John Carlos Baez on Nostr: Apparently Dante conceived of the universe as a 3-sphere! That's a 3-dimensional ...

Apparently Dante conceived of the universe as a 3-sphere! That's a 3-dimensional space formed by taking two solid 3-dimensional balls and gluing their surfaces together, completely.

In Paradise Lost, Dante describes the usual geocentric universe of his day. It has concentric spheres around the Earth for the Moon and Sun, the various planets, and then the so-called 'fixed stars'.

Outside that sphere there's a sphere for the 'first mover', the Primum Mobile. Ptolemy believed in this outer sphere, and so did Copernicus - and even Galileo did, at first.

But that's not all! Outside that sphere, Dante describes 9 concentric spheres of the Empyrean, where various levels of angel live. And as we go up, these spheres get *smaller*. They all surround a point - which is God.

At the opposite extreme, at the center of the Earth, is another point - and that's where Satan lives, surrounded by the 9 levels of Hell.

So, we have a 3-dimensional closed universe, which mathematicians call a 3-sphere!

Much later Einstein also postulated that the universe was a 3-sphere, which was kept from collapsing by the cosmological constant. This was before Hubble and others saw that the universe is expanding.

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