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But there was a stunning amount of mathematics used for all the feats of engineering you're talking about, even early on.
by throwawaymath 8y ago
But there was a stunning amount of mathematics used for all the feats of engineering you're talking about, even early on.
- superpermutat0r 8y agoWell, I'm pretty sure there was not even Euclid's geometry thousand years after he invented it in any architecture recipe book, yet they built brutally large structures. We have 13th century books from architects that built cathedrals filled with recipes with 0 mathematics, all heuristics, rules.
- throwawaymath 8y agoAre you sure? For example, the Florence Cathedral (Il Duomo) required nontrivial, novel mathematics. Brunelleschi didn't succeed in that effort simply through iterative engineering. I think in general it would be more appropriate to say that fundamental theory tends to predate its applications, and then the theory and applications evolve as one informs the other in a positive feedback cycle. Likewise a lot of improvements to rocket science are due to iterative engineering, but we couldn't get off the ground (literally) without calculus.
- zazen 8y agoBrunelleschi was working at the height of the Renaissance, in the early 1400s. They weren't short of book learning in renaissance Florence, but that's why it's called the renaissance. I imagine medieval cathedral building, e.g. Notre Dame starting more than 200 years previously, might have looked very different. They couldn't build a dome like Brunelleschi back then.
- imh 8y agoSimilarly, there's a ton of math in the applied side of neural network research too. It's not math vs no math. It's a question of foundational "General Theory of X" math.