The Eternal Doorman

See  About Logic Interview with Emily Riehl  and  Marie Durrieu - Bourbaki n’est pas un homme, ... My comments : 11:55 I think there is evidence in Euclid's Elements that there was an analytic process which preceded the synthetic theory he presented. Aristotle makes this explicit where he talks about the process of division as making the demonstrations obvious. He mentions in particular the proof of proposition 32 "In any triangle, if one of the sides is produced, then the exterior angle equals the sum of the two interior and opposite angles, and the sum of the three interior angles of the triangle equals two right angles." This came from considering lines falling across two parallel lines and is very closely connected with the formulation of the parallel postulate. There are other places where you can clearly see that several propositions are all derived from one drawing which then reappears as you connect the separate propositions together. I don't have my notes w...

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I wonder whether this can ever happen with sound or light? Here water is being modeled as a homogeneous fluid. See  All About Water and Entropy .  Subtitle could be "The perfectly reasonable ineffectiveness of mathematics in the physical sciences".  There is a French video platform for mathematics lectures  https://www.carmin.tv/​ Subscribe to  IHES .  After watching that talk I found these and it struck me that composed together they're a kind of inverse to the above problem:  In higher-order ambisonic systems sometimes you get ill-conditioning in the decoder and this produces rogue waves ( 27:37 ). The way these systems work is that they either record from a single point at the center of the space and play back from a shell surrounding the space, or they record from a shell surrounding the space and play back from a central point.  Subscribe to  EMPAC .  Persi Diaconis on Poincaré and probabity.  Poincaré analysed the probability ...

These are all very closely related, but the premisses in each case are different enough that it would take a lot to explain the connection in any detail. I don't know what the answer to this is, except to note that they all have to answer to different funding sources. See  A New Kind of Science . Andrej Bauer - Derivations as Computations See  https://www.andromeda-prover.org/ See also the SEP entry on  Substructural Logic .    Subscribe to ACM SIGPLAN .  Philip Wadler on Interpreters for free 27:13 Whilst trying to explain the idea of proving progress in a reduction relation he gets his slide projector software into a mode where it only allows him to step forwards, ...  See the book  https://github.com/plfa/plfa.github.io Subscribe to INI . An interesting talk on basic Stone duality See also  Stefan Milius - Demystifying Codensity Monads through Duality . Overview of Petri Nets and Derivations Subscribe to MSP Strathclyde .

I can imagine a process where one could use a metalanguage to derive syntactic structures with certain formal properties induced by formal maps between them. This is how I imagine Grothendieck toposes are used in Lawvere's categorical semantics. The way this would work would be like the module system in a high-level functional programming language where one could instantiate syntactic structures at any level by  concrete syntactic objects, which might be derivations in some formal deduction system, or they might be programs-cum-proofs in some type theory, or a construction in some algebraic language like a diagram algebra. However what I imagine is not a single formal system one could download and compile. Rather it would be a network of interconnected systems where syntactic structures defined in one place can be instantiated in many others. So it would not grow monolithically like a proof library, but organically like an ecosystem.    Subscribe to The Well . For more pr...

It's way more interesting than any textbook would have you believe! See  The electric storm of November 1882 . Subscribe to  Dr. Jorge S. Diaz . 

My comment : 11:41 Applied category theory was invented by Ernst Mach in around 1882, I think. From The Economical Nature of Physical Inquiry "The greatest perfection of mental economy is attained in that science which has reached the highest formal development, and which is widely employed in physical inquiry, namely, in mathematics. Strange as it may sound, the power of mathematics rests upon its evasion of all unnecessary thought and on its wonderful saving of mental operations.... No one will dispute me when I say that the most elementary as well as the highest mathematics are economically-ordered experiences of counting, put in forms ready for use. In algebra we perform, as far as possible, all numerical operations which are identical in form once for all, so that only a remnant of work is left for the individual case. The use of the signs of algebra and analysis, which are merely symbols of operations to be performed, is due to the observation that we can materially disb...

The bat-shit bonkers Brits want slaughter,... It's happened so often they think it's part of their national character.  See  Kim Iversen and Ben Swann on Pizzagate .  Subscribe to  World Affairs in Context .    Steve Jermy interviewed by Glenn Diesen. See  https://stevejermy.substack.com/   Subscribe to Glenn Diesen . And a bonus which is Kim Iversen Interviewing Dan Kovalik:  Subscribe to  Kim Iversen . 

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