Numbers and Shapes

Abstract

Abstract Pythagoras initiated the mathematical analysis of nature, a cornerstone practice in modern physics. “Things are numbers” is the most significant Pythagorean doctrine. It signifies that the phenomena of nature are describable by equations and numbers. Therefore, nature is quantifiable and potentially knowable through the scientific method. The Pythagoreans quantified pleasing sounds of music, right-angled triangles, even the motion of the heavenly bodies. The “Copernican revolution” (heliocentricity) is traced back to Pythagorean cosmology. But, finally, Einstein’s relativity clarifies a popular misconception related to it: that “the earth revolves around the sun (heliocentricity) is correct,” and that “the sun revolves around the earth (geocentricism) is incorrect.” Plato was inspired by Pythagorean mathematics, but he replaced “things are numbers” with things are shapes, forms, Forms, a noetic description of nature known as the theory of “Forms.” The quantum-mechanical wave-functions—mathematical forms that describe microscopic particles—are the Platonic Forms of quarks and leptons.