The Eternal Doorman

See  Breaking through the normalization barrier: a self-interpreter for f-omega  (POPL 2016) by Matt Brown and Jens Palsberg. Here's his earlier  video about System-F .  Subscribe to Computable Secrets . Jeremy Gibbons on his book Functional Programming Patterns   See his piece How Design Co-programs .  Why is so hard to get anyone to talk about the dual notion which is data representation by processes? If data determines algorithms, then algorithms can equally well determine data. And if those algorithms are distributed computations then it makes the data they represent very hard to alter. If you ask a computer scientists they might just say "Well, that's because they're not isomorphic." But that doesn't matter: it just means that codata can represent so-called uncomputable functions, which can actually be used in practical applications such as forward key-generation. Some physicists also don't seem to want to think about what data actually is. See  J...

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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 ...