Hi
I remember reading about the “geometric shape” of the Platonic soul. I hope I’m not misremembering here. Perhaps I misinterpreted the Platonic soul as having a shape (I’m thinking of the five Platonic solids). I’m not sure. If the Platonic soul does have a shape, what shape is it ? I couldn’t find anything on "the geometric shape of the soul " online. I look forward to your feedback.
davidmich
I think you’ll want to read Plato’s Republic and Timaeus.
There’s a summary of the latter here.
Thanks Quartz. What I’m trying to pin down is an actual reference to the Platonic soul being likened to mathematics (arithmetic, geometry, astronomy, and harmony). That is what I remember reading. I must reread Timaeus.
It’s 30 years since I read them so, unless you spark another memory, you’ve exhausted my knowledge.
I think you’re misremembering what Plato said about the five regular solids of geometry.
They are as follows: the tetrahedron (4 faces, each face is an isosceles triangle), the cube (6 faces, each face is a square), the octahedron (8 faces, each face is an isosceles triangle), the dodecahedron (12 faces, each face is a pentagon), and the icosahedron (20 faces, each face is an isosceles triangle).
It’s interesting to note that these are the only five objects which can be constructed this way. If you take a regular 2D shape (regular meaning that each side is the same length) and use copies of that shape to build a 3D solid, you will always end up with one of the five platonic solids. There are three ways you can do it with triangles. There’s only one way you can do it with squares. There’s only one way you can do it with pentagons. It can’t be done with hexagons, heptagons, octagons, et cetera. There’s only five ways to do it.
Plato decided that these five shapes must somehow explain the building blocks of the universe. This was at a time when conventional wisdom said there are four elements: air, earth, fire, water. So Plato decided the tetrahedron is fire, the cube is earth, the octahedron is air, the icosahedron is water, and the dodecahedron as the shape of the universe itself.
Of course, we now judge this model of chemistry to be whimsical at best, bordering on totally useless. But he gets a gold star for effort.
I’m pretty sure it never had anything to do with the soul.
Isn’t there a 10 sides shape, I do recall a 10 sided die in DnD type games.
If you use regular polygons, and also require that every vertex of the solid have the same number of faces, then you get the five Platonic solids. Remove that second requirement, and there are two more, the triangular bipyramid and the pentagonal bipyramid.
Actually, strictly speaking, you also need to require that the polygons be convex, or you also get a figure made up of a dozen five-pointed stars.
Could this possibly have anything to do with the neoplatonic idea of concentric circles emanating from the One?
Oops. I thought I put that into my explanation (or at least implied it) but looking again I see that I left it out. Maybe I’m not as awake this morning as I thought I was.
The 10-sided die is regular in the sense that all the faces are the same as each other, but not all the vertices are the same as each other and the faces themselves are not regular. The faces are irregular quadrilaterals and some vertices touch three sides while others touch five.
You could use a similar method to construct a 14-sided die, et cetera, but it wouldn’t be a regular solid either.
Don’t feel too bad, you’re in good company-- Euclid left out that condition, too.
Equilateral, isn’t it? For the *regular *solid, anyway.