A trippy maths program that visualises the inside of strange 3D spaces could help us figure out the shape of the universe.
Henry Segerman at Oklahoma State University and his colleagues have working to interactively map the inside of mathematical spaces known as a 3-manifolds using a program called SnapPy.
“I’ve been thinking about these things for 20 years, but we never had pictures,” says Segerman.
A 3-manifold is like a generalised version of ordinary three-dimensional space. “A 3-manifold is something that looks like three-dimensional space if you look at just a little piece of it,” says Segerman. “But it might be connected in some weird way around the back.”
Different manifolds may or may not have boundary. “There might be a place where you can’t go any farther,” says Segerman.
To understand this, it helps to think of a 2-manifold, which is a generalised version of two-dimensional space. A 2-manifold could be a flat space that goes on forever, but it could also be a sphere or a Möbius strip, which you can loop around forever but never go round the edge.
The team looked at 3-manifolds with the shape of a knot removed from them. “Three-dimensional manifolds where we’ve removed a knot from space – those have boundary where the knot used to be,” says Segerman.
This removal has strange effects from the space. For example, pink balls morph into cigar shapes as the program comes up with different geometries inside where the knot was (see video above).
“You can’t just use ordinary graphics as you would in computer games,” says Segerman. “You have to build it from the ground up.”
One of the interests of this branch of maths, called topology, is the shape of the universe. “Does it go on forever in all directions, does it somehow loop around on itself?” says Segerman. “We can’t see far enough to know.”
The team hopes that other mathematicians can use the program for visualisations that may lead to future ideas.