Monday, January 22, 2007

The Harvest of Randomness

Several days ago I described four types of Darwin skeptics. "Physicists" were described as people who love the mathematical structure of the Universe and believe this math is all encompassing. Perhaps a better designation would be "determinists". They are, I suggested, resistant to three pillars of my own faith in the statistical nature of the Universe. I mentioned Kurt Gödel’s Incompleteness theorems, Heisenberg’s Uncertainty Principle and Chaos Theory.

Heisenberg’s Uncertainty Principle implies that there is a limit to the precision with which you can know about a single atom/particle. You can know where it is or how it’s moving, but not both. I believe that this uncertainty is intrinsic, not just mathematical, and the effect of a given object on its neighbor is also subject to a stochastic response. Even identical twins don’t react to each other with perfect accuracy or predictability.

Chaos Theory basically says that a relatively complex system may well be so sensitive to precise original conditions that the future of the system is not predictable through deterministic equations. Although a system might be technically deterministic, original conditions can never be measured with sufficient accuracy to emulate reality. The butterfly in Beijing flaps its wings thrice instead of twice, and two weeks later an unpredicted hurricane threatens the Caribbean. Weather, though possibly not climate, is one of those systems so complex that physics-based models predict radically different results when a single bit is changed in the data. It may be that the required quality of the input exceeds the measurability limits specified by Heisenberg, which is to say that the Universe is neither predictable nor repeatable.

What Kurt Gödel proved is that even the mathematics of a sufficiently complex system is immune to prediction or complete understanding. There will be true things within the system that cannot be proved within the system, and false things that cannot be disproved. Even if a precise mathematical model of Life the Universe and Everything were developed, it could not be counted on to explain everything.

These three ideas shook the foundations of physical science in the twentieth century. Statistical analysis became not just a way to approximate the Truth, but an essential component of the Truth. Things are stochastic. There is an irreducible element of randomness, and Life flourishes, free of determinacy, because of it.

1/22/2007 2:05 AM

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5 Comments:

At Monday, January 22, 2007 2:48:00 AM, Blogger jj mollo said...

Forgive me. The correct link for the four types of Darwin skeptics is here.

 
At Wednesday, January 24, 2007 7:38:00 AM, Blogger Steve said...

I'm of the impression that in chaos you have the "strange attractor", a trajectory that, while unpredictable, does have structure. The structure can change suddenly as some tipping point is reached in the chaotic system, but there's still structure. That means you can make certain predictions, no? (This assumes that strange attractors are characteristic of chaotic systems in general, which I don't know.)

I'm looking forward to being enhanced, a la Kurzweil, so that I can come to absorb and understand these things better and much, much faster.

 
At Wednesday, January 24, 2007 10:01:00 AM, Blogger mal said...

p+q=1 is a very simple formula. The complexities it implies however is truly mind numbing. Apply it to evolution? Oh my *L*

I love it when the determinists (religious or otherwise) get smacked in the face with reality.

I sincerely hope the universe never loses it surprises. Life will be neither fun or interesting

 
At Thursday, January 25, 2007 12:42:00 AM, Blogger jj mollo said...

Steve,

Determinists believe that a state set has channels, which the future must follow. Anything sufficiently close to the channel will get dragged in and flow predictably downstream. The thing about strange attractors is that many of them can be characterized, but it doesn't necessarily help. If a state is at point A at time 1 and transitions to point B at time 2, it may indeed be a direct consequence of point A, but will not occur again in just that way. For if the state is "close" to state A, the closeness required to evoke something close to state B may well be smaller than any measured difference. In fact the required closeness to state A is closer than any difference you may specify. I.e., the limit goes to zero, and Heisenberg insures that there will always be a difference. Weather can never be predicted with certainty or at all beyond a certain time horizon.

There are of course many approaches to analysis that allow you to narrow the possible outcomes and characterize them statistically. Information is available, but precision is not.

I'm betting that we will eventually discover that humans are much better at dealing with chaotic systems than any proposed substitute. Enhancement is a different issue. That happens all the time. We are always riding on the backs of our new tools, new technology and improved education.

The problem with growing old is that we begin to find some of the enhancements distasteful. My mother learned to keep her car running. She learned how to use a microwave oven. She even learned how to do e-mail and surf the Net. She is balking, for some unknown reason, at playing DVDs. Oh well.

 
At Thursday, January 25, 2007 1:03:00 AM, Blogger jj mollo said...

Mal, Even if the Universe were deterministic, we would still be in for lots of surprises. We are pretty finite creatures. The theory does remind me of the doctrine of pre-destination. Why does the minister bother preaching if God already knows who will be saved and who will not be saved? What is the meaning of effort, or free will, in that scenario?

Steve, The tipping point concept is probably borrowed from Catastrophe theory, rather than Chaos Theory.

An excellent metaphor for chaos theory might be taken from Larry Niven's Ringworld series. In one scene, Luis is jumping through mazes of transporters in order to keep from being followed. No one can know whether he chose the left or right and each jump leaves him off at a dramatically different place. He has randomized his location on the planet, although it can be characterized. His adversary knows that he is near a transporter, but nothing more than that.

An example of a catastrophe, which is perhaps controlled by chaotic systems, is the surface renewal theory of Venus. According to this theory, the land remains static while heat builds up in the core for thousands of years. Once the heat reaches a crucial point, the entire surface of the planet inverts itself, renewing the surface and releasing the heat. (I haven't checked on it lately. The theory might have been refuted by now.)

 

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