Go(Φ)d is Number: Plotting the Divided Line & the Problem of the Irrational

Abstract

Plato believed that behind everything in the universe lie mathematical principles. Plato was inspired by Pythagoras (571 BCE), who developed a school of mathematics at Crotona that studied sacred geometry as a form of religion. The school’s motto was “God is number,” or “All is Number”. Pythagoras believed that numbers represented God in pattern, symmetry, and infinity. When one of its students, Hippasus told the world the secret of the existence of irrational numbers, Greek geometry was born and Pythagoras’ idea of divinity in numbers died because how could God not be perfect and symmetrical? In Plato’s Republic he discusses something called The Divided Line, which is a map, of sorts, for reaching what he calls the highest Good, which is the ultimate truth where one realizes the true state of the universe and can see the world for what it really is. Many mathematicians have attempted to plot Plato’s Divided Line only to come across a litany of problems and conundrums. Some have said that it the Divided Line cannot be plotted and is merely an allegory not meant to be plotted. This paper discusses some of the conundrums preventing the plotting of Plato’s Divided Line (not an exhaustive list), including Whole ‘vs’ Separate, Equality ‘vs’ Ontological Dissimilarity, Linear ‘vs’ Non-linear, and Infinity ‘vs’ Finite. This paper also explores a new understanding of the Allegory of the Cave in light of ‘the problem of the irrational.’ In exploring the link between the Divided Line and the ‘the problem of the irrational,’ I was able to plot it. It was found that the Divided Line is not a line in the linear sense, but a spiral, the Golden Ratio! This paper is an example of a new category of scholarly inquiry I call “Math Theory” based on scholarly mathematical axioms in theory, rather than including actual maths. In my papers I use existing mathematical equations and place them in an encompassing theory, rather than finding new formulae to fit an existing theory. Keywords: Pythagoras, divided line, math theory, highest good, all is number