Public, Peer-Review & Editing Process for Book Titled “Making Good Decisions”: Revised Version for Volume 1 – Part II – Section #6: “Hamming” on Mathematics as a “Flexible Rule”
For new readers: Please read the “Pinned Post” at the top of this Substack’s Home Page, and titled Why Use Public Peer-Review to Write a Book? - “See for Yourself”.
For returning readers and subscribers: This post introduces the Revised Version for Volume 1 – Part II – Section #6: “Hamming” on Mathematics as a “Flexible Rule”
Summary:
Section #6: “Hamming” on Mathematics as a “Flexible Rule” - This section picks up from Eugene Wigner’s application of “Number Magic” to “Small Worlds” in theoretical Physics to look at its use on “Large World” problems by Richard Hamming (1915-1998) who delivered a lecture twenty years after Wigner’s talk, and titled it “The Unreasonable Effectiveness of Mathematics”. A mathematician focused on computer and telecommunications engineering, Hamming builds up explicitly on Wigner’s essay, as can be seen from the similar titles. However, he deliberately leaves the discussion of” Closed-form Equations”, and theoretical Physics to Wigner in order to focus on Applied Mathematics from the perspective of an engineer. His essay answers the question: “Why”. Why do mathematical “Methods” provide such unreasonably effective “Predictions”? Unlike Wigner’s hopes to extend the unreasonable effectiveness of mathematics beyond Physics to include other (and softer) branches of learning, Hamming narrows the scope of the discussion to the “Process” of applying mathematics to engineering problems. His answer to the “Why” question states that mathematics works like a “Flexible Rule”, a rule that changes with circumstances. Thus, a Flexible Rule” will reasonably show unreasonable effectiveness in measuring the areas where it can be applied. Wigner’s “Number Magic” loses its “Unreasonable Effectiveness” when applied outside of the “Small Worlds” of metaphorical machinery, and Hamming shows how to regain some of this “Unreasonable Effectiveness” in the “Large World” with the metaphor of the “Flexible Rule”. Hamming’s “Flexible Rule” works as a “Repair Program” that limits Wigner’s “Rational” prescriptions of “OMG, this must be right ” of the Logic & Statistics Program to the “Task Environments” in the upper-left quadrant in the enhanced-Cipolla chart, while extending its value with observations of “Good enough, looks like it works” in the other quadrants.
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”CTRI by Francois Gadenne” writes a business book in three volumes, published serially on Substack for public peer-review. The book connects the dots of life-enhancing practices for the next generation, free of controlling algorithms, based on the lifetime experience of a retirement age entrepreneur, & continuously updated with insights from reading Wealth, Health, & Statistics research papers on behalf of large companies as the co-founder of CTRI.