The Eternal Doorman

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 . 

13:10 "Entanglement is not nonlocal!" See  Lyapunov Stability in Dynamical Systems .  Subscribe to The Institute O'farts and Ideas .  Talking about biology as if it was just physics: Subscribe to Avshalom Elitzur . 

There are control theory people who talk about a revolution in thermodynamics: see  The Port-Hamiltonian Formulation of Thermodynamics—A New Perspective  by Janusz Badur and Piotr Józef Ziółkowski.  The idea is that you can describe certain non-conservative thermodynamic systems as control systems and these have dynamical properties that can be characterised quite precisely.  See also  Port-Hamiltonian Modeling of Ideal Fluid Flow: Part I. Foundations and Kinetic Energy by Ramy Rashad, Federico Califano, Frederic P. Schuller and Stefano Stramigioli.  Subscribe to Richard Pates .  The roboticists have categorical models of hybrid continuous/discrete time systems. These are systems which undergo instantaneous discontinuities in the evolution.  My comment : There's a kind of duality between robotics and experimental physics. The robot's environment becomes the physical laboratory and the physical theories are those which explain the phenomena in ter...

I'm a sucker for good commercials. See  https://alanis.com/events . Subscribe to Alanis Morissette .

They're threatening to do this weekly, ... My comment :  Looking forward to the Dana Scott interview! Maybe there's not time to do this before then, but I would like to hear a discussion about the different views people have about models. I sometimes think that Computer scientists look for models in the zoo of mathematical theories, because they feel like this the only possible source of their legitimacy: they say something like "Well, this type system is sound because if it wasn't then ZFC would be inconsistent and you would have much bigger things to worry about than the soundness of my little type system!" But then serious mathematicians who have Fields medals come along and say "Well actually, I have these proofs that I've done in Higher Homotopy theory and I seriously doubt anyone has checked them as carefully as I did, and I am not sure that I haven't made a mistake somewhere, ..." and then they find a type system that a computer scientist ...

Category theorists, it seems, can't help but go up , making more concrete stuff that they have to find names for. They should learn about abstraction.  See  Why is Physics So Difficult?  and  David Jaz Maiers - Compositionality via 2-algebra .  See also  Richard Southwell and Norman Wildberger on the Future of Mathematics . Norman's box numbers are a multisubset of the set 1={∅} which, according to nlab is an isomorphism class in the over category Set/1, I think. See the three examples in the comma category on nlab  and  fundamental theorem of topos theory .  Richard Garner, Polynomial comonads and comodules Subscribe to  HoTTEST .  David Spivak's talk "Categories = polynomial comonads", a simple demonstration. This is great. It should give Norman Wildberger a whole lot of new ideas for stuff he can do with polynumbers! It was given in September 2020. Tom Leinster on a general notion of magnitude: I learned something interesting a...