By Donna Lu
A trippy maths program that visualises the inside of strange 3D spaces could help us figure out the shape of the universe.
“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 further,” says Segerman.
Did You See This CB Softwares?
37 SOFTWARE TOOLS... FOR $27!?Join Affiliate Bots Right Away
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, yet 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 on 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?” asks 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.
More on these topics: