I had to put this one through Claude, but it boils down to:
reply> 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.
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.
replyWhatever one might say about method, epistemically speaking, the aesthetic is prior to the mathematical. The mathematical is found in the analysis of the beautiful.
replyTruth, beauty and goodness are known as the “transcendentals” for a reason. They are linked. They don’t come one after the other.
replyMathematics and Art - https://en.wikipedia.org/wiki/Mathematics_and_art
replyWikipedia 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.