Norman Wildberger - How Physicists do Maths


For context, see A skeptical look at the Special Relativity narrative



See Algebraic Topology of Finite Topological Spaces and Applications by Jonathan A. Barmak The first chapter of this is surprisingly readable, and would be understandable too, to someone who is familiar with CW complexes and Homotopy theory in general.






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Maybe that number should be called Z? See Doron Zeilberger - An Ultra-Finitistic Foundation of Probability (Foundations of Probability seminar November 19, 2018:)




Persi Diaconis and Brian Skyrms begin with Gerolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume’s problem of induction, Andrey Kolmogorov’s general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea—that we are psychologically predisposed to error when judging chance—is taken up through the work of Daniel Kahneman and Amos Tversky.

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When we (finite individual human beings) make representations, for example, on computer gaphic displays, we typically have a matrix of (non-negative) integer pixel values. So we should never need to do anything other than exact arithmetic all the way through the process. When we make such representations we need to be able to expand the whole process model to achieve a certain fidelity of representation: See Trying to Make a Sci-Fi Movie and Sense Perception v. Sense:


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