In a review (NY Review of Books) of Debunked! ESP, Telekinesis, Other Pseudoscience, by Georges Charpak and Henri Broch, Freeman Dyson writes:
The book also has a good chapter on "Amazing Coincidences." These are strange events which appear to give evidence of supernatural influences operating in everyday life. They are not the result of deliberate fraud or trickery, but only of the laws of probability. The paradoxical feature of the laws of probability is that they make unlikely events happen unexpectedly often. A simple way to state the paradox is Littlewood's Law of Miracles. Littlewood was a famous mathematician who was teaching at Cambridge University when I was a student. Being a professional mathematician, he defined miracles precisely before stating his law about them. He defined a miracle as an event that has special significance when it occurs, but occurs with a probability of one in a million. This definition agrees with our common-sense understanding of the word "miracle."Littlewood's Law of Miracles states that in the course of any normal person's life, miracles happen at a rate of roughly one per month. The proof of the law is simple. During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hear things happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month. Broch tells stories of some amazing coincidences that happened to him and his friends, all of them easily explained as consequences of Littlewood's Law.
The link for this review came via Marginal Revolution. There, too, I came across Persi Diaconis. Another article, from Vanderbilt University, summarises Diaconis's view of coincidence thus:
What are the odds? The mathematician will answer that even in the most unbelievable situations, the odds are actually very good. The law of large numbers says that with a large enough denominator — in other words, in a big wide world — stuff will happen, even very weird stuff. ''The really unusual day would be one where nothing unusual happens,'' explains Persi Diaconis, a Stanford statistician who has spent his career collecting and studying examples of coincidence. Given that there are 280 million people in the United States, he says, ''280 times a day, a one-in-a-million shot is going to occur.''Throw your best story at him — the one about running into your childhood playmate on a street corner in Azerbaijan or marrying a woman who has a birthmark shaped like a shooting star that is a perfect match for your own or dreaming that your great-aunt Lucy would break her collarbone hours before she actually does — and he will nod politely and answer that such things happen all the time. In fact, he and his colleagues also warn me that although I pulled all examples in the prior sentence from thin air, I will probably get letters from readers saying one of those things actually happened to them.
Freeman Dyson winds up his review with these thoughts:
There are two extreme points of view concerning the role of science in human understanding. At one extreme is the reductionist view, holding that all kinds of knowledge, from physics and chemistry to psychology and philosophy and sociology and history and ethics and religion, can be reduced to science. Whatever cannot be reduced to science is not knowledge. The reductionist view was forcibly expressed by Edward Wilson in his recent book, Consilience. At the other extreme is the traditional view, that knowledge comes from many independent sources, and science is only one of them. Knowledge of good and evil, knowledge of grace and beauty, knowledge of ethical and artistic values, knowledge of human nature derived from history and literature or from intimate acquaintance with family and friends, knowledge of the nature of things derived from meditation or from religion, all are sources of knowledge that stand side by side with science, parts of a human heritage that is older than science and perhaps more enduring. Most people hold views intermediate between the two extremes. Charpak and Broch are close to the reductionist extreme, while I am close to the traditional extreme.The question of the proper limits of science has a strong connection with the possible existence of paranormal phenomena. Charpak and Broch and I agree that attempts to study extrasensory perception and telepathy using the methods of science have failed. Charpak and Broch say that since extrasensory perception and telepathy cannot be studied scientifically, they do not exist. Their conclusion is clear and logical, but I do not accept it because I am not a reductionist. I claim that paranormal phenomena may really exist but may not be accessible to scientific investigation. This is a hypothesis. I am not saying that it is true, only that it is tenable, and to my mind plausible.
... I am suggesting that paranormal mental abilities and scientific method may be complementary. The word "complementary" is a technical term introduced into physics by Niels Bohr. It means that two descriptions of nature may both be valid but cannot be observed simultaneously. The classic example of complementarity is the dual nature of light. In one experiment light is seen to behave as a continuous wave, in another experiment it behaves as a swarm of particles, but we cannot see the wave and the particles in the same experiment. Complementarity in physics is an established fact. The extension of the idea of complementarity to mental phenomena is pure speculation. But I find it plausible that a world of mental phenomena should exist, too fluid and evanescent to be grasped with the cumbersome tools of science.
Freeman Dyson is Professor of Physics Emeritus at the School of Natural Sciences of the Institute for Advanced Study in Princeton. He is the author of Disturbing the Universe and The Sun, the Genome, and the Internet.
