I Don’t Think I Believe in Infinity
Thu, Dec 20, 2007
Pointing to fractals as evidence of the infinite to me is like pointing to the existence of the word "infinty" as proof - I suspect they are both human concepts.
To my understanding, there are no true fractals in nature. However self-similar a fern's leaves and branches are there's a point at which the similarity breaks down. This is even true with our simulations of fractals: if we get close enough to the computer screen, we'll see individual pixels which no longer represent the overall pattern. Fractals are ideas, and the image or animated simulation of one is a representation of that idea rather than an example of it.
We look at the patterns we find in nature (fern leaves, the orbit of planets vs the orbitals of atoms), and being playful creatures, extrapolate them "
further than we can possibly imagine!
" (i.e. infintiy) and "
faster than a speeding locomotive!"
in the same way we see rabbits in the clouds. Much like these rabbits, a fractal is a story. A story that says, "isn't the world fascinating!"
I am inclined to agree with john and Wildcat's thoughts on the limitations of our words in defining such things. And I must say, folkert's vision of a universe with infinite possibility, but finite or novel substance, strikes me as wonderfully
would say). I can't help but think that the universe is not made of "natural" or rational numbers or mathematics - which like fractals - are practical concepts we've come up with in trying to function in a universe we can't yet wrap our minds around. Math is the story of our understanding of the universe. We've done fantastic things with it, yes. We've soared above mountains. But a bird does the same thing and has no use for math.
The universe doesn't contain "a set of some stuff" gap23, but a set of all stuff that doesn't care about mathematics. I'm convinced the universe is