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  "body": "\n## Summary\n\nAn entropic algebra is an [[algebra|QJGPT2W0FT]] in which any two operations commute with each other.\nEquivalently, every operation $A^n \\to A$ is a [[homomorphism|KBXSZC6BV1]] of algebras from the power $A^n$ to $A$.\nFor an algebra with one binary operation this is the [[medial law|VZHN6GA3TA]].\nModules over a commutative ring, semilattices and affine spaces are entropic.\nIn an entropic variety, the homomorphisms from one algebra $A$ to another algebra $B$ form a subalgebra of the power $B^A$.\n\n## Explanations\n\n### L1 human\n\nFill a rectangle with elements, $n$ rows and $m$ columns.\nTake two operations, one with $n$ arguments and one with $m$ arguments.\nYou can apply the second operation along each row and then the first to the results.\nOr you can apply the first down each column and then the second to the results.\nAn algebra is entropic when these two ways always agree.\nFor a vector space this says, for instance, that $r(a + b) = ra + rb$ and $r(sa) = s(ra)$.\n",
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