"Gothic cathedrals and Doric temples are mathematics in stone. Doubtless Pythagoras was the first in the Classical Culture to conceive number scientifically as the principle of a world-order of comprehensible things—as standard and as magnitude—but even before him it had found expression, as a noble arraying of sensuous-material units, in the strict canon of the statue and the Doric order of columns. The great arts are, one and all, modes of interpretation by means of limits based on number (consider, for example, the problem of space-representation in oil painting). A high mathematical endowment may, without any mathematical science whatsoever, come to fruition and full self-knowledge in technical spheres." ~ Spengler, Decline of the West

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n4r9 4 hours ago | parent [-]

I had to put this one through Claude, but it boils down to:

> A culture's felt sense of proportion, ratio, and spatial order manifest directly through the hands of masons and sculptors, without necessarily needing the mathematical formalism of proofs, axioms, and treatises.

Not sure how I feel about this, as the Familia was absolutely built in a context of formalised mathematical sciences.

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blitzar 4 hours ago | parent [-]

It seems somewhat important to me to know if something was done because it looked pretty, was random or because there was an intent to reflect maths, science, planetary alignment etc.

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lo_zamoyski 2 hours ago | parent | next [-]

Whatever one might say about method, epistemically speaking, the aesthetic is prior to the mathematical. The mathematical is found in the analysis of the beautiful.

	▲	hammock an hour ago \| parent [-]
		Truth, beauty and goodness are known as the “transcendentals” for a reason. They are linked. They don’t come one after the other.

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rramadass 4 hours ago | parent | prev [-]

Mathematics and Art - https://en.wikipedia.org/wiki/Mathematics_and_art

Wikipedia on "Sagrada Família" - https://en.wikipedia.org/wiki/Sagrada_Fam%C3%ADlia (see "Geometric Details" section).

Gaudí used hyperboloid structures in later designs for Sagrada Família (more obviously after 1914). However, there are a few places on the nativity façade—a design not equated with Gaudí's ruled-surface design—where the hyperboloid appears.