Miracles and Statistical Probability

 

    

    Years ago, I was in the driveway of my parents' house in Auburn, Alabama, staring at the front tag of my father's old Pontiac when it spoke to me. Alabama issues only one tag, leaving the front bumper available for personal messages, and Daddy (like almost everybody in Auburn) was a football fan, so the tag had War Eagle in orange lettering on faded blue field. It was a very particular tag, the blue faded almost pastel and a lower corner bent--evolved since its exit from a factory. 

        What prepared me to hear the tag's message? I don't know, but the message was as clear as it was unfathomable. In all the vast flow of time, from the Big Bang until then, what were the odds of a faded, bent tag reading War Eagle (a team cheer of untraceable origins) at this exact point on earth and in this relation to all the rest of the planet, the galaxy, and the  universe around it? How did War Eagle find itself in this context of leaves on the trees, grass blades bent this way or that, gravel embedded in concrete, and dirt below it down through magma to liquid iron at the earth's core?

What were the odds? Essentially zero. The probability was immeasurably close to infinitely small that all of this should exist as it did, signified by an absurd six-by-twelve plate of bent aluminum declaring in fading paint an enigmatic phrase in an arbitrary code called English. And at that exact moment. Normally, events this astronomically improbable are called impossible. And yet, there it was. 

As I realized this, living leaves flickered in the wind and a dead one skated across the driveway. A car passed on Dumas Drive, and I knew the earth had rotated a fraction of a degree, changing the tag's relation to the sun and Alpha Centauri. Another world-state had been born, dependent on the previous impossible one, and so also impossible. Everything was impossible, and yet everything existed. The War Eagle tag was a miracle. As a rule, we feel such existential wonder about major transformations, relationships or illnesses, but that blinds us emotionally, I think, to the ordinariness of the enigma. Whatever guides our lives for good or ill guides equally a faded football tag, a windblown leaf, and the fall of a sparrow (Matthew 10:29).

A kind of reply to this becomes clear if we stop looking through the lens of our egos, our desires, and our culture. If in a poker game (perhaps hard-up for money) you are dealt a straight royal flush, you may consider this unlikely, but in reality all other particular hands are equally unlikely. There is no probability difference between this hand and any other set of five cards. A given odd combination of numbers in various suits seems more likely than a perfect flush, but this illusion is a product of social rules that lump together thousands of low-ranking hands. It's culture, not reality. The probability of any specific poker hand is 1/2,598,960, but the probability of being dealt some hand in a deal is 1/1. Similarly, the likelihood of the War Eagle tag in that driveway was all but nil, but, given a material universe, the presence of something there (if only a spacial relationship) was assured.

Another model for life probabilities is the random walk. I simulated this as a teenager riding bikes with a friend around Auburn and flipping a coin at every intersection to see where we'd end up. At the endpoint of the game, when we got tired or lost interest, we were always somewhere, but it was impossible to predict where. It's common fallacy to try to calculate the odds that our species would come into being by a process of evolution and conclude that such an outcome is impossible, thus miraculous. Certainly, such an outcome seems highly unlikely, miraculous in the sense that a War Eagle tag was. But given evolving life in a complex ecosystem--and, in a world of change, evolving is inevitable--the eventual emergence of some complex species is all but guaranteed. A human being may be wildly improbable (like a straight royal flush or returning home at the end of a random walk), but some "advanced" species is to be expected, and, whenever it emerges, it will see itself as the miraculous endpoint of the process.

An itinerate laborer wandering from town to town may eventually settle in a town when his wanderlust fades and say to himself, as he sits at the door of his home, that he is lucky. What are the odds that, after all his zigzagging across the world, he should land in such a comfortable spot? My suggestion is, if he doesn't die in transit, such an outcome is inevitable. He wouldn't stop (not for long) in a barren field or any other place that isn't comfortable. He'll try to keep moving until he achieves a match that, looking back at all the wandering, may seem miraculous. Even if some wanderers are unlucky and some ecosystems hostile, the odds tilt in any surviving wanderer's favor. But again, even though an optimistic ex-hobo may feel that his final home is his providential destiny, it's a town like hundreds of others. Which one impossible to predict. 

Albert Einstein is supposed to have said (but probably didn't), “There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.” But if a miracle is, as often defined, a divine intervention in the natural order, then, logically, if everything is a miracle, then miracles are the natural order, and nothing is. It seems that "everything's a miracle" is about attitude, not logic. It mandates wonder and gratitude that (like a War Eagle tag) something astonishingly improbable has happened. "A hundred million miracles are happening every day," wrote Oscar Hammerstein, and, if faded blue car tags qualify, that is a low estimate. Life may indeed be best lived by waking up each morning with a sense of mystery, but if everything is miraculous, then what about the more assertive sense of the word? What about turning water into wine or rising after three days dead?

A few years ago, I read a magazine article about the widespread belief of Americans (over 70 percent) in miracles. I would be among the skeptical 20-odd percent because I would understand the poll to ask if I expected (or was even comfortable with) sudden violations of natural law--something like a great stone floating in the air or surface tension holding up a my hiking boots. That sounds chaotic and threatening to me--agreeable only if I assume the chaotic force is on my side. But there are millions of people on earth with conflicting interests, and I have no reason too think that I am a Chosen One. If two sides pray for victory in a battle and one wins against all expectations, the winner may well celebrate a miracle, but what about the loser? The suspicious thing about miracles is that they are always pleasant to whoever calls them miracles, and we may recall Marcus Aurelius' warning that believing that whatever pleases is us good is the "beginning of sin" (9:4). There's no popular term for a negative miracle, a unexpected divine smack-down. Anyway, interviewees in the magazine article said they believed in miracles because it gave them hope, which suggests that they expected to be Chosen Ones like the winning army. A "miracle" is seldom an enemy's answered prayer.  As Alexander Pope wrote, “Hope springs eternal in the human breast;/ Man never Is, but always To be blest."

The foundational treatment of miracles in modern philosophy is in David Hume's An Enquiry Concerning Human Understanding, where he defines miracles as violations of natural law (or humanity's "uniform experience") and concludes that no testimony in favor of a miracle is credible unless its falsity would be even more miraculous than its truth, a staggeringly high bar. Second and third-hand stories from scripture or legend--from what is sometimes called the Age of Miracles--are clearly not credible, Hume concludes. Any credit given to them would be raw faith, not based on good evidence, and even if a seeming miracle were established to have happened, there would remain the probability that it was an artifact of our imperfect and evolving understanding of natural law and only seemed to violate nature (Section X, Parts 1-2).

In Jesus Before Christianity (pp. 40-43), Albert Nolan explains that Hume's definition would have made no sense to Jesus' contemporaries, who had no concept of natural law to be violated. To them, miracles were merely unusual, wonder-provoking events in a world where everything that happened--mundane and wonderful alike--was understood to be part of God's ongoing creation. Think of miracles as purple passages in a seamless God-text. Given a distinction between ordinary wonders and "signs" amazing enough to prove his divine mission, Jesus refused to give the Pharisees the latter (Mark 8:11-13), just as he rejected Satan's challenge that he throw himself from a high place because it would be putting God to the test (Luke 4:12). Many of Jesus' miracles depend not so much on his personal powers as on the faith of other people. He couldn't perform miracles in his hometown because his neighbors lacked faith in him (Matthew 13:58).

In fact, as Nolan points out, many of Jesus' miracles resemble the "parting" of the Sea of Reeds in Exodus (explainable as tide) in they are not so much violations of nature as wonderful coincidences, conceivable in the natural order. Stormy seas do eventually calm, sometimes quite suddenly, so the miraculous aspect of the Jesus' calming the sea is all in the timing (Matthew 8:23-27, Mark 4:35-41, and Luke 8:22-25). And miraculous cures like those attributed to Jesus in the gospels have, of course, been replicated in recent times, sometimes in front of hundreds of witnesses, so they (or the appearance of them) obviously don't violate natural law. Some cures are fraudulent, of course, especially when performed as shows by professionals, but there's no reason to suspect this in every case. Illnesses, like storms at sea, may into spontaneous remission, in which case coincidence is a natural explanation. Also, belief, not of a religious kind, explains the well-documented effectiveness of placebos and the sudden relief of psychosomatic disabilities. Finally, hypnotic suggestion--call it faith--can mask chronic symptoms temporarily, and no testimony is given that scriptural cures were permanent. 

        So nearly any given gospel healing can be explained by natural processes, though the clustering of them in the gospels is dense that it seems all but impossible. Father Nolan suggests that the writer of Mark supplemented the existing sayings of Jesus by interviewing peasants who had heard oral stories of his ministry and that he remained "faithful to his sources" so that, after years of retelling, they "include embellishments and exaggerations" (pp. 42-43).

R. F. Holland argues for what he calls "the contingency concept of the miraculous." An event may be miraculous even it its elements, taken separately, don't violate natural law. In his thought experiment, a boy in a pedal car becomes stuck on a railway crossing on a blind curve. His mother hears a fast train approaching and runs toward him, but before she can reach him, the train rounds the curve. Inexplicably, its brakes are already screaming, and it stops a few feet from the boy. The mother celebrates a miracle, but nothing supernatural happened. The engineer suffered a stroke and released the throttle at the exact time for the automatic brakes to engage when they did. It was only a coincidence, or was it? The mother will always believe it was miraculous.

Most coincidences mean nothing, Holland writes, but miraculous ones carry a burden of "something which God is thanked for or thankable, something which has been or could have been prayed for, something which can be regarded with awe and be taken as a sign or made the subject of a vow" (pp. 373-374). Carl Jung calls such events synchronicities and, like Holland, regards them as significant. A friend had a dream of his grandmother saying goodbye the night she died many miles away. There's nothing necessarily paranormal here given that she revealed no verifiable secrets. He knew she was in bad health and could have (indeed may have) dreamed about her on other, less significant nights, but I would find such a dream awe-inspiring if it happened to me. The difference between a contingency miracle and dumb good luck may be religious faith, so that an event as common as a near-collision in traffic may qualify. In the same situation a skeptic may react, "Bummer! I almost totaled my car!" while believer celebrates a miracle.  

"Do you feel lucky tonight?" I heard this on the shuttle from my motel to a casino the same night that I fed ten dollars into a machine and won over three hundred. When I heard the question, I didn't understand it, but after I saw the cherries line up and heard the clang-clang-clang of fake silver dollars slamming into the tray of the old-fashioned slot machine, it was clear enough. For days afterwards, clang-clang-clang echoed in my mind, and I felt (no other word for it) lucky. It was like a chemical high, the basis of gambling addiction. I recognized this and played no more that night. "Do you feel blessed? Do you feel miracles are about to happen?" Yes, to those questions, I think, may produce a similar high and even a self-fulfilling prophecy. 

I recall an article in The Skeptical Inquirer that argued in secular terms that optimists tend to be more successful because they are more open to opportunities. Of course, they lose more often than pessimists, but (to put it in writer's terms) a manuscript you don't submit is never accepted. There are practical advantages in feeling like a Chosen One with a Godfather making offers you won't refuse, some of which may even get you into the Promised Land. Nice work if you can get it. I have known such irrepressible Christians, and maybe the optimist's advantage is reason enough to believe in personal miracles--even in flat-out, nature-violating, gifts-from-the-Lord.

With my distrust of ego (plus an ingrained inferiority complex from childhood), I can only envy such happy believers and look for a back door of reflection and humility. And I do see another reason why people need to believe in miracles, in this case nervous near-materialists rather than the Chosen. If you see the world as a rigid, indifferent machine, then you may be desperate for blessed exceptions, perhaps after a criminal conviction or a cancer diagnosis. I see the world another way. 

There is, of course, a consoling crust of reliability in nature. Objects don't fall up, and water won't explode. But beyond that (beyond what I've called Kalashnikov truths, https://www.wrestlingwithreligion.net/2019/10/kalashnikov-truth.html ), the world is, for all practical purposes, a vast and teeming complexity beyond human comprehension. It doesn't take a miracle for a terminal cancer diagnosis, a stock market prediction, or a political poll to be wrong. At the level of most of our experience, anything can happen, even a War Eagle car tag.

Works Cited

Holland, R. F. "From The Miraculous" in Introduction to Philosophy of Religion: Readings. Edited by James Kellenberger. Pearson/Prentice Hall, 2007.

Hume, David. An Enquiry Concerning Human Understanding. Project Gutenberg. https://www.gutenberg.org/files/9662/9662-h/9662-h.htm 

Marcus Aurelius. Meditations. Translated by Martin Hammond. Penguin, 2006.

Nolen, Albert. Jesus Before Christianity. Orbis, 2001.