ON THE NATURE OF CHANCE AND PROBABILITY

The following is the abstraction of a  topic currently featured in V.H. Ironside, Behold! I Teach You Superman 

            “And how could I endure to be a man, if man were not also poet and reader of riddles and the redeemer of chance!”

Nietzsche

                     There is no reality like empirical reality.

          Take the toss of a coin! The relationship between probability and randomness is nowhere more apparent than in the haphazard drop of a coin. In other words, if you

throw a fifty-pence piece into the air, say, a hundred times, the expected ratio would be fifty-fifty - heads or tails - give or take a few. The pattern is so obvious it barely needs arguing. It is, in a word, self-evident. Either/or, slanted one way or the other, is unsustainable over protracted periods. It waxes and wanes, but always in proportion to the statistical balance of probability. A system might happen to move briefly into a less likely state, but excessive or extended fluctuations of this process are, in principle, exceedingly low. As a test of resolve and persistency, as much as a matter of personal record (I didn’t spare myself!), you’ll find that they rarely if ever exceed four or five repetitions in a row. But since the mechanics of each throw are determined only by themselves, the prevailing theory is that chance may cause anomalous patterns, but that the mathematical likelihood of either heads or tails coming up will continue to be fifty-fifty.

          Or will it?

          Once again it seems that the reality principle is returning with a vengeance. And I don’t think anyone will accuse me of giving the plot away if I reveal that, in a predictable reversal, the likelihood of heads coming up for a sixth or seventh time, is inversely proportional to the already accumulated tally. ‘Conceptually’, in other words, each new attempt to stretch the tally is less probable than the last. And there is the rub! Mathematicians will argue that the probability remains the same for each throw. The conceptualist will claim that although a random fluctuation may increase, the

probability that it decreases is greater. That it has a momentum of its own - acting like an invisible rubber band whose elasticity has been stretched to the limits. The force increases, the harder you pull. Something also known as the Bell curve of probability. Just as water finds its own level, chance too, follows the path of least resistance. And most physicists view that as a statistical law. Random, but predictably so, because any such configuration has a natural propensity to move from less likely to more likely as time passes. The reconciliation of the relation between causality and probability hinges on ‘conceptual constraint’, in other words. Which is not a causal a priori law, but an a posteriorily defined perception. Nor would you  wish to place your money on ‘heads’, if heads have come up five or six times in a row already. It requires no great insight to see that. Or let me put it this way. No one can disprove that the chances of lightning

Christina Jones: Mail Carrier  Killed by Lightning Bolt 

striking twice in the same place are no less than lightning striking anywhere else, but somehow, the sheer logical force of the ‘conceptual average’ must prevail - never mind the mechanical independence of each strike, as determined by itself.  

          Point taken!

          But now we come to another kind of calculation. Does a sequence of probability consist of objective  events alone, or is a subjective observer necessary too? An entirely reasonable question since ‘the chance’ of probability theory totally differs from ‘the chance’ that is inherent in nonlinear system theory (which, too, places strict limits on certainty even though each individual variant is wholly deterministic). Indeed, as a branch of mathematics, modern probability theory has a considerable pedigree, going back to the seventeenth century and the valuable efforts of Blaise Pascal, who made a careful study of the laws of chance. More to the point, it illustrated an astonishing fact. That probability is not a ‘law of nature.’ That, by contrast, deviations from determinism appear to introduce anthropomorphous concepts such as chance and coincidence. Which is to say, that the individual experience may well exceed the limits set in  Bell’s theorem by many times the expected  average. A statistically significant violation  of the empirical bias structurally embedded in our ways of thinking. Or, indeed, of some other unguessed property that leads to the appearance of determinate behaviour as a result of statistical averaging. Implicit in which is the assumption that chance is possible only because the probability responds differently to different individuals, and the distortions are just such as to maintain the absolute character of the law of averages. And if I were to suggest how this contradiction might be resolved, I would indeed suggest a law due to the synchronicities in the human mind, and not a series of mechanical events that can act together in a probalistic fashion; “a peculiar interdependence of objective events”, in other words, “with the subjective state of the observer”(Jung).

          Some call it luck!

          In the world of perception, facts are a necessary sequel only insofar as they determine the frame of reference. But even if, by its very nature, the statistical tally is explanatory of the past rather than predictive of the future, it is no doubt true to say that facts and reason are ultimately overwhelmed by the nebulous imposition of conceptual constraint. Indeed, whether it is the punter versus the wheel, or the conceptualist versus the mathematician, no reasonable person can doubt that ultimately the ratio of the spin will always be disciplined by its own unforgiving logic.

          In other words, the older you get, the greater the chance of you dying.   

          On the face of it, there seems no ground for believing that probability is a law due to the mind, but we are apt to deceive ourselves badly as to the degree of effective impartiality even in the strictest context of causality, since among its less visible effects probability emerges as the projection of a synchronized manifestation. As the manifestation of an anthropic concept, rather than mathematical consistency. A concept which lays no claim to either causal or mathematical logic, but which is all the more conspicuous for the absence

of either. And not merely because it is the vehicle of recognized ideas and perceptions, but precisely because it provides exactly the properties necessary to constitute the great determining principle of empirical reality, if not by virtue of causality, at least as the result of what I have described as conceptual necessity. For even though what exactly happens here represents a breakdown of determinism in nature, what is clear is that reality makes little pretense of objectivity. Indeed, an essentially subjective analysis represents the absolute truth far more completely than any mathematician working by a priori methods can possibly imagine. And our demonstrating it a posteriori as a necessary consequence of the anthropic principle means that we are not studying facts, but a mathematical model that describes and codifies our perception of facts, not events, but their synchronization by human comprehension. For if reality is an illusion that can only exist in the mind, then nothing is so coercive as the cast of one’s mind...