The relationship of foundations & applications
Recorded at Geometric Structures in Logic, Physics & Computer Science, École Normale Supérieure, Paris (2000), featuring Francis William Lawvere. From the Michael Wright Collection, held by the Archive Trust for Research in Mathematical Sciences & Philosophy.
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mw0002161-cc-a_p- Format
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- Michael Wright Collection
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- Archive Trust for Research in Mathematical Sciences & Philosophy
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This transcript was generated by speech-recognition software from an archival recording and has not been hand-corrected. It will contain recognition errors — particularly for proper names and technical terminology — so please verify against the audio before quoting. Timestamps play the recording from that moment.
0:00 In the last lecture, which is the long one, so if anybody in the second part, and so the second part is for the computer to live in. The geometry is strange, it's sort of very seriously, and for example, an alternative to label transition systems is called the chemical attract machine, which I have learned is now one of the describing things.
52:30 But since Robin talked a lot about that, solution t equals zero is called synchrony, and I never, and that's really, this is a completely different. Why? Because you have a large scale interaction between bodies with information flow in zero time, it's called Newtonian mechanics in physics, and it's totally non-trivial, I mean, three bodies is not trivial, but the information flow is conceptually zero debate, and everybody knows that it's wrong, but everybody knows that it's... For example, who is using this kind of... In total theory, when you write a country equation like xt equals yt plus c, you have no time for plus, and people are very happy to be able to...
55:00 You can view it as a physical circuit, a magical machine that will solve, in no time, any set of Boolean equations provided the... How do you find these computation models? You will find them again in electronic circuits, so the delay models, and this is why we can say things about circuits, we can make them work actually in physical. You can find them in the implementation of synchronous energies, but I won't talk about that. You can find them in things like systemic arrays. If you know large-scale computing with systemic arrays, it's a typification problem. And these models relate together. What's happening is exactly what is happening.
57:30 There is no electric constant. So the natural tendency would be to suppress cycles altogether. But it's not true and you can do better. And we had to do this for reasons I won't explain. And we made some interesting discoveries about what electrons do as far as logic is concerned. All of this is true, which is totally true, and that would make sure that if you find any solution, it may not stabilize.
1:00:00 And you can see a circuit as a machine that will show that everything is connected, you know. It's a very, very expensive one, because if you add a never-seen periodic to any number, for example, 101010,
1:02:30 it goes into 100 plus 0. And this is... And so this number is... But its number is slightly different from what is explained in one word. Nothing. So, my mission is to view ABC. The definition of the circuit is that it makes an addition. The point shown in the central circuit is the evolution of the series of circuits, and I encourage you to, for example, I give totally... The thing you can do, for example, is explain all sorts of things that are, put all the bits of a number in space, and the source code of that, if you put, show that the fundamental time space, that thing I would like to say, computations are something new, but...
1:05:00 What the classical algorithm makes is trying to optimize the usage of resources, trying to make as a less, a minimal number of operations, a minimal number of memory cells, to use a minimal thing. And this may disappear. This very problem may disappear, or not disappear. We change phase. I mean, ten years ago, upon circuits, the spare resource was computing, the spare resource was computing. And now we have too many transistors to know, and you need men to do that. And computers. So there are not anymore rare resources. Things change. The notion of wanting to minimize the global time it takes to do everything about modern circuits is about speculative calculations, which means computing all sorts of useless stuff. That is, trying to... The problem is as follows. When you have a route here, you start the test. But maybe the test is long. You don't want to wait for the result of the test. You start both branches in parallel. And that may be very complicated.
1:07:30 If I try to change the world, you must make copies of them and keep the copies very, very aggressively and for IA 64 architecture by Intel, nobody changes the way, for example, it may total an algorithm, it's not necessarily true, if you're on machines, one is on chemical computing, internet computing, so very different. My personal view would mean that to optimize your computing, you consider all numbers and you are paying, you are paying for more because you may make some useless computations that are not needed.
1:10:00 All optimizations so far have been the theory of needed computing. The new large-scale computing, the problems I showed of zero-delay interaction, gives to three different fields of computing. We never see circuits, people talking to pi-calculators. It is an interesting question whether the general mathematical framework
1:12:30 are the module structure of programs the same for all these three application domains. Is there more Curry-Roward explanation than the simple one I gave? Are there Curry-Roward views? And so on. So there are a lot of questions. I'd like to ask a question in mainland about the action and bias. Can you provide a general or is it too late to solve the problem? So, I'm not going to ask you questions about that. My first question is about Kantor. What do you mean by Kantor? As a second speaker, it seems to say that Kantor, in a complicated sense, is not so useful now because of our parallelism, was the first question. Speaking of instances, so does that mean that you put the concept of classes or sets behind exactly like mathematicians who deal with sets first and then in categories? And my third question is, is it possible to be a better professor of professors and if so, what can we apply? I didn't catch the last words. Is it possible to be a better tester of your papers? And if so, what can we do?
1:15:00 I'm just about to decide whether to answer how many of your questions. You understand one question.
1:17:30 This whole conversation can represent a diverse group.
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