressive. Picard was a jet. No, I did some training. What's he around? At the time he had a mother. Where it was, they said, oh, you don't want to stay around. Oh, even the early generation. So the end of the 19th century. Just like King's Cross. A number of people are dedicated to the case right now. No, we haven't ordered yet, because they said they were only just going to be in the kitchen, so we thought we'd have a drink first and then go to the front. Oh, yes, yes, I think so, it's OK with you, yes, it's good with the person. I'm not saying that we can't offer something not spicy. Yeah, well, that's true. Thank you for watching.

32:30 Thank you for watching this video. It's the same, it's the same. The vegetable chili. Yeah, the vegetable chili. Yes, well that's what chili is. Then we have the chicken casserole. Chicken, chicken casserole. What is the understanding? Spanish chicken, casserole. I might take that as well. Or if you want something... I think that would be good. That shouldn't be here as well. I mean, yeah, those. Yeah, okay. I'm going to take the Spanish chicken. I think I'm going to stick with the Australian continent. Ah, okay, yes. We're going to have one Spanish chicken casserole, one chewy con carne with the salad, and I'll just go and find out what our friends want to do. We've got this taxi and there are two people in front of it. You might come back to me, it's cold.

35:00 We just ordered, Olivia and I, but we wouldn't want to keep you waiting, so we ordered chicken. Well, we ordered chicken. It's the usual selection. I ordered chili con carne chile with the chicken. You're going to eat later, aren't you? Yeah. Oh, you did? No, no, I mean, has it been my drink? Yeah, so did I. So I tell you, we have no more time to talk. There is a scientific name for the first term and the second term, wait. There are different people in the mix for some of them. For example, Christophe Hans Schubert was obviously in the second term and was connected with Helmholtz and both were in the first term. So they've gone for self-image. It's just that most people instinctively go for self-imaging and stuff, which was the first term.

37:30 I'm afraid that's a fairly trashy paper that you've got there, but don't trash most of the broadsheets these days. I doubt whether the Daily Mail, it's the Daily Mail I think, will carry, no, they probably will carry no, I mean they will probably carry no foreign news at all, it's very, very, well it's very lowbrow these days. It is, well it looks good. Well, it should still taste pretty good, I don't know. Yes, actually Bristol is also very good. It comes from the Mendip Hills, which are, you know, why it's so hilly around here. So it's actually filtered through all the local limestone and in fact it's very pure indeed. It comes from Aquitas in, I don't know how far below the ground, but they are a long way down, I mean, they're, it's, in fact Bath is famous as a spa town because it has natural mineral springs, it's, in fact natural hot mineral springs, which the Romans discovered when, actually they've already, They were already used even before the Romans, but the Romans built, in fact, one of the largest bath complexes in the Roman Empire. That's why the name of the town has the name, because it was the centre of this extremely elaborate complex of Roman baths, which are still there, which you can still actually go around and see them. It's one of some of the most extensive Roman remains anywhere in Britain. I should definitely go to Bath. It's a very nice city. The only problem is it has far too much tourism. Because it's a relatively small place, it tends to be suffocated by masses of tourist buses every day.

40:00 But if you go early in the morning or in the afternoon, actually the afternoon is the best time to go because the tourist buses are pretty well done by then. I have to see if the train is about in the same line as London. Yes, it is. Ah, it is? Okay. Yes, it is the same line. The train to Bath is only 10-15 minutes from here, not even 15 minutes. So it's the same line you get around here. But not all the trains stop at Bath, so you've got to make sure you get one that does. But it is the same line. It's very near Bath. And also the station in Bath is much closer to the centre of the town than near Bristol. So, what we're doing is, what I'm saying is, there's some reason that, on the vector space, there's one, O of minus one, where the unit is O to the x. I want to bring it up tomorrow for YouTube. The motivation for that peculiar element was to do with complex analysis. Yes, I think I can see what that might be to do with. But you put on to Richard the idea of finite topos. You put it to him, to call him. I think he realized what he was doing. Good, good.

42:30 Yeah, not too much in the way of the classical language, because there are always sites, sites of many categories, and these products are able to talk about binary relationships, and you can't represent them at that level. I'm curious about all sections being iso, what it implies inside the topos, or among topos. You mentioned a conjecture whether all these things... All sections of the map. Yes, every... what is the axiom? Hold on. Every... if you have a retraction, then... Oh, I see what you're saying, yeah, if you have two random maps of an object, alpha and beta, if alpha and beta equal to infinity, then so do you. You can check to see whether geometric morphisms between things like the topos are satisfying this property are essential. Right, right, right. So, only that would be interesting enough. Richard's been working on finance. Perhaps it's something that would appeal to him. Some very simple actions. We were talking about Richard that's part of this seminar. You're talking about the same Richard, yes?

45:00 I'm talking about Richard the Organizer. Yeah, right, yes, I assumed you were talking about Richard Fettinger. Yeah, sure. Well, Richard is... Yes, exactly, I know his research is about finance. And he has been, of course, making a huge effort in a very concentrated way in the last couple of months, two or three months, to learn. I mean, from scratch, which obviously is it. But yeah, it's a big work, a big, big work. But yes, the finite. I was wondering whether the finite compass might illuminate some of this business of these non-isomorphic models. That's interesting. Yeah, well, right. Very good. So there's a concrete finite set, and there's also literally just finite, non-reliant functors on finite categories, and there's a certain two categories, and this is, it has many remarkable properties that we can use. An example of a typical control club is a real different base, where the base has different properties than the whole finite set. Then that small set. The whole set. For example, every geometrical, every, every, every, every, every, every, every, every, every, every, every, every, every, every, every, every, every, But then on the other hand, if you try to axiomatically describe it, it's not exactly as simple as it may be. There are a lot of statements like that, but we don't know that one, and there are no obvious ones. The power set, as you say, is the finite one, where the finite power set is the damage-free simulant, which is the finite one, which is the finite one, which is the finite one, which is the finite one, which is the finite one, which is the finite one,

47:30 So what we were saying before about the Dedekind property or two strong properties of the finalist type, I don't know if one implies the other or not, but they're all true in these concrete models. If you want to consider arbitrary propositions, there's got to be a lot of them that satisfy the same propositions, and those are the non-standard levels. They're also temporities, because they're not based on that set. There are all sheep, whatever it is that they're based on. Well, yes, yeah, yes we did, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah, yeah. Thanks. Are you sure you don't want anything? I'm sure, yeah. It's too loaded. Yeah. Well, yeah, not just Mediterranean, but particularly anybody from a Spanish-speaking culture. This is very, very early to eat. Not from a warm country. A warm country, sure. There are all sorts of reasons why people in... South of Rome. People eat late. That's pretty sensitive. I mean, the whole, the siesta, of course, is absolutely essential to any kind of total existence in the US. It's crazy to go out. So, of course, you then go and work when it gets cooler, and you work until it gets dark, and then you eat. That makes perfect sense of how the customer works.

50:00 But it is a nightmare. As you probably can imagine, Bill, I spent quite a bit of my life working as a tour director, a tour director, but I did, and one of the biggest difficulties was always when I had to take American groups to Spain, and there I said particularly groups from Midwest where they rise very early in the morning, and they used to go and work farming hours early in the evening, and... There are no places to eat. Well, if you go to Spain, I mean, nobody sits down to eat until 9 o'clock. Whereas Americans like people a lot earlier than that, and people from the Midwest frequent them, even 6.30, and then it's quite late in the afternoon, so we kind of struck that in the end, it was one occasion when I had a group of people from Minnesota, actually, I know it's not the Midwest, who refused to believe that. They wouldn't be able to find anywhere to eat dinner at 5.30 or 5.45 in Spain, and I just told them they wouldn't be. And of course, eventually, I did actually find someone, which of course was still serving lunch. So I simply took them in there, and they didn't realise that this was just the end of lunch. It's very difficult to believe anything I tell them after that, because I tell them it might be impossible, but I don't know if we're going to be able to do it in time. So, yeah, it's interesting, the different cultures. The British are more or less in the middle between the modern and the Latin, in that respect. Although we're becoming more Latin, we're starting to need data instead. Well, yesterday you said that Davide was part of the evaluation group to check on the loading story. Yeah. So he is. I suppose there will be at some point a huge cultural appeal for punks for a small league.

52:30 I remember one time I spent a few days in a museum called Emajio. Thank you for watching. Oh, I see. Sorry. The whole thing is quite touchy though, I'm sorry. Thank you for your attention. It's said in the newspaper even that the agriculture is the most nervous thing. Probably something like that tends to shatter the, you know, the water supply in the days.

55:00 And Davide's wife, Leila, But, when I was introduced to the retreat, it was explained that she was from a place on a lake, as I was told. And actually, they lived in Loughlin. They actually lived in Loughlin when I went to work at Marist. They were actually right near the site of the event. Yes, I hope they were alive. And even that their house was relatively undamaged. There's many people able to sufficiently engage in the field of mathematics and physics, and we should be allowed to tweak some of them. It was an interesting time, originally, I think. I think it's older than well. I think it's older than well. Have you been all right, guys? Yes, thanks. I mean, the questions themselves are very interesting, apparently, even before the audience. I'm remembering now that I went to this wonderful museum to watch. The Mastodon is a sort of restored, incredible, all sorts of things. This is a span of the Mastodon, you know, it's a prehistoric, prehistoric, with the massive trunk, relative with the mammoth, not the same, different species. Yeah, what is it? It's a typical strategy of which I was quite used to. You went to the lab the other day, and the counselor you said you were used to. I will see you all next Thursday, I think. I won't be here next Wednesday. That's it. ...that they would attempt to throw out the Spanish.

57:30 I'm going to try some Austrian spices. My schedule is quite intact, however. What's the relation between... Olivia, you probably know this because you're telling me your father was originally from Naples. His parents were, yes, his family was originally from Naples. I want to know this, and I probably did, but I could not know this. What relation were the Bourbons who made the Neapolitan Bourbons, the Bourbons who ruled in Naples, the royal family, to the French Bourbons? I mean, obviously they were the same family, but they weren't the same branch, they were a different branch. I have no idea what the connection was. They were the people who managed to turn Naples into what Glanston, in one of his fics of moral outrage, described as the negation of God erected in the system of God. Well, actually, it's a description of the forehorns of, you know, probably the most reactionary regime in Europe. It's not that out of place. Thank you for your attention. Yes, I was going to say, I think they were all set up very well.

1:00:00 It's like, have fun, we'll travel. Yeah. They were a very experienced group. Yes, we were all out of a job. People needed somebody like that. It's a question of need. Need for other people to travel. Well, you could actually say that, that really ought to be the motto of the British royal family, the throne will travel, because they, of course, came over from Hanover originally. But the Bourbons of Spain and the Bourbons of France and the Bourbons of Naples, as I understand it, were all... Different branches of the family, because there was never a point at which, oh well actually it was briefly a point because that's what caused the war on the Spanish succession, but except for one brief episode when Louis the 14th tried to put his son on the ground, sorry great grandson I should say on the ground, they weren't actually the same people. But the essential point was that Mr. Steff was an honest man. Yes, yes, definitely. The Spanish ones, the ones in Naples, had not, you know, entered China by aggressing the people for a few centuries. They were just parachuted in, you know, by the royal system. Isn't the person who did the spade the sister of the extreme Greece guy who was kicked out of Greece? I think he's a suspect, you know. Well, they certainly, I mean, it seems a little bit dismissive of these people, but, you know, they're pretty dangerous. I mean, they did stage a considerable comeback. I mean, they came back in the 1970s to become, you know, stage a major European nation. They put it on the same thing in Austria and in the Republic of America.

1:02:30 So, well, Romania is still alive, the very wine that was driven out in 1944, or actually in 1946. I'm not sure what it is, but I'm not sure what it is. The evening attempt at the stage of restoration of the port, I guess. Yeah. How is your chicken? It wasn't too spicy? No, no, no, it was perfect. Excellent. To think it was one of the few which were non-spicy. Do you think it was spicy? Yeah. Or simply yes? Perhaps we are just not used to it. In the south, they eat more spicy than in the north. But since I'm in the very north, My family, nobody likes them, so my mother and grandmother always cook for us. Ah, that's always the best way. But they were excellent. I bet. No substitute for modest cooking. I'm not, but they are. The English menu doesn't have a particular taste for spicy food, in fact English food was notoriously rather bland in the cook, but what has happened is that England has now become the world centre of Indian restaurants in the last 50 years.

1:05:00 There are more Indian restaurants in Birmingham than there are in any single city in India. So, the English have got a taste because of Indian cuisine. They've got a taste for mathematics. Do you like some things for Indian food, like that kind of bread and those sauces also? There is one which is very spicy and I avoid that. I love a very spicy one. Well, I'm going to tell my bookie about that. And if you... Yes, you soon know if you've made a mistake. Yes. There is one red in pot. Oh, yes. Which is... Thank you for watching. Thank you for your attention. Thank you for watching this video, I hope you enjoyed it. But what I'm saying is that she married this man in Oaxaca who was a professional chef, so he cooks for all of us, good, and fairly spicy, but he has a secret kind of spicy. Oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh, oh,

1:07:30 Yes, you can say Mexican food is notoriously very spicy. More so than, I think, most Argentinians have seen right. Weird meat. I would assume, considering it's, you know, the beef-raising capital of the world, that they do eat a lot of beef. We have some Italian influence, but mostly we eat... Do you eat pasta every day, for example? Not every day, but it's... yes, yes. It's beef and pasta and things I would have guessed, but I don't know. But not particularly spicy? No, no, no, no. And we don't have almost none of the Asian... There is an Asian. There's some Chinese, but... Well, there's nowhere else that you can find a place where they don't have a Chinese restaurant. Even little tiny little towns in Ireland almost don't have a Chinese restaurant. Well, there are not many Chinese restaurants. What about fish? What about seafood? Are there any places that taste them? Yes, there are some places in the coast that have good fish. But getting good fish... Ah, being far from the coast is difficult. Yes, because if you're in, yes, I was getting your code a bit much later. It's a long way in land. No, no, I mean La Plata. Oh, sorry, you know, you said it. But even in La Plata, which is relatively near, you know. Actually, the turning point was when Heraldo Giuli, from, precisely, from Rotterdam, came to these lectures, and then afterwards he wanted to ask them that, but we couldn't understand each other at all. It was so frustrating to realize, I have to learn this Italian better. I had, I had this wonderful opportunity.

1:10:00 I started, rather I said, I asked the students, would you like to have English, more English, or bad Italian? Bad Italian, bad Italian! And so I just started, and there was very little, very little comprehension, but because of... Because of, well, places like this, you know, discussive mathematics, active lectures, whatever, unites and so on, it smooths out, it smooths out, so my talent is really to conceal it. Instead of, you know, instead of conjugating words, I say things like this. So I have a lot of strategies appearing to do it well, but the result is that when I'm in America, I imagine I can't, because someone calls me on the phone very hard. Yeah, but still, when we talk about the form, if I am here, if I am in Italy... Let's say 10 days, then I'm back. It's amazing how many people came to notice me on there now. Really? Well, you actually must be very good. Fatima must have helped there, I think. But anyway, of course, when you were actually living there, after a short time, you spoke to us at home. And the children. My daughter, when I met her, she, at that time, was very good at boobering. She would just be boobering and just beating it, just like all the other children. But she was so young, four or five years old, too young to remember it. When I left her, she was a god. But anyway, pretty amazing. Good. It's amazing anyway. Do you speak Italian with Fatima? Sometimes.

1:12:30 No, but even in America perhaps you practice sometimes. Sometimes, sure, sure we practice. So when you will be in Pisa, will you give your talk in Italian? Well, it all depends. If I am in Toscana, I forget. Yes, but we should arrange that after the lecture. But I need to give a very good question. As far as the general public, whereas in Pisa it's presumed a sympathetic institution, it wants to be qualified. But the rest are not even sympathetic to the general public. Okay, so it's better this way. What I really should do is have a 10-day vacation to Tuscany first. Well, why not? That's going to be the best. Well, it was a disaster, actually, in 2003, in the sense that there was a meeting. For the 40th anniversary of my thesis day, Mike was one of the main organizers, and our friend, Alberto, produced this. So, this was a very fun meeting. Thank you. Specifically, not typically, but because of all the foreign participants, the whole thing is in English, therefore I did not develop this preliminary one of the basics. Then I went, I took the train to Milan, and I thought, I figured out something, see, about dynamical systems that have a special kind of timing, so I'm very, very excited to come. Thank you for your attention. Representation, room, room, room, sala, sala di rappresentanza, non rappresentazione.

1:15:00 What does representanza mean? It means the concept that we were trying to express. So it's a movement which is used for formal occasions. I see. Because the representanza literally means... Not just presentation. Presentation. Presentation. Presentation, yes. But representation. My English is badly colored now. I hope I'm using the word representation to mean you're going to represent, you're going to pretend to be. Oh, well, upper board's well, basically. It's a way of feeling in certain places. It's a way of appearance. You represent yourself. You see, you represent yourself. That's the idea. So, anyway. So, there was a total disaster. Because I was lecturing in my bad Italian, and a large part of the audience were not my school friends. All my old friends got away with murder, and I believe it actually has clicked into me. It doesn't take me years to learn what I invented. You know, they're very friendly to me. The other professors are very nice. This was clearly, but I only realized that later, that this clearly had been much better than English. I couldn't quite really internalize the fact that it wasn't the Robertson time period. I hope my friends didn't lose any grants or something because it could have happened. I think also another reason for leaving the Tolkien Institute piece is that there might be more people studying it. And people who do not know it at all because this is the center of the Georgian philosophy.

1:17:30 No one loses his grant for your Italian. No one loses his grant. No, I don't think so, but it would be impossible, you see, because of course they were describing me as their mentor. Which is true. I would want to turn them on to the category theory of even and true, so the others in any way have a dim, low view of the category theory. If they see this illiterate guy, he's going to... I was very embarrassed when I went to Milan to give a talk three months ago, and there were only Italians, so I had to be Italian, but sometimes I was there like this evening, and also the Italian translation. I don't know how to translate literally. It sounds very ridiculous. Well, yes, literal translations do tend to sound ridiculous in all languages, and I think this is fairly down-to-earth. It's not the right term in Italian. Because part of it always gets a kick out of it. The doctors that are supposed to be faithful are usually forgetful. Yes, that's very difficult, isn't it? I've always thought that English is a much more abstract language than Italian. What do you think, as a language? Italian is very literal, which means very descriptive as a language. So, for example, when we say apple.

1:20:00 We really think of the fruit, so we build a concrete image, as you say, but when we use this word, we think of it as the collection of all the concepts. There's a computer these days. No, but I think the point is that English, I think, does make much freer use of metaphor. I've had a lot of experience with it, but it's very different from English or German or Italian or any European language in that it's, what, I mean the terms are often taken when you're European, they tend to have a very specific meaning, you know, like for example, and even professional linguists think of it, the final study of linguistics. So the professors would always have some theories about linguistics and give examples. Jefferson, Schiff, German, Vanatel, and they were all wrong. The examples were over because one of the many reasons that the professors didn't get it right was because of the particularities. And one professor asserted that... Some words have a lot of meaning, but there's one word that has only one meaning, and that's arrest. Arrest means that a policeman takes you into jail. Well, see, that is not even true in American, but it's a kind of natural head of this place. It's the main use of that. In fact, you can have cardiac arrest. Arrested motion. Arrested motion. Arrested motion. There's not just a matter of bringing someone to the state of motion, there's a more literal The word with a general meaning, they meant it in connection with some specific context. So that specific meaning remains the more or less official. The core, the core meaning for most speakers.

1:22:30 And that's a huge, huge difference. For instance, I... In Italian there is that difference between general and official. That's very, that's very striking. We also say in British English, I mean, that's a very arresting remark. So, and that would be, but I think that would probably not be such a natural thing for an American. Not at all. No. You wouldn't understand it at all. No, that's what I would do. It would be cold. That means that you're going to call the FBI. Yeah, yeah, yeah. It probably wouldn't be an everyday usage, but it'd be quite a common usage. I mean, it wouldn't just be something which academics use. I can imagine people in a pub saying, somebody says something, that's a very arresting idea, that's very arresting or not. It would not be a very common usage, but it wouldn't be completely weird. On a different note, I was interested in the last category that you were meeting. You know Jeff Eger. It seems that there was a similar discussion at some point. Jeff Eger was present and I think it was Walter Tonnen. They were discussing whether some phrase could have only one meaning. So it was Walter Tonnen or Robert Roseberg who proposed that I lost my Blackberry could only have one meaning. And Jeff contradicted by saying that he would assume that he had lost his anal virginity. Oh God, yes, I could just imagine, gruesome, yes. I thought it might have something to do with, you know, the business of the cherries. No, I thought it was going to be some innocent remark about, you know, kids blackberrying. No, no, no, Jeff made something there. That one can develop in different languages. For example, in English it's very easy to be funny. I'm considered very funny in general. But when I'm in Italy, I'm considered quite serious. But I'm the same person. And I behave the same way. But, you know, English people are inclined to love each other. And perhaps this has something to do with the nature of the language, because you cannot interpret the same thing in any other way. I absolutely agree. I think in fact it's the reason that, because I think that your, when you said that English is a more abstract language than Italian, I don't think that's quite correct. I think that...

1:25:00 German is certainly more abstract. I think English is, in fact, for the most part, every bit as concrete as Italian, but English lends itself very flexibly to metaphor. And I think it's the extraordinary, it's the absolute ubiquity and versatility and flexibility of metaphor in English that makes for the humour, because most of humour turns on this, so much English humour turns on wordplay. And I think it's the extraordinary metaphorical... So I enjoy very much English, much more than Italian, because I'm very relaxed when I'm speaking English. I'm relaxed that I'm not offending anyone, that there is always a second meaning to things, while instead in Italian one has to bring it here. And if you say something which has a double meaning like that in English, they usually laugh like hell anyway because they know that you don't mean it or something. Mrs. Thatcher got laughed at all the time because she was a very literal minded person as well as a very humorless one. And she was prone to say all sorts of things which of course have marvelous double meanings in English which caused her to be laughed at without her ever realizing. The deputy for the first few years of her administration was a man called Whitelaw, Willie Whitelaw, who was a senior Tory, who was the deputy prime minister, that she had beaten for the leadership of the party, but who became her very loyal lieutenant, and she gave an interview, she was talking about her colleagues, and she said, yes, every politician needs a Willie. We're talking about Whitelaw. Which of course in English slang means that every politician should have a penis, which of course caused huge wails and gales of laughter when she made this remark in the studio. I don't think she ever realised why everybody was laughing at her. Recently there was an interview on the Italian television of an athlete that met Berlusconi on the TV and she said, I can even be touched by you.

1:27:30 And she did a scary trick, the fencer. She said then, and since we in Italy are very, you know, concrete, then we said, oh, she wants to be touched up. She wants to be touched up by, yes, yes. Very, very close to the bottom. In this case, I think, you know, well, I wouldn't have said that in her position. No, no. It would have made more sense, I think. So, no, no, we take things very seriously. I should, I've resolved after that to always be speaking in any situation whether it's not just my friends speaking. Because you can so easily cause offense without attending, you know. It's happened to me in Italy. See, another thing about English is that they get American specials. Many people are talking almost entirely in cliches, right? In other words, instead of using a simple word, there is some particular situation in history which has become, that particular situation has become an emplacement for the black community. If you try something that doesn't work, like I say, knock the wind out of my sails, like some ancient time sailing ships, they needed the wind to move and when the wind was not there, they were in trouble. This is a very specific thing, but very specific, generalized into every possible case of a certain kind of failure of an effort. Yes, precisely because of this metaphorical tendency. Well, the metaphorical, yes, it's a capacity. Language itself provides the possibility to actually learn a cliche and do a lot more things like that. And then it can't just become a cliche, does that make sense?

1:30:00 I do it myself without even thinking. I just supply it with cliches, so I use those instead of finding a suitable word. Thank you for your attention. So that is a huge difference. I don't know. I should know more about the British dishes, but unfortunately I'm still quite a foreigner in England, so I don't use them. Because Cambridge is not England. No, it's a very... the end of the world apart. The way you speak, the way you use abstinence, Italian seems to be quite... No, no, it's not. That's because you're Italian. That's absolutely weird. I think all the non-Italians would think that Italian was a much more theatrical language. Most non-Italians have the very strong impression that Italian is a much more theatrical language. They may be wrong, but I'm sure that's their impression. Maybe that's because they think Italians are more demonstrative and emotional than theatrical people. The sentence is, I can play more, I can play more, but in English. Even though I know it much less, but I can play more, so there must be something. I'm sure there is. Or I'm a craze, so it might be another option. Nothing is related to a lot of flowers, or a lot of texts which don't say much about Larry. I want to tell you, for example, cliche that I picked up in Washington, D.C. I picked it up at the speech with all the other professors, but I never took it again. Subtitles by the Amara.org community

1:32:30 I know it's horrible, but I have such a small supply that I haven't used it. That's the sort of thing I had in mind by saying that I think most outsiders think Italian as being more a theatrical language. By the way, I didn't realize that Kasseler was a student of linguistics. Has she ever spoken? I didn't realize. Has she ever spoken? There's no question that Zell has become very interested in linguistics. He gave a rather nice talk about the application of Thomas Poole in linguistics about six months ago. But she's very interested in the subject. Being a daughter of an Italian working immigrant, she did not receive an advanced education at the end of her state, an elementary one, so when I married her, she didn't even know what geometry was. But after our children would be on Savannah, we'd probably turn 12 years old, we thought, well, they could take care of themselves. She entered the University of Buffalo. She did four years of work and three years with Paul Hayes and became, just before she was 50, she got the doctorate degree in order to prepare for the career which was going to be in the U.S. So her major was linguistics as such, and Italian literature, and actually she taught Italian in my university, but the program was to save the pre-allowed language, because it's a minority language, and at the time it wasn't clear that it was going to survive. Now with real activists like Fuyo herself... Do you know Floria Holster? I don't tell you. That was a television show with Fabio Fazio.

1:35:00 That's right. Until last year. That's right. But now not anymore. The mayor, the major, the, ah yes, the, ah okay, the sindaco, the sindaco, yes, the sindaco, yes, very bad, wacky. Thank you very much for your time. People tried to maintain language published in the United States, so she went to this undergraduate school and she started working in graduate school, but then it turned out, actually, that study in linguistics has very little to do with languages, it's not about history of languages, it has to do with the science of that practice. No, it's some fuzzy philosophy. Various idealist philosophies of sorts are published in old books, and of course you go into that stuff, and that's called linguistics courses, but really the content of them are made to imagine to be the science of language. So after several years of this, he just gave up, and as I said, meanwhile, the problem, the key of life, probably, was followed by the medical school. What's that? Was Fatma's mate the language of her head when she was a child for a year? Yes, for a year and a half. She had a very good base for learning other languages. In the town of Spillingbergo, the people speak Rulon at home, and Veneto at home, and Italian to visitors, and German to other visitors, and so many of these people have gone to Sweden to build castles there and returned.

1:37:30 So that if you go by the pubs in the town, you hear every language being spoken inside. These are actually natives. I'd love to go to the pubs in the town sometimes. But still, in spite of all that, in spite of all that, they're actually a bunch of natives. Yeah, pretty much. In Zell, for example, there's... He told me, he actually was boasting when he heard me, that after taking on the job of director, which is an incredibly busy job, especially for him, a fanatic director, he has to learn the language so that he can get speeches and so forth in that background. When I gave a talk, he introduced me to sort of an honor in my life. It was a very great job. You may have heard of it, but you've never met it. No, no, I saw people. The subject of the question is the causal representation of Marx's dialectic system and mathematics system. This is all a consciously designed revelation. Thank you for your attention.

1:40:00 Make it as if it came out of a box, and as if it came out of a box, and as if it came out of a box, and as if it came out of a box, Actually there was a professor of logic in Turing who had horrors because he once wrote lectures which were completely full of mistakes of various natures and some of them were really serious. And he obliged the students who were studying the lectures to prepare the exams for them. And when I went to him and I showed him with 100 more pages of original work that I had done in order to fill all the gaps and to correct the statements of the students, that was, that was advanced. There are a lot of things in the lecture notes, but stated without any format, and with wrong dichotomies, so a lot of creative work was needed to repair everything, and of course I wanted to understand things properly, and so I did this work entirely on my own, because all the other students didn't realize my mistakes, so I was alone, and then I went to see him, and he told me, well, Miss Caramello, you have a problem. You have a problem. You are too profound. I'm surprised you didn't say these results were your opinion as opposed to his opinion. And then he told me, you have to go and take the exam as all the other students by repeating what is contained in the lecture notes. And then I said, well, then if you think like that, that I'm completely right, because of course he had to recognize me because, you know, mathematics is not an opinion. But he was very angry, and he also told me, I'm the professor and you're the student, so this makes the thing so, you know.

1:42:30 Unfortunately, yes, it's amazing, but it's a true story, unfortunately, and a very sad one, because when I was in that situation, I was quite, you know, stuck. Well, being a student puts you on an offer. It's really a homomorphic story. Ah, okay. As I said before, a lot of it was studying linguistics, and none of this was a course called the History of the English Language. There was a lot about German that we saw. So again, the professor had prepared me for the future. She discovered many mistakes. She wrote carefully down all these mistakes, doing him a wonderful favor now, telling him simply what he has to do, but he wrecked it, you see, and I think she finally convinced him to give her a good grade anyway, but she wasn't forced to give him a good grade. But the following year, she saw young students taking his course and still using the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes with all the same notes The truth is completely touching. Yes, yes, yes. But then I was lucky enough because in Italy you can choose exams, so you are not forced to give a particular exam in the last part of your study. In the beginning there are definite exams that you have to take, but at the end you can choose. So after spending three months just on that course to write all that stuff... I faced myself with the option of abandoning, no, because I don't want to, you know, give him, I didn't want to give him the satisfaction of going there and to say, rather, and so I said, okay, then if this is your opinion, I change the course, and so at my expenses, I changed the plan of my studies and I took another course in analysis. And so I survived it, yes, but we all did. We had a very ambiguous position about this issue.

1:45:00 Yeah, so that's why... Well, probably you didn't understand the mistakes in the... No, because then I was interested in logic, so the only option for me was... To make a career in logic was to strike the pieces in logic in a way, even though those pieces were not very important, still, you know, you needed to show that you were going into that direction, and so I was forced to ask Lolly for a thesis, and he accepted, but in the world of the year, we didn't talk, we never talked about the lecture notes, so he had this very... There's this kind of stereotyped parasite of the academia, which inserts itself into this position, which is a lot of power, and that's absolutely nothing but poor and completely unacceptable. But can I ask what, slightly as an obvious question, the system in Italy may be different? And he was forcing students to regress. Did they not have external examiners in Italian universities? L'Oly was the other examiner, but not external. But they don't have, so they don't have proper external examiners for the same course. They were giving, they were examining the students together. I see, but there was no external examiner. No, no, no. That was the problem. I tried to invoke the external, and I even went to the director of the department to complain about the situation. It was so shameful, but they all protect themselves. So they put the friendship above the truth. That is something which is not even friendship. It's not even friendship, it's just the situation is really that bad. These guys are probably more difficult than we realize, and we're afraid so, we're afraid so, knowing these two examples that are accepted in three countries, and certainly not only in Carina, not only in Italy, and in some ways I think the problem is much worse in the humanities, because obviously there... At least in the case of mathematics, as you say, you can't argue about whether a proof is... Well, you can argue within 10-minute limits, but then you will reach a conclusion, of course, that whether a proof is...

1:47:30 Yes, in historical linguistics, there is a fact of the matter. There is a fact of the matter about whether it is... You know, whether your result holds for all prophecies or all sub-prophecies, and there is a fact of the matter about whether this is a correct construction in English, but of course in the interpretation of the historical event, there is no such clear count as a correct derivation. So here this sort of thing flourishes even more. In computer science, that's true. Sure. There are areas where it's... I thought it was a South American thing, you know, where there's no actual tradition of academia or very limited thing. Only a couple of hundred years, you know, our universities are very, very new. And the computer science departments are actually very new, so they were created by these kind of parasites. But after a while, I mean, I'm surprised that in a mathematics department... Yes, but that was the only, it was not the only creature that I had to deal with. There was another creature, which is a very, very good name, but I should use another name. Very appropriate. Nice coin. There is a female professor that I had in algebra, and at the end of an exam she had to give me the highest grade. And they told me, well, I had to admit, definitely not the kind of person that one can kill easily. Killed. Killed. Killed. Which in Italian is also, for the discursive that it is. Killed with courage, I see. Really? With courage. What word did she use? Kill. My, my, my. Kill me. Yes, you did. No, no, but the Italian word on it. It's like uccidere. Uccidere. Uccidere. So it was. You're going to kill him, not myself. Kill.

1:50:00 No, no, no. It's really the end. I have to admit it. No, no. There were others that I. Well, at least she was out in the open about it. I suppose at least she made no secret of her enmity. The worst of the ones, of course, who were terribly charming to your face and sort of say, oh, yes, you're going to have a brilliant career. And then, of course, stab you in the back because, in fact, they are determined to stop you. They're the real slimy creatures, I mean the ones who are these open enemies are... Did she ever give any explanation as to why she was so hostile to you? No, I always had a very shy... I'm not the kind of person that wants to exhibit, and I'm actually quite shy, so I just did my work, but I didn't do that seriously, and that was the only problem, because one day I liked it, and also I wanted it to be. I was ambitious in my mathematical thesis, and they couldn't understand that. So it was not a personal thing, it was something to do with my approach to mathematics and with my companions of thought that they couldn't understand. And the fact that they wanted to keep the environment as close as possible so that they could be mediocre without any... They can be happily mediocre and reproduce mediocrity of their students without feeling challenged. I'm afraid this is a very widespread phenomenon, not at all confined just to Latin America. I suspect it's more common in England now than it is even in Italy. I would expect these people to try and try to find other spaces in order to grow. I would never want to go into academia for the first time. It's contradictory to everything they believe in. Except that academia is, you know, the concept, the notion of academia I think is not very helpful because obviously there are places where people do world-class research and where people have, people who are bold and original. People who have challenging ideas about their subject are welcome, but there are plenty of places in, what's the term, academia, and certainly in England now, there are plenty of places where, because largely of the cultural pressures against the academy, courses have been done down in Ronnie Brown, the whole department.

1:52:30 Bangles. Closed. If you want a mathematics department, well how can you claim to be a university if you don't have a mathematics department? Well, very easily these days because, you know, the function of the university is of course to maximise income by getting bums on seats, squire, which is why we have to have more courses on media studies and that. It's become completely betrayed. Completely betrayed. Well, we should have become really worried a long time ago. I couldn't agree more. We should have become, we should have risen up against this, the destruction standards of at least more than a generation ago, but it's now become so great that the British, well I wouldn't use the word academy because I'm afraid I don't think it's a, because in fact the pretense that there is any longer such a thing as academia is actually part of the smokescreen which allows these people to continue to... The pretence that there is something called academia to which rubbish like media studies and serious mathematical research don't equally belong is part of the problem. The third is that in Italy there are a number of careers across all the universities, so the obvious for the library is the Scuola Normale, but also, yes, that is not very big like, you know, Cambridge, so, you know... I'm not sure it has a big impact on America, because being similar to France is not, I'm not sure, but of course it's really important, because otherwise Italy would be even worse than it is, but the fact is that all the other state universities are more or less the same level, and so you will find problems like the one that I faced, I think. I'll pray to Alberto Ferrucci, who Bill was just speaking of, has told us of similar problems in his account as well. Also, it depends a lot on the directors of the departments and a lot of these things, because if there is a good director, then they can't really behave in that way, because then you go to the director and the director takes your...

1:55:00 I've never seen a director like that, I must say. Unfortunately, nor have I. The sort of people who become directors tend to be people who want to do administration because they can't do research, and who have become more and more enamored of power. There are exceptions, I'm sure. And many times, those who are not able to do research are attracted to power, yes, yes, and so they go and they occupy those important positions because they manage them at the university, and so when you want to bring a good value, they say no because they have the interest to keep the situation as good, as bad as possible, and it's... I think the environment plays a very important role, because people, they all have their own character, so perhaps they are inclined to behave better, but if there is a good environment, then that prevents them in some ways, so the environment can be also very important. I like this lady for testing the children. Probably kind of... I don't know, she wanted to challenge me. She wanted some... and I didn't do anything to deserve that. I just interested in studying computer science and she gave me... A book which is called by Pesky, An Algebraic Introduction to Complex Projective Geometry. So she gave me that book to read. Which is like an encyclopedia actually, so it's not, you know, the standard reference is Atiyah MacDonald, who knew the device, right, and it's a wonderful book, so I wanted to read the letter, and she knew that, and so she decided to force me to study on the other one, which was impossible to deal with together with, because it was written in a completely different spirit, and it was for specialists that wanted.

1:57:30 Like the elephant, that you can't really learn unless you are a specialist. I was in my second year, undergraduate, so I was not in fifth year, and so she forced me to study that, and to solve all the exercises which were almost impossible, well, some of them were very, very deep, and in fact, I couldn't solve all of them, but it's funny. I spent a lot of hours working all the time, and one time I decided to tell her that I couldn't solve one of the problems, even though I had the solution, because I wanted to test her to see if she could, and she didn't, and then she told me, I can't solve the problem, and then I shouldn't have the solution, so... Oh, that is great. Well, now I think I understand why she said she wanted to kill you, right? You don't mind my saying so... No, that was at the end. Yes, yes, yes, yes. And anyway, the attitude that she was continuing to push for was this of the kind of challenge and going against my natural desire to learn and to... no, no, no, it was... Which are good notes. Graded you, graded you. Yeah, well, the fact was that I called all the highest grades in all the exams in the universe, all the highest. So, it was not a matter of grades, it was a matter of behavior. They had a very... It's this other kind of creature, which you can leave as, like, hostility. Toughening you up, but that wasn't it. No, no, no.

2:00:00 See you tomorrow Matthias, thanks. You're sure I'm not dragging you away? If you want to discuss with him... I think that makes more than one of us. I'll just finish packing and then...