When a theory is beautiful?

Philocrat

Mandelbrot is undisputedly beautiful in that it provides a sophisticated yet very convenient departure from bi-valent quantificational and logical madness. It is progressive and the beauty is in the progress. As you know, for the first time we are able to depart from the macro-world and take a cool trip into a fuzzy world. Before Mandelbrot fractals, fuzzy world or fuzzy realism was inaccessible to any logical or mathematical instruments. Mandelbrot blew open that world and provided us with a beautiful train ride into it.

And remember: the beauty is in the progress of this and the totality of it is even more so!

ryokan

There is a great level of progress in the alimentary industry, but can we relate beauty to such progress? And I don't will talk on the progress in weapons.
Surely, your reference is only to progress in scientific knowledge, with independence of its practical applications. Yet in such case, theories seem differ in beauty in a different form to their distance in the involved scientific advances. And it remains the question that aesthetic considerations can influence the form in that some scientists have elaborated hypotheses and theories. Of course, Science ever will search the progress in all its fields.

ryokan

I am in accordance:"only the correspondence with facts remains crucial". But I can also be interested on both the grade of beauty of theories and the influence of the aesthetic judgements can have in the development of theories.
On the contrary, I cannot agree with your assertion on the pragmatism of Science. I think that the aim of Science is the answer to questions, both pragmatic and non-pragmatic. To see if petals of some flowers are related to Fibonacci numbers semms to lack of any practical sense. Are Mathematics ever pragmatic?

selfAdjoint

Pragmatic doesn't mean narrowly utilitarian. Mathematicians are very pragmatic; everything is in the service of getting the answer, or proof, or whatever designated outcome.

Flower petals and seeds show Fibonacci patterns because of the rates of growth they stem from.

ryokan

[QUOTE=selfAdjoint]Pragmatic doesn't mean narrowly utilitarian. Mathematicians are very pragmatic; everything is in the service of getting the answer, or proof, or whatever designated outcome.
QUOTE]
I don't know if you and metacristi use the term pragmatic in the same sense. I agree with the pragmatism of Science in your's wide sense, not in utilitarian sense. Yet, I think that beauty and pragmatism in Science are different concepts. Pragmatism in wide sense (answer to questions) is essential. Aesthetics can be interesting.

marcus

hello selfAdjoint and ryokan,
I am posting simply for the pleasure of participating in the discussion.
I have a kind of fascination with the role of beauty in mathematical science (or with the human sense of beauty which I think is partly trainable but also partly a genetic inheritance)
But I do not have a stable consistent ideology about this. So what i say today might be different from yesterday.


If in 1903 the Wrights started out to design a flying machine so it would be beautiful this would have been impractical probably and even dangerous. But they were good engineers and they designed it to be buildable and to function---that is to fly and be controllable.

however even in 1903 one could have had a kind of Faith, almost a fanatical confidence, that if one could build it and then keep improving it year after year that eventually the airplanes would be beautiful

one would not know how it would be beautiful and one could not
use one's preconception of what beauty "is" to guide one in designing, necessarily, but one would be absolutely sure with a fanatical belief that one day one would look at the refined improved designs and realize that they are beautiful.

and they are

and I think it is cross-cultural-----that the kid in LA or Inuit kid or Bushman kid or Cambodian kid whether they live in arctic or outback or jungle or next door to LAX airport they will with some high probability think the airplanes are beautiful. Maybe that's wrong and maybe it has non-genetic explanations too. But I think its in the human bloodline, bred into us by millennia of knowing a wellmade weapon or tool.

selfAdjoint

Well, I for one find the Wright Flyer beautiful. Graceful, minimally designed for its purpose, "Less is More."

Ted Sturgeon once wrote a short story in which an alien walks down an American street, seeing the cars, which he can see through with his X-ray vision. And he wonders why they streamlined the cars on the outside, but not down in the engine.

ryokan

Yes. That is perhaps the question with Philocrat.
There was progress in the Wrights plane, but not yet refinement.
Beauty would be associated in some form to evolution of theories towards ... Simplicity? Power of prediction? Unification? I don't know, but this evolution and its final result would be perceived as aesthetic pleasure.
In the Aristotle's Poetics art is imitation, mimesis. It is possible that the beauty of a scientific theory express its mimesis, its fitness to Nature.

ryokan

Godfrey Harold Hardy wrote:
The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
A Mathematician's Apology. London 1941.

What do you think about this "test"?

marcus

both these last two posts are pretty good, ryokan

also they are short, which is nice

I dont think of anything to add

Philocrat

And a theory that helps find or discover the 'Best or Perfect Convergence formula' for structional and functional perfection would be the most beautiful of them all. Perfect Convergence formula is any theory that allows things and what are left of their final properties to survive physical destruction. Scientists should stop being demoralised and start finding this formula!

ryokan

I don't think that scientists be demoralised. On the contrary, I believe that Science is optimistic in the search of knowledge.
I see that again you identifies beauty with progress.