Motus Mentis

My friends Kevin Kim and Bill Keezer have been discussing a recent post of Bill’s, in which he argues that the Universe is “undetermined and constrained”. Bill’s post is here, and Kevin’s response, which raises some important objections but stops short, I think, of fully “grasping the nettle”, is here.

Bill’s essay begins:

For over two hundred years, the findings of science and their increasing accuracy in describing phenomena and predicting them appears to motivate the idea that ultimately one can have absolute predictability and that the laws of nature completely determine the functioning of reality.

This idea fails for several reasons. First, all the findings of science are based on measurements, and measurement inherently has error. This is why all valid scientific results are reported with a plus-or-minus value at the level of the least significant figure. Even accepted values such as atomic weights have an implied error value though it is not stated. Second, determinists think that determinism operates at the atomic level and then apply it at a cellular or higher level. Usually it is applied to nerve functions. They fail to recognize the difference in scale between atoms and molecules and the nerves they are discussing. This will be discussed in detail below. Finally, there is a failure to understand what Stephen Boltzman recognized over one hundred years ago, the statistical nature of atomic and molecular behavior.

After giving some examples of complex, unpredictable systems, and an overview of statistical mechanics, Bill concludes:

In this essay, I have attempted to show by example that both immaterial objects, e.g. a fountain, and the mind are undetermined and constrained. From this it is possible to generalize and state that physical reality is undetermined and constrained, simply because all collections of atoms and molecules follow Boltzman statistics.

I’m not going to jump in at great length, but I do have a few things to add.

First of all, I think it is extremely important to pry apart, and to keep well separated, the concepts of ‘determined’ and ‘predictable’. To do this, it is helpful to understand the idea of “algorithmic compressibility”.

The great early triumphs of modern science, particularly those of astronomy and physics, were won by finding algorithmic descriptions of the behavior of certain natural systems. A good example is the motion of the planets; whereas the Ptolemaic system layered epicycles upon epicycles, and even the great Kepler wasted much of his life attempting to fit the “spheres” of the planets into nestings of the Platonic solids, Newton, was able, at a stroke, to account for the movement of the planets by applying his newly discovered formula for the law of gravitational attraction. Suddenly the whole evolution of the system — a planet’s position at any time, past and future, as well as its path through space — could be predicted. This sort of thing became the very soul of science: the reduction of complex systems to simplifying, predictive formulas. Predictive accuracy became the measure of a scientific theory, and in many peoples’ minds, the measure of science itself.

But while some systems are amenable to this sort of ‘compression’, others are not; in order to make exhaustive model of these complex systems the necessary equations would have so many terms that they would be beyond, sometimes even in principle, any available, or even imaginable, computational engine. Such systems abound in nature: the weather, for example, or the diffusion, or turbulent flow, of gases and liquids. Anyone who is familiar with the programmed systems known as ‘cellular automata’ (CAs) — which, as Stephen Wolfram makes clear in his remarkable book A New Kind Of Science also seem to exist, perhaps with great abundance, in nature — will know that there is no simplifying algorithm for the future states of these systems, despite their being completely, uncontroversially deterministic. (You can play with them here.) Even if we know with complete certainty the rules of the system and the initial condition, there is no way to know the state of the system after a given number of steps without actually running the calculations for every intermediate step. In other words, only the system itself can give you certain information about its future state; if you want to find out what it’s going to do, you just have to let it run. But — this is so important that I’ll say it again — cellular automata are fully deterministic systems. (They’re just computer programs, after all!)

This, then, is algorithmic incompressibility. And the example of CAs suffices to show that unpredictability does not imply indeterminism. The simplifying methods devised by Boltzmann were a great insight, and of immense practical use, but what they did was not to demonstrate any indeterminism at the particle level, but simply to make possible statistical predictions of a deterministic, but algorithmically incompressible, system.

Bill’s article doesn’t say much about free will, but the question of free will is clearly the “elephant in the room”. This is the other point I think needs airing out: that even if, as Bill says, the action of the brain is not causally determined (although the argument, I have to say again, seems to me to rest heavily on a conflation of ‘determined’ and ‘predictable’), indeterminism does not buy us what we really want from an account of free will, which is originating agency. There are, in fact, ways in which quantum randomness might be amplified to the scale at which our neurons work, but so what? How is our decision-making any more our own if it arises from underlying randomness than underlying mechanicalness? How does indeterminacy in our skulls make us responsible for anything?

That’s enough out of me, I think. Go and read Bill and Kevin’s posts. And if you like, you can look at a linked series of some old posts of our own about free will, below.