Kepler asked the following question,
and nobody had ever asked that question, something incredible.
At the time there were only six planets. Only from Mercury, Venus, to Saturn.
Uranus and Neptune were not known, because they are invisible to the unaided eye.
So, he asked the following: "Why are there only six planets?
Why not 3, 20 or 50?
There has to be a fundamental explanation that determinates the number of planets".
Then he racked his brains trying to understand that.
And for him, since God was the great cosmic architect,
the explanation was a way of understanding God's plans for the Universe.
That was understanding God.
So, he racked his brains, and eventually he discovered an answer
that is based on the platonic solids.
Essentially there are only five perfect three-dimension geometric figurses.
We know two of them well: the pyramid, which is made by triangles,
and the cube, which is made of four squares.
There are three other: icosahedron, decahedron, etc.
So these five platonic solids are the only perfect figures.
What Kepler said:
"if God is a geometer, he certainly used the most perfect figures to create the world".
Then he invented a model solar-system in which the Sun was the center
(being an unbending Copernican),
then you had Mercury, a sphere circulating the Sun,
then you had the first platonic solid
and around this platonic solid you had another sphere and another platonic solid.
Each of these spheres had a planet, so Mercury, Venus, the Earth,
Mars, Jupiter, Saturn,
you had six planets. You can have five platonic solids among them
and, with that, he built the geometric model of the cosmos.
And what is amazing is that geometry determined the distance
between these planets and, when he compared this distance
with the known distances, the astronomers had already measured the distances of the planets to the sun,
and the precision was of 10%. Around 5% or 10%.
Kepler went mad, he said: "I discovered the mystery of creation.
God invented the world using these geometric forms."
For him, this was a huge success.
And in the meantime he also discovered that the orbits are not perfectly circular,
they are elliptical. That is what we mostly know of Kepler from school.
But what interests us here is that Kepler was a Pythagorean, a Platonic in Renaissance
who tried to unveil the mysteries of the world using geometry.
This transposition of the myth to Math, to knowledge
is something that goes on to the Modern Age.
When we get to the 20th Century we find another disguised Pythagorean,
who everybody knows, called Einsten.
Einstein said the same thing, that the essence of nature is geometric.
But he didn't say that god was a Judeo-Christian God, no way.
For him, god was essentially a metaphor for nature.
So, Einstein believed there was a god, who was a kind of architect,
but he believed in the human capability
to unveil the mysteries of nature using geometry, math.
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