Discussions, incl. FW Lawvere

7:30 But neither will it be injected because it will demonstrate the two definitions that are actually given by Hawking. I wouldn't say all that, but I can define this.

10:00 If I knew the general theory of how this works, I couldn't think of quantifying it. Now quantifying over those definitions is horrendous. All possible precision systems and all possible high compact and open product operations on them

17:30 I should not explicitly function or measure spaces, but just cohesive linear space, which is involved with first achievement, in other words, the technical achievement of defining a tensor product and then proving that theorem with the functions of another space, in order to make it easier, quote-unquote, for the statisticians to assume...

20:00 And so, if you want to see the general form of such an enneagram, it's a wonder of feminism to another point in the, probably not even more complex, in a sense.

22:30 So, at that time, when we exercise, something can be solved. Everybody functions on that open set, which is a cohesion of space, and what that means, what does cohesion mean, is not always clear. The point is that you can do all of this by...

25:00 But you can ask to be computed in one precise term. The Cauchy problem is d minus w, their concrete expression. Of course, it makes sense when z and w are complementary, the places are open, so you take, you know, you take the open, you open, you consider the function, now if you, if you took another function for the complementary, you open, you lose the functions of those w's, the depth of w, well, you can, you can divide it by z minus w, you know, integrate it. The precise answer is exponential growth, standard growth conditions. Then on the unbounded complement, we consider the analytic functions, the arbitrary analytic functions of exponential growth on this unbounded complement. And the point is it's biased, it's fixed.

27:30 One is represented as the two or the other to a great extent. So I can even see just from the first. So now we're talking about analytic geometry. It can be carved out, but it happened to be a concept systematically between the whole dictionary.

30:00 The basic phenomenon I think was known already in the 19th century. We're just talking about how homework is actually the whole, the play of... The phenomenon was known, but this particular formulation was then used. Systematic isomorphism is categorized as algebraic versus analytic. What does that mean? What does that mean to you? It's a bit fast, but I'd say I'm 50. I was presumed to be old, sir. I didn't know what you were going to do with me. I don't know what you were going to do with me. I don't know what you were going to do with me. I don't know what you were going to do with me.

32:30 I don't know what you were going to do with me. I don't know what you were going to do with me. I don't know what you were going to do with me. I don't know what you were going to do with me. I don't know what you were going to do with me. They're so algebraic from each other that they were extremely put all under the Gurdjieff connection now. It may have been entirely due to Sayre, if so, those of you... Again, yes, he was there for all of this. So the FAC, okay. What does it mean? It means that now these analytic spaces that we've discovered because we were looking at the functional analysis of complex medical,

35:00 Interesting, deep, macho mathematicians should be pursuing. After all, it's just a blank job. Clear formulation... Oh, by the way, we need topos to explain this. That's just a year or two of... So this is the history... Because we close meeting countries with this sign. Yeah, and meanwhile, you know, Kahn and Vanadad joined countries in 1958, which were instantly plugged into this. ...discovery of the linear case. ...57, and it doesn't mention adjoins, but then con. So now it explains to you that it's a decade, 1950-1960. It's not at all this continuity that it seems. ...analysis as pupil of charts, algebraic, everybody is actually a pupil of series. It's not at all... I think it is. One thing about complex is that that's not the point. No, that's not the point. Nor do I. You just have to recognize that there are two or three key theorems that show that it relates to A and it also relates to B. So that way you can get to that B. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. And then you finally get your Indiana farm boy, who comes along and says, oh, by the way, logic is a special case of this, too.

37:30 Yeah, and set theory is a special case of this. Well, by no means does the main case should at least be recognized, because it does have some role to play, guys. I still won't accept it. No, 45. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. For a full game. I said, from what's been pouring out of you in Belgium in the last 24 hours, I said, from what's been pouring out of you in Belgium, there's a lot pouring in as well. Yeah, I feel guilty because I didn't say that. Right. Well, in other words, college would still retain the kind of science.

40:00 But very much particularly, there are denominators, this kind of thing. And that's the expensive ones, however. Anything with respect to which certain things are done. No matter how big the degree is, it will force the product, that's algebraic, so therefore, it's not like some second order infinity, but it has a tendency to be finite, only a tendency to be finite.

42:30 But if you take any example, what's happening is that you think of it as you have a rig object so that you can try to talk about it two times as much as you can about it. Meaning, this explanation actually amounts to, which bits you want to know.

45:00 It may become more clear that in no case that the algebra is always, when algebra emerges from calculus, is the standard machine.

1:12:30 For presenting the same algebra, the linden-bound algebras emerged from first-order logic, cylindric or polyadic algebras, or, you see, again, cylindric algebras, polyadic algebras, particular kind of category, which the first-order logic was always trying to present.

1:15:00 If people didn't have even a smirkity of those kind of algebras, they would never write down the first-order axioms in the first place. Does this make sense? Yes, no, this system, this system. Objectives of algebra and presentation. Could this even be a part of the explanation of the other structures in this profoundly algebraic way? The reason that he did actually miss the electronic device to extract the reading.

1:17:30 Yes, yes. I would hope it would be preserved. Yes, you told me. I remember when I talked about Michael Redhead's structure set that...