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Non-linear dynamics: A way around the dead end of Darwinism? Maybe not …

Here’s an intro to James Barham’s argument.

To which physicist Rob Sheldon responds,

a) “emergence” is NOT a local property, it is a global property. If it were local, then it would be a method of increasing information without input. That is to say, it would violate the principle of the conservation of information, which in physics jargon, is the conservation of entropy. The way physicists get around the fact that life decreases entropy, is always to say that it is an open system. But “open” is just another way of saying “global”.

What does this mean for your theory?

It means that the “strange attractors” are not locally responsible for the dynamics, but are globally responsible. The information does not lie only in the boundary conditions, in the initial state of the system, but in the equations governing the system. It’s the complaint that Dembski makes of all these OOL theories, they are playing a shell game with information. Here the information is being moved into the equations, into the global properties of the non-linear dynamics.

b) Because of this information moving into the global parameters, homeodynamics, both robustness and plasticity, are properties of the global parameters. They do not “emerge” as a new property of the system simply by adding a non-linear term to the dynamics. Furthermore, the fact that a new equilibrium can be found (plasticity, metastability) is not a given for non-linear dynamics, but is a property of the global system. Even the number of basins, the idea that if we get perturbed out of one “strange attractor basin” we will fall into another, is a global property, not an emergent characteristic of non-linearity.

I’m just repeating what theoretical physicist Stephen Barr said in “Modern Physics and Ancient Faith” when he said that explaining one physics law by appealing to deeper symmetry (non-linear math, strange attractors, etc.) makes the problem of gaining information worse, not better, because the deeper symmetry is even more global than the local behavior we were attempting to explain. That is to say, the information content of some feature goes up as you expand the phase space. (Finding a dollar bill in your wallet isn’t very surprising, finding on the sidewalk on the way to work is more surprising, and finding it on the Moon would be even harder to explain.)

c) But this way of looking at homeodynamics doesn’t do justice to the really novel part of this picture. Turing said that if you feed the output back into the input, you no longer have a deterministic system. Those cute chaos patterns that you used to illustrate your post are “Poincare plots” where two variables of motion are plotted, (x versus Vx for example) and they were often generated exactly that way–feeding the output of one state back into the input to determine the next state of the system. The “non-determinism” part is that each dot on the Poincare-diagram lands in a general way on the curve, but not fitting any known function, they aren’t periodic, they aren’t linear, their locations are like digits of pi, computable but not predictable. However, Kolmogorov-Arnol’d-Moser showed that these points fall inside a well-defined boundary, a surface, which they called “the invariant torus” because it tended to have a hole in the middle I suppose. While we can’t predict where they’ll land inside that donut surface, we can predict where they will not land–outside the donut. This ability to predict where they don’t land, is a blurry form of determinism again, and makes many physicists feel like they can control chaos–that they’ve beaten Turing’s game, and can deterministically describe non-linear dynamics in terms of attractors etc. But as I argue next, the dream vanishes when applied to living things.

Okay, all this was for inanimate objects like the orbit of earth as perturbed by Jupiter. What happens when we plug in life? Some of the early math models were for (virtual) insect populations on an island of fixed resources. The computer insects multiply each year until they exhaust the resources and there is a population crash. The number of survivors is not the same as what they started with, so the next multiplication sequence looks different and when you examine all these crashes there is this peculiar chaotic pattern that emerges which can be characterized by Lyapunov exponents and Feigenbaum constants.

But is that what we actually observe in nature? Vaguely, but not in detail. Because in detail, the insects know they are about to crash, so they change their reproductive strategy. Plants produce less seed when resources are dropping. People have less kids when they get rich. In other words, they know something about the global conditions and modify their behavior accordingly. Lovelock’s thesis was that life modifies its environment in ways that change the strange attractor, they achieve homeostasis by actively modifying the controlling equations. This is only possible if there is global information in the system. By the time we have a set of equations that describe our real insect populations, we have had to insert that global information about their behavior, teleological information about how they “know” what to do to survive.

So we are back to the fact that homeodynamics and homeostasis are not simply properties of non-linear math, but are properties of global information. Stephen Barr is right, we can’t get something for nothing, we can’t locate the information in the system in the local part of the non-linear dynamics.

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