Beautiful Ideas.

[Khandro]

Do you find the natural world beautiful?
Does this world embody beautiful ideas?

[jim360]

Beauty can only take you so far -- which might seem a pity, but it actually not. Indeed, you should be far more thankful from the deviations from "perfect" beauty. Without them, we would almost certainly not be here.

[jomifl]

That's a bit profound jim...are you prepared for the inevitable questions?

[jim360]

Yup :) Well, hopefully.

[mibn2cweus]

Beauty is inherent in that which gives rise to and makes its eventual perception, evaluation, appreciation and understanding possible apart from which the existence of beauty is meaningless, without purpose and unfulfilled.

[Khandro]

To be honest, I learnt this a long time ago, so long I'd forgotten the details, but this (above) is only the first part, and jim you probably know the astounding fact that these harmonious sounds are connected to weight !!!

Instead of adjusting the screw to tighten the string as a violist does, P. had weights hanging down the edge of the table on the ends of them from his zither-like contraption;

https://www.google.de/search?q=image+of+pythagoras%27s+string+experiment&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwjM-o6o9LPKAhUIwHIKHS_jBUsQsAQIIQ&biw=1400&bih=739

What is remarkable (you must agree?) is that the tones are in harmony if the tensions are ratios of squares of small whole numbers - higher tensions correspond to higher pitches, so a 1:4 ratio produces the octave and so forth.
"This second relationship is even more impressive than the first in that things are hidden numbers. The relationship is better hidden because the numbers must be processed - squared to be exact- before the relationship becomes evident."

[Zacs-Master]

Were talking Fibbonaci here aren't we.

[jim360]

I don't do much musical harmonics, so actually you're probably better-read in it than I am. Not really sure I get why that weight relationship is more beautiful just because it's y going as x^2 rather than y going as x, though (not that I'm disputing its beauty per se, but it seems based mainly on the surprise of someone who had never realised that things don't have to be linear).

[Old_Geezer]

It's possible we learnt to find them appealing. Other cultures, Indian for example, would sound strange to western ears until sufficiently experienced. Or on the other hand why shouldn't we find certain ratios appealing ? Seems natural to me that we would. I think this is a case of spotting patterns and drawing unjustified conclusions from them. There is no evidence of intent.

[Khandro]

O.G.//Other cultures, Indian for example, would sound strange to western ears until sufficiently experienced.//
Perhaps worth spending 8 minutes of you life listening to this. :0)

[jomifl]

It may use smaller intervals than semitones and lots of slides but it uses the same principls as western music.

[jomifl]

The world only embodies ideas in that ideas are in our brains and we are part of the world.

[Old_Geezer]

Not an area of my expertise but smaller intervals has to mean more notes per pitch range which in turn means different chords. Thus different sounds. Yet different folk learn to see an idea of beauty in different sounds. I think that supports the idea that it is learnt not simply there from an external intelligence.

[Khandro]

jomifl; The world only embodies ideas in that ideas are in our brains and we are part of the world.//

The relationship between mind-matter-beauty, is heady stuff! The point I am attempting to make here is that the mathematics embedded in that trinity existed before P. discovered it, and before we came on the scene, and will exist after we are gone, and I think it is safe to say it exists throughout the cosmos.

We didn't invent mathematics, like we invented the bicycle, we only discovered its underlying principles, and if we are receptive, find beauty within them. I'm in pretty good company in thinking this; Galileo Galilei, Johannes Kepler, Isaac Newton, James Clerk Maxwell and more searched and found it.

As Leibniz said, (with my parenthesis)
"When God [insert here; He, She, Them, It] sings to himself, he sings algebra."

[Old_Geezer]

When God [insert here; He, She, Them, It] sings to [insert here; himself, herself, themselves, itself], [insert here; He, She, Them, It] sings algebra.

:-p

[Khandro]

Thanks OG! :0)

[jim360]

One of the facts about the natural world I've always found slightly beautiful, in a crazy way, is how so many apparently totally different systems can be described with (essentially) the exact same equation, or set of equations. If God were obsessed with beauty, he was also pretty lazy (or perhaps, more charitably, economical)!

[Khandro]

jim; I don't think it's laziness, though it can be a virtue. Field Marshal von Moltke
in categorizing his officers put at the top of the list the 'Intelligent and Lazy' - "I make them my commanders because they make the right things happen, and find the easiest way to accomplish the mission".

The hallmarks though, of beauty in nature's artistic style are;

'SYMMETRY - a love of harmony, balance, and proportion.
ECONOMY - satisfaction in producing an abundance of effects from very limited means.'

Frank Wilczek

[woofgang]

But like the tree in the quad, is something beautiful if a sentience has never experienced it and judged it beautiful?

[jomifl]

Khandro, the relationships existed, we invented maths to as a tool to explain the relationships. Mathematics did not exist before mankind invented it.

[jomifl]

Woofgang, I think your question hits the nail on the head, beauty is subjective, end of.