No More Learning

Another noted American astronomer, William Henry Pickering, categorically stated that, although heavier than air flying machines were possible (he had to say that because the Wright brothers had by then already flown) they could never be a serious practical proposition:
The popular mind often pictures gigantic flying machines speeding across the Atlantic: and carrying innumerable passengers in a way analogous to our modern steamships . . . It seems safe to say that such ideas must be wholly visionary, and even if a machine could get across with one or two passengers the expense would be prohibitive . . . Another popular fallacy is to expect enormous speed to be obtained.
Pickering goes on to 'prove' by means of authoritative calculations on the effects of air resistance that an aeroplane could never travel faster than the express trains of his day. On the face of it, the 1945 remark of Thomas J. Watson, head of IBM, 'I think there is a world market for maybe five computers' sounds similar. But this is unfair. Watson was surely forecasting that computers would become ever larger, and in this he was wrong; however, he was not downgrading the importance of the computer in the future, the way Kelvin and the others were downgrading air travel.
Those banana skin stories are, indeed, awful warnings of the dangers of an over-zealous scepticism. Dogmatic disbelief of anything that seems unfamiliar or unexplained is not a virtue. What, then, is the difference between this and my avowed scepticism of astrology, reincarnation and the resurrection of Elvis Presley? How are we to know when scepticism is justified, and when it is dogmatic, intolerant short-sightedness?
Let's think about a spectrum of stories that people might tell us and meditate on how sceptical we ought to be of them. At the lowest level are stories that might be true, and might not be true, but that we have no
particular reason to doubt. In Evelyn Waugh's Men at Arms (1952), the comic character Apthorpe frequently speaks to the narrator, Guy Crouchback, of his two aunts, one who lives in Peterborough, the other in Tunbridge Wells. On his deathbed, Apthorpe finally confesses that in fact he has only one aunt. Which one did he invent, Guy Crouchback asks. 'The one at Peterborough, of course. ' 'You certainly took me in thoroughly. ' 'Yes, it was a good joke, wasn't it? '
No, Apthorpe's was not a good joke, and it is precisely this that makes Evelyn Waugh's joke at Apthorpe's expense funny. There are, no doubt, many elderly ladies residing in Peterborough, and if a man tells you he has an aunt there you have no particular reason to disbelieve him. Unless he has some specific motive for lying to you, you might as well believe him, though if a great deal hangs on it you'd be wise to check the evidence. But now suppose somebody tells you that his aunt can levitate herself by meditation and will-power. She sits cross-legged, you are told, and by thinking beautiful thoughts and intoning a mantra she raises herself above the ground and stays there, hovering. Why be any more sceptical than you would be if a man simply told you that his aunt exists in Peterborough, for in both cases you have the word of a claimed eye- witness?
The obvious reply is that levitation by will-power is not explicable by science. But that just means present day science. It brings us straight back to Clarke's Third Law, and the important point that any era's science doesn't have all the answers and will be superseded. Maybe, some day in the future, physicists will fully understand gravity and build an anti-gravity machine. It is conceivable that levitating aunts will become as commonplace to our descendants as jet planes are to us. Does Clarke's Third Law then entitle us to believe any and every yarn that folk may spin about apparent miracles? If a man claims to have witnessed his aunt in cross-legged levitation, or a Turk zooming over the minarets on a magic carpet, should we swallow his story on the grounds that those of our ancestors who doubted the possibility of radio turned out to be wrong? No, of course these are not sufficient grounds for believing in levitation or magic carpets. But why not?
Clarke's Third Law does not work in reverse. Given that 'Any sufficiently advanced technology is indistinguishable from magic', it does not follow that any magical claim that anybody may make at any time is indistinguishable from a technological advance that will come in the future. ' Yes, there have been occasions when authoritative sceptics have come away with egg on their pontificating faces. But a far greater number of magical claims have been made and never vindicated. A few things that would surprise us today will come true in the future. But far more things that would surprise us today will not come true in the future. The
trick is to sort out the minority from the rubbish - from claims that will forever remain in the realm of fiction and magic.
If faced with an amazing or miraculous story, we can begin by asking ourselves whether our informant has a motive to lie. Or we can assess his credentials in other ways. I recall an entertaining dinner with a philosopher who told me the following story: One day in church he noticed that a priest, in a kneeling position, was hovering nine inches above the church floor. My natural scepticism of my dinner companion was increased when he went on to relate two further eye-witness experiences. He said that, among his many careers, he had once been warden of a home for delinquent boys, and he discovered that all the boys had 'I love my mummy' tattooed on their penises. An improbable story in itself, but not impossible. Unlike the case of the levitating priest, no great scientific principles would be called in question if it were true. Nevertheless, it seemed to provide a useful perspective on my neighbour's credibility. On another occasion, said this prolific raconteur, he had observed a crow strike a match while raising one wing to shield it from the wind. I forget whether the crow actually took a drag on a cigarette, but in any case the three stories, taken together, seemed to establish my companion as an unreliable, though diverting, witness. To put it mildly, the hypothesis that he was a liar (or a lunatic, or a hallucinating fantasist, or that he was researching the credulity of Oxford dons) seemed more probable than the alternative hypothesis that all three of his far-fetched stories were true.
As a philosopher, he would have known the logical test set out by the great eighteenth-century Scottish philosopher David Hume, which seems to me unassailable:
. . . no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavours to establish. 'Of Miracles' (1748)
I'll follow through Hume's meaning with respect to one of the best attested miracles of all time, one that, it is claimed, was witnessed by 70,000 people, and within living memory. This is the apparition of Our Lady of Fatima. I quote from an account in a Roman Catholic website which notes that, of the many claimed Marian sightings, this one is unusual in being officially recognized by the Vatican.
On October 13th, 1917, there were more than 7o,ooo people gathered in the Cava da Iria in Fatima, Portugal. They had come to observe a miracle which had been foretold by the Blessed Virgin to three young visionaries: Lucia dos Santos, and her two cousins, Jacinta and Francisco Marto . . . Shortly after noon, Our Lady appeared to the three visionaries. As the
Lady was about to leave, she pointed to the sun. Lucy excitedly repeated the gesture, and the people looked into the sky . . . Then a gasp of terror rose from the crowd, for the sun seemed to tear itself from the heavens and come crashing down upon the horrified multitude . . . Just when it seemed that the ball of fire would fall upon and destroy them, the miracle ceased, and the sun resumed its normal place in the sky, shining forth as peacefully as ever.
If the miracle of the moving sun had been seen only by Lucia, the young woman responsible for the cult of Fatima in the first place, not many would take it seriously. It could so easily be a private hallucination, or an obviously motivated lie. It is the 70,000 witnesses that impress. Could 70,000 people simultaneously be the victims of the same hallucination? Could 70,000 people collude in the same lie? Or if there never were 70,000 witnesses, could the reporter of the event get away with inventing so many?
Let's apply Hume's criterion. On the one hand, we are asked to believe in a mass hallucination, a trick of the light, or mass lie involving 70,000 people. This is admittedly improbable. But it is less improbable than the alternative: that the sun really did move. The sun hanging over Fatima was not, after all, a private sun; it was the same sun that warmed all the other millions of people on the daylight side of the planet. If the sun had moved in truth, but the event was seen only by the people of Fatima, an even greater miracle would have to have been perpetrated: an illusion of wow-movement had to be staged for all the millions of witnesses not in Fatima. And that's ignoring the fact that, if the sun had really moved at the speed reported, the solar system would have broken up. We have no alternative but to follow Hume, choose the less miraculous of the available alternatives and conclude, contrary to official Vatican doctrine, that the miracle of Fatima never happened. Moreover, it is not at all clear that the onus is on us to explain how those 70,000 witnesses were misled.
Hume's is still an argument about the balance of probabilities. Moving to the far end of our spectrum of putative miracles, are there any speculations or allegations that we can utterly, and for all time, rule out? Physicists agree that if an inventor applies for a patent for a perpetual motion machine you can safely turn down his patent without even looking at his design. This is because any perpetual motion machine would violate the laws of thermodynamics. Sir Arthur Eddington wrote:
If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is
found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
The Nature of the Physical World (1928)
Eddington is cleverly bending over backwards to make overwhelming concessions in the first part of the passage, so that his confidence in the second part has the more impact, But if you still find it too cocksure; if you think it is asking for trouble at the hands of some as yet unimaginable future technology, so be it. I won't press the point, but will take my weaker stand, with Hume, on relative probabilities. Fraud, illusion, trickery, hallucination, honest mistake or outright lies - the combination adds up to such a probable alternative that I shall always doubt casual observations or secondhand stories that seem to suggest the catastrophic overthrow of existing science. Existing science will undoubtedly be overthrown; not, however, by casual anecdotes or performances on television, but by rigorous research, repeated, dissected and repeated again.
Returning to our spectrum of improbabilities, fairies would fall somewhere between Apthorpe's aunt and a perpetual motion machine. If tiny, butterfly-sized humans, wearing wings and fashionable but miniature clothes, were authentically discovered tomorrow, no great principles of physics would have been violated. It wouldn't be nearly as revolutionary as a perpetual motion machine. On the other hand biologists would have a hard time fitting fairies into their existing classificatory scheme. Where did they spring from in evolution? Neither the fossil record nor existing zoology shows us any primates equipped with flapping wings, and it would be surprising indeed if they suddenly and uniquely evolved in a species sufficiently close to our own to have co- opted - as some famous fake photographs which excited the notoriously gullible Sir Arthur Conan Doyle clearly showed - 1920s-style clothes a la mode.
Alleged creatures such as the Loch Ness Monster, the Yeti or 'Abominable Snowman' of the Himalayas, and the dinosaur of the Congo, lie in the spectrum somewhere on the more probable side of Conan Doyle's fairies. There really is no particular reason why a relict population of plesiosaurs should not survive in Loch Ness. I can't tell you how delighted I, and all zoologists, would be if they did; or if an authentic dinosaur were found up the Congo. No biological and certainly no physical principles would be violated by such a discovery. The only reason it seems unlikely is that the last known dinosaur lived 65 million years ago, and 65 million years is a long time for a breeding population to remain concealed and unfossilized. As for the Yeti, the prospect of a surviving population of Homo erectus, or Gigantopithecus, would fill me with elation, if only I could believe it. I dearly wish I thought the idea more probable than the
Humean alternatives - hallucinations, lying travellers' tales or honest misreadings of sun-enlarged animal footprints.
On 50 August 1938, Orson Welles's still famous radio dramatization of H. G. Wells's The War of the Worlds provoked widespread panic and even some rumoured suicides among listeners who thought its opening scene was - as it purported to be - an authentic news bulletin announcing a Martian invasion. This story is often held up as evidence of the laughable gullibility of the American nation; rather unfairly, I have always thought, for an invasion from outer space is not impossible and, were it to happen, a sudden newsflash on the radio is exactly how we'd probably first hear
of it.
Flying saucer stories are perennially popular, but they tend to be disbelieved by the scientific community. Why? Not because a visitation from outer space is impossible or even wildly improbable. It is because, once again, the alternative explanations of fraud or illusion are more probable. As a matter of fact, numerous flying saucer stories have been painstakingly investigated, in wearisome detail, by teams of conscientious amateur and professional scientists. Time after time after time the stories have crumbled under investigation. Often they turn out to be straightforward hoaxes (lucrative for the perpetrators, because publishers pay good money for such stories, however poorly documented they may be, and whole industries of T-shirts and souvenir mugs can be supported). Or the 'saucers' turn out to have been aircraft, airships or balloons, seen, or illuminated, from a peculiar angle. Sometimes they are mirages or other tricks of the light, sometimes sightings of secret military aircraft.
One day, maybe, we shall be visited by extraterrestrial spaceships. But the odds that any particular report of flying saucers is genuine are low compared to the odds of the Humean alternatives of fraud or illusion. In particular, the thing that for me subtracts verisimilitude from most flying saucer stories is the almost comical resemblance of the reported aliens to ordinary humans, or to the latest fictional creations to have appeared on television. Many of them resemble human males sufficiently closely to want to copulate with human females, and even produce fertile offspring. As Carl Sagan and others have pointed out, abduction-crazed humanoid aliens seem to be the modern counterpart of seventeenth-century demons and witches.
Abetted by the prestige of television and the newspapers, astrology, paranormalism and alien visitations have a privileged inside track into the popular consciousness. If I am right that this tendency exploits our natural and laudable appetite for wonder, we have here paradoxical grounds for encouragement. We should take comfort from the thought
that, since the appetite for wonder is fed so much more satisfyingly by real science, it ought to be a simple matter of education to combat superstition. But I suspect that there is an additional force at work which may make things more difficult. It is quite an interesting psychological force in its own right, and my purpose in the rest of this chapter is to explain it, because understanding it may help us to limit the damage it can cause. The additional force I am speaking of is a normal and, from many points of view, desirable credulity in children which, unless we are careful, can spill over into adulthood, with unfortunate results. I'll begin with a personal anecdote.
On All Fools' Day one year, when my sister and I were children, our parents and our uncle and aunt played a simple trick on us. They announced that they had rediscovered in the attic a little aeroplane which had belonged to them when young and they were going to take us up for a ride. Flying was less commonplace then, and we were thrilled. The only stipulation was that we had to be blindfolded. They led us by the hand, giggling and stumbling across the lawn, and strapped us into our seats. We heard the noise of the engine starting up, there was a lurch and up we went for a bumpy, swaying, reeling ride. From time to time we evidently passed through the high treetops, for we felt the branches gently brushing us and a pleasant, rushing wind in our faces. Finally we 'landed', the lurching ride came to an end on terra firma, the blindfold was removed and amid laughter all was revealed. There was no aeroplane. We had not travelled from the spot on the lawn where we had started. We had simply been sitting on a garden seat which our father and uncle had lifted and slewed and bumped around to simulate aerial movement. No engine, only the noisy vacuum cleaner, and a fan to blow wind in our faces. They and the tree branches brushing against us had been wielded by our mother and aunt standing by the seat. It had been fun while it lasted.
Credulous, faith-filled children that we were, we had looked forward to the promised flight for days before it happened. It never occurred to us to wonder why we must be blindfolded. Wouldn't it have been natural to ask what was the point of going for a joyride if you couldn't see anything? But no, our parents simply told us that, for some reason unspecified, it was necessary to blindfold us; and we accepted it. Perhaps they fell back on the time-honoured recipe of 'not spoiling the surprise'. We never wondered why our elders had kept from us the secret that at least one of them must be a trained pilot - I don't think we even asked which one. We just didn't have the sceptic's turn of mind. We had no fear of crashing, such was our faith in our parents. And when the blindfolds were removed and the joke was on us, we still didn't stop believing in Father Christmas, the tooth fairy, angels, heaven, the Happy Hunting Ground and the other stories that those same elders had told us. Incidentally, my
mother has no memory of the incident, but she does remember the occasion in her own childhood when her father played the identical trick on herself and her little sister. His patter was even more far-fetched, because his plane 'took off' indoors and the children were told to duck as they flew out through the window'. She and her sister still fell for it.
Children are naturally credulous. Of course they are, what else would you expect? They arrive in the world knowing nothing, surrounded by adults who know, by comparison, everything. It is earnestly true that fire burns, that snakes bite, that if you walk unprotected in the noon sun you will bake red, raw and, as we now know, cancerous. Moreover, the other and apparently more scientific way to gain useful knowledge, learning by trial and error, is often a bad idea because the errors are too costly. If your mother tells you never to paddle in the lake because of the crocodiles, it is no good coming over all sceptical and scientific and 'adult' and saying, 'Thank you mother, but I prefer to put it to the experimental test. ' Too often, such experiments would be terminal. It is easy to see why natural selection - the survival of the fittest - might penalize an experimental and sceptical turn of mind and favour simple credulity in children.
But this has an unfortunate by-product which can't be helped. If your parents tell you something that is not true, you must believe that, too. How could you not? Children are not equipped to know the difference between a true warning about genuine dangers and a false warning about going blind, say, or going to hell, if you 'sin'. If they were so equipped, they wouldn't need warnings at all. Credulity, as a survival device, comes as a package. You believe what you are told, the false with the true. Parents and elders know so much, it is natural to assume that they know everything and natural to believe them. So when they tell you about Father Christmas coming down the chimney, and about faith 'moving mountains', of course you believe that, too.
Children are gullible because they need to be if they are to fulfil their 'caterpillar' role in life. Butterflies have wings because their role is to locate members of the opposite sex and spread their offspring to new food plants. They have modest appetites satisfied by occasional sips of nectar. They eat little protein by comparison with caterpillars, which constitute the growing stage in the life history. Juvenile animals in general have the role of preparing to become successfully reproducing adults. Caterpillars are there to feed as rapidly as possible in order to chrysalize into flying, reproducing, dispersing adults. To this end they have no wings but instead have stout munching jaws and voracious, single-minded appetites.
Human children need to be credulous for a similar reason. They are information caterpillars. They are there to become reproducing adults, in a sophisticated, knowledge-based society. And by far the most important source of their information diet is their elders, above all their parents. For the same kind of reason as caterpillars have chumbling, hoovering jaws for sucking up cabbage flesh, human children have wide open ears and eyes, and gaping, trusting minds for sucking up language and other knowledge. They are suckers for adult knowledge. Tidal waves of data, gigabytes of wisdom flood through the portals of the infant skull, and most of it originates in the culture built up by parents and generations of ancestors. It is important, incidentally, not to take the caterpillar analogy too far. Children change gradually into adults, not suddenly, as caterpillars metamorphose into butterflies.
I remember once trying gently to amuse a six-year old child at Christmas time by reckoning up with her how long it would take Father Christmas to go down all the chimneys in the world. If the average chimney is 20 feet long and there are, say, 100 million houses with children, how fast, I wondered aloud, would he have to whizz down each chimney in order to finish the job by dawn on Christmas Day? He'd hardly have time to tiptoe noiselessly into each child's bedroom, would he, since he'd necessarily be breaking the sound barrier? She saw the point and realized that there was a problem, but it didn't worry her in the least. She dropped the subject without pursuing it. The obvious possibility that her parents had been telling falsehoods never seemed to cross her mind. She wouldn't have put it in these words but the implication was that, if the laws of physics rendered Father Christmas's feat impossible, so much the worse for the laws of physics. It was enough that her parents had told her he went down all the chimneys during the few hours of Christmas Eve. It must be so because Mummy and Daddy said it was.
My contention is that trusting credulity may be normal and healthy in a child but it can become an unhealthy and reprehensible gullibility in an adult. Growing up, in the fullest sense of the word, should include the cultivation of a healthy scepticism. An active readiness to be deceived can be called childish because it is common - and defensible - among children. I suspect that its persistence in adults stems from a hankering after, indeed a pining for, the lost securities and comforts of childhood. The point was well put in 1986 by that great writer of popular science and science fiction Isaac Asimov: 'Inspect every piece of pseudoscience and you will find a security blanket, a thumb to suck, a skirt to hold. ' Childhood is, for many people, a lost Arcadia, a kind of heaven, with its certainties and its securities, its fantasies of flying to the Never Never Land, its bedtime stories before we drifted off to the Land of Nod in the arms of Teddy Bear. With hindsight, the years of childish innocence may pass too soon. I love my parents for taking me for a ride, high as a kite,
through the treetops; and for telling me about the Tooth Fairy and Father Christmas, about Merlin and his spells, about baby Jesus and the Three Wise Men, All these stories enrich childhood and, together with so many other things, help to make it, in memory, a time of enchantment.
The adult world may seem a cold and empty place, with no fairies and no Father Christmas, no Toyland or Narnia, no Happy Hunting Ground where mourned pets go, and no angels - guardian or garden variety. But there are also no devils, no hellfire, no wicked witches, no ghosts, no haunted houses, no daemonic possession, no bogeymen or ogres. Yes, Teddy and Dolly turn out not to be really alive. But there are warm, live, speaking, thinking, adult bedfellows to hold, and many of us find it a more rewarding kind of love than the childish affection for stuffed toys, however soft and cuddly they may be.
Not to grow up properly is to retain our 'caterpillar' quality from childhood (where it is a virtue) into adulthood (where it becomes a vice). In childhood our credulity serves us well. It helps us to pack, with extraordinary rapidity, our skulls full of the wisdom of our parents and our ancestors. But if we don't grow out of it in the fullness of time, our caterpillar nature makes us a sitting target for astrologers, mediums, gurus, evangelists and quacks. The genius of the human child, mental caterpillar extraordinary, is for soaking up information and ideas, not for criticizing them. If critical faculties later grow it will be in spite of, not because of, the inclinations of childhood. The blotting paper of the child's brain is the unpromising seedbed, the base upon which later the sceptical attitude, like a struggling mustard plant, may possibly grow. We need to replace the automatic credulity of childhood with the constructive scepticism of adult science.
But I suspect an additional problem. Our story of the child as
information caterpillar was too simple. The programming of the child's credulity has a twist which, until we understand it, is almost paradoxical. Let us go back to our picture of the child needing to absorb information from the previous generation as swiftly as possible. What if two adults, say your mother and your father, give you contradictory advice? What if your mother tells you that all snakes are deadly and you must never go near them, but next day your father tells you that all snakes are deadly except green ones and you can keep a green snake as a pet? Both pieces of advice may be good. The mother's more general advice has the desired effect of protecting you against snakes, even though it is too sweeping when it comes to green snakes. The father's more discriminating advice has the same protective effect and is in some ways better, But it could be fatal if carried, unrevised, to a distant country. In any case, to the young child the contradiction between the two might be dangerously confusing. Parents often make strenuous efforts not to contradict one another, and
they are probably wise to do so. But natural selection, in 'designing' credulity, would need to build in a way of coping with contradictory advice. Perhaps a simple override rule, such as 'Believe whichever story you heard first. ' Or 'Believe mother rather than father, and father rather than other adults in the population. '
Sometimes the advice from parents is specifically aimed against credulity towards other adults in the population. The following is a piece of advice that parents need to give their children: 'If any adult asks you to come with him and says that he is a friend of your parents, don't believe him, however nice he seems and even (or especially) if he offers you sweets. Only go with an adult that you and your parents already know, or who is wearing a policeman's uniform. ' (A charming story recently appeared in the English newspapers in which Queen Elizabeth the Queen Mother, aged 97, told her chauffeur to stop the car when she noticed a crying child who was apparently lost. The kind old lady got out to comfort the little girl and offered to take her home. 'I can't,' wailed the child, 'I'm not allowed to talk to strangers. ') A child is called upon to exercise the exact opposite of credulity in some circumstances: a tenacious persistence in believing an earlier adult statement in the face of what may be a tempting and plausible - but contradictory - later statement.
On their own, then, the words 'gullible' and 'credulous' are not quite right for children. Truly credulous people believe whatever they have most recently been told, even if this contradicts what others have told them before. The quality of childhood that I am trying to pin down is not pure gullibility but a complex combination of gullibility coupled with its opposite - stubborn persistence in a belief, once acquired. The full recipe, then, is extreme early gullibility followed by equally obstinate subsequent unshakeability. You can see what a devastating combination this could be. Those old Jesuits knew what they were about: 'Give me the child for his first seven years, and I'll give you the man. '
7
UNWEAVING THE UNCANNY
. . . though no great ministering reason sorts Out the dark mysteries of human souls
To clear conceiving. . .
JOHN KEATS, 'Sleep and Poetry' (1817)
The eminent fertility specialist Robert Winston imagines the following advertisement, placed in the newspaper by an unscrupulous quack
doctor, aimed at people who want their next baby to be, say, a son (the sexism underlying this assumption is not mine but could be found unquestioned all over the ancient world, and still in many places today). 'Send ? 500 for my patent recipe to make your baby a boy. Money refunded in full if I fail. ' The money back guarantee is intended to establish confidence in the method. In fact, of course, since boys turn up anyway on approximately 50 per cent of occasions, the scheme would be a nice little earner. Indeed, the quack could safely offer compensation of, say, ? 250 for every girl born, over and above the money back guarantee. He would still show a tidy profit in the long run.
I used a similar illustration in one of my Royal Institution Christmas Lectures in 1991. I said I had reason to believe that among my audience was a psychic, clairvoyant individual, capable of influencing events purely by the power of thought. I would try to flush this individual out. 'Let's first establish,' I said, 'whether the psychic is in the left half or the right half of the lecture hall. ' I invited everybody to stand up while my assistant tossed a coin.
Everybody on the left of the hall was asked to 'will' the coin to come down heads. Everybody on the right had to will it to be tails. Obviously one side had to lose, and they were asked to sit down. Then those that remained were divided into two, with half 'willing' heads and the other half tails. Again the losers sat down. And so on by successive halvings until, inevitably, after seven or eight tosses, one individual was left standing. 'A big round of applause for our psychic' He must be psychic, mustn't he, because he successfully influenced the coin eight times in a row?
If the lectures had been televised live, instead of recorded and broadcast later, the demonstration would have been much more impressive. I'd have asked everybody who watched it whose surname begins before J in the alphabet to 'will' heads and the rest tails. Whichever half turned out to contain the 'psychic' would have been divided in half again, and so on. I'd have asked everybody to keep a written record of the order of their 'willings'. With two million viewers, it would have taken about 21 steps to narrow down to a single individual. To be on the safe side I'd have stopped a bit short of 21 steps. At, say, the eighteenth step I'd have invited anybody still in the game to phone in. There would have been quite a few and, with luck, one would phone. This individual would then have been invited to read out his/her written record: which would have matched the official record. So this one individual succeeded in influencing 18 successive tosses of a coin. Gasps of admiration. But admiration for what? Nothing but pure luck. I don't know if that experiment has been done. Actually, the trick here is so obvious it probably wouldn't fool many people. But how about the following?
A well-known 'psychic' goes on television, a lucrative engagement fixed up over lunch by his publicity agent. Staring out of ten million screens with hypnotically smouldering eyes (nice job by Make-up and Lighting), our imaginary seer intones that he feels a strange, spiritual rapport, a vibrating resonance of cosmic energy, with certain members of his audience. They will be able to tell who they are because, even as he utters his mystic incantation, their watches will stop. After only a brief pause, a telephone on his table rings and an amplified voice in awed tones announces that its owner's watch stopped dead within seconds of the clairvoyant's words. The caller adds that she had a premonition that this was going to happen even before she looked down at her watch, for something in her hero's burning eyes seemed to speak directly to her soul. She felt the 'vibrations' of 'energy'. Even as she is speaking, a second telephone rings. Yet another watch has stopped.
A third caller's grandfather clock stopped - surely a weightier feat than stopping a little watch whose delicate hairspring would naturally be more susceptible to psychic forces than the massive pendulum of the grandfather! Another viewer's watch actually stopped a little before the celebrated mystic made his pronouncement - is this not an even more impressive feat of psychic control? Yet another watch has been more impatiently susceptible to occult forces. It had stopped a whole day before, at the very moment when its owner looked at the famous mystic's photograph in the newspaper. The studio audience gasps its appreciation. This, surely, is psychic power beyond all scepticism, for it happened a whole day early! 'There are more things in heaven and earth, Horatio . . . '
What we need is less gasping and more thinking. This chapter is about how to take the sting out of coincidence by quietly sitting down and calculating the likelihood that it would have happened anyway. In the course of this, we shall discover that to disarm apparently uncanny coincidences is more interesting than gasping over them anyway.
Sometimes the calculation is easy. In a previous book I gave away the number of the combination lock on my bicycle. I felt safe in doing so because obviously my books would never be read by the kind of person who would steal a bicycle. Unfortunately somebody did steal it, and I now have a new lock with a new number, 4167. I find this number easy to remember. 41 is imprinted in my memory as the arbitrary code used to identify my clothes and shoes at boarding school. 67 is the age at which I am due to retire. Obviously there is no interesting coincidence here: whatever the number had been, I'd have searched my life for a mnemonic recipe and I'd have found it. But mark the sequel. On the day of writing this, I received from my Oxford college a letter saying:
Each person authorized to use the photocopiers is issued with a personal code number which permits access. Your new number is 4167.
My first thought was that I'd undoubtedly lose this piece of paper (I quickly lost its equivalent last year) and I must immediately think of a formula to fix it in my memory. Something similar to the mnemonic by which I remember my bicycle combination, perhaps? So I looked again at the number on the letter and, to borrow a neat line from Fred Hoyle's science fiction novel The Black Cloud, the figures on the piece of paper seemed to swell to a gigantic size. I didn't need a new mnemonic. The number was identical. I rushed to tell my wife of the amazing coincidence, but on more sober reflection I shouldn't have bothered.
The odds of this happening by chance alone are easily calculated. The first digit could have been anything from 0 to 9. So there is a one in 10 chance of getting a 4 and matching the bicycle lock. For each of these ten possibilities, the second digit could have been anything from 0 to 9, so again there is a one in 10 chance of matching the bike lock's second dial. The odds of matching the first two digits is therefore one in 100 and, following the logic through the other two digits, the odds of matching all four digits of the bicycle lock is one in 10,000. It is this large number that is our protection against theft.
The coincidence is impressive. But what should we conclude? Has something mysterious and providential been going on? Have guardian angels been at work behind the scenes? Have lucky stars swum into Uranus? No. There is no reason to suspect anything more than simple accident. The number of people in the world is so large compared with 10,000 that somebody, at this very moment, is bound to be experiencing a coincidence at least as startling as mine. It just happens that today was my day to notice such a coincidence. It isn't even an added coincidence that it happened to me on this particular day, while I was writing this chapter. I had in fact written the first draft of the chapter some weeks ago. I reopened it today, after the coincidence occurred, in order to insert this anecdote. I shall surely reopen it many times to revise and polish, and I shall not remove the references to 'today': they were accurate when written. This is another way in which we habitually inflate the impressiveness of coincidence in order to make a good story.
We can do a similar calculation for the television guru whose psychic miasma seemed to stop people's watches, but we'll have to use estimates rather than exact figures. Any given watch has a certain low probability of stopping at any moment. I don't know what this probability is, but here's the kind of way in which we could come to an estimate. If we take just digital watches, their battery typically runs out within a year. Approximately, then, a digital watch stops once per year. Presumably clockwork watches stop more often because people forget to wind them
and presumably digital watches stop less often because people sometimes remember to renew the battery ahead of time. But both kinds of watches probably stop as often again because they develop faults of one kind or another. So, let our estimate be that any given watch is likely to stop about once a year. It doesn't matter too much how accurate our estimate is. The principle will remain.
If somebody's watch stopped three weeks after the spell was cast, even the most credulous would prefer to put it down to chance. We need to decide how large a delay would have been judged by the audience as sufficiently simultaneous with the psychic's announcement to impress. About five minutes is certainly safe, especially since he can keep talking to each caller for a few minutes before the next call ceases to seem roughly simultaneous. There are about 100,000 five-minute periods in a year. The probability that any given watch, say mine, will stop in a designated five-minute period is about 1 in 100,000. Low odds, but there are 10 million people watching the show. If only half of them are wearing watches, we could expect about 25 of those watches to stop in any given minute. If only a quarter of these ring in to the studio, that is 6 calls, more than enough to dumbfound a naive audience. Especially when you add in the calls from people whose watches stopped the day before, people whose watches didn't stop but whose grandfather clocks did, people who died of heart attacks and their bereaved relatives phoned in to say that their 'ticker' gave out, and so on. This kind of coincidence is celebrated in the delightfully sentimental old song, 'Grandfather's Clock:'
Ninety years without slumbering. Tick, lock, tick, tock.
His life seconds numbering. Tick, tock, tick, tock.
It stopped . . . short. . . never to go again When the old man died.
Richard Feynman, in a 1963 lecture published posthumously in 1998, tells the story of how his first wife died at 9. 22 in the evening and the clock in her room was later found to have stopped at exactly 9. 22. There are those who would revel in the apparent mystery of this coincidence and feel that Feynman has taken away something precious when he gives us a simple, rational explanation of the mystery. The clock was old and erratic and was in the habit of stopping if tilted out of the horizontal. Feynman himself frequently repaired it. When Mrs Feynman died, the
nurse's duty was to record the exact time of death. She moved over to the clock, but it was in dark shadow. In order to see it, she picked it up - and tilted its face towards the light . . . The clock stopped. Is Feynman really spoiling something beautiful when he tells us what is surely the true - and very simple - explanation? Not for my money. For me, he is affirming the elegance and beauty of an orderly universe in which clocks stop for reasons, not to titillate human sentimental fancy.