Abstract

Symmetry: Culture and Science
Volume 33, Number 3, pages 267-287 (2022)
https://doi.org/10.26830/symmetry_2022_3_267

SEMIOTIC AND CATEGORY-THEORETICAL CONSIDERATIONS OF THE GOLDEN RATIO AND FIBONACCI NUMBERS

Sungchul Ji^*

^* Emeritus Professor of Theoretical Cell Biology, Department of Pharmacology and Toxicology, Ernest Mario School of Pharmacy, Rutgers University, Piscataway, New Jersey, USA.
Email: sji.conformon@gmail.com

(This paper is dedicated to my wife, Jaehyun Lee, with love, who passed away on May 17, 2022, at the age of 68, while I was completing this manuscript.)

Abstract: It is proposed that there are two types of the Golden ratios; (i) the qualitative (approximate, phenomenal, or material) Golden ratio widely observed in nature and culture, and (ii) the quantitative (precise, mathematical, or formal) Golden ratio that appears in geometry and algebra. There are two possible relations between the phenomenal and the formal Golden ratios; (i) ‘causality’ meaning that one is the cause of the other, and (ii)‘codality’ meaning that the similarity between the two Golden ratios is the consequence of sharing a common historical precursor. A category theoretical argument based on bio-evolutionary data was advanced to support the history-based (i.e., codality-based) relation between the two types of the Golden ratios. From a semiotics point of view, the two types of Golden ratios are signs referring to something other than themselves called referents or objects and induce in the mind of the interpreter models of the same referent. It is suggested that the referent of the Golden ratios is the regularity called Gnergy inherent in Ultimate Reality.

Keywords: golden ratio, the Fibonacci numbers, golden spiral, semiotics, category theory, complementarity, ultimate reality, Gnergy, matter-form duality, hylomorphism.

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