Discussions, incl. FW Lawvere, M Wright

0:00 Two separate ones, which I didn't know about. I didn't realize that either, but they're two separate areas. Graubunder, yes, is the German name for it, and Kantar. What does the word receive in two kinds? A tiny little twig. Oh, the twig, that must be Slavine, of course, yes, because it comes from Slavine. Yes, I was just looking at this little bit and thinking that it was actually a separate region from the... No, no, it's not a separate region, it's the whole Slovenian area. Yeah, they are speaking... Yes, I didn't realise there was a little Slovenian... Well, they don't have... There's something called Vindish which comes in there, right? There's a language called Vindish. Oh, Vindish, yes, which is... Yeah, I've heard of that. Is it still spoken? Is it still a living language? I think so. It should be, it should be read in there. And some languages which have become extinct, or actually even show us which have become extinct, like Cornish, because they have been revived, I think there are about 3,000, I think it's around 3,000 Cornish speakers, but they're all members of the Cornish Nationalist Party who have learnt it from studying it, none of them was actually the earliest speaker, the last latest speaker. It certainly wasn't a region of Gaelic speakers in Brittany as a little over-ambitious. There was probably some Breton nationalists who, because it's my understanding that it's only really in the small communities along the coast of the Far West... You said we actually had a couple in Catalan. And it's a country of course for that. Ah yes, so they're probably, you know, they can promote. I'm sure of it.

2:30 Oh, that's right, Faroese also have their own language, which amazes me. I assume they spoke Danish. Well, that's because the Welsh and Breton are both the Soviets, and then these are the Gaelic, Scots and Irish. And I hadn't realized that Manx had, in fact, died out. I thought that was sort of terrible. Being re-established, they claim that it's an ideal. I mean, it's now a certain agenda, much more, but my impression is...

27:30 ...some of the stuff on his website, which I didn't know. They just hope that God will set them free and rescue them when they...

32:30 Well, isn't that just expository articles in American math? Keep it all implicit. Can you tell me what you said?

35:00 Well, maybe he's got that.

37:30 I'm very sure that John Mabry wasn't able to.

40:00 He would have had an opportunity to talk to them sometime. You come over here next time. Now I understand. Now, he said, do you do that? He came back just after, a little after. No, I do come back first, and then I saw him a little while later, and that's the first thing he asked. Do you know who first called that for that? I had to admit I didn't, but I've seen how the question came from. Four years of struggle. He's actually, all along, basically his attitude for the third half of the fourth year. Now, I'm basically this totally naive person. How could I possibly believe a shred of Marxism?

42:30 No, I think people like pride, I've come across this before, and you ought to say that too, that you have this kind of, it's a little bit like divine right doctrine, the doctrine of the Laubir's two bodies. You know, there's the Laubir who does. Of course, at the same time as you have this 40-year relationship with people, there's been the 40-year struggle with you and Steve Schengel. It's like we can continue thinking to eternity.

45:00 The set theorists even talk about that. They'll even say, in some ordinal number, they'll talk about the gods who could do this or that, or the super gods. We actually talk that way at least one time a day. But in any case, these are two distinct levels of idealization. Not that one should reject the latter, because it's partially a useful model for a continuation of faith in these things. Inevitably, non-inconsistency, absurd results continue to push. Of course, what logicians are trained to do, they're trained to push the bad aspects of mathematics. Which can be enumerated out into an item. This idea about the relative. By the images of Grumby, Topos, and Sokolov. As soon as you have a truth value object. And then you will also have an exact number out there, that's dedicants, provided you have the dedicant infinite objective, an unreasonable picture of the objective, the non-subjective, and the graph of something, that's the dedicant infinite, so the very idealization of truth, you see, it's also, when I say idealization, it means objectification of the subjective.

47:30 The objectification of the subject of truth essentially implies, together with the other reasonable objectification of matter and motion, implies the B-model made a definition of the no-minimal model, which is such that, of course, in the side of truth, there are two things, which it is the equalizer, do not go to another part of your total. It could be just the truth value of that, and everything is...

50:00 The idea of topos is that everything is equal. Every sub-object is equalized and matched into two sides. It's kind of universal. As I was saying, once we have this basic idea, which could easily be, if no one's written this down, but if we could do so, it would take a minimal understanding of co-minimalism, so a little bit beyond the understanding I have, and make it into a category, and then take a group of topos and generate it. Again, I think the crucial point becomes, you see, this point that geologicians have redesigned as instantiated in many different ways. The function types are somehow not as extreme as the power types. The existence of the space of maps between two geometrical objects, even though infinite dimensional, is not anywhere near as productive of nonsense conclusions as The power set, namely ultimately the truth value object itself, the power set, once you have a truth value object, is just a particular explanation as well. To what extent, to put it simply, could you have a Cartesian closed category, i.e. one with full explanation, which still had this property, only finite components, against basically an own animal, while you're dealing just with the function of it? The naive expectation would be that they were to automatically create many components, too, although that didn't happen with apologies, to be honest. It's not that likely. One doesn't have to block the thing's length in that space-dwelling curve.

52:30 That might be the idea of this construction. No, the idea that the O-minimal already has no space-dwelling curve, Once you've introduced function space, the question to get it right is could you have a curve that builds function space? Yes, that's smart. That's one. The other is more of a number of connected components. It's slowly becoming a sort of thing, sort of retained topology and retained functions involved. The notion of function space is not on the face of the subject. You might expect that it doesn't have, in fact, so this is, apart from actually learning more about what the old minimalists are doing is one thing I would like to discuss with Angus is, I mean, here is a crude, not precise, real algebraic geometry, but if you consider the space of maps and the lines of the line, what are the space in the number line? Polynomials.

55:00 Polynomials have degrees. Yes, of course they do. There seems to be at least a sum of countably many finite-dimensional spaces, so the idea is that if taking the degree of the polynomial is an internally smooth map of the actual natural morphism in the topos, whose co-domain is the, you know, Dedekind-Lemire natural numbers, then we're screwed. I mean, we're not necessarily, but I mean, that's... That's the outline of an argument about who can be gotten around, but it might be that it can appear in natural numbers, but some are semi-continuous models. In fact, that's very likely, because a natural map has to do a lot more than just map points to points. Here the points are polynomials, and here the points are natural numbers, and so we imagine a degree is just a map there. Actually, it has to apply to polynomials with coefficients in arbitrary variable rings and remain natural and all that. Well, of course, it's one number there, it's not something perfectly rich, it's not good. No, the theory of real closed fields is decidable. That would start to be the original result, which is complicated. There is no computer yet which is programmed to do all of it, but huge chunks, you can actually decide that. A popular statement about Goethe's fields is, who are not, which basically means about the real numbers, the polynomials.

57:30 That was the starting point. Added to the polynomials, you can find lots more sets, intersect them, but still, you'll get down to just the dot, dot, dot. These are the set of both finite signs, I know. Yeah, yeah. Beyond the polynomials. And not only that, also... Where they're close in spirit to what Grozny, Kofman were. So that's why after I told Dan DeVries about Grozny so that we knew the answer to that... Yeah, shtick off, it's about taking politics. Did he not give credit for that before? Well, he certainly didn't mention me. I didn't want to tell him, he knew nothing about it before. I mean, he had to know all the severe words, so... I was all excited, you know, I kept hearing it's going to be a useful, useful terminology. No, of course he might have written Grozny, but... I did, but he gave more credence for himself by appealing to the great authority. I don't think he's actually gotten anything. He's from the, he probably suffers from the same, because he probably left with a hard and fabric freedom, but also, you know, he wanted to throw Angus out of the church. Steaming in church. Well, no, just by applying logic to geometry, this is counter to the true spirit of pure animation. I don't think either Angus or Hewitt are likely to be intimidated by atomic freedom, I have to say.

1:00:00 Well, in his case, one might put it down to ignorance rather than panicism. Yeah, I think that's right. The kind of ignorance we're literally not claiming to know. Was it you, Donny, that she told me had once said to you, oh, yes, you ought to be a toposther, it's not very mainstream, is it?

1:22:30 There's quite an interesting email here from my friend Mike Stenton about, with of course all the focus on Iraq. He's asked about some of the things that have been going on in, you know, earlier, some of the dry run for the American imperial project with some of the techniques of news management.

1:25:00 Do you want to do your emails now? ...a wooden table up here and have, you know, Colin and John... Now, all of this is my... I have a... It's like half iron as well. Almost, yes. The trouble is, it's almost impossible for one... That was where I had my bong farm. It burned all the rubbish back then.

1:27:30 But it can't keep on top of it. This needs another good cut. They would know how to do it properly. Good peasants, they would know. They would do an incredible amount. Oh, I'm sure they would. That reminds me, actually, I went to a... I went to a place last year in Italy which I wanted to swallow a very small fish. It's alright. It was just some tiny insect, not a flower or anything like that. Don't beat yourself up just like that. Now last year I went over an absolutely fascinating place called Quintero. Don't you know I heard of Genoa? Yes, near Genoa, which is this baggy coastline which was reclaimed by the incredible labourers of these working people. ... and vineyards and little farms out on the rocks, you know, by the most interesting ways. And it was in the... it was an area of very strong presence in the small producers. And there was a very useful one about this business of the murals, which allows you to get to it.

1:30:00 So it's not actually in Ireland, but it's... It's virtually in Ireland. Yes, it's just connected by a very thin... and, of course, just up to send some of them to you. Do you want to do your own emails now? Uh, yeah. Well, I think I've done everything. I've got all the phone numbers now. Colin, I don't know where Colin got it into his head that he was going to get in at about 5 o'clock. He's not. He's going to get in much earlier than that. In fact, there's no reason at all why we shouldn't be able to get him to 5 to get in the car. Why would we be able to pick him up before? Yeah, well before Angus gets in. Angus doesn't get in until 5.30. Colin, in fact, by my eye, actually gets in to Charles de Gaulle at 9.35 tomorrow. So if you get to the train directly down from L'Arche, Laval or Rémy, it's probably in Berlin, isn't it? I don't know how to do it. You just have to go into the general internet, that's all you have to do.