The Eternal Doorman

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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...

John Baez interview with Latham Boyle Notice that he hardly ever mentions the theory and actual observations, just the deductions that they have made from them ( 2:47 ). To me this sounds like a state of almost complete ignorance. Sure, it's simple enough, but why is this interesting? Is it because he thinks he has shown that we don't need to assume anything special about the initial state of the Universe, and that it spontaneously produces all the structure we could ever abstract from observations of its present state? 14:10 When you look at the cosmic microwave background now you find it is far from scale-invariant because of the gravitational clumping that's been going on since. Personally I think this just means that it was all so long ago that not even God knows anything about it. See this talk on coupled oscillators as associative memories for compositional inference . Subscribe to John Baez . Mike McCulloch on what sort of things would happen if you found that some ...

41:31 That point of perspectivity is invisible from the perspective of the camera!   See Coxeter's Projective Geometry on the Internet Archive .  Subscribe to  Richard Southwell . This is a placeholder for Norman's upcoming video on polynomial functors in terms of slice categories and adjunctions or something, ...  Well, Norman didn't show up, so I found this talk by Simon Willerton on the Categorical notion behind the Legendre-Fenchel Transform. 1:06:16 Interesting question about the Cauchy completion of the rationals. It reminded me of the theorem of Kronecker for some reason. See Lawvere's 1984 paper  State Categories, Closed Categories and the Existence of Semi-continuous Entropy Functions . I think that if you just consider a finite complete lattice then you will get most of this structure (of the Legendre-Fenchel transform) in a topological space. Then maybe you can extend it to an infinite lattice using some model in projective geometry. So one s...

I missed this bit the first time I listened to this talk: at 9:02  The magnitude of a finite category is the Euler characteristic of its classifying space and the magnitude of the poset of simplices of a finitely triangulated manifold is the Euler characteristic of the manifold.  It's quite hard to find out what the classifying space of a category is: see  What Does the Classifying Space of a Category Classify?  by Michael Weiss. See also  Terence Tao Formalising Riemann-Stieltjes Integrals in Lean Mathlib  where I wrote "... an Abstract Simplicial Complex which satisfies the Augmentation Property is a Matroid, and a Finite Simple Matroid is a Geometric Lattice. Then Simplicial sets are used to define quasi-categories, a basic notion of higher category theory. A construction analogous to that of simplicial sets can be carried out in any category, not just in the category of sets, yielding the notion of simplicial objects." 48:35 Diversity measu...

Subscribe to  Mike McCulloch . My comment : 14:00 I can't believe he just said that out loud. [Maybe what he said was "Please make your instruments sensitive enough in these respects x, y and z, so that we can test this theory."]  [Experiments intended solely to confirm a calculated predicted have been a tradition in physics since at least the Eddington experiment in 1919.]  Subscribe to  London Institute for Mathematical Science .