The Shape of Things

Folks have been trying to figure out the shape of the universe for a long time. Early answers included “a big tree” and “flat, supported by elephants on the back of a turtle”. One of the latest ideas is a Picard topology, sort of a horn shape with a really long end.

I notice that the term “pringle” has replaced “saddle” when describing areas of negative curvature…

4 thoughts on “The Shape of Things

  1. Okay, call me unimaginative, but I don’t understand how the universe could be finite. Wouldn’t that indicate an “outside” as well as an “inside”?

  2. Not necessarily. It’s the difference between “finite” and “bounded”. Finite means that the area is a defined number, while bounded means the area has edges. For instance, the surface of the Earth is finite in 2 dimensions, but no matter how far you travel you’ll never find the “edge” — it’s unbounded.

    The illustration with the article isn’t very helpful, because it makes the Picard topology look like a 3-dimensional horn. The actual shape is a 4-dimensional volume, so it connects to itself in ways that can’t be shown on the 3-dimensional figure. They tried to note that (with the space ship description) but it’s hard to visualize when it looks like there are hard edges.

    We have a pretty decent book by Rudy Rucker about this, _Spacetime and the Fourth Dimension_. It’s his master’s thesis, actually, but still a good description (if I remember correctly.) He has another one called just _The Fourth Dimension_ which is longer but more entertaining.

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