The Eternal Doorman

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1:06:18 He's a Taoist, ... I suppose that shouldn't be a surprise. Subscribe to European Mathematical Society . 

Here's the whole blackboard: I had to time-travel to get that picture, so please look at it! My comment : This is great material you're presenting, but the tech you're using is several steps back from a chalkboard or a pen and a piece of paper. I need to see what's been written to be able to refer back to definitions when you use them later, and I can't do that without rewinding the video. You've serialised a manifold isomorphic to R^3!  I have a problem with the bit right at the beginning though. It's not clear to me what is S^2 and what is Q. Clearly the points q_1 and q_2 are on S^2, and q then seems to be path of points on S^2 and t_1 and t_2 are on the real line? So the path function q picks out for each t in the interval [t_1,t_2] a single point in the general configuration space Q. So what we are trying to ascertain is whether there is some sort of canonical representation of the dynamics of the system that fixes the trajectories it can take through ...

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My comment : 2:30 If we knew the initial conditions perfectly, .... But but but, .... you have a model, right. Your model has some representation of state, and some set of functions mapping state changes as a function of time. So the "initial conditions" you are referring to are the initial states as represented in your model. Surely yes, because even if your model was using states of individual atoms then it would only represent them with some finite amount of data, so to a limited resolution. So your model is always representing not actual physical states, but statistical distributions of physical states. So there is no real way I can understand what knowing initial conditions perfectly could mean. Even if the model was subatomic, there is no notion of perfect knowledge of the state, because, even if it exists, it's hidden until you measure it. The reason I am making a fuss about this is that it is getting the notion of determinism wrong. There is an idea around that d...

I'm sure this will be great Scott. Ask Bertrand Russell if you don't believe me. See the centenary talk Scott gave on Strachey  and also Scott, D. Some Reflections on Strachey and His Work . Higher-Order and Symbolic Computation 13, 103–114 (2000). https://doi.org/10.1023/A:1010018211714  and Toward a Mathematical Semantics for Computer Languages (1971) by Scott and Strachey. 2:03 From Scott's Strachey centenary talk: Let us now return to λ-calculus and Strachey’s use of it. Christopher told me once that Roger Penrose (now Sir Roger!) suggested to him that he ought to look into using the λ-calculus for the kind of function definitions he wanted to do. At this moment I cannot track down or verify the story. (Perhaps people in Oxford might ask Penrose personally about this?) See  Curt Jaimungal Talking With Roger Penrose  and the reference Penrose made to S. W. P. Steen's graduate course in Mathematical Logic. In 1973 Steen published a book  Mathematical Logic ...

That's fun. He doesn't mention it, but I think they're using Topos theory behind the scenes. If they're not then they probably should be! See  Richard Southwell Being Norman Wildberger . On that early Universe/Scattering Amplitudes duality, see  The Category Enriched over the Category of Finite Sets, The Finitely Triangulated Manifold and the Magnitude of a Finite Category . See Another Two Talks on Cosmology and  Clark Barwick on Factorisation Spaces and "doing physics" in Spec ℤ .  Subscribe to Institute for Advanced Study .

See the full interview here:  About Logic with Andrej Bauer  and this discussion at 40:14 . You can support Deniz by helping with production costs via  https://buymeacoffee.com/aboutlogic . My comment : The good old completeness theorem is my favourite theorem! Can you  and Thorsten interview Paul Taylor some time and ask him why they wrote Proofs and Types in such a bizarre way. Was it to drive people insane if they were stupid enough to try to understand logic and computation? Subscribe to About Logic . My comment : I am wondering whether I am the only person in this subset of people who understand some part of this video, ... Subscribe to Sheafification of G .  See Dana Scott's Stochastic Lambda Calculus: an Extended Abstract  and Lattices Everywhere . This whole way of doing topos theory just doesn't seem right to me. If it's all based on constructive mathematics then why can't it all be described in one language? These people keep inventing new langu...