Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and EverythingElse

by Jordan Ellenberg

Scronch geometry has laws of “conservation of horizontal and vertical”; if two points are joined by a horizontal or vertical line segment, so are their respective scronches. Lorentzian spacetime is much the same. A point in spacetime is a location and a moment; the special line segments conserved by Lorentz symmetries are those joining two location-moments whose two locations are separated by the exact distance light would cover in the amount of time between the two moments. The speed of light, in other words, is built into the geometry. The question of whether light can reach location-moment A to location-moment B has a definite answer, which is the same whether you get on the bus or not. The scronch plane is like a baby version of Lorentz spacetime. You might think of it as what relativistic physics would look like if, instead of three dimensions of space, there were only one, joining with the one dimension of time to make a two-dimensional spacetime.