A mathematical doughnut, a torus, sits on the boundary of a three-dimensional world where gravity acts. You can crumple and stretch it, and physicists decided to see how it behaves. Inside this world, space can be flat like a table, expanding like a soap bubble, or curved like a saddle. The doughnut boundary refused to stay smooth. Folds spontaneously appear on it, and sometimes it intersects itself, like a ribbon twisted into a ring that pokes through its own side.
The authors rewrote gravity in the language of temperatures and energies — much like calculating the thermal properties of matter. It turned out that crumpled doughnuts are not just a fun picture. Under certain conditions, they beat smooth ones. For example, in a world with a negative cosmological constant (where space itself tends to contract), folded shapes win if the boundary curvature falls within a narrow range of values.
But the most intriguing part is entropy. Some of the found solutions possess enormous hidden complexity, like a black hole. Inside such a doughnut, an entire universe with its own thermal history might be hiding, even though from the outside it looks like a modest geometric figure. This echoes the old idea that gravity is just a shadow of a deeper quantum reality.
So from a simple doughnut, we arrive at the structure of spacetime. Smoothness turns out to be not the rule but just a special case. And folds and self-intersections are the key to understanding how gravity works at its deepest level.
Three-dimensional gravity is much simpler than our four-dimensional one: it has no gravitational waves, and black holes behave almost like ordinary particles.
In Neal Stephenson's novel 'Anathem', scientists study a cosmos where the geometry of space changes depending on the observer's point of view — much like in this work with crumpled doughnuts.