Abstract
The Greek culture evolved in the shadow of two dominant and sophisticated economies: the Chaldeans (Babylonians), with their strong arithmetical and administrative culture and the Egyptians, who contributed a geometric orientation. In the shadow of these two traditions, the Pythagoreans and Plato assimilated a mystic perspective of an ideal world of mathematics. Later Greeks developed a system of fair division that absorbed an arithmetic dyad. Aristotle analyzed two-party isolated exchange using the harmonic proportion introduced by the Pythagoreans whose “ideal types” influenced later market perspectives. These traditions informed modern regulated political, legal and economic institutions.
Received: September 24, 2009
Revised: October 30, 2009
JEL classification: B00, C00, N00
Mathematics Subject Classification (2000): 00-02, 01A05, 11-00
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Notes
- 1.
It has been surmised that Pythagoras’ exposure to the existence of regular crystalline forms used by his father in his jewelry trade informed the development of Pythagoras’ concept that the universe is composed of regular solids.
- 2.
Plato’s emulation of Pythagoras’ secrecy is reflected in the absence of any discussion of irrational numbers in his writings. This secrecy regarding irrational numbers was also perpetuated by Euclid and was apparently also characteristic of Nicomachus, who wrote an extended book on arithmetic at the beginning of the second century AD, much of which is lost. Iamblichus wrote a book on Pythagoreanism dating from the late third or early fourth century AD, but the chapters on arithmetic, apparently drawn from Nicomachus, have also been lost. We have to go to Boethius’ writing in the late fifth and early sixth century AD, for a record of Nicomachus’ work, but Boethius’ commentary does not elaborate the problem of irrational numbers.
- 3.
An exhaustive analysis of the uncanny number of correlations implicit in this ratio can be found in Le nombre d’or by Ghyka [6].
- 4.
The basic problem is that Aristotle’s text on exchange is rather sketchy and has probably suffered from centuries of re-copying and translation, frequently done by people who did not clearly understand the subject matter.
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Lowry, S.T. (2010). Pythagorean mathematical idealism and the framing of economic and political theory. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 13. Springer, Tokyo. https://doi.org/10.1007/978-4-431-99490-9_8
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