This is a question rather than an answer.Shmuel Weinberger wrote a (to me, amazing) book about a decade ago, entitled
"Computers, rigidity, and moduli. The large-scale fractal geometry of Riemannian moduli space" (Princeton link)
Has the "grand project" promised by this book flourished, or at least evolved, in the last decade?I don't mean this question to be critical, I am just curious where his line of thought(e.g., "logical complexity engenders geometric complexity") standsten years after.