[hammock]

Designing in an era where calculus exists, using chains and weights strikes me as gratuitous or onanistic.

The Ancient Greeks and Romans also used the same or similar empirical geometric methods to generate ellipses, parabolas, and hyperbolas in their architecture. The difference is, they were still 1000-2000 years away from having formalized calculus.

[srean]

He is solving differential equations but with an analogue computer.

Doing it faster and with less doubts over fidelity and existence of a solution too.

Solving partial differential equations numerically and vetting the solution so obtained is not a trivial matters. Many things can go wrong in non obvious ways.

Analogue computers are a worthy alternative when applicable.

[hammock]

No doubt. I call them empirical geometric methods, you call it an analog computer, same thing. He didn’t invent anything though. The method of hanging a chain and adding custom weights to find the ideal shape for a complex masonry structure was invented by Giovanni Poleni in 1743 to fix the dome of St. Peter’s basilica. Poleni himself was extending Robert Hooke's 1675 inverted chain concept for optimal arches. The techniques Gaudi used had already been in use for hundreds of years.

[srean]

I did not know of Poleni, thanks for that story. I always thought that the notable insight was by Robert Hooked.

Oh wait I misread, it was Robert Hooke as you said, but Poleni used and developed it.

I find the study of funicular shapes very gratifying.

[MengerSponge]

Calculus exists, but analytic solutions generally don't. Gaudi's chains and weights serve as an incredibly elegant mechanical computer that were only surpassed in the last few decades by CAD. Designers used mechanical splines until the advent of CAD in the 70's/80's.

[anthk]

Ahem https://en.wikipedia.org/wiki/Archimedes_Palimpsest