Skip to comments.Goldblatt on Polkinghorne, The Coin Toss, and The Monte Carlo Fallacy
Posted on 03/29/2002 7:39:58 AM PST by cornelis
. . . . here's a thought experiment: Suppose I toss a coin in the air. The odds are exactly equal it will land heads or tails. Suppose, then, it lands heads. If I toss the coin again, do the odds change? No, the fact that the coin landed heads the first toss has no effect on the second the name given the superstition that the first toss affects the second is "The Monte Carlo Fallacy." Even in the unlikely event that the coin turned up heads twelve times in a row, on the thirteenth toss the odds would still be exactly equal. I can never, in short, predict the very next toss based on what's happened before. Paradoxically, however, if I toss the coin a million times, I know the outcome will be half heads and half tails. Though individual tosses are unpredictable, and though no previous toss affects a subsequent toss, the result of many tosses is certain in advance; it's so certain, indeed, that if the result didn't turn out equal, I'd know the coin had been tampered with.
Question: How does predictability emerge from unpredictability? How is it possible that no single coin toss affects another, yet the cumulative weight of many tosses somehow binds together independent outcomes?
The agnostic reply is that it's the law of averages. Yet that only begs the question, only assigns the phenomenon a name. The deeper issue is why the law of averages works. What unseen will shepherds the coin through the indifference of individual tosses, never letting it stray too far from the necessity of its fate? The necessity holds, moreover, whether one coin is tossed a million times, or a million coins are tossed simultaneously; the result will be half heads and half tails.
Likewise, on a subatomic level, quantum physics instructs us that we cannot predict the behavior of individual electrons, but the concerted behavior of billions of them is certain. Indeed, the very fabric of the universe depends on the seemingly inexplicable working out of such probabilities.
It was just such an insight, long before quantum theory, that led Aquinas to argue that God's creation of the world shouldn't be understood as a one-time event what we'd now call the Big Bang but as an ongoing creation that underwrites the world as it is. It's God's ongoing creation, in effect, that ensures probabilities become actualities over the long haul. The English theologian Richard Hooker called God's sustaining principle "the law of nature" and asked, rhetorically, "See we not . . . that obedience of creatures unto the law of nature is the stay of the whole world?"
But of course we're less concerned, and rightly so, with the behavior of tossed coins or subatomic particles than with human behavior. So much fashionable agnosticism notes the beastly ways people act towards one another and asks if it's possible, or even worthwhile, to believe in a God who allows terrible events to occur. The traditional response to such objections has been that God gave people free wills and that freedom entails the possibility of bad outcomes. But if that's the case, if people are really free, is God really in control?
The British physicist-theologian John Polkinghorne has recently suggested a way to understand this paradox how God might have made people free yet still held absolute sway over his creation.
Polkinghorne likens the fate of individual lives to the behavior subatomic particles or, for that matter, to coin tosses. What happens to one person is inherently unpredictable. But what happens in the aggregate is absolutely determined. That is, you and I are free to create our own fates. But the course of history, the outcomes of multitudes of fates, is subject to God's guiding hand. In this view, good triumphs over evil in the long run for the same reason that order emerges from the seeming chaos of electrons or that coin tosses eventually come out even. All are manifestations of God's ongoing creation of the world.
"Dionysius Periegetes gives it his best toss"
The one who is faithful must show reliability in his relationship with his world...On this view the laws of nature are signs of God's fidelity. The one who is love will grant a generous measure of independence to his world, for love is grounded in the free interchange between lover and beloved...Faithfulness might be expected to find its expression in order but a genuine freedom granted to the world opens up the possibility of disorder...The world created by the God of love and faithfulness may be expected to be characterised by both the openness of chance and the regularity of necessity.
Time to open a window.
This is where the coin toss analogy falls flat. The toss of the coin, as either heads or tails, is one of necessity and therefore excludes the good. Hauling in the good by the giving necessity the mark of certainty with the name "law of averages" misrepresents the feature of providence that love brings.
As Romano Guardini pointed out in Power and Responsibility (Die Macht: Versuch einer Wegweisung):
May we say, for instance, that a storm, an epidemic, a lion has power?
Obviously not, save in a fuzzy metaphorical sense. In the natural forces we do not have effective objects capable of producing specific results; but what is lacking is something we include involuntarily when we think of "power," namely, initiative. The things of nature have or are "energy," not power. Energy becomes power only when concsiousness recognizes it, some will capable of decision directs it towards specific goals. Only in one limited sense can we apply the word to natural energies: when we conceive of them as "powers"--in other words, as mysterious beings somehow endowed with personal initiative. However, this conception hardly fits our present-day picture of existence. It belongs rather to the mythical image of the world in which the essences of things act, meet, conflict with one another, or join forces. Such "powers" are of a religious nature, evolving more or less clearly as "the gods."
Man, on the other hand, is a spiritual being. Although he's limited by physical reality, he can exercise his will to determine his actions and effect his world. How a man acts is not determined by statistical chance, it's determined by his own reason.
Man was made in the image and likeness of God. That means that whatever can be observed in this world, is mirrored in heaven. God has a Free will. There was nothing to force, or cause Him to be good. The choices He made were His own and certainly did not result from some grand sum of statistical action. Just as Jesus was not coerced, no man is coerced. God teaches, through His son, who came for that very purpose, and through the Spirit.
So it is with man. He was given Free will unconditionally. There are no limits placed on the wills of men by God, they are all Free to make their own choices. The grand outcome of all that man has done, will be up to men, not God's will. Else there is no Freedom and God has only created puppets.
There is no glory gained from creating beings that act as directed, but there is in creating them, blessing them with the gift of Free will, forgiving their tresspass, and rewarding the ones who, to some essential degree, have chosen and acted according to His own Spirit.
What does this all mean?
Mandatory seatbelt laws are evil.
The Orthodox affection for an iconic theology of presence becomes easier to accept when one recalls mans creation as proto-icon. Because the loving providence whose image is stamped on the coin thus endows it with personhood, the coin is no longer object but subject. Freed from the compulsion to render unto Caesarean necessity, the God-stamped coin is enabled to render unto its Prototype in the freedom granted it.
Conversely -- the other side of the coin, if you will -- even in gross structures (I think of human beings I have known) we see that its through the grace of a continuing Creator and a Redeemer who transfigures fallen nature into a eucharist that the inchoate, faithless unreliability of quantum chaos resolves into cosmos -- ordered, reasoned, reconciled beauty.
Redemption from both chaotic alienation and slavish laws of necessity is what Good Friday is all about, after all.
Returning the winnings was unethical...
ROS: Eighty-nine (times in a row a coin toss has landed heads up.).
GUIL: It must be indicative of something, besides the redistribution of wealth. List of possible explanations.
One: Im willing it. Inside where nothing shows, I am the essence of a man spinning double-headed coins, and betting against himself in private atonement for an unremembered past. (He spins a coin at Ros.)
GUIL: Two: time has stopped dead, and the single experience of one coin being spun once has been repeated ninety times...(He flips a coin, looks at it, tosses it to Ros.) On the whole, doubtful.
Three: divine intervention, that is to say, a good turn from above concerning him, cf. children of Israel, or retribution from above concerning me, cf. Lots wife.
Four: a spectacular vindication of the principle that each individual coin spun individually (he spins one) is as likely to come down heads as tails and therefore should cause no surprise each individual time it does. (It does. He tosses it to Ros.)
ROS: Ive never known anything like it!
GUIL: The equanimity of your average tosser of coins depends upon a law, or rather a tendency, or let us say a probability, or at any rate a mathematically calculable chance, which ensures that he will not upset himself by losing too much nor upset his opponent by winning too often.
This made for a kind of harmony and a kind of confidence. It related the fortuitous and the ordained into a reassuring union which we recognized as nature. The sun came up about as often as it went down, in the long run, and a coin showed heads about as often as it showed tails.
Then a messenger arrived. We had been sent for. Nothing else happened. Ninety-two coins spun consecutively have come down heads ninety-two consecutive times...and for the last three minutes on the wind of a windless day I have heard the sound of drums and flute..."
Probability is not a law like the law of gravity. Nothing is required to conform to it. Probability is an observation of how one can expect things to behave where there is reasonable equalibrium of causes, and none are determinant, but they don't have to act that way, and sometimes don't, thank goodness.
I think the author makes an interesting point here, and it is not the one he is trying to make.
We see this argument very often, expressed as "inexplicable working out", or "irreducible complexity", or, in the good old days, credo quia absurdum. It means, in all its forms, the same thing:
"I don't understand X; therefore, God exists."
Whether this is a good or a bad argument, it raises a methodological problem. It leads to the view that, if X were to be understood, then God's existence would become, in some degree, less defensible, less certain.
This seems to me to set up an almost inevitable confrontation between Faith and Reason - between a faith that builds on a lack of understanding and a reason that tries to understand. And we've seen this played out, right here on FR: "You can't explain X (blood clotting, the eye, the bacterial flagellum, ...)", followed by "Follow this link to 12,345 scientific papers explaining what you claim cannot be explained", followed by the usual degeneration into bald assertions and insults.
As I see it, there is an alternative. A religion that works on the principle
"I do understand X; therefore, God exists."
There is indeed such a religion. It's called by some Natural Religion, and by others Platonism. One of its best living exponents is Paul Davies. I recommend his books highly.
--I hope not by you! Of course you know all about Socrates too.
I think the author makes an interesting point here, and it is not the one he is trying to make.
It is one that Descartes tries to make in his meditations. Infinity is coeval with his finite cogito ergo sum.
But what must be underscored here is that rationality does not exist in vacuo. And the larger context of knowledge, especially all that is not directly a function of reason, is not best expressed as irrational. This is a careful distinction and a helpful one; it saves us from the tyranny of flip-side logicism (ghost of Fichte!). An antidote to this is Levinas.
I think he's talking about Aquinas' insight regarding essence and act of existence; that what a thing is is different from the fact that the thing exists (or doesn't exist). Aquinas' insight shed light on the mysterious "I AM" of Scripture: GOD IS. God is the only being whose essence and act of existence are the same.
I've never seen this mentioned, but I think this is one of the most persuasive pieces of evidence for the inspired nature of Scripture. If God didn't reveal the name "I AM" to Moses, who did? A philosophical genius living among primitive nomads hundreds of years before Aristotle? A philosophical insight that wasn't fully understood for another 2000 years?
And even if such a person existed, how would he put those words in Moses' mouth? After all, the scribes were so scrupulous regarding the copying of Scripture that they left in the passage in Genesis: "we created man in our image" which certainly at least appears to contradict monotheistic theology.