Crazy Algebra

Stream: Equational

[Mario Carneiro]

Looking at finite magmas has reminded me of the crazy operation from Malbolge. Is this operation in the database? Does it have any interesting laws?

[Terence Tao]

I mean, it obeys a bunch, of which the shortest nontrivial one is equation 8 x = x ◇ (x ◇ x), but I don't recognize any of the others as ones we have encountered elsewhere.

[Mario Carneiro]

it satisfies none of the 3 variable laws. Is that common?

[Mario Carneiro]

1654 - x = (x ◇ y) ◇ ((y ◇ x) ◇ x) reminds me a bit of the weak central groupoid law, but associated the other way around

[Terence Tao]

General heuristics suggest that random n x n magmas are unlikely to obey any 3-variable or higher laws (one is asking for n^3 equations with n^2 degrees of freedom - highly overdetermined set of constraints).