Saturday, December 25, 2010

A static pattern of infinite variation

Christmas day and lazily watching television. Something sciency. I was paying half attention while carefully dissecting a chocolate Santa. They were talking about chaos. The idea that began with/spawned the saying about the butterfly and the tornado. I was thinking, boring, idiots, how couldn't you see? I've known, somewhere deep inside, always. The tiny details that tip the scales, creates tidal waves, that somehow fit into a greater pattern that yet still cannot predict the wave. I got interested at first because it amazed me that generations of great mathematicians seemed to have been baffled at the realization. The idea that chaos in the general sense is something that doesn't truly exist; it's simply another form of order.

But as they went on...

Not even nature can keep track of all the details. Micromanaging has never been the way to win a war. It's about initiating very simple patterns, that will lay the land for the winning strike, although you can never be sure when or how it will happen. Like a tree that repeats itself, smaller and smaller into branches, like our blood vessels, like river streams. Suddenly I saw the connection from math - to fractals - to nature - to the patterns of humanity and the world - back to the math that we spawned because of it. Feedback; an infinite, clever loop based on a very simple concept. A single pulse of the bat sonar, and another shard of clarity taken away from it.

Perhaps there is no need to know the details, perhaps no need to understand the small things, only to know the simple premises and how they build on each other? A difficult thing for me to accept, because it turns my beliefs about science upside down. Is it possible for humanity to understand the world we live in? An hour ago I would have said no, never, absolutely not. But maybe understanding it does not mean to know exactly where lightning will strike; rather to know the premises under which lightning will surely strike - sometime, somewhere.

It strikes me that it might be what my knowledge of people builds upon. As I get to know a person, a simple equation takes shape that will explain all behavior - but not predict it. I have always known that I'll never be able to predict. Too many small variables for a human brain to compute, probably also for a supercomputer. Bigger patterns of behavior are much easier to predict, but the actions of a single individual may also change the course of that behavior so drastically that predictions will always be just predictions; guesses.

Perhaps I even believe in evolution now, although that's a bit trickier. It means progress requires small mutations in all systems, which again removes the capacity to ever understand anything, because the tiniest change in the premise of the pattern can drastically change the outcome. Butterfly and all that.

Which brings me back to the idea that a system in motion, one that contains living, growing, evolving things can never be accurately understood or described, especially not by those inside of it.

Fractals have taken us closer to a math of nature than I previously understood. But can humanity ever understand everything? No, never, absolutely not.

But clearly there are underlaying, static patters that create a world of infinite variation. Can those be found and understood? Maybe. Maybe.


Kristin said...

I'm reminded of that xkcd strip about centripetal vs centrifugal force. Newton's laws as they are generally constructed only allow for a centripetal force, but if you construct the laws in a rotating system there is a centrifugal force instead.

I somehow feel that it's vain and stupid to always try to observe from the outside. No matter how hard you try you can not put yourself outside the world - so why work so hard? Why not accept the way things are and work from the inside?

Riklurt said...

You're essentially summing up every single one of my religious, scientific, and philosophical beliefs in this post.

I... have nothing further to comment, because obviously I agree with you :P

Yeonni said...

I agree with Kat also, and have always done. This idea to try and understand a system we're inside from the outside is... very very difficult to imagine would be possible. I'd almost call it ridiculous.

Kristin said...

Not just that. Even if we succeed it does not describe the reality we experience! And that's what really matters, at least to me. Why else would I play all these games?

Kristin said...

Yes. If you waste all your time on trying to describe the centripetal force to a kid riding a carousel you'll miss all the fun in feeling the centrifugal force while riding it!

Yeonni said...

Ah, well, it's important to remember to experience life and not just observe it. Knowing that the centripetal force exists and how it works may save lives or give you great personal wealth by inventing carousels, however.

Nallenon said...

Wait, you didn't believe in evolution?

Yeonni said...

I accept evolution as a scientific theory, I'm just not 100% convinced that it's 100% true.

Also, can the underlaying static patterns that create the world of infinite variation be understood... well... I'm kinda negative on the maybe now. More like, unlikely.

Nallenon said...

Oh. Well that's just being scientific about it, I don't think anyone is 100% convinced that it's 100% true. Anyone who is is very likely wrong anyway, so..

Riklurt said...

Accepting evolution as a scientific theory has less to do with believing that macroevolution actually happened, and more to do with accepting that it's a good assumption to use when doing biological and medical 'speriments.

You can use the model of macroevolution and not actually believe that it happened just fine. It's no different from using the theory of ether to calculate things moving quickly in space - the theory is incorrect, but the math pans out correctly anyway.

Also: I have had some conversations with my dad on this subject, of understanding the universe. He likened it to a game of Nomic: It's possible to understand the rules, but only as they appear right now. Trying to understand the entirety of Nomic is impossible, because the rules can change the rules can change the rules.

There is, as I have often mentioned, mathematical proof that mathematics are unreliable. That, if anything, should be good enough proof that the world can never be understood using reason alone.