Narrative & rationality (contd.)

0:00 One is the m-category, the problem, the issue. The other is this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, this, If you worked with him, couldn't he just be saying the same things all the time? What commutative geometry is doing is just spewing out of him the new learned storylines. Storylines about whenever we saw commutative algebra in the past, we can always find non-commutative versions of these. And just as the algebra is related to geometry of the past, whenever we have non-commutative algebra, we call it non-commutative geometry. I think there's something particular about this program that lends itself to... It seems to have an important narrative within it, in terms of what it wants to do, because it's always trying to take things that it's already got there and do things with them in a certain kind of way. So, I suppose, you're not necessarily going to be having an eye on the past. There's so much more to that. Well, many interesting things to discuss, but I think I made it very short. Suggestion and then an initial clarification. The suggestion is that at some point you were making this point that if you are interested in understanding the development of new conceptual frameworks and understanding mergers, if you are interested in that logic is going to be of use, I guess, I have actually seen your tendency to do it. This tendency of having a very clear-cut way of understanding what logic is.

2:30 But actually, I mean, in a way, to be honest, the variation around is very clear in logic. All kinds of different approaches to logic, meaning which I would tend to say, oh, yes, that should be labeled differently. So logic is a very similar system and unknown. It's something that is being transformed all the time. For instance, Schopenhauer's theoretical approaches to logic, which many people think, or at least a large group of people, take. If you start thinking in that way, of course it is not so clear. I just wanted to point that out. So Jessica, as long as you're tagging with your picture, this equation of logic is 1000 plus 100. Right. You can't rule out what formalism could one day... I'm very, myself, I'm very much against the formalism, so I sympathize so much. Of course, one could never rule it out. But of course, much of what is happening is, well, they try to capture some kind of modification of formalism, but I think, in fact, the approach that is leaving the side of the world is more formal. But whenever these things do anything useful, they do something useful in computer science, you know, we do all this work on modal logic, doing sacrilege or something like that, modal logistic, but I mean, you know, it doesn't tell me about possible worlds, you know, we end up using it in model checking in computers, program specification, I mean, this is where these things work. Now, the other issue of communication is that one of the regularities of this language was the... I sent Insta from a paper from Bates and somebody else, I think, recently. Yeah, they were. On this, I'm capturing an analogy between physics... Yeah, the Rosetta Stone I did. And actually, I don't know, I just had an image of the measure of space and space time, and I was a little bit uncomfortable with it, because I think you didn't... I don't see the point in the analogy you're making.

5:00 I just wanted to know if they know if they actually know the next, the next oh the next yes I mean that's like another space space time with the right rules and conferences do they really elaborate on this in the paper or do we need some substance oh this wasn't actually that's not from them this is from There's, do you know this stuff, this topological quantum field theory, they're trying to, this was Witten and Atiyah, wasn't it, and everything's beautifully phrased up so that one of these things is a functor from a certain geometric space to a certain algebraic space, and these guys are trying to extend it, they're trying to add another layer in there so that you don't just deal with, like, I don't know, say circles. And then pairs of trousers going to other circles. So that's classically a cobaltism between two circles and a circle, a new pair of trousers. And then we map this to something geometric, something algebraic, so perhaps something like vector spaces so that the ends get mapped to a vector space of some kind and the cobaltism between them gets mapped to an operator and then you've got a vector space corresponding to the other end. So this is the work of Witten in terms of trying to do that kind of thing. Now what stops you from going a little stage further and saying you now have manifolds with corners, so you don't, so you start with a point, a cobordism to an end point over there, and then you can also, what do we need to do, we need to, we can then make that line, transform that carving out to two dimensional space, we take that line now, amorphism. We've got an anamorphism over here, and then we can fill in between that, so suddenly these manifolds that have edges can be seen with three layers, the edge bits, there's a line joining an edge bit here and an edge bit there, and then there's a two arrow sweeping out the two space, and now we need to send that sort of thing to something algebraic, but it's got to have three layers to it, it's got to have two vector space, it's got to have its special kind of transformations. So they're trying to model, they're trying to bring matter as the edge bits, the filling in between the edge points of mediation between the bits like that.

7:30 It's, yeah, I mean, yeah, absolutely. In fact, you know, I said he gave up this type of theory of physics, at least in mathematics he could make it. Could you put Leo Corley, because you made him the end of the proposition and he made a new position. So, what I done, there is something that I don't understand in this proposition. The thing that has been, which is the single reason, is the object of the study of research and the study should try to understand. And convey it. Understand. Then, the thing that might be, why not learn, is not the story of professional business. But, what does it mean to understand the thing that has been, if it does not mean to understand that it has been in this way and not in the other way in which it might be? They have been, if I'm not compelled, this way, being with another possible way of being and saying, okay, things are going in this way because, one, two, three, it is understanding. Otherwise, there is no understanding. So, I cannot see how these things can be opposite one to the other. I am an historian that to try, I tell, no, no, no, no, no. Because, no, sorry, I can understand that you are a historian that does not want to understand. Okay, possible. A world historian, to tell a story, is to say things as things in this way.

10:00 Okay, no problem. It's not my work, but I can understand that this is a possible work. But Leo says, the object of the story... You should strive to understand and convey, so I take Leon's point of view, not mine, not the other, his point of view, to understand, and I ask, what does it mean to understand? It does not mean to compare the real and the possible. It doesn't mean it. What does it mean? In the quote, when he says, what might be, he's talking about what might have been in 1900, for instance. Or he's talking about the future, really. Oh, no, no, no, no, the 1900s, yeah. He's talking not about the future, from today. No, no, no, no, he's talking about the future. No, he's very much... The past's future. Yeah, it's very much we should, you know, think about how mathematics is... And they may... So, can you defend Leo at all? I mean... Are we going to use Leo to defend Leo? I think there is a problem there, which is basically I want to have a lot of information. You cannot be against it. No, you know, I would be against it. I'm very good at it. Could you tell us more about this? Yeah, perhaps I can tell you more about it. Because I can certainly see ways in which what he's saying is kind of completely in controversy. He's saying, oh yeah, things might be something to consider. Oh, it should be a limit. If you could put the end of the day and then our final data, what might happen? Or he might be saying we shouldn't consider it at all. If he says we shouldn't consider it at all, that's very extreme. He says it should be something that's considered for the course of better understanding.

12:30 So I'm just wondering what... Yeah, yeah. Dig up from my mind. I mean, he was certainly interested in... What is the aristotelical difference with poetics? That's about what should have... Do you know Aristotle's ideas on poetics? What should have been... I think there's a sort of... Perhaps if you put should have been, it almost would have been... The thing that should have been is another thing. That would have been much less controversial. The opposition between what has been and what has not been, how should it be? I understand. But this opposition I don't understand. But what scope is there for the good? Can you as a historian have a notion of a step being taken for a good reason? What does that mean? Why was it good? Or bad, if you think it's a bad thing. But that's typically not the case with historians. The point I wanted to make before was simply that I see a good methodological reason in promoting this kind of perspective. And I see, so part of, actually, history is a discipline. So it is a formative importance for future historians to have them develop a clear eye for distinguishing what may be more speculative philosophies and what is more, you know, harder. And yet, on the other hand, I don't see why anybody would want to be a pure historian. There are a lot of pure historians. To be a good historian, my point is, to be a good historian, you have to master that kind of... Yeah, right. And then you can be something else, probably, and maybe a more interesting character, by not being a pure historian. So this is the sense in which I am for you. There's a question. Yeah, okay.

15:00 In fact, the first one I really wanted to talk to you about was about mathematical education, but since this has come up, I think it's extremely dangerous for generalised science that we need to have all these particular conceptions of what can be characterised in the subject matter of this video. And I think that is understood, it's connected with almost all, almost all practicing professional historians. Hold, what they termed, counterfactualists, which is a very, very steep, in fact, regardless, is completely off limits for the profession. It's sort of something, you know, you work, you do, and you're off, you get out, and you're going to get it out, and you've left, and that's what it's about. I think that's perhaps one of the most important things. There's a set of differences, but sometimes you've got the best of two interests. Yes, that is. I wanted to ask you about the, what do you mean by the connection of categorization? Categorization, the real thing, the super-science shadow that has started to come up in capitalism, and the example that you then gave about the kinds of geometries, and the equations of the stabilizers, Oh yes, yes. The initial stage of the world of the ladder of capitalization of geometrical structure, and at that time we were in Germany. Would it be fair to say that at each stage, when one ascends this ladder of structural engineering and capitalization, one is typically looking for a five-foot-tall? Five-foot-tall? Well, in this context, I was convicted, I was afraid, I was afraid, I was afraid of geometrical structures. If you want to hear what you've discussed, go to each of our other groups' reports, as long as you have a general setting for the algebraic answer. I don't think it's very important to just go. Well, really, yeah. Here's the point that you made in your blog recently. You said there was a question of the length of the graph here.

17:30 And there were some of the spectrums that you had in mind in this description. What was the discussion of? Of points. Oh, that lovely paper. It's so interesting to see how things act up, in a way. There's some interesting stuff in terms of the way the levels can factor out. It's a good thing when you have two things at a certain level and a map between them that you sort of comb out, if you like, layers. The projection can be combed out into different stages. And it's something very close to logic going on there. I mean, you can sort of think group, they've got this notion, this stuff, for example, it's made up of stuff, which then has a structure. So there's a nice, typically when you have a logical theory, a type is going to get set, sent to a set, down by theory for groups.

20:00 But anyway, I mean, you would need, you know, we do the multiplication here first, and leave this one alone, and then we do the multiplication on these two. It's got to be the same, let's do it the other way around, leaving this one alone and multiplying those two. So there you're seeing this highest level of truth value, an axiom. The axiom of associativity is the two you multiply first. The axioms are telling you about how you can shift the whole thing up another level. So that's this idea that we need some two-logic around it. Your propositional logic hashed out the items of the property given model. We definitely need a sort of two-logic where your highest level is increasing apart.

22:30 I have to say, syntax, the character occupations in syntax is very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, very, ...trying to get these bits together. There's definitely one line of thought and then there's plenty of other work on categorical logic and I thought we'd be really able to sit down and see how it all fits together. Absolutely true. Hasn't been properly done yet. Well I think there's a great, and again this is not quite a compilation, but there's a great scope for a great validity of the investigations alone on the various grounds which were formed from different sounds to represent either the realisation of or some sense of conceptual... Fundations for capitalism in some are proponents of being the whole of the end-capitalist program, categorization. But there's also the old rule of law that says that there are five categories of capitalism. There are two categories of capitalism, and there are other categories of capitalism. And there is no generalization of capitalism. All of these ideas were broken down and sent there, which made the right kind of panel for both the academy and the pro-academy. I think that's a huge project that the research is kind of in the good philosophy of Will Lam should be focusing on, while the key people who created the confounders, et cetera, are still alive and kicking and not expensive enough to contribute.

25:00 That was not the way it was done. You certainly learn things a lot more. I mean sometimes you know you can go back to the 70s philosophy of science and come away with an impression of people thinking kind of quite rigidly but I mean like this just isn't like that you know there are also rigid thinkers around but they tend not to interact very well with anybody else like great fluidity I mean whether you can go to the other extreme have too much fluidity. There are mathematicians who want conceptual re-instruction of the subject. There are mathematicians who want grand narratives. Not necessarily quite the same thing, and there are others who want very different things to learn, because they think that's where we have to work with. I've been very impressed with historians that they venture into these fields of the past and unearthed this. I think that was very difficult to do. Yeah, almost overwhelmingly too much, surely. Even individuals change their way. Anything you say, there's something for this at a certain point. Given what it's like now, what it's like now, you must have been like that. Well, I suggest you go to the questions to open the discussion. I have a question to leave the stage. Thank you very much. Two minutes in order to resolve the debate.

27:30 I would like to talk to you about the topic of the meeting tonight. I'm sorry, I didn't mean to interrupt. It's been too long. Are you talking now?