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  "body": "\n## Summary\n\nA self-distributive operation is a [[binary operation|0M418FE7BB]] that distributes over itself, on the left or on the right.\nLeft self-distributivity reads $x * (y * z) = (x * y) * (x * z)$.\nConjugation in a group, the join and meet of a lattice, and the operation $2x - y$ on an abelian group are self-distributive.\nLeft self-distributive magmas are called [[shelves|PDFC0MRYR8]]; together with racks and quandles they are used in knot theory and in set theory through the [[Laver tables|9H65YDXMGJ]].\n\n## Explanations\n\n### L1 human\n\nThe usual [[distributive law|0KBEMAJAYA]] says that multiplication spreads over addition: $a(b + c) = ab + ac$.\nA self-distributive operation spreads over itself.\nActing with $x$ on a combination of $y$ and $z$ is the same as combining the results of acting with $x$ on each of them.\nThink of $x * y$ as \"move $y$ by the symmetry attached to $x$\".\nThen the rule says that moving a combined object is the same as moving its parts and combining them.\nFor example, $x * y = 2x - y$ reflects $y$ through $x$, and reflections behave in this way.\n",
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