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@@ -52,4 +52,6 @@ people who are "good with numbers" usually aren't doing harder math — they're
arithmetic works. that's actually strange. why should the abstract rules governing numbers — which are themselves abstract objects — map so perfectly onto physical reality? why does 3 apples + 4 apples always give 7 apples, never 8?
-this is a baby version of wigner's "unreasonable effectiveness of mathematics" question that becomes much more dramatic at the [physics](/wiki/stem/physics) level. but it starts here, with the fact that addition works on apples, dollars, people, photons, and ideas — despite these things having nothing else in common.
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+this is a baby version of wigner's "unreasonable effectiveness of mathematics" question that becomes much more dramatic at the [physics](/wiki/stem/physics) level. but it starts here, with the fact that addition works on apples, dollars, people, photons, and ideas — despite these things having nothing else in common.
+
+and these same four operations generalize far beyond numbers. [[structural/linear-algebra-as-thinking|linear algebra]] extends arithmetic to vectors and matrices — you can add vectors, scale them by numbers, multiply matrices. the operations feel familiar because they *are* arithmetic, lifted into higher dimensions.
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