The Flaws of Probability
by Asa Boxer
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In “What is a Scientific Fact? Laying Bare the Heuristics,” I explained that mathematical probability could not establish any laws of physics or nature because probability is actually a clever workaround (heuristic device) for what we do not know and cannot predict. The best it can do is give us a roundabout purchase on phenomena we perceive as random and involving chance or luck. There is a reason for this limitation.1 Probability was developed to help describe the phenomena of gambling. According to Britannica, probability originated “in the study of gambling and insurance in the 17th century.” A further entertaining bit of trivia from Britannica:
The modern mathematics of chance is usually dated to a correspondence between the French mathematicians Pierre de Fermat and Blaise Pascal in 1654. Their inspiration came from a problem about games of chance, proposed by a remarkably philosophical gambler, the chevalier de Méré.
Any application of probabilistic math to gambling makes a decent fit, but still cannot reveal the outcome of the next spin of the roulette wheel or roll of the dice. Such math can represent, augment and test common-sense observations about the likelihood of rolling another double six or of a ball falling into another red slot with a kind of accuracy that helps the house establish betting rates and gamblers decide whether the bet is worth it. When you think about it, though, probability isn’t establishing any laws; it merely enhances one’s sense of the odds.
The most troubling problem is that this gambling math has been repurposed for other uses in science where it has very little relevance and arguably muddies more than it clarifies. Since pointing out these limitations, I have continued to stew over probability. I’ve been reading Stephen C. Meyer’s Signature in the Cell: DNA and the Evidence of Intelligent Design, where Meyer spends a lot of time considering the probability arguments supporting Darwinist notions of the role of chance in evolution. Meyer makes a distinction between origin of life science (or first-life) and evolution; the latter examines historically progressive, biological phenomena, while the former works to understand a one-off event.
It’s been a brain-tickling read, Meyer’s careful critique of probability as a tool to support the theory of undirected processes in creating the first life. He takes probability on its own terms and shreds it; in fact, disproves the role of chance and accident in the assembly of DNA, RNA and the information coding and decoding that goes into nucleic processes. That’s right. The odds are against the information-rich computing system of life having come together by mathematically defined, random processes. Many fascinating ideas emerge from Meyer’s consultations with some of the world’s leading probability mathematicians, one of which I’ll share at the end of this barstool bit.
But the overall takeaway I’ve had is that when bundled with statistics and applied to things like populations, economies, moral actions, happiness and public policy, evolutionary theory, quantum physics and climate modelling, the math is misapplied. What was a clever workaround tailored to one set of phenomena to begin with is now repurposed to apply to categorically different phenomena. Not only that, but the application is often reversed (as in Neo-Darwinism and big bang theory), starting with the outcome (the now) and imagining or (predicting. . . or should it be postdicting?) the origin; then working up the invented origin by hypothetical and probabilistic processes to the presently observed state. (Which sounds a lot like confirmation bias through storytelling.) The result is a bad fit and impositions of assumptions regarding the phenomena that no one would assume were it not for the math.
This clumsy cannibalising goes further to my point that present-day science erroneously imposes its models on phenomena, trying to make the phenomena fit the models. This cognitive error gets so far out of hand that scientistic persons (including many scientists) often forget that the phenomena come first and models are secondary derivations. Instead, they posit that their models precede the phenomena with underlying “laws.” On the heels of this epistemological error, they attempt to make various phenomena fit their models by dreaming up ad hoc phenomenological attributes like dark matter, virtual particles, wavicles, missing links and parallel universes.
More specifically, the application of probability to a phenomenon assumes the phenomenon is a game of chance in some kind of casino. Nonsense? No. Whether we’re talking big bang or Darwinist evolution, the operating assumption that allows us to apply probabilistic concepts in the first place is a “laws of Nature directed” but otherwise random knocking about of energy and matter or a number of other undirected collisions. But in what sense “random”? In the sense that no conscious intelligence is directing things—not externally from beyond the cosmos, and most definitely not centrifugally from any internal agency in any of the myriad life-forms that inhabit our planet. Human consciousness is an impossible fluke, as unlikely as flipping a coin and getting one-hundred heads in a row.
The assumptions thicken. The idea that the universe has developed into what it is by an accumulation of chance incidents is a casino analogy that recruits the notion of do-overs, repeated turns at the roulette or craps table. This is where we impose the model, suggesting the existence of multiple universes for each possible outcome. These universes however are phantom vestiges arising from the math. There’s nothing wrong with considering the possibility. But you ought to be aware when doing so that you’re no longer investigating a phenomenon, but instead a dreamt up fiction, an intriguing fallout of mathematical thinking that is likely just a blind alley.
In reality, we ought to assume that the universe we occupy is the only one to have developed. In any event, it’s all we have to investigate (at present). Probability sprouts imaginary universes. It’s a tool to dream with. And it’s productive in that domain. Too productive. It plays too big a role in shaping our worldview and our behaviour.
How does probability get us anywhere, scientifically and interpersonally speaking, if it necessarily imposes these hypothetical alternatives that never happened or will never happen? That’s not really science anymore. It might be mathematically directed philosophy, sure. But science? Granted, its measures can glean keen and useful distinctions when applied in numerous rational endeavours. But stats and probability make up much less of the picture than popular scientism admits.
One might argue that the vast variety of species, elements and molecules points to a random distribution or at least fits with the idea. Such varieties as we observe are the outcomes of cosmic do-overs at a roulette wheel made of matter and energy. Accidental or undirected combining and recombining of these limited elements by happy coincidence evolved into ever more complex roulette wheels from the original simple one.
Not a bad excuse to apply the mathematics of probability to notions of development and evolution… See where it sticks. That would lead to some tentative hypotheses. Okay. But we’re always left with the problem of the original roulette wheel. At some point, we’re going to have to face that issue if we hope to actually resolve the question. What sets first-life thinking apart from evolutionary thinking is that the origin of life is a single instance (supposedly): the emergence of the first amoeba. How did the first organism organise itself? By agency or accident? If the human mind is imposing the probability game by analogy (a likelihood considering it’s after the fact), how do we know it corresponds to the actual shape of the phenomena? And if we are in fact reading the phenomena for what they are, then how did the cosmic roulette wheel come together in the first place?
One of the insights I’m after is that the mathematics of probability cannot support accidentalism, or the idea that the world and life and consciousness as we know it is all a big accident arising from undirected processes.
This is not a failure of probability. (We will get to its failure in a minute.) It’s a misapplication of the heuristic. How do we know? Because the reasoning breaks down into self-contradiction. Rather than assuming accidental processes, probability assumes design. It assumes a game, a framework, an aim, a purpose, a vector of potential and significant outcomes. How do we get a meaningful result from a probabilistic measure if we don’t presume a significant possibility? There needs to be a casino with games designed to yield an array of certain specific results, right? There’s no probability measure for throwing the roulette ball out the window or the craps dice into a toilet (unless we change the parameters of the game). To impose the measure, we must delimit the game, and in doing so, we set up a designed context. (Same goes for game theory.)
Rather than assuming accidental processes, probability assumes design. It assumes a game, a framework, an aim, a purpose, a vector of potential and significant outcomes.
Unwittingly, then, those atheists who insist on accidentalism as a principle of cosmic and evolutionary development, introduce principles of design to make their point when they recruit probabilistic measures. What are dice without markings? What is a roulette wheel without numbers and colours and a ball? In other words, we need to assume significant context to even get the probability ball rolling. The infinite regress of development-by-chance hypotheses is stupefying. The idea that a study of chance reveals definite directing laws of nature (the “laws of probability”) turns accident into necessity—a fundamental contradiction. I am aware that some (like Richard Dawkins) have argued that chance is not accident because governed by the laws of probability. But they decide to stop thinking there. Implications go out the window, and they wind up expressing a belief in accidentalism anyway.
And now. . . for that probabilistic anomaly I promised to share earlier from Meyer’s book. We have this through mathematician, William Dembsky: he pointed out that if you were to flip a coin one-hundred times and record the sequence of Hs and Ts, you would wind up with a unique series of outcomes; in fact, so unique that the odds of getting that particular sequence—1 in 2100—would be the same as getting one-hundred Ts or one-hundred Hs in a row. Meyer uses roulette to help elaborate his point, explaining that the odds of winning 100 times in a row are 1 in 10158. But if you were to record the series of outcomes of 100 spins of the wheel, the odds of that particular sequence of outcomes occurring would be exactly the same as the odds of winning 100 times in a row (Meyer 182-3).2
In other words, according to probability, we are always participating in a sequence of events that is highly improbable and unlikely. Intriguing. And I think most of us would tend to agree on that point. But the probabilistic analogy is unrealistic. The math recruits a fiction to confirm a truth. How does that happen? Let me explain.
Common sense tells us the math here doesn’t agree with experienced reality because we will never witness the phenomenon of coin flipping result in one-hundred consecutive tails or heads, never witness the phenomenon of a roulette player winning at 100 consecutive turns of the wheel. These are fictional hypotheticals. The math however insists, Why not?! Any sequence of 100 spins or flips is equally unlikely. Hmmm. Looks like we may be using the math to recruit a fiction to make a rhetorical point, not a mathematical one.
My barstool intuition tells me to probe my common sense here to explain how we know with such certainty that we will never witness 100 consecutive Hs. I think we understand at some level that the combinations and recombinations we’re going to get are restricted by an incommensurable element, like the infinite, non-repeating decimals we find in π, φ and ψ. These incommensurable numbers are key to understanding the unfolding of Nature. They are also key to describing electromagnetic phenomena. And as I’ve pointed out before, these numbers indicate a gaping flaw in our mathematical heuristics because we can only approximate them by present means.
One last, sobering observation from the barstool: probability distorts our thinking about the world and our place in it. Nevertheless, probability and statistics rule the developed West like a primitive god. Our economies are built on them. Our education. Our sports. And via the insurance companies, we are made to rent our holdings and guard them like they were our own. And your property better be up to code. Your concert on the farm too. That fence along the gorge marks the insurance man’s territory. He oversees the wilderness… the banks. He regulates the traffic the way He regulates the solar system, the galaxy, the cosmos. Your retirement. He taketh and hopeth never to dispense; and where He can, He wheedleth out. He rules over the living and the dead. He replaces what is taken by earthquake, flooding, hurricane and fire. (*But He doesn’t cover acts of God or Big Pharma.) He is measuring the height of your balcony railings. He wants to know what you eat, when you last saw a doctor. How’s your cholesterol? He knows what you are pooping. We live in the insurance man’s casino where we are the games; where we are the thing they’re betting on. And the buy-in—not to play, but to be played—is mandatory.
Asa Boxer’s poetry has garnered several prizes and is included in various anthologies around the world. His books are The Mechanical Bird (Signal, 2007), Skullduggery (Signal, 2011), Friar Biard’s Primer to the New World (Frog Hollow Press, 2013), Etymologies(Anstruther Press, 2016), Field Notes from the Undead (Interludes Press, 2018), and The Narrow Cabinet: A Zombie Chronicle (Guernica, 2022). Boxer is also a founder of and editor at analogy magazine.
For the record: by pointing out the flaws of probability, I am not denying the powerfulness and utility of the tool. My aim is to suggest that we diminish our reliance on it, our treatment of it as a central doctrine.
Meyer, Stephen C.. Signature in the Cell: DNA and the Evidence for Intelligent Design. New York, New York: HarperCollins, 2009.