[jerkstate]

I visited this and several other Gaudi buildings about 15 years ago in Barcelona, and many of them are truly breathtaking, or at least dramatically original and unique. I went to the Gaudi museum as well and found it fascinating that the architect himself was not a professional mathematician - he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains. Really interesting to hear about how he also heavily used ratios and symmetry. I love how artistic taste can be partially derived from math (but the math itself isn't sufficient to develop artistic taste)

[lo_zamoyski]

> I love how artistic taste can be partially derived from math [...] the math itself isn't sufficient to develop artistic taste

Strictly speaking, it isn't "math" as math is the science of quantity and structure, both of which are objective features of reality. We all perceive structure and quantity as it is instantiated in concrete things and ensembles of concrete things and so on. We all respond to and reason about quantifiable and structural properties of reality at varying depths all the time. All math does is pursue them intentionally and methodically. It isn't surprising, then, that a competent artist should intuit various mathematical truths. Indeed, quantity and structure as essential to art. The artist is therefore closer to a domain-specific application where such properties are understood in relation to the subject matter. This introduces a domain-specific aesthetic dimension that is not present in abstracted properties, though one can certainly make aesthetic judgements about abstracted properties.

[rramadass]

https://news.ycombinator.com/item?id=48860150

[RetroTechie]

> he did not use hyperbolic cosine to calculate the dimensions of the catenary curves, he traced the outline of hanging chains.

In a way that's like doing the math, but using real-world physics as your 'calculator'. No doubt Gaudi was a smart dude.

[embedding-shape]

> No doubt Gaudi was a smart dude.

He also died crossing the tram track, presumable not looking both ways before crossing. To be clear, I've also nearly been hit by the Barcelona tram too, so I don't blame him, but "smart" is always relative.

[imp0cat]

He was smart, but not street smart.

Also, I do belive the story was that he had the appearance of a homeless man and thus received sub-standard care. When someone finally recognized him, it was already too late.

[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