A transformation T of a structure D is structure-preserving if T(D) has the same symmetry group as the original one: Aut(T(D)) ~= Aut(D).https://twitter.com/literalbanana/status/982816860566532096 …
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Why did Alexander believe there was a correct choice among the three? Perhaps as an architect, symmetry across the horizontal axis is less important, since gravity always breaks it. His preferred elaboration resembles an object standing on legs! cc:
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his original degree was in math I think - but “structure-preserving transformation” isn’t formalized in the math way I don’t think
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Yeah, what I'm arguing I think is that group actions are one language to (very rigorously) describe some of these notions, not all of them. Certainly when you look at something like https://en.wikipedia.org/wiki/Islamic_geometric_patterns … it's almost necessary.
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But it tells you nothing about why he prefers the third rectangle, except by omission.
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