Unpredictable Tao

DIVERGENT SEQUENCES ARE UNPREDICTABLE

According to the popular image of science, everything is, in principle, predictable and controllable; and if some event or process is not predictable and controllable in the present state of your knowledge, a little more knowledge and, especially, a little more know-how will enable us to predict and control the wild variables.
This view is wrong, not merely in detail, but in principle. It is even possible to define large classes or phenomena where prediction and control are simply impossible for very basic but quite understandable reasons. Perhaps the most familiar example of this class of phenomena is the breaking of any superficially homogeneous material, such as glass. The Brownian movement of molecules in liquids and gases is similarly unpredictable.
If I throw a stone at a glass window, I shall, under appropriate circumstances, break of crack the glass in a star-shaped pattern. If my stone hits the glass as fast as a bullet, it is possible that it will detach from the glass a neat conical plug called a conic of percussion. If my stone is too slow and too small, I may fail to break the glass at all. Prediction and control will be quite possible at this level. I can easily make sure which of three results (the star, the percussion cone, or no breakage) I shall achieve, provided I avoid marginal strengths of throw.
But within the conditions which produce the star-shaped break, it will be impossible to predict or control the pathways and the positions of the arms of the stars.
Curiously enough, the more precise my laboratory methods, the more unpredictable the events will become. If I use the most homogeneous glass available, polish its surface to the most exact optical flatness, and control the motion of my stone as precisely as possible, ensuring an almost precisely vertical impact on the surface of the glass, all my efforts will only make the events more impossible to predict.
If, on the other hand, I scratch the surface of the glass or use a piece of glass that is already cracked (which would be cheating), I shall be able to make some approximate predictions. For some reason (unknown to me), the break in the glass will run parallel to the scratch and about 1/100 of an inch to the side, so that the scratch mark will appear on only one side of the break. Beyond the end of the scratch, the break will veer off unpredictably.
Under tension, a chain will break at its weakest link. That much is predictable. What is difficult is to identify the weakest link before it breaks. The generic we can know, but the specific eludes us. Some chains are designed to break at a certain tension and at a certain link. But a good chain is homogeneous, and no prediction is possible. And because we cannot know which link is weakest, we cannot know precisely how much tension will be needed to break the chain.
If we heat a clear liquid (say, clean distilled water) in a clean, smooth beaker, at what point will the first bubble of steam appear? At what temperature? And at what instant?
These questions are unanswerable unless there is a tiny roughness in the inner surface of the beaker or a speck of dust in the liquid. In the absence of such an evident nucleus for the beginning of the change of state, no prediction is possible; and because we cannot say where the change will start, we also cannot say when. Therefore, we cannot say at what temperature boiling will begin.
If the experiment is critically performed – that is, if the water is very clean and the beaker very smooth – there will be some superheating. In the end, the water will boil. In the end, there will always be a difference that can serve as the nucleus for the change. In the end, the superheated liquid will "find" this differentiated spot and will boil explosively for a few moments until the temperature is reduced to the regular boiling point appropriate to the surrounding barometric pressure.
The freezing of liquid is similar, as is the falling out of crystals from a supersaturated solution. A nucleus – that is, a differentiated point, which in the case of a supersaturated solution may, indeed, be a microscopic crystal – is needed for the process to start.
We shall note elsewhere in this book that there is a deep gulf between statements about an identified individual and statements about a class. Such statements are of different logical type, and prediction form one to the other is always unsure. The statement "The liquid is boiling" is of different logical type from the statement "That molecule will be the first to go."
The matter has a number of sorts of relevance to the theory of history, to the philosophy behind evolutionary theory, and in general, to our understanding of the world in which we live.
In the theory of history, Marxian philosophy, following Tolstoi, insists that the great men who have been the historic nuclei for profound social change or invention are, in a certain sense, irrelevant to the changes they precipitated. It is argued, for example, that in 1859, the occidental world was ready and ripe (perhaps overripe) to create and receive a theory of evolution that could reflect and justify the ethics of the Industrial Revolution. From that point of view, Charles Darwin himself could be made to appear unimportant. If he had not put out his theory, somebody else would have put out a similar theory within the next five years. Indeed, the parallelism between Alfred Russel Wallace’s theory and that of Darwin would seam at first sight to support this view.
The Marxians would, as I understand it, argue that there is bound to be a weakest link, that under appropriate social forces (notice the use of physical metaphor, inappropriate to the creatural phenomena being discussed. Indeed, it may be argued that this whole comparison between social biological matters, on the one hand, and physical process, on the other, is a monstrous use of inappropriate metaphor) or tensions, some individual will be the first to start the trend, and that it does not matter who.
But, of course, it does matter who starts the trend. If it had been Wallace instead of Darwin, we would have a very different theory of evolution today. The whole cybernetics movement might have occurred 100 years earlier as a result of Wallace’s comparison between the steam engine with a governor and the process of natural selection. Or perhaps the big theoretical step might have occurred in France and evolved from the ideas of Claude Bernard who in the late nineteenth century, discovered what later came to be called the homeostasis of the body. He observed that the milieu interne – the internal environment – was balanced or self-correcting.
It is, I claim, nonsense to say that it does not matter which individual man acted as the nucleus for the change. It is precisely this that makes history unpredictable into the future. The Marxian error is a simple blunder in logical typing, a confusion of individual with class.