Notes: Chapter 17c: Entropic Epistemology: How We Know What We Know

Chapter notes for “Chapter 17c: Entropic Epistemology: How We Know What We Know”

Notes

¹ Adrian Bejan, The Physics of Life: The Evolution of Everything (St. Martin’s Press, 2016). Bejan’s Constructal Law — “for a flow system to persist in time, it must evolve to provide easier and easier access to the currents that flow through it” — is applied here to knowledge flows. Accurate models provide easier access to prediction and coordination, conferring a thermodynamic advantage on epistemic systems that carry them. The extension from physical flows (rivers, vasculature, lightning) to informational flows (beliefs, theories, cultural transmission) follows from the convergence between the Constructal Law and the Free Energy Principle established in Chapter 3.

² The Feynman Point (six consecutive nines beginning at the 762nd decimal place of π) is named for a joke attributed to Richard Feynman: that he would recite π to that position and conclude “nine nine nine nine nine nine, and so on,” implying a false pattern. The attribution is apocryphal. There is no record that Feynman made the remark, and the earliest documented version is Douglas Hofstadter, Metamagical Themas (New York: Basic Books, 1985), recalling his own ambition to memorize π to the 762nd digit; some have proposed calling it the Hofstadter point instead. The six-nines fact itself is correct. For the digit string, see David Blatner, The Joy of π (Walker & Company, 1997). The Feynman Point illustrates the distinction between local regularity (a coincidence in a normal number) and thermodynamic basin (a stable attractor that systems fall into and remain in under perturbation). For the statistical properties of normal numbers and the inevitability of such digit strings, see Ivan Niven, “Irrational Numbers,” Carus Mathematical Monographs 11, Mathematical Association of America (1956).

³ The concept of Schelling focal points (coordination equilibria that emerge from shared cultural attention rather than from any intrinsic property of the coordinated-upon object) is from Thomas C. Schelling, The Strategy of Conflict (Harvard University Press, 1960). The Feynman Point functions as a Schelling focal point for mathematical culture: memorable because it confirms a pattern-seeking bias, not because it carries thermodynamic significance. The distinction between culturally sustained focal points and thermodynamically stable basins is central to the epistemological test proposed in this chapter.

⁴ The “constructal epistemology” argument, that truth has a thermodynamic advantage because accurate models outcompete inaccurate ones over sufficient timescales, has antecedents in evolutionary epistemology. Donald T. Campbell, “Evolutionary Epistemology,” in The Philosophy of Karl Popper, ed. P.A. Schilpp (Open Court, 1974), 413–463. Karl Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (Routledge, 1963). The thermodynamic grounding adds a substrate to Campbell and Popper’s mechanism: the selection pressure operating on beliefs is the same physics that operates on dissipative structures.

⁵ The π Spiral visualization accompanying this chapter (768 digits of π mapped onto an Archimedean spiral, each colored by value, with the Feynman Point ringed in gold) was originally created by Marius Comper and Claude on Pi Day 2026 (source: https://github.com/mariuscomper/pi-spiral). Adapted for The Deeper Law as an interactive companion diagram illustrating the epistemological argument. The Archimedean spiral is itself a constructal form: equal angular spacing maximizes readability as data grows outward, a geometry of efficient flow access applied to visual information.