u/non-orientable

It is an open secret that many JPRG worlds (such as Chrono Trigger's) are not spheres, as you would expect; they are >!tori!<! In fact, games that properly take place on a sphere aren't entirely common, even in the present day.

Why? We explore two major mathematical obstructions: the Gauss-Bonnet theorem and the hairy ball theorem.

Read the full post on Substack: Chrono Trigger and the Hairy Ball Theorem

Mathematics offers a unique possibility: the ability to conclusively prove that there is a solution, without ever actually producing it. Indeed, explicitly constructing the solution may be a separate (and much harder) challenge. For mathematical beginners, it is often difficult to understand how this could possibly happen; this post gives a simple example involving the game Chomp, and Zermelo's theorem from game theory.

Read the full post on Substack: On Constructive Proofs that there is a Solution