Theory of Form

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furonius
Is there a such thing as a perfect circle or a perfect line that naturally occurs? Also is it possible to artificially create a perfect circle or straight line in science? Or is it all flawed to some degree?

rudester
well im not sure about the perfect line, ut the perfect circle can be seen in fractal science.

http://www.youtube.com/watch?v=yUM7e0tIFi0&feature=related

Little Caesar
Originally posted by furonius
Is there a such thing as a perfect circle or a perfect line that naturally occurs? Also is it possible to artificially create a perfect circle or straight line in science? Or is it all flawed to some degree?

As a Google intellectual I can say that perfect shapes in nature probably come into existence and disappear but they don't last long enough to observe and record.

Astner

rudester
dear god I don't know but I remember watching a documentary about it.

Astner
Originally posted by rudester
dear god I don't know but I remember watching a documentary about it.
Fractals are mathematical sets with a certain property, this property can be partially illustrated by an iterative process which structures repeated shapes in respect to zooming.

But they're not found in nature.

Mindship
Originally posted by Astner
Fractals are mathematical sets with a certain property, this property can be partially illustrated by an iterative process which structures repeated shapes in respect to zooming.

But they're not found in nature. But aren't these fractal in structure? Or perhaps better put: fractal geometry effectively represents these natural patterns...

https://emedia.leeward.hawaii.edu/harvest/spring06/WinnersPages/Art/photo_folder/S-bare%20tree.jpg
http://citybythesea-nyc.com/blog/wp-content/uploads/2010/07/Joni-Sternbach-Ocean-Surface.jpg

As for that video: I think it did a poor job explaining the subject matter. For one thing, to say people are like cells sounds like the Doc was confusing fractals with holons. For another, it wasn't necessary to introduce chakras.

Not a good video, imho.

Symmetric Chaos
Those fractals break down if you zoom in far enough. For all sane purposes these are fractals, for philosophical and mathematical purposes they are not.

"Perfect" shapes that can be described mathematically can't exist in reality because reality is made up of stuff that can't be infinitely subdivided. For example if you make a ring of protons with the circumference of our galaxy it would still only be a polygon with lots of sides.

Mindship
Originally posted by Symmetric Chaos
Those fractals break down if you zoom in far enough. For all sane purposes these are fractals, for philosophical and mathematical purposes they are not. Yeah...that's why I second-guessed myself with, "perhaps better put: fractal geometry effectively represents these natural patterns," ie, as opposed to other mathematical descriptions. I believe this was Mandelbrot's initial incentive/application: how to better map, for example, coastlines.

Another example: fractals generating a representation of a mountain...

http://upload.wikimedia.org/wikipedia/commons/6/6d/Animated_fractal_mountain.gif

And indeed, the pure geometry eventually "outpaces" the reality.

Astner
I think that the opening poster meant geometric objects existing in nature, and not simply geometric object that can be used to find good values for surface areas of various objects.

Either way. An open string could theoretically take the form of a perfect line, and a closed one as a perfect circle, because they're one dimensional, but there's no way to observe that.

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