How One Line in the Oldest Math Text Hinted at Hidden Universes

that now we have something to compare our measurement with. If the universe is flat, the angle we measure in the sky should be the same as we expected. But if the universe is curved like a sphere, the angles of the triangle would have to add up to more than 180 degrees, so the angle we would measure would be larger than expected and this peak would shift to the left. Similarly, if the universe has a hyperbolic geometry, then the spots should appear smaller than expected and this peak would shift to the right. So what do we measure? This is data from the Plank mission, which is almost exactly what you would expect if the universe were flat.

This mission also gives us the current best estimate of the curvature of the universe, which is 0.0007, plus minus 0.0019. That's basically zero within the margin of error. So we are pretty sure that the universe we live in is flat. But living in a flat universe seems to be surprisingly fortuitous. (contemplative music) At this time, the average mass energy density is reduced to the equivalent of approximately six hydrogen atoms per cubic meter. If, on average, it were just one more hydrogen atom, the universe would have had a more spherical curvature. If there were one less, the curvature would be hyperbolic geometry.

And so far, we're not entirely sure why the universe has the mass and energy density that it does. What we do know is that general relativity is one of our best physical theories of reality, and at its core are those paradoxical and seemingly absurd geometries, which we found because

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