Process Maths

John Baez was the first person I ever heard use the term functor. He used to (maybe he still does?) publish a newsletter called This Week's Finds in Mathematical Physics which I sometimes read with bemusement when I was in the first year of studying undergraduate maths.

This is all about representing diagrams and processes. See Two Interesting Videos on Groups.

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Gerald Jay Sussman talking about scheme programs as wiring diagrams, ... (1986)

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Jonathan Sobel talking about Categorical Semantics (December 2004). He starts talking about the equivalence of Turing Machines and Lambda Calculus with capture-avoiding substitution. See Ian Grant's Weather Report agosto 01, 2022 for more on logical frameworks for formally specifying semantics, and Gerald Sussman on Rewriting Systems for more about ways to think of rewriting systems as biological and chemical reactions.

Att 15:24 he quotes Dana Scott on the origins of the idea of a Cartesian Closed Category (Eilenberg and Kelly, Closed Categories, 1966) which was around the time John H. Conway was giving his Cambridge course on Regular Algebra and Finite Machines. See Ian Grant's Weather Report julio 23, 2022.

As an exercise you might care to think about simulating a Universal Turing Machine using recursive Lamba expressions for each state and lists for the part of the tape behind the head and the other part underneath and in front of it. It's not too hard [NB: I'm breaking the second law!]. But defining a Turing Machine that carries out normal-order lambda reduction is not so easy.

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