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How Obsession with Improbability Closes Scientific Minds
Before autonomous vehicles become an indispensable part of our lives or Mars one of our frontiers, are we prepared to face the accidents inevitable in pioneering new technology and territory? To be blunt, are we capable of preventing another disaster like what happened to Space Shuttle Challenger and managing the next pandemic? Asking these questions may sound inconvenient. However, even driving cars, getting vaccinated, and being X-rayed are not 100% safe due to Chance, “a force assumed to cause [improbable] events that cannot be foreseen or controlled.” (dictionary.com) Therefore, through experience and data, we endeavor to master Chance with probability theory, the science of chance.
Oddly, New Atheism, which is supposed to be at the forefront of science, has become impractical and rigid amidst the proliferation of probability, a framework for solving real problems and promoting scientific minds. Obsessing with the improbable, New Atheism makes liberal use of the concept of Chance to bypass probabilistic reasoning and scientific methods, which favors the probable. On the other hand, recognizing that there are chance elements in both causes and effects makes us scientific thinkers. In addition, the virtues of the ideal scientific thinker can be quantified and hopefully automated and empowered in AI.
Notes
- The usage of Chance as a real force implied in New Atheism will be capitalized and printed in Boldface throughout the rest of the article.
- The title is inspired by “Lost in Math: How Beauty Leads Physics Astray” by Sabine Hossenfelder.
Two Responses to Accidents
As humans, we take two different stances in responding to accidents, depending on our moods or the contexts in which we find ourselves: either assuming “stuff happens” and moving on, or believing “everything happens for a reason” and digging in.
The two stances profoundly clash when we bring them to the debate on abiogenesis, presumably life’s first accident, in which its building blocks were formed on the primordial earth. The explanation of abiogenesis could point to humanity’s place and purpose in the universe, with which New Atheism is most concerned. Did it happen by chance or for a reason? Taking the first stance and refraining from further inquiry, according to New Atheism, are we comfortable regressing to our ignorant and timid past? Taking the second stance and asking reason after reason, according to Aristotelian philosophy and the intellectual tradition of western Christianity, do we agree that there is the final cause, God?
As a result, New Atheism hails the first stance as the way to see ourselves in the universe. However, modern societies, despite outwardly appearing atheistic, are practically concerned with striking a balance between progress and safety, and therefore, have doubled down on the second stance as a discipline that goes beyond emotionally primitive reactions, inquiring “what went wrong” with an accident, followed by “how to prevent it.”
Besides, in today’s data-driven and AI-focused technology landscape, where “every piece of data counts” because “everything happens for a reason,” the first stance struggles to fit in, while the second stance finds itself at home.
Lost in Comedy
Imagine that a horrible tragedy has happened. While the nation anxiously asks for the cause and demands a solution to prevent it in the future, a scientist steps up to address an anxious audience:
We have caught Chance red-handed, reigning over the often-thin line between life and death. You should be awed by the realization that we live on (and are at the mercy of) a planet that is far more unstable than our short lives perceive. We live in a world of mistakes, governed by chance, and it’s not just a matter of Chance that you were born, it’s Chance that helps keep you alive, and it’s Chance that might very well kill you. Our Chance-driven world is a profound revelation. It is astonishing that blind Chance is the source of all novelty, diversity, and beauty in the biosphere. One recourse in the face of such claims is simply to deny Chance. But should we have the courage to accept the pervasive role of Chance? If we are here by accident, not by Design, what are we supposed to do? How might we live in the face of this knowledge? (Carroll, 2020)
The audience is perplexed, murmuring, “who the hell is Chance?” Watching the disturbed audience, the scientist seeks support among comedians:
Next to scientists, the one group of people that seem least inclined to think everything happens for a reason, and that blind Chance governs the world, are humorists and comedians.” [They] have rejected traditional beliefs about humanity’s place and purpose while making us laugh at the absurdity of some of those beliefs. (Carroll, 2020)
A humorist steps up responding to his scientist friend:
When someone says everything happens for a reason, I push them down the stairs and say, ‘Do you know why I did that?
Of course, the comedian tries to impress the audience, who conversely sees mocking a disaster as anything but a comedy.
Troubles with Certainty
Even though I make up this clown-show story, the scientist’s words are taken literally from “A Series of Fortunate Events,” written by Sean B Carroll, an evolutionary developmental biologist. The words of the comedian are from show host Stephen Colbert.
These quotes exemplify New Atheism, or what I call Chance Atheism, inspired by Neo-Darwinistic Chance, an over-simplified abstraction of the universe’s probabilistic nature spawning from our ignorance. Positioned as an advocate for science, New Atheism takes a hardened stance against its “superstitious” and “irrational” ideological foes in education, politics, and media. As seen through Carroll’s words, New Atheism takes issue with people believing, for the sake of certainty, that everything happens for a reason, or technically speaking, every effect has a cause. However, as mathematician Emile Borel said
No one would be able to go on living if he did not possess a few practical certainties regarding himself, his environment, his home, the town in which he lives, and so on. (Borel, 1963, p.117)
The New Atheists dismiss such a need for practical certainties as digressive, concerned it allures people to explain everything away with God. However, it is also what motivates us to seek patterns and regularities that establish scientific certainty. Hypocritically, Carroll pleads his readers to stop believing in and looking for reasons. At the same time, he explores the probable causes behind which a single ancient genetic toolkit generated the full spectrum of biological forms from fruit flies to ourselves in his “Endless Forms Most Beautiful” (Carroll, 2005), one of my favorite books on evolutionary biology.
How has this double standard developed? Do we advise ourselves to “thank our lucky stars that we are here at all’’ (a favorable review of the “A Series of Fortunate Events”)?
Chance and Necessity
Nobel-winning molecular biologist Jacques Monod arguably inspired New Atheism. In his seminal book “Chance and Necessity” (Monod, 1971), “necessity” refers to an effect inevitably following a cause, such as the fact that an enzyme must function according to its structure. Chance concerns an effect that might be fraught with too many unexplained causes or subject to free will. For example, a bacterial cell seems to have free will to “choose” whether or not to synthesize an enzyme responding to the surroundings. Such a choice is, in turn, a necessity governed according to the high-level free will of the bacterium as a whole, which makes choices through chance genetic mutations. Notice how Monod refers to free will as Chance.
Thus, the evolution of life involves intermixed instances of Chance followed by those of necessity. This finding was a massive revelation to Monod. Since Chance appears to demand no cause or reason, there is no backward causation path to God, the final cause, or the first cause if we follow forward causation. From here, Monod jumped to the conclusion that abiogenesis must have been a pure accidental emergence of amino acids, following which earth necessarily evolved into an increasingly complex and diverse biosphere. In a confessed ideological generalization, he asserts
[Chance] alone is at the source of every innovation and all creation in the biosphere. Pure [Chance], absolutely free but blind, at the very root of the stupendous edifice of evolution. (Monod, 1972)
Monod believes “the most important scientific results have been to change the relationship of man to the universe.” Neither a scientific study nor a linguistically precise definition of Chance concerns him, despite the central role of Chance in his thesis.
Monod’s understanding of Chance, as a real and supreme force, certainly would not listen to prayers. More importantly, we could not appeal to it or expect it to explain. Chance would be no different from an irrational and unpredictable God who rules without giving reasons.
So, what can we say more about Monod’s all-powerful, all-encompassing, God-like Chance? Carroll tries to define Chance as:
By Chance, I mean a rare, unpredictable, or random event, or one that entails so many variables or forces that are near enough to be random. (Carroll, 2020)
This definition begs the question: Should we consider it Chance that we predict, on average, a newborn has a not-so-rare 48:52 chance of being a girl?
The Frequentists
One may wonder how New Atheism’s obsession with improbability, such as The Blind Watchmaker analogy for evolution (Dawkins, 1985), leads to its assertive narrative about Chance. Before further exploration, let’s try to measure the rareness (or frequentness, so to speak) of Chance as a probability, a numerical measure taking a value between 0 and 1, with 0 meaning impossible, and 1 definitive. There are two camps of probabilists: the Frequentists and the Bayesians.
The Frequentists evaluate the probability of an event by the frequency of how often it occurs over many observations. How does a Frequentist know a phenomenon, such as males newborns outnumbering females, is statistically significant and not caused by sampling errors, human biases, and other unknown factors that we collectively call chance? He strives to keep himself checked by making the null hypothesis the adversary, suggesting the phenomenon in question is nonsignificant or happening by chance. The Frequentists refer to this process as Null Hypothesis Significance Testing, which is the foundation of the Scientific Method of Karl Popper (Popper, 2002).
In the case of the sex ratio of newborns, the null hypothesis yields an equal chance of having more males or more females. Given the null hypothesis, the Frequentist calculates the p-value, the likelihood of the phenomenon under study, for example, male newborns outnumbering females. He also sets a threshold for the p-value, for example, .05, below which he would reject the null hypothesis, thereby proving the alternative. Physician John Arbuthnot used 82 years of birth records in London to calculate the p-value as one divided by 2⁸², or 4,836 sextillion (1 followed by 21 zeros). The male newborns outnumbered the females for each of the 82 years. This study and later ones have rejected the null hypothesis. Accordingly, they established a ratio between female and male newborns consistently at 48:52 in a sufficiently sizable human population across races, geography, and time.
The Bayesian
Another view of probability, named after Reverend Thomas Bayes, is what French polymath Pierre-Simon Laplace referred to as “the probability of causes and future events, derived from past events.” Laplace’s fellow countryman Borel described to what extent, on a scale from 0 to 1, one was willing to bet on his belief (McGrayne, 2011). The idea can be represented by Bayes’ rule as shown in its most basic form for only one probable cause:
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For a hypothesis that a probable cause C is true, P(C) and P(C|E) are the old and new degrees of how much we believe in C, respectively, before and after the effect E is observed. Hence they are referred to as “prior” and “posterior.” The likelihood P(E|C) represents how likely it is that C has caused E. The Frequentists reserve the use of probability for events only. In contrast, the Bayesians use probability also for degrees of believability.
Bayes’ rule revises how much we believe in a probable cause according to the likelihood and our prior belief. After one iteration of Bayes’ rule, the resulting posterior becomes the new prior in the next iteration. Notice that given an effect, updating the posterior requires considering both the likelihoods given the hypothesis being true and false.
Bayes’ rule summarizes how we interact with the largely unknown universe. We propose probable causes to explain observed effects, which are necessarily imperfect due to noise, corruption, or partial interpretation from our incomplete knowledge. Thus, the Bayesian view of probability requires a reasoner to
- Admit ignorance by expressing it with the prior
- Recognize data imperfection by describing it with the likelihood
- Account for the counter hypothesis by including its likelihood and the prior in the posterior calculation
Practical Certainty
How exactly do a Frequentist and a Bayesian go on living and satisfy their needs for practical certainty if the former forever challenges himself with null hypotheses and the latter constantly evaluates probable hypotheses? Geophysicist, Harold Jeffreys, describes how acquisition and accumulation of scientific knowledge lead to practical certainty:
Every scientific advance involves a transition from complete ignorance, through a stage of partial [and incomplete] knowledge based on evidence becoming gradually more conclusive, to the stage of practical certainty. (McGrayne, 2011)
Borel depicts how we find practical certainty in “the single law of chance,” or simply Borel’s Law, as follows:
[Improbable] events with a sufficiently small probability never occur, or at least we must act, in all circumstances, as if they were impossible. (Borel, 1962)
Borel’s Law applies to chance events, such as a lottery or even random microscopic behaviors in a gas. Borel provides different threshold values for “sufficient smallness” on four scales: human, terrestrial, cosmological, and super-cosmological. For example, though aware that there have been and will be winners, a sane person will not bet his living on winning a jackpot since the likelihood of winning by chance is sufficiently tiny on the human level. However, a person obsessed with his winning odds might still bet his life savings despite looking insane. On the other hand, no personal preference or opinion can override scientific laws such as Newton’s Laws of Motion and the Second Law of Thermodynamics since the probability of violating them is negligible on the cosmological or super-cosmological scales.
However, what happens when a presumably “improbable” event on the cosmological or super-cosmological scales occurs, such as male newborns outnumbering females for 82 years in a row? We should use the Null Hypothesis Significance Testing to challenge the chance assumption leading to the “improbability.” Seeing the sufficiently small probability as a p-value below any conceivable threshold ensures that there must be some reason behind the event. Hence, we can amend Borel’s Law as:
When a presumably improbable event occurs, we must challenge the chance assumption and look for probable non-chance explanations.
When a presumably improbable event occurs, we must challenge the chance assumption and look for probable non-chance explanations.
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Here is one attempted counter-example to Borel’s Law in the debate over how the Great Sand Dunes National Monument was formed. The New Atheist author assumes that each grain of sand could choose whether to land in one particular, tiny area of the valley. He concludes that the probability “that all these grains of sand drifted into the given zone is 16 orders of magnitude smaller than the threshold for impossibility stated in Borel’s Law” and erroneously claims he disproves Borel’s Law. The author should have considered the amended Borel’s Law and agreed that there must be some non-chance explanation.
“If it is not Chance, then what is it?” a New Atheist might jump up. “Are you suggesting that it is God?”. According to the New Atheists, the answer to their questions must be either Chance or God, and the latter is forbidden. We can indeed find a non-Chance explanation for the dunes formation without prompting a Chance vs. God debate.
According to New Atheists, the answer to their questions must be either Chance or God, and the latter is forbidden.
Obsession with Improbability
The narrative of the amended Borel’s Law directly opposes that of the New Atheists, who insist on improbable events being positive evidence of the cosmic power of Chance. Facing an improbable event, a New Atheist freezes in amazement without questioning the improbability. We can attribute this obsession with improbability to Monod, who claims:
This central concept of modern biology [Chance] is no longer one among many other possible or even conceivable hypotheses. It is today the sole conceivable hypothesis, the only one that squares with observed and tested fact.
Yet, Monod omits the following basic assumptions in probability:
- There should be at least two hypotheses for any scientific study: the null and the alternative hypotheses, according to the Frequentists.
- For any hypothesis, there should be at least one other hypothesis, the counter hypothesis, according to the Bayesians.
Nevertheless, the Chance Hypothesis of New Atheism, according to Monod, follows:
Among all the occurrences possible in the universe, the a priori probability of any particular one of them verges upon zero. Yet the universe exists; particular events must take place in it, the probability of which (before the event) was infinitesimal. (Monod, 1972)
What exactly is the “a priori probability”? We can refer to Monod’s hypothesis as the null hypothesis and call the “a prior probability” the p-value. Then, according to probability practice, Monod effectively provides no alternative hypothesis and accepts the null one, despite the infinitesimal (improbable) p-value, presumably below any practical threshold.
When under criticism for promoting the improbable, New Atheism often blames the critics for its problem: the Chance Hypothesis. In defense, it claims that the critics overlook how life, through Natural Selection, climbed the evolution staircase. However, what would be the null hypothesis for testing the staircase theory? Well, the null hypothesis would say that the staircase happened by chance and is nonsignificant. It is none other than the Chance hypothesis! If a New Atheist follows the Scientific Method of establishing a theory by testing the corresponding null hypothesis, he has to choose between Chance and science or playing with a double standard.
A New Atheist has to choose between Chance and science or playing with a double standard.
Closure of Scientific Minds
From both a Frequentist and a Bayesian perspective, observed facts, which are confused as definite proof for a hypothesis in New Atheism, have chance elements in them that can potentially “disprove” the hypothesis. We should discard a hypothesis that renders the observed facts improbable, instead of upholding it.
Unaware of the difference between hypotheses and observed facts, Richard Dawkins, one of the most outspoken New Atheists, remarks:
Evolution is a fact. Beyond reasonable doubt, beyond serious doubt, beyond sane, informed, intelligent doubt, beyond doubt, evolution is a fact. The evidence for evolution is at least as strong as the evidence for the Holocaust, even allowing for eyewitnesses to the Holocaust. (Dawkins, 2010)
However, one of the most distinguishing characteristics of modern science is the humble admission of ignorance. According to Popper, in the spirit of the Frequentists:
… whenever we propose a solution to a problem, we ought to try as hard as we can to overthrow our solution, rather than defend it. (Popper, 2002)
Likewise, Yuval Harari says, in the style of the Bayesians:
[Modern science] accepts that the things that we think we know could be proven wrong as we gain more knowledge. No concept, idea, or theory is sacred and beyond challenge. (Harari, 2018)
Thus, science-denial, which is how New Atheism likes to label its critics, is an oxymoron. On the other hand, dogmatism can be in any name, including science. The desperation to abolish the final cause ends up making Chance New Atheism’s final cause.
The Ideal Scientific Thinker
The ideal scientific thinker, who has a different view of Chance and necessity, would say
Because we can seldom be certain that a particular cause will have a particular effect, we must be content with finding only probable causes and probable effects. (McGrayne, 2011)
In other words, Chance is not a counterpart of necessity as Monod, Dawkins, Carroll, and their colleagues would like to see. Instead, there are chance elements in both causes and effects.
There are chance elements in both causes and effects.
Mathematicians refer to the process of exploring probable causes that lead to observed effects using Bayes’ rules as Plausible Reasoning (Polya, 1954) (Jaynes, 2003). It explains almost a full range of our mental activities seeking patterns and regularities from ancient survival instinct and common sense to detective skills, math & science geniuses, and engineering wonders. There has been an unbroken line of plausible reasoners from hunter-gatherers to modern-day scientific thinkers.
If our hunter-gatherer ancestors had only thanked their lucky stars without using plausible reasoning, we would not be here at all. As believing everything happens for a reason is what made us humans, recognizing chance elements in both causes and effects makes us scientific thinkers. Today, a scientific-thinking atheist will not jump to a choice between Chance and God. Likewise, a scientific-thinking believer does not let her faith get in the way of her quest for intermediate causes.
If our hunter-gatherer ancestors had only thanked their lucky stars without using plausible reasoning, we would not be here at all.
In my article, The Limit of Logic and the Rise of the Computer, I described the quest of the perfect logical thinker as answered mathematically in symbolic logic. In the same token, the following virtues of the ideal scientific thinker find their mathematical counterparts in probability:
- Humility in admitting ignorance
- Honesty in recognizing sense imperfection
- Open-mindedness in accounting for alternative views
We will see if the industry perpetually embeds these virtues in AI to keep us rational and honest about ourselves so that we can fulfill the quest of Jaynes:
How could we build a machine which would carry out useful plausible reasoning, following clearly defined principles expressing an idealized common sense?
Bibliography
Borel, E. (1962). Probabilities and Life (M. Baudin, Trans.). Dover Publishing.
Borel, E. (1963). Probability and Certainty. Walker and Co.
Carroll, S. B. (2005). Endless Forms Most Beautiful: The New Science of Evo-Devo. W. W. Norton & Company.
Carroll, S. B. (2020). A Series of Fortunate Events: Chances and the Making of the Planet, Life and You. Princeton University Press.
Dawkins, R. (1985). The Blind Watchmaker. Norton & Company, Inc.
Dawkins, R. (2010). The Greatest Show on Earth: The Evidence of Evolution. Free Press.
Harari, Y. N. (2018). Sapiens: A Brief History of Humankind. Harper Perennial.
Jaynes, E. T. (2003). Probability Theory: The Logic of Science (10th ed.). Cambridge University Press.
McGrayne, S. B. (2011). The Theory That Would Not Die. Yale University Press.
Monod, J. (1972). Chance and Necessity: An Essay on The Natural Philosophy of Modern Biology (A. Wainhouse, Trans.). Collins.
Polya, G. (1954). Mathematics and Plausible Reasoning. Princeton University Press.
Polya, G. (1954). Mathematics and Plausible Reasoning. Princeton University Press.
Popper, K. (2002). The Logic of Scientific Discovery (2nd ed.). Routledge.
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