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  "body": "\n## Summary\n\nA commutative magma is a [[magma|9689SFPVE9]] whose operation does not depend on the order of the two arguments.\nCommutativity does not imply associativity, and commutative magmas are the natural setting to see the two conditions apart.\nExamples include the average of two numbers and the operation of \"rock, paper, scissors\".\n\n## Explanations\n\n### L1 human\n\nIn a commutative magma, combining $x$ with $y$ gives the same as combining $y$ with $x$.\nBut brackets may still matter.\nTake the average of two numbers: the average of $0$ and $4$ is the average of $4$ and $0$.\nYet averaging $0$ with $4$ and then with $8$ gives $5$, while averaging $0$ with the average of $4$ and $8$ gives $3$.\n",
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