Today we went to a math tournament, so I might as well write a post praising math. Plato thought what we see in the physical world is a dim reflection of the metaphysical, intellectual world. Math—particularly geometry—is certainly a great way of understanding reality. When you look at a line, plane, triangle, or square, you are looking at "shadows," which do not represent our three dimensional world. But when you add a z-axis and construct cubes and tetrahedrons, you take the first steps out of the cave.
In fact, Plato was such a great fan of math that he stressed the study of geometry in his Academy in Athens, which had a entrance sign that said, "Let no-one ignorant of geometry enter here." Inspired by Pythagoras, he taught math as a branch of philosophy, and the Academy's students learned math and science for 10 years. Plato is known to have identified 5 regular symmetrical 3-dimensional shapes, which he maintained were the basis for the whole universe. The shapes are the tetrahedron (represented fire for Plato), the octahedron (air), the icosahedron (water), the cube (earth), and the dodecahedron ("constellations on the whole heaven").
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| "Let no-one ignorant of geometry enter here." |
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| Platonic Solids |
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