Workbook for Volume 1 – Part II – Section #10: The “Number Magic” of “Probabilities”
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 #10: The “Number Magic” of “Probabilities”
Summary:
Section #10: The “Number Magic” of “Probabilities” - This section looks at the types of “Word Magic” and “Number Magic” associated with the use of probabilities. We see what we understand, and understanding probabilities proved more complicated than expected. Probabilities add more optional views to an already long list of possible mathematical views of reality. The last five sections showed that: (i) Wigner saw the “Unreasonable Effectiveness” of “Closed-form Formulas” in theoretical Physics, (ii) Hamming saw Mathematics as a “Flexible Rule” that placed empirical “Motions” first, Proofs second, (iii) Huygens saw fairness in calculating “Expected Values”, (iv) Bernoulli saw morality in using “Expected Utility” instead of “Expected Values”, (v) Secrist saw a world of increasing mediocrity from “Regression to the Mean”, and (vi) Peters saw a “Prediction” of institutional outcomes, not individual outcomes, in non-ergodic “Ensemble Averages”. This section shows that: (a) “Classical Probabilities” see probabilities as characteristics of the observed, and specifically the characteristics of “Small Worlds” games of chance, (b) “Frequentists Probabilities” see probabilities as characteristics of the observed, and specifically time series with features that do match the “Axioms, Assumptions & Hypotheses” required for the valid use of “Small Worlds” statistical “Tools”, and (iii) “Subjective Probabilities” see probabilities as judgments made by the observer, subject to changing information over time. This means that when we use probabilities to share our understanding of reality, we also need to state our specific view of probabilities in order to be understood.
See the downloadable pdf below:
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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.