On being Trumped: Probabilities and Actualities.

David Lidov*

If you bet on a horse despite 4-to-1 odds that your horse will lose, maybe you will win big. If you do, it does not mean the odds were wrong. My understanding of the mathematics of probability says we could only check out how smart the odds were by re-running the same horse race, say 100 times. If your horse does not win something like 20-30 times out of a hundred, then the odds were very probably misleading, but we have to say “probably” because the test could have been a fluke. Flukes happen. After Trump’s election, there was much talk that the polling had been wrong. Why? The polls, in aggregate, had suggested that DJT had roughly a 1-in-4 chance of winning.   That this horse beat the odds does not contradict them.   We don’t deny, of course, with hindsight, that polling methodologies might have been sharper. That is a different conversation.

In normal daily life, we are very dependent on notions of probability not just for horse races but also for thinking about the weather, planning pensions, choosing routes and modes of transportation based on estimates of traffic, and so on. Yet, the interpretation of probability is a problem dicey enough to have attracted careful treatment from various philosophers, statisticians and others. They sustain subtle disagreements as we should expect and respect, but we are generally comfortable with the idea of probability despite the tenuousness of its logic and physics. Thinking about probability as a sign, as I do in this fantasy-bagatelle need not broach or decide expert issues. I express my curiosity with no pretence to launch a theory.

At present, probability is a bothersome theme in metaphysics. Semiotics might properly want to stay aloof from debates about the foundations of physics, but even if we can not help the physicists, courtesy demands we acknowledge that physicists themselves have identified some of their metaphysical issues as semiotic, a failure to find, outside of mathematics, representations that “make sense” to our imaginations for worm holes, superposition, entanglement and some other weird phenomena which include, of course, the probability densities that describe the locations of sub-atomic particles before they make up their minds where they actually are by getting measured.

 

What I’m curious about is whether the reports from the frontiers of physics, whatever our various capacities are to absorb them, are hitting a sore nerve not simply because of novelties we can’t readily digest, but also because of conundrums we habitually sweep under the rug and don’t want to be reminded of. What do we usually take probabilities to represent and on what basis? What should be clear after that frightening election, is that probabilities, by their design, refer symbolically (that is, as governed by rules) to possibilities and that nevertheless, we conveniently take them as icons referring to future actualities.

In The Implicate Order,[1] most of which he laboured to make intelligible to lay readers, physicist David Bohm lobbied for a full resetting of our acquired frames of understanding for space, time and causation. He recognises the frame, which he calls an “order” and what some of us might call an episteme, as culturally acquired and subject to transformation. Probability is a hinge pin in the reigning “order” and was excluded in the Newtonian order. The scary problem in Newton’s order, not only for Newton’s opponents but for Newton himself was that gravity acts at a distance.[2] Within a century or two, that problem was pretty much swept under the rug and gravity taken for granted. Eventually the problem seemed to be solved with the supposition that gravitons or gravity waves make the connection covering the distance. But gravitons giveth what quantum entanglements taketh away: We still must suffer action at a distance; same dirt under the rug but beneath a different wrinkle.   To think about it hurts a bit now, but if quantum computing starts to be economically useful, we might just agree not to notice.

In life down here on earth, probabilities are derived from past and present actualities, such as a sample of voters’ actual intentions at the moment they were interviewed. Probabilities are, nevertheless, representations of possibilities that may in the future become actualities, or not. What sorts of relations connect the possibilities to future actualities? No physical principles. Up there in the clouds and the physicists’ cloud chambers, probabilities may seem to have a partly different basis as their immediate derivations may be calculated from law-like physics equations rather than directly from data records. This difference is perhaps not so deep. In neither construal, on earth or in the clouds, does anyone see probabilities as somehow exercising a determining influence on outcomes. For now. Maybe our order will change. That is what Bohm was pleading for in proposing an implicate order that embodies the hidden variables which—so far—escape our perception in the explicate order. A short part of his book requires more mathematics of the reader than I can bring to the table, but nothing in the English part suggests that he has a real theory rather than a wish list. From what he says about it, I understand the math part as meant to tighten the screws his wishes respond to, not to give an answer.

When I said, “no physical principles” I was skipping over the option, which may seem consensual in physics or close, of accepting randomness itself as a physical principle. For example, we can say it is a law of physics that a balanced coin without any physical bias will, in the long run, land heads half the time. Much can be derived from that one postulate.[3] But it is essential to recognise that this postulate which currently fits common sense is merely an empirical inference, not coherent as part of an axiom set, and remains totally unexplained. In physics, our episteme continues a shaky relationship with reality.

Of course, I, David Lidov, am not asserting that the postulate of randomness is wrong. I am not endorsing Einstein’s refusal to believe that God played dice. (Goodness, Albert, for an omniscient being, dice would be the best game in town!) All I am saying is either way, our representation of the territory continues to include some degree of mess to which we willingly blinded ourselves in the past and may again.

Except that it is a sign, we can not easily assign an ontological category to probability or to the objects that probabilities refer to, possibilities. Peirce identifies Firsts as possibilities, but the converse does not hold. All possibilities are not Firsts. A stick hitting a ball is a possible second; me hitting a home run is an impossible Third, or at least it has a Third (home run) as a component. A probability is a terrific example of Habit in Pierce’s sense because, although it can be deduced from data about actuals by well studied, empirical rules of thumb, it can not be deduced from rigid physical ‘laws’.

Probability expresses a habit (a Third) that actual events have: for example, the habit of penny tosses to aggregate towards a fifty-fifty split of heads and tails. In the hundred years Peirce’s notion of habit has been on the table, no one I can think of has come up with a better conception for recognizing the coin toss principle or for accounting for the dependability of the probability densities of quantum superpositions. If semiotics has one bone for the metaphysicians of horse races, quantum collapse and multi-universe theories, it might be Pierce’s notion of habit. Perhaps Peirce’s systems in the context of contemporary physics should bring to life for us his fascination with regard to the difference between “real” and “actual”.

From the standpoint of semiotics, if not physics, another model may more graciously distribute the dirt under the rug. The notion of other ‘planes’ or ‘dimensions’ of reality beyond that of our business-as-usual, four-dimensional space-time and quotidian sensory capacities is quite alive in various spiritual communities. We are free to imagine that in those spaces, Platonic forms, morphogenetic fields and probabilities are casting spells of influence on our temporally unfolding world. David Bohm was never dissuaded from such speculation nor were all of his colleagues.
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*David Lidov, emeritus and senior scholar of the Music Department of York University is currently revising for an online publication his Elements of Semiotics, 1999 (a theoretical system which studiously avoided the type of questions toyed with in this essay).

 

[1] David Bohm, Wholeness and the Implicate Order, 1980, Routledge, New York and London.

[2] A short and clear discussion, drawing on Janiak will be found in the second of Noam Chomsky’s Dewey Lectures, p667, Journal of Philosopy, 60:12 (December, 2013).

[3] A cleaner, if vaguer solution should be to choose a class of physical phenomena that we believe to be random, such as penny toss results or Geiger counter click spacing at a specific locale and then speak of another class of events as having a distribution that is equivalent to the first.