Francis William Lawvere / Ted Bastin / Viv Pope Aspects 2000 Tape 2 2000
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Recorded at Aspects 2000 Tape 2 (2000), featuring Francis William Lawvere, Ted Bastin, Viv Pope. From the Michael Wright Collection, held by the Archive Trust for Research in Mathematical Sciences & Philosophy.

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mw0002168-cc-b_p
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Michael Wright Collection
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Archive Trust for Research in Mathematical Sciences & Philosophy
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0:00 Quantities and or dimensionless or dimension things go together. Build this out of pure mathematics and then fit that to what you see. But there seems to be something there. In a way, it's like trying to guess the lottery. I mean, I put my numbers in. Cases, they might be bits of information and they might be lots of things.

2:30 Which of those things they are, I'm studying, well, there are two ways of looking at it either, one can look at it ontologically or epistemologically, take the epistemological route because I like it better, I'm studying perception in a generalised sense, even without specifying, I just want to say, before you say any more, before you say any more, I just want to say, before you say any more, As you said the other day, your method is not to be relational. He said, no, he said, for sure, no.

7:30 There can be no outside intervention. So in order to make the another 15 minutes be able to start asking questions, when you were talking about generation and discrimination as two separate operations,

25:00 it's with Jameson's simplification of the quantum numbers when we start to do scattering theory. It's interesting looking at this again. It may be useful to both of us, even though our points of view are different, so there's not much convergence. A more general question, from either point of view, it's forgiven that you had as one way to represent the combinatorial higher brain or whatever, and this is...

30:00 I mean, you certainly guess to a clicker right away, because we get quaternions, and we already have in the work I did with Lou Kaufman, the bed-string model, which in fact came out of a...

32:30 A suggestion of Beloch's a long time ago, looking at Stein, referring it to the Feynman half-integral approach. We know how to get from this a discrete version of that. See, I have a much more physical root. Subtlety about the commutation relations were complicated.

35:00 I think we know how to solve that now. That is something we did this spring and hopefully then we can put these two things together and we have a finite and discrete model for the interaction vertex in QED, but that means then if we do in program universe if we've got and then which interact...

37:30 There are two things which came to my mind. The first is that the bit strings, well, yes, they are pretty well bit strings in the conventional sense, as far as the computations are concerned, except that one must take into account the number of leading zeros. The number of leading zeros? How many zeros do you have before you start getting zeros, before the first one? The second thing is that the operation itself is actually a generalization of the exclusival. Yes, a generalization though, isn't it? It's not a exclusival. But if we go back down to the simple case... Then it is, right. Would I understand a model called generalization? Well, yes, Exclusivall compares, as an operation, it compares two bits. It says, how's it, what, will it be the same one? So, if they're the same, it may give one, but it may give two. So what's the generalization that isn't that? It's a bit singular, but that's also different, but it's one, perhaps, I wouldn't explain it unless I would like to tell you.

40:00 They ask questions. What is to Clyde about addition, even if it is a reservation against Mike? And the question is, what would you mean? These are really the same question. I mean my answer to the first question is that when the second operation occurs it must be physical. You have to work with the first one in order that the addition should be distributive over the other.

42:30 In the very early days, the operation was much less Frederick and others at the Language Research Unit, because if you write the hierarchy out in Frederick's way with what you see is operating on the vectors, things together, things a few years ago, I mean, I think this has an answer.

45:00 Because, you see, if somebody doesn't accept the original theoretical basis, like process and so on, we don't need the same kind of theoretical explanation for the second relation. We don't accept the first, where we don't know about the second thing, and regardless, we know how it would work anyway. Yes, I could add something to that. I think that there is a way of introducing addition which, oddly enough, Eddington in a very muddled way got somewhere near in fundamental theory because when he writes B numbers out, and sometimes he thinks he's just doing the Dirac algebra and that's that, but sometimes he writes four of them down. Without coefficients, that is to say, coefficient unity, we still have something like E1, 2, plus E3, 4, or something like that. And what he is doing in those parts of the book is simply using this plus as a way of grouping them together. He could equally well have written them with commas in between, of course. And if that's what you want to do with...

47:30 I'm quite happy with addition, so long as it doesn't mean any more than that it's a way of looking at things. So that, for example, I could write a DC subset, instead of writing it as A, B, and A discriminated as B, as AB, I could write it as A plus B plus AB. And then I could define the distributive law as As holding, it would be all quite straightforward sort of thing. But I think you're really asking for a bit more than that kind of purely formal. Oh, yeah, yeah. There's a little way towards, I don't know, I think Ted might agree with this. I mean that Eddington, some parts of fundamental theory, Eddington uses a purely formal addition. Actually, this is really nothing new. It's only like at the beginning of this century when vector analysis was just coming along and people... Both physicists and mathematicians saw it as a funny sort of thing. We've always written the electric field as E1, E2, E3, or EX, EY, EZ in brackets and commas in between. Now we have to write it as IE1 plus JE2 plus IE3. And they must have said to themselves, what do you mean by adding these things together? So I don't mind addition like that, but there is quite a careful distinction to make sure that what you were doing was in this purely formal way and not something surreptitious. My question is about the construction of the Converterial Hierarchy by two ways. One way is mathematics and mathematics and I understand how it was done. Another way is the slot theory by Parker Rogers in which he introduces twins which are not the same but also are not the same.

50:00 Both, and in this approach, the combinatorial hierarchy numbers appear as ranks of the sorts, not sets, but sorts which are constructed. And I don't see, I don't see a correspondence between these two ways of construction. And I don't understand why these two ways of construction give the same hierarchy numbers. Are they corresponding? I think this is a very interesting question, an extremely deep one. I'll give a short answer and then I'll ramble on for a long answer. And the short answer is that I could never understand the theory of indistinguishable in that book. It was just too hard. Do the combinatorial hierarchy. It's carefully constructed. The quick answer is, certainly you're right in entirely the same way. There's a lot more structure. Yeah, there's a lot more numbers as well. But they're certainly different. Now, the question gets a bit deeper. Totally unrelated in this way. And the odd thing is, this gets us back to what we were saying earlier, which didn't actually say it. Seems to me, I've come to the conclusion, one can look at the history of what they needed. One sees this most clearly in the binary logic.

1:00:00 The logic, yeah, but you might get somewhere down. I take this would be it would be finally in the formal discussion as far as I'm concerned yeah yeah you nothing more to say I think no no something to ask but it's a big question maybe how do you get space There we are going. I didn't know the clock was ticking. We'll take note of your questions. Okay, so I should officially wind the meeting up at this point. Everybody who stayed to the bitter end, I think, was perhaps at least twice as many people as we've ever had before at this point. It's surprising how this was. No, it's not the appropriate word at all. In fact, I think it's gone extremely well. And I hope we can keep a similar sort of format for next year. I think it's been successful. Well, I think you should be congratulated, both of you really, on subtly engineering this process. Certainly there weren't horrible gaps and there weren't embarrassing dead ends and all those sorts of things.

1:02:30 Generally, running the type shift. Let's give them a hand. I'd like to remind everybody yet again to return for 30 minutes. There he goes. I hope some discussions ever see you this afternoon. I'm not returning. You're not returning. That's exactly what I intended to do. Thank you very much. We stay in contact as being the categorical part of the thing. Yes, I think that would be an extremely good thing to do. We try. Thank you. Peace and very much. Goodbye. Next time. We'll stay in touch. Very shortly, I think. Take care. ...or use some money for the empathy. Do you know how much it is? It is 30 quid. Well, who do you pay them to? Ambulance. Three pounds. I'll talk to you. I'll do nothing. You've got a return train ticket, haven't you?

1:07:30 Now, here it is. The cube is equal to 1 over n minus 1 over 3. Okay, so the cube spots at n squared over n squared is equal to 1. Okay, so that's the sum of... But if you say but one, you see, if that is the probability, then you say the positive square root of that, if the two roots, then, let's say the two roots of q equal one plus n squared over n squared, this interprets as probability one. This is what I would call adding in quadrature.

1:10:00 We have all of these arguments. But now you're saying you want to interpret the two roots of this, the symmetric roots, of this whole left-hand side or just this whole left-hand side, The two factors are that the benefits of the two factors are that the benefits of the two factors are that Yeah, now there is a more, you see there is a more extensive discussion on what I call anti-inflation, in connection with everything from out of man, and from one of the whites, and from one of the whites, and from one of the whites, and from one of the whites, and from one of the whites, I never turned this around. I always heard you were very good at math. I can't do those things. See you later. Okay, cheers. But I owe you on my music. I hope we can get through the rounds and get through them all. This is yours, and yours is mine. Yeah, so you get this one here. So, are you going to publish? So I will just go. Oh, right. Yeah. I just need to take these because otherwise if I don't, yes. So, what do you do when you're not here? I hope you enjoyed this video, if you did, please like, share, and subscribe to our channel.

1:12:30 I mean, this is, okay, you see, okay, this is asymmetric. If you go back, if you go up, there's the same, you see, that's just derivation of the, you know, of the, of the, of the, of the, of the, of the, of the, of the, of the, of the, of the, of the,