Workbook for Volume 1 – Part IV - Section #4: Foundational Papers of the 19th Century & Before – Euclid, Fibonacci & Huygens
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 a Revised Version for Volume 1 – Part IV - Section #4: Foundational Papers of the 19th Century & Before – Euclid, Fibonacci & Huygens
Summary:
Volume 1 – Part IV - Section #4: Foundational Papers of the 19th Century & Before – Euclid, Fibonacci & Huygens - Growth, and growth rates provide some of the most visible, differentiating features of living organisms. Life, business, and investments convert energy and information into growth. In this context, C. G. Lewin’s 2019 paper “The emergence of compound interest” starts this chronology of foundational papers with the oldest financial concept, as evidenced by a Babylonian clay tablet dated 2000 to1700 BCE, and showing what appears to be a compound interest problem. Compound interest calculations quantify multiplicative growth dynamics. However, to compare and communicate patterns of growth we need to summarize observations with quantitative tools such as averages. Averages take us back to the 3rd century BCE. Euclid’s “Book V, Proposition 25” states the following: ᾿Εὰν τέσσαρα μεγέθη ἀνάλογον ᾖ, τὸ μέγιστον [αὐτῶν] καὶ τὸ ἐλάχιστον δύο τῶν λοιπῶν μείζονά ἐστιν. “If four magnitudes are proportional then the (sum of the) largest and the smallest [of them] is greater than the (sum of the) remaining two (magnitudes).” A special case occurs when the middle terms are the same, in which case this proposition gives us a corollary: “The arithmetic mean of two magnitudes is greater than their geometric mean”. The inequality of the arithmetic and the geometric means has been known for a long time. As we shall see in this workbook, it took two millennia to move from an geometric understanding of this difference to interpreting the practical meaning of the difference between the means. Recently, Ole Peters showed the limits of this “Expected Wealth” as a decision criterion in Section 2 “Origins of probability theory” of his 2011 paper “The time resolution of the St. Petersburg paradox”, and his 2019 paper “Comments on D. Bernoulli (1738)”. Peters showed that “Expected Wealth” amounts to a 17th Century view of “Expected Value” [the arithmetic mean] as a decision-making criterion to choose between two gambles of equal duration, and in the absence of the contributing effects of decision time horizon, and discount factors. We now understand that this 17th Century idea (“Expected Wealth”) of embedding current reality in as many alternative scenarios as possible is akin to averaging over parallel universes instead of averaging over the passage of time. This form of averaging reflects the typical (“Ensemble Average”) outcome of the “Casino” instead of the typical (“Time Average”) outcome of an individual player. This means that the inherent, collective bias in the arithmetic of the Average, the Arithmetic Mean, the Expected Value, the Expectation, the Expected Wealth, or the Expected Return does not make these decision criteria a good enough basis for individual decision-making. We see what we understand, and we have just started to understand that framing & bias exist at the core of the mathematics of Financial Economics, in addition to the psychological narratives of Behavioral Economics.
Developing…
”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.