Three dimensions can be so limiting.

Mathematicians, freed in their imaginations from physical constraints, can conjure up descriptions of objects in many more dimensions than that. Points in a plane can be described with pairs of numbers, and points in space can be described with triples. Why not quadruples, or quintuples, or more?

There is the minor difficulty that our nervous systems are only equipped to conjure images in three dimensions. But that doesn’t stop Étienne Ghys of the École Normale Supérieure in Lyon, France, from visualizing the four-dimensional dynamical systems he studies: “I live in dimension four,” he says.

And you can too. Ghys has now created a series of videos teaching others to visualize four dimensions the way he does. His work is in collaboration with Jos Leys, a Belgian graphic artist and engineer, and Aurélien Alvarez, a mathematics graduate student at ENS Lyon. [LINK]

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