For a game whose rules can be taught to a small child, chess is surprisingly complex—it is possible games of chess than atoms in the physical universedespite the world’s predictions the superior intelligence of the brainit seems it is impossible that the game will ever be “settled.”
But! In general, two-sided chess (or its diversity) is not enough for you, be happy, because thanks to the efforts of the YouTuber mannymakeswho keeps a place for mind bending types of chessnow you can play chess on the hyperbolic plane!
If you’re not familiar with the concept of hyperbolic space, it’s one of those two-dimensional spaces where the laws of Euclidean geometry don’t apply. Okay, but what does this really mean?
Euclidean geometry is the kind you were taught in school, the world of sines and cosines, and the square on the hypotenuse is equal to the squares on the other two sides. Its rules—the first were laid down by the Greek mathematician Euclid nearly 3000 years ago in his book. Things-can be reduced to five simple axioms.
Four of these are easy to prove, but the fifth is not. In fact, the question of how to prove it has stumped mathematicians for millennia. The postulate itself is simple enough: it says that two parallel lines can never meet. On the face of it, this statement seems self-evident—but the reason it has resisted evidence for so long is that it isn’t true.
For example, consider a circular area. If you draw two parallel lines due north from the equator, those lines the will get together. They meet together in the northern part of the sphere. The surface of the circle has two sides, but it is also curved, forming a closed loop. As well as allowing parallel lines to meet, this also means that if you go far enough in either direction, you will always end up where you started.
So what is hyperbolic geometry? It is actually the opposite of spherical geometry. In hyperbolic space, parallel lines diverge, and instead of closing in on themselves, the hyperbolic plane gets progressively larger as you move away from the origin. This can be hard to visualize, but as it turns out, examples exist in the real world. You can crochet a hyperbolic surface, but if crafts are not your bag, nature has also provided an example: the humble coral lettuce, whose leaves take up more space as they grow away from the stem of the plant.
The hyperbolic board used by mannymakes in his game has octagonal tiles, which extend to a radius of four tiles from the center of the board. This sounds like it would be too small for a chess setup, but it’s not: this board already has 161 tiles, and adding another layer will add another 448 of them. (An old 8×8 chessboard, by contrast, has 64 squares.)
So what is it like to play chess in this strange place? However, it is … different. As its founder explains in a interesting video In the project, translating the “regular” chess rules to a hyperbolic chessboard with octagonal squares is not always easy, and the game remains a work in progress. The whole thing is complicated by the fact that, instead of being just black and white, the hyperbolic board needs three colors to avoid having adjacent tiles of the same color.
Like most such games, the gaming experience is more fun than it is, you know, pleasure. But if you want to get lost in the cyclopean depths of non-Euclidean space, where geometry is wrong, and Brown Jenkin he lurks beyond the measure of genius, his thin bearded face crying as he rubs his hands in anticipation of your next move—well, hyperbolic chess awaits! You can arrest a fellow masochist or even play the computeralthough at the end, manny made warnings that the site’s AI has not been updated for new variants, so it may be as confusing as you.
