Jones Polynomial & Yang-Baxter Equations from the Ising Model (contd.)

0:00 Sigma I, Sigma K. Remembering that the K is the line, the row, and the L is the vertical corner. And now we consider an m by m lattice. In other words, you know, I don't... just m points by m points on that. Now then, to marivate this rather than prove it in general, Consider a typical configuration. Those are my spins, one particular feature. Now when the two end lattices are different, sorry, the spins at the end of the bone is different colouring. So I've got one there, I've got one there, I've got one there, and I've got one there. Yeah, that's obviously how the chromatic polynomial gets things out, doesn't it? Yeah. In the current problem. I've actually now changed the notation round, I'm sorry, I knew I was able to do it. It's almost inevitable that whenever VJH is working on it, it will do a slightly good choice. k is now vertical and L is horizontal. I'm sorry. I suppose it keeps picking on the toes.

2:30 All you can do is just change things. And then let me have a look at the horizontal. You can see that. So that means I've got four verticals. and S equals 2 horizontal. R is going to be the number of vertical bonds I've got. S is going to be the number of horizontal bonds I've got. In this particular case, vertical bonds I've got four, and two horizontal bonds, one being defined by when the two spins at the end of the bonds are different. So now if we look at the vertical, we have R unlike, The lattice is m by m, which I've got of course, and z is s unlike with m minus s like. OK, so now I've got all the bonds labelled. Right. Because when they've got like, they're in top energy. When they're different, they're energy level two. So I've really divided them off into the two energy states. Do these, I'm sorry, the trace of the four-calorie theorem, the chromatic-paroleinomial? Well, no, but it's obviously, you said yourself at the beginning, that it's coming, no, no, no, but do they use, I mean, that, of course, is a computer-generated proof, isn't it? I mean, it's never been done by hand. I mean, I've checked the individual portions of it, but it's far too long for any one person to actually go through it. I mean, is that because of the huge number of matrices that you've got, the huge size of the matrices? I just wondered if any of the software that devised for that has, I mean, this may be

5:00 you know, grandmother suck eggs has actually been tied to the protein-colding problem since there's obviously at least some structural homology between the two problems. No, I was not hearing about the chromatic polynomial for the first time, but it just strikes me that... Turning a page in that book and suddenly seeing the full colour thing in the... But it's just that, obviously, the structure of this problem, that essentially is an icing... That's the box model. Yeah, but this is an icing, which is obviously related to all of, you know, the polymer folding problem. Yeah, yeah. The shortcuts that they've used to get the proof of the four-colour fit, and whether they would have any application to the periculum solving problem. Because that was written before the four-colour problem was solved. Yes, it was solved. Oh, yes, it wasn't solved. It was solved about 83 or so. Because it was the first really significant computer-generated proof, wasn't it? This is probably old ancient stuff. What I'm doing is I'm working out what a partition function is in terms of bonds. This is where the linear graphs come. Okay, going into the integration of Uniscount and bonds, this is where it comes from. And this is actually no temperature. expansion. There are two expansions, of course, that one uses in the IT model. One is the low temperature expansion and the other is the high temperature. So one, you're coming into the critical point on the low temperature and on the other one you're coming into the high temperature. And what the duality does is enables you to meet a mirror and so make Okay, so there's a dual relation between the high temperature and the low temperature. One is on the dual lattice and one is on the ordinary lattice, and that's where the... This is for the cubic. Oh, it's quite rapid. Okay, so that's where I'm going, just to keep you in mind that I'm not just... Showing lots of... OK. So, now, I want to know what to put in here, in terms of problems. So if I consider that K sigma, I just call it sigma, I'm just .

7:30 People don't know how to come to me, so . Never mind. K times M minus R like, plus R unlike, and therefore that means that K is equal to M minus 2R. Because when it's unlike, it's a minus sign, when they're likely to have a plus sign, and therefore the total energy is an adequate. And so then I can do the same for L sigma minus sigma K, and that is just l into m minus 2s. So all I've got to know is what the number of r's or the number of s's is, and I've solved my problem. That's where the colouring of the graph comes in. Now I want to introduce the dual lattice. Okay, so I'll just rub this off. I'll do the dual lattice on you. I really haven't got enough lattice yet, but I shouldn't have put light on it. So the dual lattices put the centre... So, an ideal like this is a square, you generalize this with a star triangle. This is easy. Now then, you've got to do something. Draw a coloured line. So let me put the spin.

10:00 I'll do exactly the same as I've got here. Now let me draw a colored line every time there is a different spin at the end of the bond. They're different. Minus, plus, through a line, through a line in the color. Plus, plus, leave it alone. Plus, plus, leave it alone. Plus, plus, leave it alone. Plus, minus. Plus, Plus, minus. Plus, minus. I think it's a bit square, isn't it? No, it goes on. Yeah, it's a square. I'm sorry, I've drawn this too close. Come on, you get very nice. Now you see, if you put on the left the yellow cloud, then that would actually be a bit square. Yeah, yeah. Well, I mean, if I were to complete this, what you find is that you get... You want to... I just want to do an example of it. What I'm trying to motivate for you is that what the dual lattice does is to isolate all

12:30 minus points so you can generalize you've got big polynomials you've got big polygons with a sea of minuses inside yeah and then you've got another polynomial with a sea of minuses and the crosses are outside the polygons so the The red polygons divide the plane into up-spin domains and down-spin domains. And then the partition function is equal to 2 exponential mk plus l sum of propellant exponential minus 2 L R minus 2 K S. All I've done is just tidy this thing up and put it back, no physics has gone in, it's just a question. Rewriting this with these two terms. But these are now polygons, and some of them are all polygons. And this idea of the coloured polygons dividing up the whole plane into, off and down to spin the Well, that's what you'd have to do anyway. Your point is, you've got an ensemble of spins, and they're all equal-probable, remember you did an ensemble of those. So just throw them down, and then, and you work out the partition function, and that's the way to do it. You know, you don't write down infinite-dimensional matrices, as you saw. When I did it with matrices, it was incredibly obscure.

15:00 But this thing is what I was doing before, only in terms of something which is much easier, which is embedding graphs in the estimation. In this case, I'm looking, this is on the dual lattice notice, this is on the dual lattice. OK? That's the low temperature. And we'll find the high temperature are polygons on the lattice. And therefore you've got a relationship between the low temperature and the high temperature. So you've got a relation between the lattice and the fuel lattice. So you've got this interplay between lattice and dual, structure and dual, so you've got a very deep duality. Really Onsaga. He was Mammoth and Banya. Those are the two guards who were going on. Onsaga, I think, probably did the most. But Onsaga did it via the impersonational matrices. Who did, who started the diagrams going, I'm not sure, historically. Tempoli certainly. But that was specifically in the context of the Eisen model. Yeah. Yeah. And Don certainly did, because I learnt what I know from Don, and Sipes, and Fisher, who was the free king to work. It's just that it all ties up so beautifully with the results in combinatorial theology I'm just wondering if people have looked at the origin. So the partition function may not necessarily have anything to do with temperature? No, no, no, absolutely not. Which is what puzzled me, why Luke Houtman was using partition function for much? You know, where's the temperature, I guess? It's got nothing to do with temperature. It's like purely... Essentially purely common authority. Common authority. Yeah, well, I was interested also in seeing, you know, when it comes in, you go off it, when you put it in the iron here, underneath.

17:30 But to sort the other thing out in the first place, it's just purely combinatorial. Okay, let me now... Here's a hunch. temperature. Now I'll do it, first of all, and I'll leave the graphs, I'll do it with just one there. Now you can see, sorry, I should say, why is this low temperature? because the bigger terms are going to be the order of r and x, yep, because that's the temperature, as I get the higher orbit of L squared, if it's low temperature, L squared should be, oh, because it's minus. Yeah, the terms get smaller. As I expand this out, I only need the first few terms. And that's why it's the low temperature expansion. Now I want to do the opposite. I want to go to a way of looking at it where... I want to expand it as I give the susceptibility, where the terms go to zero, the higher order terms go to zero, and the temperature's large. Okay, now how do we do that? We do that simply by the following. We take exponential A sum over ij. I'm not doing two bones anymore. I'm just doing one bone. This is any, any structure you want. It doesn't have to be a lattice or anything like that. You just label the points. One, two, three. Okay, and you've got to have some way of defining what is the nearest neighbor, but obviously

20:00 you've got to have some structure behind there with the nearest neighbors going on it, but you can see it actually comes out. Right, now we can write that there simply as a product over ij exponential k delta sigma i sigma j oh notice this is not the isomodal This is where pure graph theory comes from. Okay, so now let's take that and expand it, and that of course is just going to give us 1 plus exponential k minus 1 delta sigma r, sigma j. That's where I just expand it turn by turn. Now I don't get it split into hyperbolic cosine and sine because delta squared is equal to delta, delta cubed is equal to delta. So I've just got the exponential, and the only thing I've got to worry about is that there's a... a one that doesn't have the delta function attached to it. That has a one with a delta function attached to it, but I don't want it when I expand that, so I'll take it away. Okay? So then I want to write Zn

22:30 and the sum over sigma phi i j, one plus V delta sigma i sigma j. OK, where V is equal to, in this case, V is equal to exponential k. OK, let's have a look at some terms in there. 1 plus V delta sigma 1, sigma 2, 1 plus V delta sigma 2, sigma 3, 1 plus V delta sigma 1, sigma 3. In other words, I've just got three points. 1, 2, 3. Okay, now, to find that out, I'm going to get 1 plus V sigma 1 sigma 2 plus V sigma 2 sigma 3 plus V sigma 1 sigma 3. Then I'm going to get terms with V squared, sigma 1, sigma 2, sigma 2, sigma 3, plus V squared, sigma 1, sigma 2, sigma 1, sigma 3, plus V squared delta sigma 2 sigma 3 delta sigma 1 sigma 3 plus V cubed times delta delta delta Look, I want to just explain it out

25:00 that you're not going to do it Now then Whenever I see a delta, let me put in a line. So one, two, it's called one, two, three. This would correspond to two, three. This would correspond... Yep. This will correspond to, uh, 1, 2, 2, 3, so that's 1, 2, 2, 3. This one will correspond to 1, 2, 1, 3, this one will correspond to 2, 3, 1, 3, 2, 3, and this one will correspond to the same. So what I've done, essentially, is taken three bonds and coloured the bonds. And each term corresponds, this term corresponds to one bond, this term corresponds to two bonds, this term corresponds to three bonds. Now I still have, I haven't summed over, this is just the product, but I've still got to do the sum over all the bonds. Okay, so the bonds I've got now, I'll go back up the top here again, the bonds have the same sign, if they don't have the same sign these deltas are going to vanish. graph as L-bonds and C-connected components.

27:30 So let me take one of my terms, and that is just C equals 2, So if I want to find my partition function is just sum of all graphs 2 to the c times v to the n. because every time I draw a bold in, that's a big contribution to it. But now I hope you can see how we're getting close to the colour problem. In this particular interactional handbook that I've got there, it's now a colouring problem, but I'm going to get points and I just colour in those. But it also gives me the partition function as a high temperature expansion because V is exponential K. So when k is j over kt, so if t is pi, k over k is small, exponential is k. Therefore, I mean, I want the first u to the one. Because I'm expanding it. The other one I'm expanding at u to the minus k. Do you see what I said? It's just counting there. Yeah. It keeps grinning at me when I say, Well, I'll tell you, there's quite a lot of work to do before you start counting. Yes, yes. Well, you could say the same about the solution to the four-calibre problem. There's all counting, just getting the setting thing up before which the buddy computers could do the counting for them. And it was one of the, you know, it was one of the everestes one of the everestes of mathematics, that problem, isn't it? The counting is not as easy as you think it is. No, no, certainly not, no, it's not like that.

30:00 There are some beautiful counting theorems that Martin Starks developed, which we use, which are really, very... Yeah. I'd like to know more about those counts. You're always counting what went wrong. But there's excluded volume walks. You've never counted the number of volume walks. Excluded volume walks, you counted what went wrong. And then you do the ordinary random walk, it doesn't matter whether you know what the result is for an ordinary random walk, crossing, nuclear, etc. Or you just take off the ones that go wrong, and you start through again. So there is a one that goes wrong. So, you know, it's not a... you have to be a little bit smart. They like to take away figoids, take away tadpoles, take away dumbbells. It's quite a... OK, very nice stuff. OK. Just one more, just to finish it off. Yeah, OK. Yeah. Yeah, I wish I could stay longer than that. Now, when we go to the two-dimensional icing model... partition function is just cross a. Now I'm doing a two-variable thing to bring up the sum of the sigma pi So, 1 plus V signal I signal chain, I 1 plus W signal I signal chain, so you get simply products. and V is equal to tanh K, and W is equal to tanh L. Just remember what W is again? W is tanh L. Right. Oh yes. OK? Now the reason for that is remember I expanded the exponential in terms of kosh and shine. I take my koshes out, I get the shine with the kosh underneath, that's essential.

32:30 These tricks don't work in three dimensions. The duality tricks. Everything else goes through in three dimensions. If these dual tricks worked in three dimensions, they would have solved the protein-folding problem by now. Probably. I think that's pretty well, you know, would say, because it seems, you know... Yeah, yeah. You've got the Nobel Prize for that. You can see what you have to think in three dimensions, numerically, counting graphs. But you can't use this technique, you certainly can't... You can't use this technique, and that's why I wonder whether not theory was going to provide the clue. Okay, well, if not there is provided the clue that solves the floating problem, as I say, you and Lou will end up with, you know, a whole price, at least. Yeah, probably. You can get it. Yeah. It's not an easy thing. I don't understand anybody's message. Okay, so what you've done, if you product these out, you see, you're going to get Vr, Ws, sigma 1, N1, sigma 2, N2, sigma 3, N3, et cetera. So you've got our horizontal lines, I've probably gone back again. I probably changed the notation back again, I'm sorry. And Ni, I'm going to finish. Your notation is like the magnetic pole, it just keeps reversing polarity at irregular intervals. I'm sorry, I'm very sorry. That's all right. That's what we're used to. I'm very sorry. All you've got to do is pay attention when you go through it yourself. All I'm doing here is giving you a feel of the problem. is the number of nines with sag i as n-point.

35:00 Now sum, sum over sigma, and since sigma is equal to plus or minus 1, the result won't unless terms can vanish, unless N1, N2, N3, et cetera, are even. And then we get the contribution 2 to the N Vr of Ws. Now, if they're all even, they're going to be polygons. And therefore, the final Zm is equal to 2 to the A, cos K, cos L, Rm. So they're all the polygons, Vr, Ws. And the other one was different in front, but the sum of the polygons was different. So that's the high temperature, the low temperature is M equals 2 exponential M A plus L sum over Exponential. Minus 2 L R minus 2 S. Or I should say, yeah, let me, these polygons are elements of the lattice, these polygons are elements of the dual lattice. Remember, when we did this, we did it on the dual axis. When we're doing this, I haven't mentioned the dual axis at all. Now, these two partition functions are exactly the same.

37:30 They're exact. They're not oscillating for like that. They're just exact. They're different ways of writing the partition. And therefore, the free energy should be equal, and that's the way we get put it in. So it's the relation between the dual lattice and the lattice. Yeah, you've got to equate these two, so you've got to equate the free energies. And what you do to get them the same is you introduce E to the 2L, of course, Taj K star and E minus two K equals Taj L star. Remember I used that before? Yeah. And I didn't tell you where it came from. Well, you did not. I'm still not telling you where it comes from but in order to get these two the same So it's another duality. Well, it's the same duality. It's the same duality. And that duality, you know, because it's self-due. You have that K-style, L-style, L-style. And that you should commission it. It's a lovely poem. So notice it's graph theory is the real key to the whole thing. And then duality changes the whole thing. And now the exciting thing is in the stack at the same time, in the 1-0-0-0-0-0-0-0, and what I'd love to see is how this connects up with the suspected darts and some people that will connect up with the non-conversity.

40:00 And with the origin of spin. Well, I don't know, but, well, I think the origin of spin is all to do with that knock on the computer. That's very deep, very broad speculation. You mean the possibilities of two values. So I've built this on two values, let's see what you want to do. Yeah. Well, Baxter is actually taking up to Q. There is a Potsmutter. Yeah. That's Q. In other words, Q possibilities on each side. Yeah. Do you want me to go on? I mean, I've never looked at these relationships when you look at that kind of character. They want to get a character and look at them. Well, anyway, they want to get a character and look at them. But it's really just duality. Yeah. And that's where the left arm and the right arm feel about, is the mindset of duality. And that's why you're getting that type of character. I must let you have your PhD thesis, because I've got all this, I imagine a number of people are going to want to look at it, including Grant, I'm so sorry, I've kept it for much too long, it's just there's so many other stuff I've been looking at, to be honest I haven't really got around to studying it, but I would like to, you know, things that they've known for my reading list, but I will, no, I won't be north, I'll bring it back next week.

42:30 I think in fact I've got high temperature and low temperature expansion, but I don't think I did with the neutrality, as well as it didn't mean much to me at that stage, and it was only later when Rome and I were going through the left shift, I don't know, the classical ecology of it. Left shift, is that it? Left shift. Well, there's two. There's also a guy called Lepschetz, who was also a topologist. It's for topologists, it's not the physicist. I think it is Lepschetz in that case, yes, yes. Classic book on topology. Yes, back in Spania, you know, the two big books. We went through that, our example I took a picture. Yeah, I got some classic early. And that was, yeah, but that was because we were finding the dual between F and F star, you know, the... Yeah. Yeah. Because there, there's a duality between the electromagnetic tensor and the cube. that's where we started because we were doing just a pathological yeah this is what got david interested in this is how he got all connected the other stuff goes buried and doesn't come up again, but it's to do with the homology and the polymorphs. Yes, of course. Sorry, when you get one down in the details, you've got to stand back. Yes, no, it is, and that's what's really... So this is what I should be looking for here, the connection between the homology and the polymorphs. Yeah, well, the very... The homology is on the lattice, and the polymorphs is on the dual lattice. I think that probably will turn out to be too simple, but you should be looking for homology and co-homology. I'm quite sure. What I suspect is fairly relevant there is the way that this partition function divides up the plane.

45:00 Yeah, yeah, yeah, perhaps. But certainly, in the study of left shifts, I then went on to that some visial complexes with, you know, and a new mode of description. That was the next step. And then, you took it out of it. Yeah, you did that one, you did that one. Oh yes, that is, that is very, very well known, that is known, well that is well known, I think it is understood that, you know, the hoplons were brought about a few hours. Oh, it is in the sort of big text books on the Molotov, we'll get the Molotov. The thing is, pathology is really increasingly transformative to the 1960s, but you can say, looking back to the 1940s, because really people are no longer thinking of the structural is the base of structure. For example, that is coming out of something more general, which is, well, explain it in these dualities, and it still can sort of do with these notion figures, which apparently is an idea that he got broken because he was reading last on the KMS papers, and also that he was going to sign my application for membership of the LMS. Yeah. Long since. Yeah. Which paper is that, sir? It's all right, I'm not going to ask you if you're true, you don't want to. Oh, no, no, I'll ask you. I thought you were going to stick that one on the TV on your site. I'm sorry. No, no, no, no, it's okay, I'm not, I'm not bitching, I'm not bitching, I'm not bitching. No, I can't expect you to do all that happening. The trouble is, you know, that you haven't got a copy of it.

47:30 Well, it's all right, I'll copy it next time. I won't, I'll sue you for it now. I'm sorry, I won't have time to read it for a minute. Is that the 1949 smile, yeah, the one that you were saying, really, the modern potential is already in there. but there's an absolutely fascinating paper which you should read which is is is is readable because it's written to be you know read by interested you know historians of mathematics by cartier french mathematician oh yeah the big noise a great algebraic uh and got the Fields Medal, you know, as a member called Barkis. He's in his 70s now, well retired. It was done as a kind of memorial, sort of survey paper, as a general source, I think the 50th anniversary of the Foundation would be IHES, you know, which is the French equivalent of the Princeton Institute. you and it's called a mad day's work uh a mad day's work uh space progress it's all to do with with the world and it's on it it's on the net yeah yeah and i'll send it to you uh it's called it's called a mad day's work and it's uh it's about ideas uh about homology, co-homology and space and points as not being the basic notion for understanding space, but the idea that points are not the basic structure but there's all sorts of deeper structure built into the notion of a point as it ran from it's called A Mad Day's Work which happens to be the subtitle it's a very clever allusion it's the subtitle The Marriage of Figaro actually the Beaumarchais play which was made into the opera but that's combing very sort of a cultural yeah yeah it is it's in the well there's a website for IHES just do just do a google search on Cartier C-A-R-T-I-E-R Pierre, first name Pierre just do a google search on Pierre Cartier and it will come up with amongst other things link to this paper, but if you don't get it through that, I promise I'll bring it along

50:00 next week. That's provided I'm here. Oh, no, wait a minute, I'm not going to be here next, because I'll be in Paris, but I'll be down in the jail, looking at my new house. So I won't be here for fortnight, but I will definitely bring it along. I've already printed out two or three copies of it. It's a nice paper, it's not very long, it's about 28, 30 pages long, and it basically tells in, very much in language, accessible to any kind of... No, it's just accessible to non-topologists, because it gives lots of heuristic motivation, and it's mostly words rather than, you know, rather than French notation. The only thing is, he doesn't, the only thing is that he doesn't, of course, mention how important Bill O'Hill was in all of this, because he was the third member of that trio. But he, of course, is the man who didn't believe in the non-commutative generalisation, generalization, but he's certainly the man who understood the depth at which, you know, homology and photomology, the idea of spaces as the carriers of, you know, homology and photomology structures were key to generalizing the notion of spaces and generalizing the notion of points in ways which I think do connect with this idea that process is more as an object. So it's all very interesting stuff, indeed. Right, well, I'm going to make tracks. I will... Are you going to walk down with Bob? Yeah, as soon as Bob comes by. Anyway, gossip on the way. I've gotten that buggered because Milan was going to sign my application for membership of the LMS and so was our letter well our letter I'm sure would still be willing to do it excuse me I upset Milan No, no, okay, fair enough, fair enough, fair enough, right, it's a little bit too raw at the moment for, um, I'm sure I'll see the funny side of it in 20 years time. Uh, I was going to say, um, what a, is, you're not a member of the MMS, are you? No, I'm not. You're not, no, I'm not. Well, that's right.

52:30 Sort of, you know, Bas Heider beer pub, yeah. No, well, I'll ask Arletta, because you need two sponsors, and Arletta is great to be one. Are you all right? No, the only reason I want to join is because you get web subscription to math reviews and loads of other stuff, which is wonderful, and you can use the UCL library without having to pay, you know, if it's something good. You don't have Paul Lovine's paper on Jones's polynomial, I wish I could. He hasn't done a paper specifically on Jones's polynomial. He hasn't done a paper specifically on Jones's polynomial. Has he? Bloody hell, in that case, I'd better have a look on my website's collection. Well, he's got a collection of all his, but do a Google on him, and you'll see on the links to his own site at Buffalo a complete list of all his publications. Weirdness. Do you see versions of it? Not all of them, but most of them certainly are now archived. I think almost all of them are archived. It's only some of the early ones, very early stuff, like, you know, the experience of Cassie, so something that did back in 1960s, that's how he's... Oh, 60, this is back in 80, I think. No, I think everything he's done since about 1975 is now in the archive. But if it's not, he's going to be here on the third of April, so I'm just bloody well asked him to bring it along. I didn't realise he'd ever done anything on Temple Eample, it's very interesting. It's a paper which is recommended, unfortunately I haven't got the reference here. Yeah, who recommended it, Maurice? Jones. Oh, Jones. Well, he must have even known all about it. I think it was Jones. Yeah, yeah. So the Jones we're talking about here, the Jones who did all the work on Noctea in the Jones polynomial, is not Vaughan Jones, is it? It's not the chap at Bangor. Oh, it's that Jones. I'm sure it is. Oh, right. He knows Bill very well. In fact, I once went with a 1989 Bangor category meeting. I went out to dinner with them. Sure. Because Vaughan Jones made the mistake of telling a sort of story, a rude story about Stalin, which got Bill very upset. Oh, God, of course, I do not know how to mention the war. Don't mention the war. Well, you can, just make sure that you know. What are you saying about things?

55:00 Tell him not to watch the History Channel, though. No, no. Because I just had a real go at Stalin. Well, I completely agree with the History Channel. are completely fatuous and childish. I wasn't stalling. He does keep off the subject. But if he starts batting on about it, you just have to kind of smile and, you know, humor and say, well, that's interesting. Well, no, I never heard that. That's really, really extraordinary. Well, well, well, you learn something every day. You know, that's the way to handle it. Just basically, you know, baby him along. I mean, without making it too obvious that you're, you know, just being patient and patronising. man can be an absolute genius man can be an absolute genius in his field as a mathematician and completely oh christopher was the big traitor oh no he betrayed he betrayed he betrayed socialism he betrayed the whole until 1953 they were gradually progressing you know, towards the Happy's Gorge, some of those uplines. Oh, no, I mean, Gorge was just a sort of out-and-out capitalist stooge and, you know, sort of, you know, American agent. Khrushchev probably was as well, but he was, or Khrushchev might just have been corrupt, you know. They were just, they just sold the pot. No, the revisionists were all very, very bad people. They sort of betrayed all of everything that, you know, kind of old Joe built up, you know. I mean, occasionally had to be a bit, he was a bit, you know, occasionally had to be a bit rough with the opposition. had to show them a few pointers and uh you know had to had to lay down the law occasionally in ways which in the ideal world he might have been i would just deny it existed he you know he thinks the whole and i told you he is politically an absolute child well yes bluntly but it doesn't mean at that level i mean i still regard him well not only obviously he is a very very great mind but he's also actually a very nice guy but like a lot of very nice people he has got He's just got one complete weird blind spot, and that blind spot is politics, so you just have to try and keep off with something. And if you do, if he will insist on getting on to it, then the best way is just, as I say, to humour him and then to gradually stir him back onto Max. I'll start with nothing to me and my family, sir.

57:30 No, but what of course is deeply embarrassing, in all seriousness, what is deeply embarrassing is when you're stuck with him at meetings, as for instance I was, in Bangor and in Como, where he is banging on like this to people from the former Soviet Union. For instance, there was this session where the Georgian, Yanna Lidsey, and the various capitalists in Georgia, you know, who would come to sit at his feet, you know, knowing that he's the great man who virtually created that subject, and they listened with their mouths, I mean, literally, you know, the expression of people's jaws dropping out of them, but I mean, you know, I literally saw these people's jaws dropping out of their chest as they listened coming out with this garbage about and these were people who told me afterwards many of them, in fact almost all of them had members of their own immediate family had been killed or murdered or imprisoned or sent to GULAD by a starly and of course you know if they said that if they said that to him he'd just say oh no that's not sort of a lie, oh lie it's just trepidly it is but then it's very often the case that people who are extremely highly developed intellectually in one direction childish you know in the 40s and 50s well even then it was inexcusable to anybody who really bothered to have conscience or you know who was at all but but you still have the oh they're just blackly with me well you have a lot of people who are in denial but the people as it were on the other side of the hill the people on the right were in denial I mean people who denied the existence of the gas chambers or you know the color course which is the exact intellectual you know in terms of the numbers of dead yeah but I mean these people are rightly regarded as completely beyond the panel you know you just don't give them house run in institution you know this is all people who write kind of letters in green ink to you know the Queen saying that the Jews are sending rays out of their television sets or you know people who obviously you know basically they go all the way to Upminster, you know, if I stop the unbarking but people on the left you know, who think the same thing about Uncle Joe I think there are very few left, but there are one or two there is one, are still regarded as within the pale of civilisation, it's just as it were a slightly embarrassing

1:00:00 or in the eyes of some people even slightly charming eccentricity if you're actually talking to one of the people whose Not at all enchanting or eccentric. But the problem is, I suppose I'm a bit gutless. I've never actually turned around to him, because I do value his friendship, and obviously an enormous stimulus of listening to him talk from the past, you know, maths and that, you know, in particular. And said, you know, Bill, I think there's one thing I'll have to tell you. I think that, you know, your views on politics in general, and style in particular, just a load of shit. Not only shit, but really, really unpleasant, you know, opiate. It's at this point that my mother's insistent that I should never talk about politics. Really wise. A wise woman, a wise woman. That sort of comes to the fore. Well, I haven't, I mean, I'm normally quite enjoyed talking politics, but not to be able, I just stake it. I mean, you always talk politics to those people you love, and I only want to wind them up. Oh, on the same planet, yeah. Well, anyway, even if you do wind them up, you know they're good enough mates not to take it personally. Actually, I did it a few times with Owen when I first met him. I played the part of the kind of extreme, you know, right-wing bastard. You see, the thing is, we actually ended up, you know, I would like to think, because, you know, he's a good mate, because you realise at the time that I was just doing it to wind him up, you know. Well, I'm not the right one to ask him. Well, by his status, I probably am, but I don't know. I didn't know anything, I don't know anything about Peter Holm's politics and everything. Yeah, I know lots of them, you know, trots. Mind you, because Bill's even more down on them than he is on Ford, because... Well, do you know that Phil Smith at the LSE? Yeah. Yeah, he was a militant Trotskyite, and actually Moshe Makhrava and John Bell were both some very interesting people and good logicians. They were both, well, John Bell was a kind of Trotskyite, he was certainly, and he was a very nice guy, actually, a bit of an Eeyore, he was a bit of a misery guy, he was depressive, he was depressive. Well, you could when you really got to know him, if you got on his wavelength,

1:02:30 but it was an uphill struggle. I got there in the end. You had to sit through an awful lot of, you know, the history of his personal traumas, and also he was a great devotee of modern serious music, by which I mean, you know, second Viennese school atonal Hindemith, you know, Schoenberg. And I literally had to go, if I wanted to listen to him talking about stuff that really interested me in philosophy of maths, that would be the deal about logic, the smooth internet, and that sort of stuff. I had to sit and listen to bloody Hindemith, all this, you know, atonal apples for about two hours, pretending to enjoy it before I could finally kind of steer him on to on to sort of statistical analysis or on to general intuitionism and general stuff on philosophy and that the funniest thing I've ever seen I mean long before Abner came along and the character of Sackley you know the wise child of the hippie mother long before that I saw John Bell's son also called John when he was about 11 years old when his dad was the hicks He was a creeper in the corner of the room, listening to music, literally coming into the room. He was a kind of young kid, you know, in his dressing gown at about two o'clock in the morning. So I bang up on the door, kind of classic rollercoaster, and he said, Father, for God's sake, turn down that place. Couldn't have you existed. I was just ending up laughing. You know, he was this kind of middle-aged child and, you know, hopeless hippie father still stuck in a kind of emotional time warp of age, well, never growing up. It was exactly like, as I say, Saffy and Adina in Aftab. He was a lot happier since he moved to Canada. He felt a lot more fulfilled over there. He wasn't there as soon as he was. of course he was one of the ones who, well unlike all academics of his generation, he would have went on and on and on about the horrors of Mrs T. Fair enough, but off he'd heard it for the 400th time. There was a certain amount of, let's change the subject John,

1:05:00 I mean, we've heard, we have heard it, you know, we know your views on that one. Erm... No, he wasn't, I suppose... Well, he was slightly born to win. Yeah, right to suffer. Oh, I'm... Okay, I know you're the same, I'm... I don't know what about her, what's she fucking about? Well, she had a scribe, didn't she? Oh, did she? I don't know. I'm sorry, I disagree with you, I think she will go down in history as the bloody saviour of the religious universities in the long run. Shaken them up. Still needs to be shaken up. I don't expect you to. Now you're going to turn around and give me a couple of black eyes. No, I'm only saying that. I'm not going to rise for that. Well, there was a stage where I felt Thatcher should have been shocked, but that was too good. Well, I agree. She didn't do a great deal at the university. So on the other hand, there was a... No, I think... Let history be her judge. I think on the whole history will judge her very well, except that that will certainly be one major block on her record. But in overall... Shrub's going to really go down in history. Shrub? Bush Jr. Oh, God. Yes, I think he is actually much more evil than people give him credit. He's actually he's actually benefited from from this In the impression of just being a dyslexic nincompoop in fact, he's a good deal nastier than Yes, and the father as well. I had a long conversation with John Mabry. You know my friend at Bristol logician at Bristol who's a very sharp guy. I mean, not having extremely good, you know, an interest in foundations and philosophy, but also knows Ed Nelson very well. But, you know, very interesting on politics. And his dad was a corporate lawyer in, back in the South Carolina State School, John was in the Hale Center, I think it was a guy in life. And he knew, well, it's a bit of a long story, but there was this guy who was one of the real local mafioses, a hell of a corrupt, and he'd come to so many tight corners,

1:07:30 and his name was Ed, I forget what his name is, anyway, he was summoned to Washington, and various of his business cronies went to John's father, and said, John, you know, before Ed goes off to Washington, sit down with him and have a really, really serious talk, because if he goes to Washington, if he carries on in Washington, the way that he's carried on, you know, whether it was in the county of Illinois, with the kind of scams he's called and, you know, the crooked deals, and then he's going to end up in Leavenworth, Fort Leavenworth, so there will be no people in town. You just can't go on like that, but for God's sake, you know, take him and have a real hard part and get it through, but he's got to clean his act up. So John's dad went and had a hard part with this guy about how he needed to clean up his act, was in Washington, Bush had appointed him Secretary of State for Agriculture, and he was up to his neck, this was Bush Senior, the father of it, and he was up to his neck in the S.L., no, the savings and loans scandals, and how the hell he avoided going to jail, but in fact, well of course the point was that it was born in on John, on John's dad, direct the old job. But the point was he had hopelessness, even though he thought he was quite a downly old bird, he was quite worldly and cynical about the way things work, but he had completely underestimated how bend and corrupt they all were inside Washington, and particularly inside the Bush administration. And he said the Bush is basically a very nasty outfit. I mean, Southern Republicans, and especially Texan Republicans, are really a bunch of very, very sort of greedy reptiles indeed. I mean, look where the money originally senior, his father, was actually jailed after the war for trading with the enemy. No, no, they did. That's true. No, no, that's absolutely true. No, his father, the grandfather of the present president, his father of George Bush. He, of course, was an out-and-out, no, pro-narch. But Bush's grandfather, as I was going to say, father of George Bush senior, Shrubb's granny, granddad, yeah, was actually jailed. He served about six months, because of course he used all his pull to, you know, to have a... But he was...

1:10:00 Yeah, exactly. He used to wrap a little cover. No, but he literally, they were done for trading with the enemy. I mean, they were actually selling, you know, spare vehicle parts to the German army while the Americans were in the war and fighting in Europe. He was actually making money out of killing. He was probably selling spare parts, as I was saying. Well, he certainly was, of course, because, as we know, I mean, the whole point about Rumsfeld and Cheney and the rest of them is that they were the people who equipped Saddam with Barthes and Arsenal to begin with. When he stands up and says, you know, we know Saddam's famous sort of weapons of mass destruction. Because we know, because we sold them. Yes, I know, that's it. They've actually had a son about that on the radio there that I've ever seen in this bush. Has he got weapons of mass destruction? I cannot prove it. Sure I can, because my daddy sold them to him when he was fighting with Iran. that he was me to my daddy and for that he sure will pay. Oh, but as I say, all of that, the impression of Bush is just a moron. Why Blair? Why Blair? Because he's been told by the senior civil servants, he's been told by the people with whom the buck stops in Whitehall that there is simply no way in a real way that since, well, since when, well, certainly since 1940-41, I'll give you this about 1917, that if push comes to shove, that in any real crisis where, you know, where it involves we have to take either the side of the Americans or go against them, that we can possibly go against them. In the last resort, we are just chained to their charitable rules whether we like it or not. That's the advice he's getting. You know, and of course he's trying to reconcile himself to it by saying, well, you know, we can still be more You know, we can be a kind of kind, civil... No, no, no, I'm saying I agree with this analysis, but I'm saying that that undoubtedly is where he's coming from. No, no, we don't really need the Brits anyway, so... No, but that's what I'm talking about. But then if you think... Yeah, but just think... Well, no, that's what I'm talking about just being nasty and direct. But on the other hand, think what Blair is now hearing from Washington. Well, you know, we got it from... I mean, from the really bright people in think tanks. Well, we got it all wrong through the 50s and 60s and 70s um and you know just kept you hanging around at the um what we now realize is there's going to be a new world order we're the only hyper power we're going to dismantle all of the existing international institutions and arrangements there'll be a new world and don't worry you guys

1:12:30 you are the one guy you know you're the one one real ally we've got and believe me you can be 15 20 25 percent of this you know you just don't know how big this is going to be and you'll be the only people on the inside and everybody else will be outside you know because again that's what he's hearing yeah uh and his politics so they'll they'll certainly shaft us um but i suspect that that is the answer to the question why is what he's doing shunted himself up in a quick look i'm i'm only too delighted to be going to France, and I shall actually make rather a point of it, I'm not, you know, the greatest post-Groët man in the world, but on this occasion, it all has become hysterical, childish, racist abuse they're taking from those kind of radio-shock-chopters of Adelaide. But what might give a sense of European opinion is, you know, really... Yes, well, even the B.C. first of all, I'll leave you on that page, if it's even without the French B.C. I'll leave you on that page. I'll leave you on that page. The French are just being used as the ripping part because where would it happen it could be, and because he hasn't been able to hate the French. Sorry, it's Iraq, Iraq, Iraq. Thank you.