Approx of entailment theories (2nd part) / lunchtime conversations (& others)

0:00 But S, take this atomic sentence, kept nice and simple, S will satisfy the mappings under the structure, this pair, this ordered pair, that belongs to that relation in D squared. Okay, so now it's a fact that satisfaction can be extended recursively to cover any sentence whatsoever in the first order language. Let's do note the set of all structures by strut, and it's not really a set, but I'm assuming that I'm working always with sets and that any construction gives me sets. So let capital X and Y be sets of sentences each, and let R, the restriction, be a subset of strut. This is notation. S will satisfy the whole set capital X if it satisfies each member of X. This is the crucial definition. Very simple. Mod R of X, the restricted set of models of X, is those in R which satisfy X. So you can see immediately that mod R of X is a subset of R. That's it. Then we can define the restricted in carbon. By analogy with ordinary entailment, x entails r y if and only if mod r x is a subset of mod r y. Ordinary entailment, given by mod r, so I say that entails r truly generalises ordinary entailment, not restricted entailment.

2:30 These properties are used to prove the properties of the domain that I've defined in this. So the first one is restricted entanglement is an antimonotone in its restriction parameter, so that's what I mean by that. If I is a subset of J, then entanglement J is a subset of entanglement I. What do I mean by that subset? Entanglement J is really a relation between There is a partial converse to this property if j is full and I explain what I mean by full below. So if J is full, and if we assume that entails J is the subset of entails I, then we can conclude that I is the subset of J. Now what is full? It's a very simple idea. First of all, it depends on the idea of elementary equivalence. So two structures are elementary equivalent if they satisfy the same sentences. Then I is full if it's passed under elementary equivalence. So the full expansion of I is structures that are element equivalent to some number of I. We have this fact that entails I actually equals entails the full expansion of I. So we need that. That's the notation. To note the family of all subsets of struct by P struct. Then the above three propositions that I've spoken about. Any non-identity family of restricted entailments has a greatest lower bound, where the order is subsets.

5:00 It's rather easy to compute, well theoretically anyway, if E is a subset of P straight, then the greatest lower bound of a collection of restricted entailments is just the restricted entailment got by taking the union of the I's as I varies through E. So any collection of restrictive entailments has a greatest lower bound. You don't have to be careful about how you choose them. Let's move on to talk about the domain. So I'll call that domain Enter. That is just a collection of restrictive entailments. It's a complete partial order which I'll just remind you of below. If you take the less than to be superset, the bottom to be restricted in government of the empty set, and the union to be that greatest lower bound. What is a complete partial order? Well, we need to check three properties. And it's not too hard to check these. Check that any directed subset of n has a least upper bound in n, but this is true because, as I said earlier, any subset of whatever has a least upper bound in n. If you are talking about a domain, you want to know what the compact elements are, and this characterises the compact elements. So any restricted entailment less than i, or entails i, is compact, if and only if the set of equivalence classes There are a number of elements of I, which is finite. It's not so startling when you think about it.

7:30 So in particular then, if you start with a finite I, then the entire I will be compact. So we need, then, this K will be complex, then the upper bound of A, then there will be a member of A. So those are the compact elements. The rest is a matter of chugging and checking conditions. So I won't spend too long on this. We need to check that the CPO is algebraic. Well, in particular, if we denote by a props x the compact elements below x, we need to know that the props x is directed. Well, it turns out it is. We need to check that for any element it's the union of the props x, and then we need to check the domain conditions. Well, it is algebraic, and Any pair of compact consistent elements has at least an upper bound, because any element in it has an upper bound. So that concludes the definition of the domain. So let me move, I think we must have struck a record this morning because I'm also ahead of time. To finish early, no one complains. By way of conclusion, let's just make some remarks. The upper bound is a member of n, so equal to the least upper bound of the compactor entailments below it, the upper bound of the ones with finite restrictions.

10:00 Now, it's not hard to show that if these conditions are satisfied, so the restriction set is finite, for example, the structures in R have finite demands of interpretation, the structures in R are all computable. And only finite sets of sentences X and Y are considered for membership of the relation S and R, then it's decided whether finite sets X and Y belong to R or not. So that's easy, or it's not too difficult for sure. I wasn't satisfied with my last slide so I rewrote it. Terms with finite restrictions are computable. Think of a domain of interpretation of a structure which is, say, an unaccountable set. So, what to do? Well, I don't know what the answer to this is and I'm still working on stuff. However, if instead of just consists of structures over the full vocabulary of the language, a place to write this, let's suppose that every structure in strut has a vocabulary V. The constant symbols, the function symbols, the relation symbols. And let's suppose every member of struct has that vocabulary, is defined over that full vocabulary V. What we need to look at is structures T, where the vocabulary of T is possibly a proper subset of the vocabulary of S. This is my thought.

12:30 Key terms may include, for example, algebra, mathematics, geometry, algebra, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, Which, let me say, have vocabularies such as this approximated. In fact, the finite ones want the finite vocabulary. The trouble is in getting these pairs to behave appropriately rather as I've shown you stepwise along in my talk. To produce the kind of approximations for the entailment restricted by elements that look like that. Some part of the way along, and I haven't nailed down all of the details yet. What kind of specific connections you're trying to get to AI and computer science? Can you say something about those? Could you make it louder, please? Big question louder. I thought I stopped louder than you did. What are the connections you're looking for in this AI and cognitive science? The motivation comes from cognitive science. However, if we can compute approximations to ordinary values, imagine you can do some kind of, say, numerical analysis. All you're doing is... We're lucky to move the approximations together to get the full detail before we can't do that completely, but you can approximate along the way, so maybe there are applications, but I don't have detailed examples.

15:00 I tried to connect things together with what's known about using the compactness theory in the first order logic. Where formulas, so to speak, give the basic neighborhoods, and the compactness theorem for first-order logic shows that the space is compact. Then we know that the open subsets of a compact house or space form a blue kind of lattice. So don't you think there must be some direct connection there between what we know about the topological statements and what you're doing with the entailment relation? Well, thanks for that idea. I am not familiar with the details of that. Ask the guy standing next to you. Thank you anyway. Any other questions or comments? Okay, let me remind you that we resume today at 2 p.m. and there is a revised schedule. I think Marcus Gatto is speaking at 2, which is a change in schedule, so you need, I think there's still, if you didn't pick one up earlier, I think there's still copies to be had before the conference. Let's close by thanking all of our speakers for coming. Thank you for watching this video, I hope you enjoyed it. Sorry, can you squeeze past? Oh, that's okay. Sorry, forgive me. Excuse me? Yes, of course. Thank you. I apologize for delaying you. Hang on.

17:30 Thank you for your attention and see you in the next lecture. You have some interpretation of the type as usual written by the Cartesian closed category or the structure of the category you are in and you bracket it by the neutral terms of the type and the normal forms of the type. These are the bodies so we are... So the normal forms are the long beta eta normal forms, and the neutral terms are the bodies of the things that come after on the ladder. So variables apply to normal forms. So, I have no, I mean, I don't know. You play the same game, really the same kind of game. No, no, no. You can read an expression on the Newtonian line, or you can read a mutual expression on the Newtonian line, or you can get the whole class. Is there a proposed lunch at Atiyah? Uh, is that a good idea? Uh, yeah. Oh, I see. And what you're suggesting is that the way Errol builds on these things. He's the same way. Okay. He's the same way. I don't know. But... You're right. It's simpler. You don't need a top. You can just take the bottom. Bottom. Bottom. Bottom. Bottom. Bottom. Bottom. Bottom. Bottom.

20:00 Bottom. Bottom. Bottom. Bottom. Bottom. Bottom. Bottom. Thank you very much for your attention and I hope to see you again soon. Directed to complete. Well, it's a well-defined notion for any relation. Thank you for watching!

22:30 Do you have information as to where there are places to eat, and do you know that they're up here, or are you just as it were? We do know that there is a lecture organised by the conference. Oh, there is, is there? Oh, something you said that we were on our own lunch, but then I think something was arranged. But that may just have been a latrine rumour. Yeah, there's people down there, it's not going to be for a little while, is it? Because our session ended so early, the others are still going on.

25:00 I'm fine as well. Testing 1, 2, 3, Testing 1, 2, 3, Testing 1, 2, 3, Testing 1, 2, 3, Testing 1, 2, 3, Testing 1, 2, 3, Testing 1, 2, 3.

30:00 I should really like to understand that more better, because I think it's a very mysterious topic.

32:30 Thank you for your attention. I'm not disturbing you if I come here.

37:30 Apart from the domain, there are only about four or five workshops going on, and I'm only staying for the domain theory workshop, so I should be finished. In fact, I'm going to be hanging around on Monday with people I want to talk to, and then get back on Tuesday, but I suspect there'll be far more people here in the middle of the week. It looks like a bunch. It really is an enormous meeting. Yes, all the people who are into the detailed programming applications and the protocols and that stuff will be here. Are you staying for the whole week or? I'm staying for the first part of next week. I'm here for the formal methods I'm so sorry, I haven't got my badge on. My name is Michael Wright. Nice to meet you. I'm from London. Excuse me, I need to go back and see if I can get a refill. Can I just leave those there? Thank you for watching this video, I hope you enjoyed it and I'll see you in the next one. We've come to the stage now where we have four groups. Three of them have come discharged.

40:00 What's more important is the corpus discharge. There are three cases of the discharge, I'm sorry, there are four cases of the discharge, three of the four, and we're left with one niggling bit of a clash in the fourth space, and that's how we actually encode it in there, and it will go away. So, the story is very down-to-earth. So, we've got a reasonable story, haven't we? Thank you for your attention. I think that I've done the proofs by hand. I just don't have proof that I can say them out now, whereas I'm not going to stand with the proofs. The BBS is actually pointing out the properties where they have a conversatory mix with handwritten proofs, which is so damaging. It looks a very interesting workshop and let me start the clashes with the domain theory. Thank you very much for your time, and I look forward to seeing you again soon.

42:30 Well, they do quite a lot of big international meetings these days. I've noticed they do it particularly at large physics conferences, especially if you're going to turn that, you know, they're charging these sorts of prices. They usually have somebody there actually making webcam recordings of most of the speakers and presentations, and then offer those afterwards to people, precisely for people who... Who were not able to get all the workshops and who have an interest in more than one field and of course they also can power them out afterwards or so on to interested corporations or university research departments or institutes and I think in fact it does actually generate quite a profit as well as being a very useful service. Plus it preserves, plus it preserves the proceedings. And I'm surprised that for some reason mathematics conferences in general And logic, computer science conferences in particular, don't seem to have got around to the idea, but nowadays the people, the physics people, I'm told by my colleagues, because I'm interested mainly in shapes and photographers, I attended a couple of conferences where there were a number of people that wasn't really a physics conference. And I noticed in doing this, and in fact it turns out that this is now more of a standard procedure in most of our physics conferences and in quite a number of other areas, the Newton Institute did it with all their means, but apart from that it doesn't seem to have become a widespread practice. I think it ought to be encouraged because, as you say, not only does it preserve the physics, but it actually generates, it is actually a public center. This kind of ideas, this kind of education, nobody understands. I teach business classes and they're all video. Exactly. And when can I actually send them on? Yes, and now there's, of course, as I say, with webcam, you can even do sort of interfacing conferences in real time.

45:00 But for some reason, I have noticed that mathematicians in general, and perhaps mathematicians in particular, seem to be just not shut up about doing it. It's particularly curious in a conference which has got so many applications directed in computer science that nobody thinks of doing this. I'm just simply making recordings without being able to see the overheads is often not very much valid. Let's give it some value. But there are going to be people who, for whatever reason, are just simply not able to get them. And it seems, you know, that it seems... Well, perhaps one should diplomatically put it to the organizing committee for next year. I was going to say, well of course I suppose if it did become the norm then you can see why people, or conference organizers might not be too keen on that, because it would mean fewer people actually traveling to conferences. But I think people are always, if they can, find the time. There's no substitute for that. It's not as if you're going to have a video conference and taking over for a very long time. I think that would make a very good idea. Absolutely. I discovered, you know, quite late in the day, that they already do this now almost as a matter of course in large international physics conferences. It's something, and it pays for itself. In fact, it's more than pays for itself. It actually generates a quite significant conference center, longer term, for the conference organizers.

47:30 So I would have thought, it may just be that they, you know, people on the organizing committee, these kind of things, just think that it would be too much trouble. But of course they don't have to do it themselves. They can always get in professional people to do it. Thank you. Hmm. Absolutely. I mean, I'm really surprised that it hasn't become a widespread at this point, after all, in the 21st century. If you wanted copies of those, you'd be paying at least the cost of production, but in fact it would be the additional profit sent to the organiser, so I can't say. I'm very surprised that people haven't done more of that. Well, as I said, it already seems to be more or less the norm amongst the physicists, and perhaps it's going to come back in the... into... And as a matter of fact, I think that very large conferences with an awful lot of subdivisions like this and some of the other large conferences I've attended, I'm not sure that having them all at the same time in the same overlap is necessarily a very good idea. I think something like video conferencing for some subjects might actually work a lot better. All the workshops I attended were really quite small focus workshops. Yes, indeed, but of course logic now is such a huge contrary of overlapping disciplines and becoming more and more of a problem with communicating between different branches of the subject.

50:00 Thank you for your attention. And I usually go to a very focused conference. I come in draft, I go in psych, I come in print, and I go to the first meeting with everyone who comes to that. Yes, yes, of course. That's such fun. We don't have to go to the meeting. All right, yes. This is all about school. Start with school. Oh, I have to get to see the kids. I think you're going to be cool, right? That's where the whole state is. It's not the five-pound Chicago. I'm going to Chicago. It's not even that wide. It's in Indiana. We are south of India, just across the border of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India, south of India. It's interesting, I have two, I have two friends. They're both from Paris, they're both American mathematicians, both of whom actually grew up in England, and I'm a teacher there, and one of whom has lived in Britain now for over 30 years. One of them, who's here, Bill Lorvier, of course, he teaches at what, until he retired recently, he taught at Bursa, but he's actually in the Arnhem and Arnhem region, I think. Not quite on this one. Well, his name, that's Lorvier, a very big name in domain theory, but he's quite well known as one of the co-creators of John Hoss theory. The other is a chap called John Mabry, who is a model theorist, and does a bit of work in functional analysis. Thank you for your attention.

52:30 Yes, yes, and of course, yes, graph theory is a very active area indeed at the moment because of the interlinks with knot theory, which is now a huge area, topology, knot theory, and a huge area in mathematical physics and all these topological quantum field theory programs. Thank you very much for your attention and I hope to see you again soon. He's, is he still at Oxford, Robin Wilson? Is he still at Oxford, Robin Wilson? Is he still at Oxford? I thought he was an opening... Oh, he may well be, he may well be. Of course, he could be a foe. I know he does quite a lot of their first, second year programs, yeah. Thank you for your attention. Yeah, he must have been his late years by now. It's amazing, I still think of him as a kind of young man, because I knew him from the time of... Oh, he was here, I certainly did know that, as a matter of fact. I met him quite by chance when, long before he became a mathematician, and in fact even before his father was Prime Minister, they used to go on their holidays to the Scilly Islands. And when I was a child my parents used to take me to the Scilly Islands, and this was in the 1950s. And we actually used to play with the Wilson family on the beach there, not knowing, as I say, at that time. Although he was, you know, a politician, he was fairly, he was in opposition. This was some years before he even became leader of the Labour Party and I used to know, I knew Robin Lawson and actually his younger brother Giles who was rather closer to my age and we, just as children we used to play on the beach in Silly Isle.

55:00 Robin I didn't really, well I knew to talk to him, you see he was quite a bit older, he was about five years older and of course when you're a child of seven or six, seven, eight, five years is a huge difference. Then I knew him later when I was a graduate student. He was already a research fellow at Oxford. Yes, it's very sad. It's very, very sad about his father. He was a very brilliant man and of course he unfortunately... Not long after he went out of office, he had a very serious operation for cancer, which means he was under for, yeah, for, well, over three weeks, he was on the operating table for about 13 hours, and the effects of the anaesthetic, the very prolonged anaesthesia and various other problems he had. He led to a very, very rapid medical decline in the last years of his life. He was brought to this completely unnecessary trip, almost completely. Very sad because he was from 64 to 68, no from 64 to 70, well he was twice actually, he was Prime Minister twice. He was Prime Minister from 64 to 1970, and then he came back two years from 74 to 76. Rather to his surprise, because I don't think he expected to win the election, what happened was he was called a snap election in February 1974 because of the miners' strike, thinking that he would win it on the hookah. But in fact it resulted in more or less a hung parliament. It resulted in the Tories losing the majority. In fact they actually also ceased justifying a smidgen of that 262, the largest parliament. And he tried desperately to cobble together a pact with the Libyans, but that failed. And Wilson was asked to form a government again, which he did. He was already conscious at that time that his powers were failing, that he had got serious health problems.

57:30 Which he, of course, you know, hadn't made public, but I think he was already aware that he was not a well-mannered man, and he certainly, and then very much to people's surprise, he resigned almost immediately after his 60th birthday, I don't know, 70th birthday, yeah, and it wasn't made public at the time, but in retrospect, it was pretty obvious that he had already been told by his documents that he had to leave. It was very sad because he was, and in his prime, I would say he was intellectually the most impressive I don't think he was a very successful prime minister, you know, there were all sorts of, actually it's quite interesting. I think very high intellectual gifts are often not at an advantage and frequently a distinct disadvantage in politics. I think having a very forceful personality and... Disciplined, but essentially reactive and unoriginal mind. Probably, on the whole, more of a recipe for success in politics than having an absolutely first-class intellect, but without the... You've got a forceful personality to go with it. You can think of quite a few examples. And if you think of it in American politics, Monarch is the most... Well, exactly, I was going to say, I mean, you could argue that in the 20th century, the most intellectually impressive, the most intellectually impressive president to have probably been passed was Wilson. And, um, Huber. All three of them are regarded, well, perhaps, as Wilson's son in a way, but certainly Huber, regarded as probably amongst the biggest failures of... ...of any of the American presidents, although there was definitely a farmer, a new farmer, a farmer, and had a far better grip, a far, far better understanding of the economic problem.

1:00:00 He was just extremely unlucky, in fact. And Carter's problem, it seems to me, was certainly actually far more impressive. I have to say Clinton was pretty awkward with him when he chose to apply himself. ...which was that he could not delegate. He had absolutely no ability to choose competent subordinates and delegate to them. He tried to do everything himself. And that I feel is why very much... He was extremely unlucky in terms of the point of the economic cycle, where he became an economist. And also because of the Iranian crisis in the last few years. All of that. But events were very much against him. But then, you know, you can say that to any politician. But the main problem, I think, is mainly that, and of course he wasn't a Washington insider, but say the same about Fenton and what he got away with. I think his big problem was Carter's problem. He was very right. He was much righter than many of the people around him. He could not delegate. He did not know how to pick subordinates and delegate. Whereas Reagan, or Dickens, a B-movie actor who could scarcely do more than read Nantes and Kierkegaard, because, I think it's just the fact that his mind was effectively promoted and managed him to do all the picking for him, but the fact was that he did get extremely effective support. ...and give them a very broad remit and then just simply lay back and really take the occasion to make big decisions, which he was... In terms of his historical record, really, he was extremely lucky because he was very close to the point where the collapse fell down by that much anyway. And Gorbachev came along, which is obviously a huge change. So... He gave to the circumstances that he comes and look at Yair Yadav... Absolutely, absolutely. He lowered everything. He lowered everything. I mean, no, he makes great of the topology, brilliant. But also, I have to say, although I agree with him, which is obviously completely dumb, the fact is he also appears to act.

1:02:30 ...to be quite effective at choosing subordinates. Although, in fact, it may very well be not him who chooses them. It's his advisors. I suspect that his... well, the fact that he chose most of his fathers, a lot of his fathers, so he didn't even have to do that to himself. No, I agree, he's absolutely done it. And also, of course, the one... The thing that he had going for him was that he was not Clinton. Because of all the sleaze that was received by Clinton. It's now a joke because in fact... Yes, but yes, he's just being an alternative. I mean, now, look at all the financial scandals that were hired in a corruption internet. And of course, he was very close to all those people in Enron and the county's going. I mean, he wasn't elected in the first place. Well, no, I was going to say, he hasn't even been elected the first time. It was his brother who saw it first. But I saw when I was in the United States last year, I saw quite, it was before September the 11th, of course, so I can't imagine they would have had the money to resolve that. I was in Florida, and there was a car driving ahead of me which had quite a good bumper sticker, and I saw it in one of the other places, which said, re-elect Gore and Lieberman in 2000 and 2004. Jeff Bush's daughter got arrested. Yes, I saw that, for violating the drugs. Well, please accept that is so ludicrous, isn't it? I mean, the Americans having drinking laws whereby a 21-year-old girl can't learn how to buy a drink in line is so absurd. I mean, many teenagers do that, which is the fact that you are... But the thing is, they weren't even teenagers. They were 20 and 21, I think, respectively. Or 20, I don't know. I mean, it is absolutely ludicrous. A very high proportion of Americans, because of the legacy of the Puritans, do have this quite astonishing... It's a startlingly anal or attentive attitude towards drinking, towards any alcohol consumption at all. And it is absolutely weird that you've got states where a 16 year old can go and buy a handkerchief, or where an 18 year old can illegally go and buy an automatic rifle, but where they can't buy a bottle of beer.

1:05:00 I mean it's just, obviously to an outsider, it does seem to defy logic, but still. I suppose we have a number here for you. Really? They still have something there? That's again anti-biblical, yes. Well, of course, I mean, there are, I think I might have to say that there are still one or two individual counties in some states that are still trying to pitch down that. One or two individual counties. You can't buy a car. Oh, you can. You cannot. We used to have quite restrictive Sunday trading laws in England until about 20 years ago. I think there's one county in Wales where they still have Sunday closing of the pubs. There's one very religiously conservative county. There used to be two or three, but I think it's now down to just one county in Wales. They have a referendum once every ten years on whether to allow the pubs to open on Sunday. But each time it comes a little closer. The last time it was split about 51 to 49, and as the old strict Methodists die off, it will eventually obviously come down. Well, in the US they don't want to be followed by a class that wants to lead. If they have certain laws they want to stick to, they are rewarded with understanding. Oh, I do realize that. They have very little understanding of the rest of the world. I mustn't generalize, obviously, we have very good, brilliant, well, good scholars and scientists, but of course we have to be there, because we have to remember that there are, after all, sort of 6,000 miles of ocean on one side and 3,000 miles on the other. It's not as if they have ever... Yes. And because, after all, it is ocean, it's also a continental economy. And the astonishing thing is... I think that is considerably less than 50% of Americans even have a passport. I think something was said about you. I got full grades probably.

1:07:30 And I went to Zimbabwe the next year. And at that point the officers... In the Department of State in Peru, we had the officer visit us to talk about Cuba and she said it was alarming. She was alarmed to see that, not only the economy was predicted, but Congress perceived elections coming out less than usual. 30% of them have asked questions, and 20% of them have been outshined. Bush, in fact, at the time that he came to Paris, the first time he had ever been. I'm not sure if it was the first time he'd ever been outside the West, but certainly the first time he'd ever been to France or, hopefully, Britain. I think he might have been. Oh, and unbelievably so. It is quite astounding the extent to which they are unaware of the rest of the world. There's just nothing but domestic years. Yeah, the international use of mathematics is much better now. I know, I know. They have virtually no... and they can't place an awful lot of... For instance, I'm sure that anyone, even in your position, coming from the subcontinent, has a thread in the time track that may make them even aware... I mean, the one thing is that the British, for obvious historical reasons, you know, India does loom very large on their mental map of the world, I mean for obvious historical reasons, but for Americans, it is astonishing. I mean, most people are sort of not aware of it. It is by far the largest democracy in the world. If you tell them that they're not the largest democracy in the world, they get most offended. They say, well, yes, actually, there is this little physical India. It has a population of well over a billion now. In the 1970s, there was more than one million people. For example, Indianapolis, for example. No, I think a lot of them were talking about that. No, I can well read that. No, I do, because I do deal with quite a lot of narratives. I wear another hat. I actually have a small travel company, so I do know a little bit about these. I call it a turban. I wear many different turbans, and that is a turban. I hate to say it, but I imagine that you have had quite a lot of problems with the ignorance of your members that I meet. I mean, I hope you don't mind my asking, but did you actually find yourself receiving any hostility because they don't actually understand the difference between a seeker and a human? I've lived in the US for 25 years, wherever I've lived, I've been the only person to serve in the US, and now and then I'll get out.

1:10:00 There's quite a substantial Sikh community in the United States at the moment. But I'm not an Indian, I was going to say, I'm not an Indian. And also I noticed in West Ontario, across the border, Toronto has got a huge Sikh community. Yes, of course. I've never been to the West Coast, I've never been to Vancouver, but I have been to Toronto. So gradually they're beginning to become aware of it, or as it were, aware of it. Which is so grotesque, isn't it? Because they think that it's something to do with physics. I mean, even the most people. In the case of the Sun Reapers, would know that Sikhs were not Muslims, that they were not Arab. In America, even quite educated people say, even people like the congressman, would not be aware of the Sikhs. Well, the problem is, as you say, because it is such a vast nation, it's economically effectively a world to itself, it's culturally a world to itself, and it has an awful lot of geographical space insulating it from the rest of the world. I must tell you a little story about that which may amuse you. Again, I'm sorry, I don't know what it seems to sound like. It does underline the point you just made. In 1993, I went to a little congress in the Mediterranean.

1:12:30 And we began to stay with friends at Case Western Reserve. It's four, but higher, for a few days. We got a car and we picked up a car in New York and we drove across to Cleveland in about two or three days and stayed with Colin McFarland, a friend of Peter's, so we were then going to go across to, actually to London, Ontario, which is where the Congress was, and it occurred to us that we hadn't actually checked to see whether we were allowed to take the car out of the United States of America, so we thought we'd better ring, so we rang the Kirk's office. In Cleveland, which as you know is actually on the lake, and which is on, well, on a very clear surface, you can just about see the Canadian shore, and it's probably about 70 or 80 miles, but anyway, it's certainly no more than that, and you can be in Canada in an hour. So we rang up the manager of the PERTS office this week and said we've got this car here, we bought it in New York, blah blah blah, this is the reference number. We just wanted to check, we're going across to Ontario. ...to London for a few days. Is it okay, you know, on these documents, to take a car outside the state of Canada? We should have checked on that. It goes into lots of bits, you know, computers going, oh yes, there's no problem at all, you may take the car out, you may take the car out to Canada. Any time. The only condition on the higher is that you cannot leave the continental United States. Well, yeah, I'm sorry, that's just what we, anyway, it was fairly obvious after going around the circle a couple of times that this guy, who must have had at least a high school education, probably, I mean, he was the manager of their office, you could say. He was not a functional literate, he was the manager of a, you know, a financial service business. He's living somewhere within an hour's drive of the Canadian border, and he's quite unaware that Canada is a separate sovereign state from the USA. I mean, I think that probably would be unusual. I don't need to say he was typical, but it gives one some idea of the kind of levels of ignorance about Canada. The fact that it's non-zero, the number of such people, what's it do? I know, it is quite scary. Now, had it been in New Mexico or somewhere, I would have made allowances, but it's not

1:15:00 Well, I have had that experience myself, again, taking people, wearing another hat. I do work sometimes with them. And I've also taken American groups on the Eurostar. And the number of times that I've had American high school students, in some cases, in the university, and in the world. ...save me, having gone through the ticket barrier in the Eurostar Terminal at Waterloo, when you go up the escalator off the platform to get on the train, have turned around and said absolutely seriously, are we in France, is this Paris? And I literally thought she went through a barrier in London and emerged. And also years ago, at the time when the Berlin Wall was down, and a number of times when I was in Berlin. But mathematical is in a backpack of people in their 20s who would say things like, the war had been one of the central factors, the symbol of the Cold War and the vision of Europe for 30 years. Yes, of course, for about 30 years. Certainly for 25 years. You could not possibly have seen any reference to more than an hour or two without seeing some reference to Berlin Wall. The number of times I've had a keynote would simply say things like, you know, we can't get this into mind. Would you tell us, why is this, why is this, why do we keep driving and we keep coming to this point? They just had absolutely no idea about the history of Europe post 1945 or of the geographical subdivision of Germany. If you look at the typical law of middle school in India, they would know all of our second stories. Oh no, I have no question at all that the standard of secondary education in India is far higher than it is in the UK. For you, as a graduate student back in the 70s, you know, all international students, everyone had what's called a foster family, a volunteer family to make kids feel at home.

1:17:30 So I had a foster family, my wife and I. They invited us over again. That was a few weeks after we agreed to be there. Thank you for your attention. So they brought out a nice dinner for us. What they thought was not very nice. Towards the end they brought out ice cream and we asked them, have you had ice cream? Do you have ice cream in India? Oh dear, oh dear, that reminds me of a love-or-loving story. I had a friend, a friend of September's like at Cambridge, who now teaches at Lancaster, a story called Feroz Yasmine, whose family were originally from Punjab, but his father, his mother spoke English, and we'll come on to it shortly. The first day or second day or so that he was in his, he was in Dix, you know, and... His landlady came rushing into his room at about 8 o'clock in the morning and literally kind of shook him away because he was so excited. Oh, we're still here, we're still here, we're still here, sir. Please, get up, get up. Please, come and look at this, sir. Come and look out of the window. You've never seen this before in your life, sir. It's called snow. Of course, he's all, poor old Bruce, he's all dragged out of bed. Oh dear, oh dear. It is astonishing how little... I suppose a little less so now because of the post-September the 11th events in general, and obviously because of the recent tension between Pakistan. But it is absolutely astonishing how little the whole subcontinent registers on America's mental map of the world. I suppose there are historical reasons for that.

1:20:00 I think in the US they become aware of the current topic and because the media is so strong, they only bring in their self-interest. But they think in the US they become involved. I mean, they know about Vietnam. It's not because they fought the war. Well, and they lost the war. Yes, indeed, although they don't remind them about the war. They don't. And Korea, and now Afghanistan. But they don't fight those countries. Oh, no, no. It is incredible how little awareness they have about the rest of the world. And I mean, when I find people, let's say, with high school grades, or even with, in some cases, underbarreted degrees, who are baffled to discover that you have to actually either cross or get up under salt water to get from Britain to the mainland of Europe. I absolutely refuse to believe that it's not joined on. I'll just try it straight across. You can reach me back to Robin Wood since you have the kind of sense of humor. I've heard him speak many times. When nobody comes over, I do it. He always starts listening. He'll be back in a couple of weeks. Yes, I hope they get the joke. They sometimes think there's a sense to it about that. I know, I know. He does it on purpose. He's a nice guy. I have to push over and chat to a couple of my... And you! Very nice to meet you. I'm now trying to go on to one of the full systems meetings. So you're on power?

1:22:30 No, but it's nice to meet you. I enjoyed your talk this morning very much indeed. Oh, Michael Wright. Where are you based? I'm based in London. Well, no, I'm not with any institution these days. Here we'll tell you my strange official history. So we see people haven't really grasped the fact that sub-objects are not the same thing as a corresponding map of the eucalyptus. Of course not, it's not in any of them. The thing that they get into major problems with is not wanting to identify projective sets. Yeah, I mean they'll want to take a particular set, say the base would say a model rather than a particular object, and then they'll start to say, okay, these are different. We want to do constructions in which we really need to identify them, and they make mistakes, you know, you tell them, you know, at some point you sort of tell them, okay, for me this is distinct, if you do that, you're going to make a mistake. No, no, no, no, we're not going to make a mistake. And then you have to wait until they do, and at that point sort of pull it out of them, and you're reminded, you're told at the start that they were going to get into this stuff, and then of course, you know, five minutes later they'll do the same. What's up within the area is that they do really identify things, simply identify, like this image in the Kodama, which is disastrous, and somehow they don't realize it's a disaster, so it's time for them to adjust it. It's terrible.

1:25:00 There is a certain sort of ritual that one has to follow, in fact, fortunately, lectures that were taught in the last half of the last half of the last half. No, but I mean, you see, there's a definite flavor about any lecture. But this is, in large part, just going through some notes, kind of with the, I mean, I'm reminded of my son once, his paper was marked wrong, because he was in junior high school, the formula for the area of a rectangle. It's L times H, not H times L, nor any other letters. That's why we have this sort of ritual, not to recognize the constants of the other functions, but to say you've got functions that are already in character. Even though they may occur sometimes. The world of the rituals that we learn from is quite different from what we're used to. There are some rituals that are distinguishing between predicate, unary predicate symbols and non-sensical symbols. I mean, typically one of them distinguishes between non-sensical symbols and predicate symbols. Because they have different code of events. Yes, but it's amazing, not only for these people, but for the rest of the world, for the rest of the world, for the rest of the world, for the rest of the world, for the rest of the world,

1:27:30 There's a positive aspect of this. Dr. Eilendorf, who was an extreme mathematician, said that mathematics is really a question of habits. Of course, there's that idea that you adjust your habits to fit the situation, not the same ones you do in high school. He was very fond of saying that the main discovery is the associative aspect. All sorts of complicated things that other people did, and he managed to choppa choppa choppa them, and in essence there's nothing left to associate them with. That sort of thing, he was very... So that kind of habit, you see. But habits have to be adjusted, and the habits become the trivial part of the... Subtitles by the Amara.org community I think the computer scientists are of two sorts. One is the mathematics background, who I think tend to be more mathematically sort of like some of the others with the computing background. They tend to have a better idea of the computing and they tend to be quite rigid about the mathematics and have some sort of despair of them. The problem with the mathematicians is that they can be completely computer-based, so they'll say something like, well I've basically modelled this thing, whereas if you actually get to understand the computer phenomena you think, well no really, you've sort of found the easy part, because you haven't really got a part of it. It's getting much better. I mean, I remember I had these countless arguments about that they'd be happy when they had a definition and some examples, and they wouldn't see the point of having a theorem, but they said, we don't need theorems, we can do the science. I mean, it sort of feels strange that you actually have to explain to them why you need to have theorems.

1:30:00 So you mentioned that max is 20,000 kilometers per second. Does that mean we just need to do it? Well, that was a joke, right? I know. But it means that everyone knows those. Because, I mean, I think we all know that joke. Thank you very much for your time, and I look forward to seeing you again soon. When you said yesterday, it was monkey around with a set of products that he was using. Well, if anything would pull you. Yeah, if anything would, yeah. Don't worry. Yeah, and he was very keen on, I think, very systematic notation. So, yeah, talking about a limit in a bicategory is a very dangerous concept, in fact, and it had to be a pilot. Even if people understand the decisions in concept, the very thing I'm using is this definite choice of terminology. There's a lot going for that kind of thing, but it goes from there occasionally. Yeah, I mean it's an excellent point, but there comes a point if you're writing a paper and if you're trying to address people. You're going to confuse them, and they're going to get lost if you keep them in algebra for three months, and somebody's going to say, by three, I mean this thing has an aftereffect. I have a paper called Adjoint, Eminent among Bicategories. There's plenty of Bicategories out there. By saying that, well, there are some technical complications concerning our association with this composition, but it's full of additions, you see, so I thought, again, it was best to just refer to that without getting into it, because the other issues seem more pressing and more relevant.

1:32:30 I remember that. But that's also the sort of part which you want to be in by 20,000. The commons are way from maximum. There you go. What's it by category? And I said, because he'd obviously read it somewhere else. I said, it's the same thing as the two category. And he said, I don't believe you. I don't believe you. They wouldn't have two different words. That's right. Actually, I had to explain a bit. After the explanation, he realized I could stick with two guys. Scotty, actually, we have to... I don't know how you're... You're the one that they tried to ambush. Oh, yes. I did go... They didn't have a meeting. Yes, they did. I understand. It was a very interesting meeting. But I mean, I have a little guarantee that one side of the way is where you've been getting all that from. That's very much kind of trying to generalize quantiles from a quantum view. I mean, they're no more enriched or less, but they allow several objects, which is almost invariably the natural thing to do when something is not positive at all. Probably they really send the objects around, not just one. But we also had a talk on the subject of the non-convective. I was reminded of your discussion of intersectional forms taught back in France.

1:35:00 We must go into this in order to get over here, so let's keep up the front. Um, there was a guy called Freddie Lucas. Yeah, yeah, he's a radio host. Yeah, he's a radio host. Yeah, and he's, um, he's a very funny guy. Um, yeah, and he... Yeah. He gave a talk on Thursday, which unfortunately I missed.