2D flatland and multi-dimensional hyperspace make fine playgrounds for the mind, but our bodies seem stuck in a space of three dimensions. Why not two or four, or five or more? Recently, physicists trying to meld gravity and quantum theory, and so explain the nature of space and time, have begun to revisit this old question.
String theory, one route to quantum gravity, gives an unsatisfactorily vague answer: space can have anything from zero to 10 dimensions. That drives theorists to anthropic arguments: universes of all possible dimensionalities exist, but we see what we see because beings like us require a 3D habitat.
In 2005, Andreas Karch of the University of Washington, Seattle, and of Harvard University came up with a more mechanistic explanation of the mystery of threeness. They created a model in which many universes of different dimensions float around inside an expanding 10-dimensional hyperspace of the kind popular in string theory. When these universes collide, they annihilate one another. The that three and seven-dimensional universes are the ones most likely to survive such catastrophes.
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If you accept the premise, that almost answers the question 鈥� but why shouldn鈥檛 we live in a spacious realm of seven dimensions instead of our cramped 3D universe?
That might be explained by looking at space not as a uniform whole, but as a construction built up from tiny pieces. A European team with higher-dimensional analogues of the triangle, the simplest unit that can be stuck together in different ways to make curvy universes. Quantum theory says that the 鈥渢rue鈥� shape of the cosmos should be the sum of all these possibilities. By requiring that their model universe should adhere to strict cause and effect, the team found that the result has just one dimension of time and exactly three of space.
There is a twist. At the very smallest scales, the structure of space changes: one dimension of the three melts away to leave only two dimensions. Perhaps, if you look closely enough, we live in flatland after all.
Read more: Beyond space and time