Do the Gambler Fallacy Hold at the Quantum Level?
The title of this microessay embodies the question that it is intended to ask, but I fear some clarification may be required before the question can be clearly understood.
By ‘quantum level’ I mean the sub-microscopic domain far below the atom, where all materialistic illusions have been abandoned, leaving nothing but statistics and probabilities. There is no “causal force” at the quantum level, no mechanical connection between any event and any other event. There are only events and their probabilities.
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By ‘gambler’s fallacy’ I mean the belief – commonly held to be fallacious – that the number of times something has occurred in the past has a direct (causal?) influence on the occurrence or non-occurrence of something in the future. Note, however, that even if past performance does not cause future performance, it can be a good predictor.
My question, therefore, is essentially this: if past performance does not cause future performance, then why is past performance a predictor of future performance? If it is unreasonable to posit “invisible” causal forces between events (and I agree that it is), then how do we explain the accuracy of predictions based on past performance?
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The only explanation I can think of is that, at least at the quantum level, the gambler’s fallacy is not a fallacy, it is a legitimate form of reasoning.
Here’s an example at the macro-level: If one laid prone at some particular location in the 18th Century, there was a certain (very low) probability that one might be killed; if one laid prone at that same location in the 21st Century, the probability that one might be killed is much greater, given that that location is now a lane on the autobahn.
Another example at the cosmological level: Prior to the big bang there was a certain (very low) probability that a particle of cosmic mass might appear out of quantum vacuum; however, once such a particle had appeared and exploded under its own gravitational forces, the probability of the appearance of a universe like ours was greatly increased.
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Of all the given possibilities at any moment, with all their various statistical distributions, the realization of some possibilities, as opposed to others, seems to have a significant affect on the predictability or probability of certain subsequent events. Preceding events have greatly altered the probabilities of those subsequent events.
If, therefore, we eliminate “invisible causal forces” (which I am prepared to do), how do we account for the fact that the realization of past probability distributions influences the predictability of future probabilities? It seems to me (intuitively) that the only solution to this problem is that the gambler’s fallacy is not fallacious, at least at the quantum level.
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