Manifold Garden and Hilbert's Hotel

“Manifold Garden” is really a marvel of puzzle game design, inviting players into an ethereal world where gravity is a toy and infinity a canvas. I played it during my freshman year and want to introduce you to this feast for the eyes.

Developed by William Chyr, this game stands as a monument to the beauty of architectural impossibilities (Hilbert’s Hotel; see the end of this blog) and geometry (mostly Euclidena but also has a rubber-sheet flavour). Its puzzles cleverly play with perception, rewarding exploration with stunning, mind-bending visuals. The experience is meditative, almost otherworldly, offering a peaceful yet exhilarating escape into a realm of infinite horizons.

Hilbert’s Hotel

Hilbert’s Hotel is a thought experiment which illustrates a counterintuitive property of infinite sets. It is named after the German mathematician David Hilbert, who introduced it in 1924. Imagine a hotel with an infinite number of rooms, all of which are occupied. According to the rules of infinity, the hotel can still accommodate more guests, even though it appears to be full. If a new guest arrives, the hotel manager can move the guest in room 1 to room 2, room 2 to room 3, and so on, ad infinitum, freeing up room 1 for the new guest. This concept can be extended to any number of new guests, even infinitely many, by applying a similar shifting strategy. Hilbert’s Hotel is often used to explore the strange and fascinating concepts of infinity, and it challenges our everyday notions of space and capacity.