This is a really nice idea. Le Livre de l’Incomplétude (The Book of Incompleteness) is an “artistic appropriation of Gödel’s incompleteness theorem,” initiated by artist Débora Bertol. The superficial understanding of that theorem is that every consistent formal theory contains truths which can’t be proved inside that theory, so the book’s conceit is that it will catalogue as many different arithmetic formulas as possible that evaluate to each of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
I think it’s a really charming take on one of the most abstract and hard-to-understand subjects in maths.
When you go to the site, you’re presented with a column of forms, one for each number. You can submit as many formulas as you like for each number; clicking the ? button submits what you’ve entered for verification. Valid formulas are immediately tweeted by @l_incompletude, and once there are at least 100 formulas for each number they’re going to start publishing an ebook.
The claim that each proposed solution is verified automatically made my pedantry finger twitch, so I of course immediately entered the following:
Gödel’s first incompleteness theorem states that a system is either incomplete or inconsistent; the Book of Incompleteness seems to have plumped for inconsistency.
… which sort of undermines the project. So maybe it’s just a bug.
Anyway, thinking up new ways of expressing the same number is a relaxing, meditative exercise, like raking a zen garden. I might spend a while submitting $0 = n-n$ for different $n$ for a while.
More information
@l_incompletude on Twitter