Discussions, incl. FW Lawvere, G Khatcherian & M Wright on general analysis of geometry & logic

0:00 Sorry, say that again, Bill. Yeah. I don't know precisely what you're... No, I'll show you the stuff. Differential forms are acting on vector bundles. Yeah. Over a fixed base space. Yeah. You're working in a particular... Yeah. ...on this fixed base space. The morphisms don't move the base space. They just move the vectors around. Yeah, yeah. ...more or less. Yeah, yeah. Whereas here... Mm-hmm. In the growth topology, even if we just look at one space, the map F is an endo-map of that space that really makes a translation on the base space. Now, I don't know exactly... Yeah, I think that's the distinction. I can see that... just what I meant by saying that I think this co-Greek and contra-Greek and differential forms is a more restricted construction than this. But I need to look at it again anyway. I'll show you in the morning. I'm too tired to do anything more tonight. And I must try and remember, yeah, if you do remember the example of the, I think it was left and right, well, yeah, I think it was in terms of left and right-sided ideals, something you showed us when I was talking with Carboni. Maybe I'm wrong, maybe I think something completely different. No, no, it's probably all right. Yeah, I think it was an example, definitely. Yeah, yeah, that's right, yeah, that's right. Where generalized maths are bimodules. That's right. That's it. That's the one. Where the intensive quantities are just left modules and then extensive ones are left modules and intensive ones are right modules.

2:30 Yeah. Yeah. Yeah, that's it. I mean, in fact, there's no need. You said it. I mean, you said it, Tony. The integral, you see, is the potential product which reduces to just the vector space. That's right. That's the one. That's the other one I was trying to remember. Actually, in some ways, that was the most helpful example for me in terms of seeing what was going on here. But this just links so many ideas in such a beautiful way. Don't you find this interesting? Well, I must explain to you the other example where extensive quantities are certain kinds of spaces over. In other words, the objective quantities, where you just think of the object itself as its own measure, or perhaps of its element of the bird-side rig as its own measure. Even there, there's a distinction, because certain kinds of spaces that were extensive and certain kinds were intensive, but the nullification and all that gets pulled back. Can't you do that in the morning? Yeah, I'm sorry, I just, I really can't, I just can't think anymore tonight, but this is wonderful. Thanks. Sure, sure, it's John... Markover sent a letter to John Bell, sorry, to John Mabry, I should say, which was for, well, I'm not sure, Markover's letter, I think, no, I do not, no, no, I was just saying to you, that's one, no, it's okay, it's here. You bet, it's one of the first things I'm going to get, in fact, I'm going to get it on Monday. Sure, but this... No, John Mabry sent this letter to, sorry, Moishe Markov sent this letter to John Mabry immediately after the conference, which he sent a copy to me, and I assume to other people who had been at the conference whose addresses he had as well, and in fact he... and I was actually very disappointed in Moishe's letter. This is John's reply to Moishe's letter, and... I wanted to get Bill's reaction to the articles, you know, to John Mabry's articles, to get an answer.

5:00 Anyway, just let me make the bed up for you, Gerry, and we'll crash out. So, just remind me one more time, Bill, what did you call the construction of which the CCRs were the immediate specialisation? The one we were talking about? The live, actually. The live, oh yes, that's right, of course, the live bits. The real point is that the Leibniz formula itself is derived by differentiation from the special case of this formula. This is the one we proved here. This is the special case. The special case must make the derivative to get the Leibniz formula. Now, what's... OK, dumb question, this is beautiful, but what's... And what's the payoff for the physics? So we've shown we can derive the CCRs, they arise in this way. What do you mean, if you want? What? It means the representations of the CCRs, which are the common abstract C-star algebra method, in other words, you have to have a C-star algebra on which the group of, let's say, homomorphisms of... And so on and so forth.

7:30 Well, it's a tantrum in another category that's associated with that. That's right. I started off with the topos X. The chosen notion of extensive quantity, I mean of intensive quantity, goes right to another category in which an object is base X. A morphism is a pair. An object is a pair X lambda. I mean, it's an extensive quantity, a pair consistent with a space in a given intensive quantity, but morphism is an F, which goes from X to Y, which has the property that… Sorry, this is a pair consistent with a space in an intensive quantity, and this is a… The same thing again, another space with a given intensive quantity. Yeah, again, an intensive quantity. And then a morphism is a… Ordinarily math F was a property that that extensive quantity is exactly the one you get by substituting F into C. Right. So a representation of the CCRs is really a functor on this category.

10:00 It could go into anything you want, linear spaces, Hilbert spaces, category of Hilbert spaces, and bounded linear transformations. So that would say to each space equipped with an intensive quantity, We assign a Hilbert space of x-tensive quantities, basically, thought of as bearing over that space, but if you change, say by a translation again, you apply a motion, any possible motion to x, but it must preserve this given intensive quantity, then you get a bounded linear transformation, so that the morphisms of x-hat act by means of, are represented in the C-star algebra of bounded linear operators. But in a way that's conditioned by these given intensive quantities. Yeah, right. And which preserves the functions of this kind of... Yeah, that's a co-variant term. Actually, in C-star algebra theory, one uses a thing in this integrated form and not in a differentiated form. They don't use the Heisenberg commutation relation, but the vial commutation relation, which is just the integrated form of it. I see. To avoid, because the bounded operators... Do not include differentiation. P is P of X times D by DX, but that's an unbounded operator. If you exponentiate it, you get a bounded one. That was Hermann Weyl's idea to study within the realm of bounded operators. But essentially, in other words, instead of considering differentiation, you consider the one parameter group of translations in the direction of that differentiation. First, again, you said the one parameter group is translated in the direction. Yeah, I mean, differentiation is really a vector field. You see, p of x times is a certain vector field in the multidimensional case. So that p is really a vector field. Well, if you can integrate the vector field and measure one parameter flow in the direction that the vector field says,

12:30 so you work with that flow instead of the vector field. The action of this flow on L2 and so forth is really a bounded operator. You can study its commutation properties with respect to multiplication by Q, and that's what the commutation relation that those satisfy is called the Hermann-Weil, the Weil form of the commutation, instead of using the differentiated form of the vector field, which is not a bounded operator. But the unbounded form has a different advantage from this point of view, not just from the other side of the structure, but from the domain itself, because it's just, you know, this could be any kind of topos or distributive category or whatever, you don't have to explicitly introduce the differentiation into the foundation of the thing. The crucial point is just this inevitable comportment of the intensive and extensive when you push them forward and pull them back and multiply them. It's really quite an obfuscation to pretend that the Heisenberg commutation relates to some kind of quantum mechanical discovery. It's just a basic property of quantities as they vary on spaces and what that might be. It doesn't have anything to do with a particular idea of dynamics or what exactly intensified these are or extended. It's just the fact that you have them. The C.C.R. Heisenberg commentation is true in classical physics. Namely, Leibniz discovered it. It's incredible. Let's see, it took me 37 years to realize that, just as an indication of the weight of the obscurantist system of education that we have in physics. Well I know very intelligent people far far further than I could ever hope to be who haven't understood it yet. I mean I can't wait to show this to Simon Saunders. I'd be absolutely shattered to see his reaction. He'd be fascinated.

15:00 You know, my friend Oscar, who wrote the book on algebraic QFT, algebraic quantum field theory, knows about as much about C star algebra as he knows about W. Incidentally, isn't the W in W star algebra is named for Weyl? What is that? No, I think it stands for week. Oh, it's just, you know, let's see. Yes, that would make more sense, yeah. What is it? It's a steep star algebra, which is weekly, which is the dual space of some, some Bonac space. Yes, yes, actually, it is the dual space and the Banach space. The reason I know that is because I've just been reading Holdsworth's article about quantum logic, which he mentions this fact. I wouldn't have known it otherwise. No, it's just a condition on the topology. It means that the convergence of operators can be tested by individual linear functional tests rather than being sort of global. It's like the Kurtzweil integral thing. See, the usual Riemann... What's usually called the Riemann definition has this delta constant, because the size of the elements of the partition has to be bounded by a single constant delta, whereas if delta is variable, it means you can test the question of whether a partition is smaller than delta quite locally by individual linear functions. When are you going to publish this, Bill? This seems to be to be tremendously conceptually important. Oh, is this already in SBE? 1174. Oh, is it? Oh, now, you told me the other day that you had got that relation after you'd... No, this date is in 1174. This age. That's the one that isn't. It's not. Oh, right, right. Yes, this is widely known but kept secret. This is why they're known too, but for some reason not mentioned. Oh yeah, I'm sorry, wasn't I here when you were talking about that? I don't remember you saying anything about the stone. Stone's theorem that... Yeah, that must have been when I was out of the room. The irreducible representation of the CCR is in fact multiplication by a function of differentiation with respect to it.

17:30 Yeah, I'm sorry, I wasn't here when you were talking about that. Yeah, and that's in Stone's book. The Weyl commutation relations can be realized by translation and multiplied by a constant, and then there's some additional technicalities involved with differentiation to get it down to this form, to the Leibniz or Feld-Heisenberg form. If there's somebody just beginning to learn math, this doesn't involve a lot of hard thought, darling. Thank you. Just, I don't understand it. So... This sort of thing is... I don't have it right in mind right now, but when I teach these management students about... You can do it all with money, right? You buy the wheat, you see, and you buy the cows and all that. Yeah, I understand better than that. The basic fact that you have to push forward to extend their quantities... Pullback, intensive ones, and the pulling back reserves products is quite essential in those kind of transactions as well. Yeah, yeah. Well, you know, I should like to hear some of the illustrations. They might be quite limiting. You'd better be careful, otherwise we might end up denouncing as the teacher of bankers, Lorvier. Ah, very good! Apparently he doesn't have my, on the end paper, have you seen it? 1980... I'm being in honor of Charles Erisman, in the Cahiers de Topologie de France, they took him there. Somehow, I think, 78 is... 1980. Yeah. Will, you give me your address.

20:00 Yeah, yeah, I'd really like to see this. And there was another paper you mentioned today, too. It's got a lot of engineering calculations in it. And by the way, it refutes the claim made in Lavendome's paper that I never did anything. Lavendome? Lavendome was here. Thank you very much for your time. Which is a common slander against myself. He's not unique in that. But he doesn't give this 1980 paper any bibliography because it refutes that. It's got lots of calculations. Is it he missed it or he just ignores it? Well, I don't know. It's in his library. I looked, I checked, and it was there. It's actually in that library. Are they stereotyping you or what? You often hear this said about Bill, actually. I mean, I've heard this said. Oh, yes, Bill. Bill O'Vear, he has, you know, is too busy having deep ideas over to do any real mathematics. That's right. But I think the taco paper is real mathematics. Yeah. Well, I didn't convince you that you're Bill O'Vear. There's an old term. No, the word is conceptual. Oh, very conceptual. Very, very deep conceptual ideas, but you never have to produce any proofs. But you see the importance of the struggle here, right? In other words, it's not a question of my own honor. It's a question of how the reactionaries are attacking from all sides in the mouths and hands of various relatively innocent people like John Bell or... Or love and dome and so forth. But the reactionary currents of philosophy, you see, so the common idea, you see, is that... Dome is a great admirer, I see. I know, I know. Deep admirer. So a common idea, you see, is this conceptual stuff, subjective logic stuff. So the first line of defense is it doesn't exist at all. Right. But then when they're forced to admit that it exists, then you say, well, it's something... It's something detached. You can admire it from a distance. It doesn't actually apply to our calculations or our actual thinking.

22:30 We have to contemplate the Holy Trinity. That's the kind of thing, you see. So it's not the proper assessment of what the whole movement of category theory is about. Because the same standard is made against Grothendieck, too. He is a great man. In the sense that he did lots of calculations to claim that SGA4... So, for example, Deligna, Grotendieck's star student who won the Fields Medal and all these things, and he wrote a book in which he slanders Grotendieck as, you know, SGA4 is 2,000 pages of useless generalities. I'm using diversion, but ultimately there's no value in solving the naked vector. See, he says things like this. By all accounts, Godendieck gave back as good as he got. It's simply false, though. It's simply false because it's Godendieck who calculated exactly how many vector bundles there are in the Riemann sphere. I mean, a very particular example. That's just one famous example, but a whole series of very particular... The calculations were done by Grosendieck as well. He wasn't just giving an amusing but ultimately useless diversion of 2,000 pages. Well, that's ridiculous, because here is a man who has created the concepts necessary to all this progress. Yeah, but according to this philosophy, these concepts are not necessary to the progress. But didn't Delaney himself use just these concepts when he proved the coherence of him? Of course he does. This is an inherently inconsistent philosophy, but that doesn't prevent it from being foisted off on the youth who must study his book. So that's why I react against this characterization of my work. I mean, even if the calculations that I did are more modest. This TACO thing is relatively modest, or category of sets, you know, relatively modest in comparison with vector bundles on a sphere, and many other things that Gruden did, but the essential detachment, you see, of the conceptual constructions with the actual examples is what this propaganda is trying to do. And as such, to the... Who's behind all this stuff? Is it just sound grades?

25:00 No. Sour grapes can be used, can be harnessed to it. It's essentially the trend that Lange pointed out, or Duprony. Students should learn exactly that minimum necessary to do their job within the calculus system, not any more. So should they learn epsilon more conceptualization that is needed to do their assembly line job, then it's a danger. Funnily enough, they also say they calculate better if they don't know what they're doing. Exactly. Or reliable slaves. You know the ultimate reason why Bishop Barclay did not get his money for the university because somebody somebody in Parliament said that we're not going to do this look we already we already set up the Trinity College in Dublin look at all the trouble that that's caused. I guess they made the same objection against creating universities in India. And, of course, later, well, in the 19th century, indeed in any form of education in the empire. I mean, Barclay's plan of having it on Bermuda was probably better than Trinity in the sense it's so isolated that the students could be completely detached from their own tribe. A bit like the people in Georgia. Yes, yes. Oh, this is so interesting. I want to go through it again to see if I have understood it.

27:30 So really there's no, so really, damn, I just noticed that bloody plaster's gone and cracked and I only plastered it about six months, less than that, about four months ago. You mean? Yeah, I literally only plastered that three months ago. It's already cracked and it's bad. I'm afraid that it will crack and come again. Yeah, it's just, oh, it's not structural, no, but I just hadn't noticed it. Anyway, uh, yeah, well, we could go up tomorrow to this pub on the hill to have lunch, which I think you'd enjoy, it's very nice. But I will make my number one priority if you're taking out the tapes. You don't have a camera, do you? No, I don't, unfortunately, no. You wanted to at this moment. Yeah, I wanted to as a matter of fact. Anyway, you're coming to Italy, you promised that. You're going to move, coming to Italy. Oh, to move. Ah, yes. No, really. Well, I might rather like that idea. If you come, come and visit us. Oh, yes. Have you ever been offered a post at Rome, have you, by any chance? I was offered a post at Cosenza in 1975. At the time, I, you know, we had the financial problems with sending children to university. Yeah, yeah, yeah, right. Yeah. Yeah, we did. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. Yeah. But I mean your work is probably more respected and admired in Italy than almost anywhere else, wouldn't that be true? That's the impression I have.

30:00 Especially as a philosopher. I was prepared to be a philosopher. Oh, well, we have declared you to be a philosopher in England now. I don't know if anybody's listened to it. Thank you, sir. That's what we've been up to. Yeah, that was the idea behind it. It's exactly what it's all been about. What was I going to ask? Oh, it's about... No, I don't think they were going to make him a professor of teaching at Bangor. Well, actually, this is quite interesting. I'd like to know, as much as I'm thinking of concrete examples about this, to teach bankers to exploit the masses. Oh, yes. Don't worry, I don't need convincing of that, Jerry. Certainly don't need convincing of that. Also, I want to think more, though, about these very basic, naive, as you mean, naive ideas about mappings that I think... Innocent, let's call it. Innocent, yes. Let's say innocent. Well, don't. Unsophisticated, innocent ideas about mappings. Don't talk too much about that, because it almost lessens the calcareous aspect. We want to get away from elements. Well, but in a sense we do get away from elements when we get, precisely when we go to the case of these identical particles that don't have the, you know, the same, I mean the calculatory aspects of that category are not the same, they don't parametrize the same morphisms as in the case of the, you know, the category of finite sets. I'd like to understand more about that. But I just want to understand the consequences for the mathematical physics of this, though. So really this is, in a sense, You don't start from dynamics. I mean, this is an instance of a much more general functional relationship between quantities, as you say, it works, you don't have to have any dynamics built in to derive the CCRs. No, they don't in general anyway. In the usual presentation, the dynamics is determined by Hamiltonian, which is a function of the particular operator, which is a function of...

32:30 And so on and so forth, and so forth, and so forth, and so forth, and so forth, and so forth, Well, first of all, the states are generalized along the delta there. The states become extensive, or extensive quantities instead of, and then, even that would not be non-classical if dynamics acts on x, and since E is a functor, it also, if time acts on x, then it also acts on E of x, because E is a functor. But quantum dynamics does not act on x. It acts only on e of x. Probability distribution at one time evolves into another probability distribution. This is true even if you started with a delta distribution. It evolves into a non-delta distribution. The dynamics on e of x does not leave x invariant. The process of statistical mechanics also takes e of x as state space. But the dynamics is considered to be lifted up from dynamics on X by means of the functionality of E.

35:00 The value of some quantity, let's say the stock market goes up, what does that mean? That means tomorrow, if we calculate it, we have to know the value of tomorrow as well as the value of today. But tomorrow we have to know both. We have to be carrying over a present value as well as the actual new value. And who's going to make the difference? There are two out there that use the A to mean the difference between the M and A tomorrow. The two adding the numbers. The A5 would be just carrying the thing over. The A arrow would be the action. The A5 would be the mistake.

37:30 That's actually the state now. The A5 action state. The state now remembers tomorrow. Whereas the A arrow action would be the actual mistake tomorrow. So, when you compose these things, there are many, many compositions over a few days, and we've tried from now to get at least three things, a few days out of less than a day, three hours out of less than a mile, and we've also reached the actual time limit, so we can get at least three things in a day. So, I've composed them in two kinds of things for several different reasons. I think it's quite a lot of different categories of math that you can take from each of those categories, the math of the categories, and the presentation of those categories. Anything to be adjoined? They would be terrible to think. And I don't even believe those things. Each of y'all might just come up with an A, and another pair comes up with an E. There are several different types of problems. One of them is that you can go down and see and back up and you can study these math theories and you can get together and you can change the age. You know, you're changing the age. So it's kind of a different type of thing that's going to do it.

40:00 Well, if you want to stay up, why don't you stay up? Yeah, okay. Give me a mattress and some warm blankets. I've got you a mattress. I've made a bed up for you. It's not very comfortable, I'm afraid, because I haven't got... You've got a mattress and some warm blankets. Yeah, well, I've got those, yeah. What I haven't got, unfortunately, is any spare pillows. I've got films and only two, and... Don't worry about it. Just give me a big book. Yeah, you can use your own fleet system. It's a soft one. It's a hard one. No, I know you're joking. I'll just grab a blanket or something. No, I've got blankets. No, no, I've got something actually in the... We need to set you up nicely with a nice photocopier. Good editor. We might even, hearing the troubles they've had publishing books, we might even... Well, I'm confused as to whether we'll ever see it. Well, we will see it. No, we might be able to. It's a possibility, isn't it? This is a book of my time, George. The proceedings of the workshop. Mm-hmm. No, no, this is the one that you brought over to the building. Oh, this was your museum? No, no, no. Oh, well, no, no, I've already got this in the book. Uh, this is the thing that you wanted me to look at, and this is where I'll see it. Mayberry is really an elegant man. An elegant man. Yeah, I agree. Yeah, I agree. That's why I wanted the guy to be here at the meeting. I mean, I've thought that for a long time. Thank you very much for your time, and I look forward to hearing from you again soon. Well, it just is absolutely necessary for the study of process. I mean, this is an extraordinary little thing. A function may represent motion, but only in highly rarefied form.

42:30 This is nonsense. I mean, anything which represents does so in rarefied form, by definition. It is not itself a motion or process of any kind. Well, nobody ever thought it was, except people. You know, this is very strange, I think. Well, actually, it obviously has enormous talent, the musicians, but not, I think, the other things about them. There's nothing I've seen as instructive as totally convincing. In a puppet theater, there's a puppeteer that controls things. But if you have to place him on the stage, he becomes a creature of good like his own very head. Someone must step in before his strength. Yeah, absolutely. I.e., I.e., constructive citizen. Exactly. Leading to objective ideas. Who's going to step in and accept that, right? Yeah. Yes, I'm almost good about basing mathematics on the theory of linking objects. There's a social general way of explaining it. Oh, he's a very fine stylist. As well as being a very intelligent man, he's a very good stylist. Now that he no longer thinks he knows he's got to put his mind to a little bit of air, like he did back in the day, but this idea never entered his head. He's I think a little bit strange. I think if he was writing that paper today, he'd certainly... You know, the one thing I really want to understand a bit, though, is the general level. This is not the subject. There's a couple of questions about this. Just at the general level, I do want to say more about this relationship between quantum physics and quantum physics, and the lack of any sort of knowledge about it. I mean, I don't agree with the position of that, and I'm sure you don't either, but I like it.

45:00 Because it's so well, you know, sort of, you know, hand-held, again, even at the lower, I mean, okay, at one level, you're already considering it, yeah. Yeah, I don't know, I mean, there's a lot of things that come up, and some of the things that come up, it's just nothing, really, it's like, it's nothing, nothing to do with all that. Can I ask one slightly downer question? Why did you have to go through all this business about the, I mean, the business about the dance, the, the, the, the, why not just simply count the holes? I mean, you get, you, you, you've got the, I mean, the mapping, you know, the mapping in the case of the, the, the basics, you know, you, you have, you know, you make it clear, you know, what the needs are. Yes, I agree, it is, I absolutely agree, it is a mini-theory, and just as the category of classical sets is a mini-theory, yeah, but to see the difference between the mini-theories, to see the difference between the mini-theories, I think we have to go through all this remote marking and everything. Can you try to say it? Oh, okay. You do say that. That is a polemic against the... You do indeed say that. The garbage that they put on. They say we can't label the elements. We can't name them. And then I'm saying, well, in the classical world, we don't need to. Of all kaboodas, there's hell of them.

47:30 So we don't need to use physics. I think that we have the right to use physics. If you read Gauch, for example, even Baye, Baye, Baye, Baye, he didn't speak history. Well, he didn't, Baye. So what, what, what, what, what does that mean? Well, that means, what does it mean? It means I'm not here. You didn't speak life, I think, though. That's what I'm saying, yes. No, I'm not, I'm not, I'm not, I'm not. The way you think about the, I mean, the relations, the, the, the relations. Which I made sense of, but it's classical mathematics, which I made sense of, but I think it's a good piece of the road. I think that's quite a bit we've come from the main thing. We can't get everything to be real, we can't get everything to be trivial, we can't get everything to be real. So that's what we're trying to do. And then what are we going to do? Well, we're going to do a few things. We're going to do a few things. We're going to do a few things. You know, the specific point about the English, well, there's a whole point of the paper, is the fact that there's a lot of contrast between the, the contrast between the two. Between the standard real numbers, you've got, oh, 2,000, 1,000.

50:00 Yeah, yeah, it's not that much different. Well, but it is, it's not that you say 2,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000, 1,000. You know, to get at the very end of it. The work on the surface is the thing that everyone wants to do. Can I come to this on a regional and international level? Take your time.

52:30 I mean, I'm not, I'm not really, I'm not really, I mean, only if you want to. Only if you don't want to be shot. What if I read it when I wake up? Yeah, how about that? I think we really should get it done without being... It shouldn't bother you. I can do it much better just... Yeah, I really think that's not a bad idea. He's now 25 years old. He doesn't deserve it. He deserves it. He deserves being slept on like any serious piece of work at this time in the morning. Which people are those, Jack? Oh, no, this may be the question. This is a bit about arrhythmia and what they do. How he thinks about sets. Yeah, show me where I'm supposed to sleep because I'm very... I'll show you there. Well, I think we all say you are a night owl. All the very same point that you were on about, in the way you think about finite collections, about the structure of the category of finite collections, I think it may be quite exactly the same as yours. It is, yeah. Yeah, one way. Is that alright? I'm sorry, this is the best I can help you. I wouldn't even have a choice. Well, no, I don't sleep there. Oh, you're going to sleep there. Phil's sleeping in my room. Oh, I see, so if I sort of keep telling him... Yeah, no, it's alright, I can sleep in my room. But I'll see you in the morning. Have you run the dryer yet? No, never. Hang on, I didn't, and I'll do that first thing in the morning. Same plan as I get. It is. In fact, actually, I'll tell you what I'll do. I'll do that tonight. I have a word for you. Yeah. It's called pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky. Pullbacky.

55:00 Pullbacky.