## Plato

3/27/2011

Most of us probably think of Plato as a philosopher, but what is difficult for modern folks to understand is just how intertwined mathematics and philosophy were back in the day.

Much of Plato's philosophy was inspired by looking at the natural world and the world of mathematics (and we should probably also include a shout-out to Socrates here).  Many people may know of Plato's allegory of the cave where he compares our experience of the world through our senses to people seeing shadows on the walls of a cave and thinking those shadows were real forms.

Plato's cave theory is closely linked to his idea of the Realm of the Forms.  He postulated a realm of perfection where every imperfect object we experience here in the world would exist in a perfect state.  Why postulate such a realm?

Let's think about shapes for a minute.  Take the sphere, for example.  We understand the concept of a sphere, but does it exist in it's true, perfect form here in the world?  The earth is round, so is the moon, but they are not perfect spheres. They're bumpy.  Have you ever seen a perfectly spherical stone?  Even the marbles we manufacture today aren't perfect spheres--they have tiny imperfections.  Perfect spheres don't exist in the natural world, but we understand them conceptually.  Mathematical objects like spheres helped shape the idea for Plato's Theory of Forms.

Plato also has some mathematical objects named after him.  The Platonic Solids are the three-dimensional shapes that can be made with sides that are all identical (and the sides have to be regular shapes like squares or equilateral triangles).  The cube is the most obvious example:  All its sides are squares.  Four other shapes can be made from other regular polygons:
• The tetrahedron is a four-sided shape made up of triangles
• The octahedron is an eight-sided shape made up of triangles
• The dodecahedron is a twelve-sided shape made up of pentagons
• The icosahedron is a twenty-sided shape made up of triangles