The kh{\^o}ra and the two-triangle universe of Plato's Timaeus

TL;DR

This paper explores the mathematical foundations of Plato's Timaeus, emphasizing the connection between mathematical principles and physical cosmology, and introduces a new translation of a key passage to clarify this relationship.

Contribution

It provides a new translation of Timaeus 31b-32b and offers an innovative analysis of the primary elements in the kh{ ext^o}ra as two right triangles.

Findings

The kh{ ext^o}ra can be reduced to two right triangles.

The translation clarifies the link between mathematics and physics in Timaeus.

First in a series exploring the concept of kh{ ext^o}ra.

Abstract

The main purpose of this article is to try to understand the connection between the physical universe and the mathematical principles that underlies the cosmological account of the Timaeus. Aristotle's common criticism of Plato's cosmology is that he confuses mathematical and physical constructions. Namely, the Timaeus is the first cosmology founded on mathematical physics. We give a new translation of Timaeus 31b-32b, an important passage to understand the connection between mathematics and physics in Timaeus' cosmological construction. This article is the first of a series about the kh{\^o}ra. We will restrict our focus here to the much-debated question of the primary elements in the kh{\^o}ra, the components of the whole physical world reduced, in an extraordinary elegant construction, to two right triangles.