There really were fairies, tiny people with wings, flitting about among the flowers.

  Elsie and Frances were making it up, and faking the photographs.

  It’s really no contest, is it? Children play make-believe all the time, and it is so easy to do. Even if it were hard to do; even if you felt that you knew Elsie and Frances very well, and they were always completely truthful girls, who would never dream of playing a trick; even if the girls had been given a truth drug, and had sailed through a lie-detector test with flying colours; even if this all added up to its being a miracle if they told a lie, what would Hume say? He would say that the ‘miracle’ of their lying would still be a smaller miracle than the fairies they claimed to show actually existing.

  Elsie and Frances didn’t do any serious harm with their prank, and it is even rather funny that they managed to fool the great Conan Doyle. But such tricks by young people are sometimes no laughing matter, to put it mildly. Back in the seventeenth century, in a village in New England called Salem, a group of young girls became hysterically obsessed with ‘witches’, and started imagining, or making up, all sorts of things which, unfortunately, the very superstitious adults of the community believed. Numerous older women, and some men too, were accused of being witches in league with the devil, and of casting spells on the girls, who said they had seen them flying through the air, or doing other strange things that witches were popularly believed to do. The consequences were extremely serious: the girls’ testimony sent nearly twenty people to the gallows. One man was even ceremonially crushed under stones, which is an appalling thing to happen to an innocent person, purely because a group of children made up stories about him. I can’t help wondering why the girls did it. Were they trying to impress each other? Could it have been a bit like the cruel ‘cyber-bullying’ that happens today in emails and on social networking sites? Or did they genuinely believe their own tall stories?

  Let’s come back to miracle stories in general, and how they get started. Perhaps the most famous instance of young girls saying weird things and being believed is the so-called miracle of Fatima. In 1917, at Fatima in Portugal, a ten-year-old shepherd girl called Lucia, accompanied by her two young cousins, Francisco and Jacinta, claimed to have seen a vision up on a hill. The children said the hill had been visited by a woman called the ‘Virgin Mary’, who, though long dead, had become a kind of goddess of the local religion. According to Lucia, the ghostly Mary spoke to her and told her and the other children that she would keep returning on the 13th of each month until October 13th, when she would perform a miracle to prove she was who she said she was. Rumours of the expected miracle spread around Portugal, and on the appointed day a huge crowd of more than 70,000 is said to have gathered at the spot. The miracle, when it came, involved the sun. Accounts of exactly what the sun is supposed to have done vary. To some witnesses it seemed to ‘dance’, to others it whirled round and round like a Catherine wheel. The most dramatic claim was that

  … 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.

  Now, what do we think really happened? Was there really a miracle at Fatima? Did the ghostly Mary really appear? Conveniently, she was invisible to everybody except the three children, so we don’t have to take that part of the story very seriously. But the miracle of the moving sun is supposed to have been seen by 70,000 people, so what are we to make of that? Did the sun really move (or did the Earth move relative to it, so that the sun appeared to move)? Let’s think like Hume. Here are three possibilities to consider.

  The sun really did move about the sky and come crashing down towards the horrified crowd, before resuming its former position. (Or the Earth changed its rotation pattern, in such a way that it looked as though the sun had moved.)

  Neither the sun nor the Earth really moved, and 70,000 people simultaneously experienced a hallucination.

  Nothing happened at all, and the whole incident was misreported, exaggerated or simply made up.

  Which of these possibilities do you think is the most plausible? All three of them seem pretty unlikely. But surely Possibility 3 is the least far-fetched, the least deserving of the title of miracle. To accept Possibility 3 we only have to believe that somebody told a lie in reporting that 70,000 people saw the sun move, and the lie got repeated and spread around, just like any of the popular urban legends that whizz around the internet nowadays. Possibility 2 is less likely. It requires us to believe that 70,000 people simultaneously experienced a hallucination involving the sun. Rather far-fetched. But however unlikely – almost miraculous – Possibility 2 may seem, even that would be far less of a miracle than Possibility 1.

  The sun is visible all over the daylight half of the world, not just in one Portuguese town. If it really had moved, millions of people all over the hemisphere – not just those in Fatima – would have been terrified out of their wits. Actually the case against Possibility 1 is even stronger than that. If the sun really had moved at the speed reported – ‘crashing down’ towards the crowd – or if something had happened to change the Earth’s spinning sufficiently to make it look as though the sun had moved at that colossal speed – it would have been the catastrophic end of all of us. Either the Earth would have been kicked out of its orbit and would now be a lifeless, cold rock hurtling through the dark void, or we’d have careered into the sun and been fried. Remember from Chapter 5 that the Earth is spinning at a rate of many hundreds of miles per hour (1,000 mph if measured at the equator), yet the apparent motion of the sun is still too slow for us to see it, because it is so far away. If sun and Earth suddenly moved relative to one another fast enough for a crowd to see the sun ‘crashing down’ towards them, the real movement would have to be thousands of times faster than usual and it literally would be the end of the world.

  It was said that Lucia told her audience to stare at the sun. This is an extremely stupid thing to do, by the way, because it could permanently damage your eyes. It also could induce a hallucination that the sun was wobbling in the sky. Even if only one person hallucinated, or lied about seeing the sun move, and told somebody else, who told somebody else, who told lots of other people, each of whom told lots of other people … that would be enough to start a popular rumour. Eventually one of those people who heard the rumour would be likely to write it down. But whether or not that’s actually what happened is not what matters, for Hume. What matters is that, however implausible it might or might not be for 70,000 witnesses to be wrong, it is still far less implausible than for the sun to have moved in the way described.

  Hume didn’t come right out and say miracles are impossible. Instead, he asked us to think of a miracle as an improbable event – an event whose improbability we might estimate. The estimate doesn’t have to be exact. It’s enough that the improbability of a suggested miracle can be roughly placed on some sort of scale, and then compared with an alternative such as a hallucination, or a lie.

  Let’s go back to that game of cards we talked about in the first chapter. You remember we imagined that four players were each dealt a perfect hand: pure clubs, pure hearts, pure spades, pure diamonds. If this actually happened, what should we think about it? Again, we can write down three possibilities.

  There has been a supernatural miracle, perpetrated by some wizard or witch or warlock or god with special powers, who violated the laws of science in such a way as to change all the little hearts and clubs and diamonds and spades on the cards, so that they were perfectly positioned for the deal.

  It is a remarkable coincidence. The shuffling just happened to produce this particular perfect deal.

  Somebody has performed a clever conjuring trick, perhaps substituting a previously doctored pack of cards which he had concealed up his sleeve, for the pack we all saw being shuffled out in the open.

/>   Now, what do you think, bearing in mind Hume’s advice? Each of the three possibilities may seem a bit hard to believe. But Possibility 3 is by far the easiest to believe. Possibility 2 could happen, but we have calculated how unlikely it is, and it is very very unlikely indeed: 53,644,737,765,488,792,839,237,440,000 to 1. We can’t calculate the odds against Possibility 1 as precisely as that, but just think about it: some power or force, which has never been properly demonstrated and which nobody understands, manipulated red and black printing ink on dozens of cards simultaneously. You might be reluctant to use a strong word like ‘impossible’, but Hume isn’t asking you to do that: all he’s asking you to do is to compare it to the alternatives, which in this case consist of a conjuring trick and a gigantic stroke of luck. Haven’t we all seen conjuring tricks (often involving cards, by the way) which are at least as mind-boggling as this? Obviously the most likely explanation for the perfect deal is not pure luck, still less some miraculous interference with the laws of the universe, but a trick by a conjuror or a dishonest card-sharp.

  Let’s look at another famous miracle story, the one I mentioned earlier about the Jewish preacher called Jesus turning water into wine. Once again, we can list three main kinds of possible explanation.

  It really happened. Water really did turn into wine.

  It was a clever conjuring trick.

  Nothing of the kind happened at all. It is just a story, a piece of fiction, that somebody made up. Or there was a misunderstanding of something far less remarkable which really did happen.

  I think there is not much doubt about the order of likelihood here. If Explanation 1 were true, it would violate some of the deepest scientific principles we know, for just the same kind of reason we met in the first chapter when talking about pumpkins and coaches, frogs and princes. Molecules of pure water would have to have been transformed into a complex mixture of molecules, including alcohol, tannins, sugars of various kinds and lots of others. The alternative explanations will have to be very unlikely indeed, if this one is to be preferred over them.

  A conjuring trick is possible (much cleverer tricks than that are done regularly on stage and on television) – but less likely than Explanation 3. Why bother even to suggest a conjuring trick, given the lack of evidence that the incident occurred at all? Why even think about a conjuring trick, when Explanation 3 is so very likely, by comparison? Somebody made up the story. People invent stories all the time. That’s what fiction is. Because it is so very plausible that the story is fiction, we don’t need to trouble ourselves to think about conjuring tricks, still less about real miracles that violate the laws of science and overturn everything we know and understand about how the universe works.

  As it happens, we know that lots of fiction has been made up about this particular preacher called Jesus. For example, there’s a pretty little song called the Cherry Tree Carol, which you may have sung or heard. It’s about when Jesus was still inside his mother Mary’s womb (that’s the same Mary as in the Fatima story, by the way), and she was walking with her husband Joseph by a cherry tree. Mary wanted some cherries, but they were too high on the tree and she couldn’t reach them. Joseph wasn’t in the mood to climb trees, but …

  Then up spoke baby Jesus

  From in Mary’s womb:

  ‘Bend down, thou tallest branch,

  That my mother might have some.

  Bend down, thou tallest branch,

  That my mother might have some.’

  Then bent down the tallest branch,

  Till it touched Mary’s hand.

  Cried she, ‘Oh, look thou, Joseph,

  I have cherries by command.’

  Cried she, ‘Oh, look thou, Joseph,

  I have cherries by command.’

  You won’t find the cherry-tree story in any ancient holy book. Nobody, literally nobody who is at all knowledgeable or well educated, thinks it is anything but fiction. Plenty of people think the water-into-wine story is true, but everybody agrees that the cherry-tree story is fiction. The cherry-tree story was made up only about 500 years ago. The water-into-wine story is older. It appears in one of the four gospels of the Christian religion (the Gospel of John: none of the other three, as it happens), but there is no reason to believe it is anything but a made-up story – just one made up a few centuries earlier than the one about the cherry tree. All four of the gospels, by the way, were written long after the events that they purport to describe, and not one of them by an eye witness. It is safe to conclude that the water-into-wine story is pure fiction, just like the cherry-tree story.

  We can say the same thing about all alleged miracles, all ‘supernatural’ explanations for anything. Suppose something happens that we don’t understand, and we can’t see how it could be fraud or trickery or lies: would it ever be right to conclude that it must be supernatural? No! As I explained in Chapter 1, that would put an end to all further discussion or investigation. It would be lazy, even dishonest, for it amounts to a claim that no natural explanation will ever be possible. If you claim that anything odd must be ‘supernatural’ you are not just saying you don’t currently understand it; you are giving up and saying that it can never be understood.

  Today’s miracle, tomorrow’s technology

  There are things that not even the best scientists of today can explain. But that doesn’t mean we should block off all investigation by resorting to phoney ‘explanations’ invoking magic or the supernatural, which don’t actually explain at all. Just imagine how a medieval man – even the most educated man of his era – would have reacted if he had seen a jet plane, a laptop computer, a mobile telephone or a satnav device. He would probably have called them supernatural, miraculous. But these devices are now commonplace; and we know how they work, for people have built them, following scientific principles. There never was a need to invoke magic or miracles or the supernatural, and we now see that the medieval man would have been wrong to do so.

  We don’t have to go back as far as medieval times to make the point. A gang of Victorian international criminals equipped with modern mobile phones could have co-ordinated their activities in ways that would have looked like telepathy to Sherlock Holmes. In Holmes’s world, a suspect in a murder case who could prove that he was in New York the evening after the murder was committed in London would have a perfect alibi, because in the late nineteenth century it was impossible to be in New York and in London on the same day. Anyone who claimed otherwise would seem to be invoking the supernatural. Yet modern jet planes make it easy. The eminent science-fiction writer Arthur C. Clarke summed the point up as Clarke’s Third Law: Any sufficiently advanced technology is indistinguishable from magic.

  If a time machine were to carry us forward a century or so, we would see wonders that today we might think impossible – miracles. But it doesn’t follow that everything we might think impossible today will happen in the future. Science-fiction writers can easily imagine a time machine – or an anti-gravity machine, or a rocket that can carry us faster than light. But the mere fact that we can imagine them is no reason to suppose that such machines will one day become reality. Some of the things we can imagine today may become real. Most will not.

  The more you think about it, the more you realize that the very idea of a supernatural miracle is nonsense. If something happens that appears to be inexplicable by science, you can safely conclude one of two things. Either it didn’t really happen (the observer was mistaken, or was lying, or was tricked); or we have exposed a shortcoming in present-day science. If present-day science encounters an observation, or an experimental result, that it cannot explain, then we should not rest until we have improved our science so that it can provide an explanation. If it requires a radically new kind of science, a revolutionary science so strange that old scientists scarcely recognize it as science at all, that’s fine too. It’s happened before. But don’t ever be lazy enough – defeatist enough, cowardly enough – to say ‘It must be supernatural’ or ‘It must be a miracle?
??. Say instead that it’s a puzzle, it’s strange, it’s a challenge that we should rise to. Whether we rise to the challenge by questioning the truth of the observation, or by expanding our science in new and exciting directions, the proper and brave response to any such challenge is to tackle it head-on. And, until we have found a proper answer to the mystery, it’s perfectly OK simply to say, ‘This is something we don’t yet understand, but we’re working on it.’ Indeed, it is the only honest thing to do.

  Miracles, magic and myths – they can be fun, and we have had fun with them throughout this book. Everybody likes a good story, and I hope you enjoyed the myths with which I began most of my chapters. But even more I hope that, in every chapter, you enjoyed the science that came after the myths. I hope you agree that the truth has a magic of its own. The truth is more magical – in the best and most exciting sense of the word – than any myth or made-up mystery or miracle. Science has its own magic: the magic of reality.

  ACKNOWLEDGEMENTS

  Thanks to: Lalla Ward, Lawrence Krauss, Sally Gaminara, Gillian Somerscales, Philip Lord, Katrina Whone, Hilary Redmon; Ken Zetie, Tom Lowes, Owen Toller, Will Williams and Sam Roberts from St Paul’s School, London; Alain Townsend, Bill Nye, Elisabeth Cornwell, Carolyn Porco, Christopher McKay, Jacqueline Simpson, Rosalind Temple, Andy Thomson, John Brockman, Kate Kettlewell, Mark Pagel, Michael Land, Todd Stiefel, Greg Langer, Robert Jacobs, Michael Yudkin, Oliver Pybus, Rand Russell, Edward Ashcroft, Greg Stikeleather, Paula Kirby, Anni Cole-Hamilton and the staff and pupils of Moray Firth School.

  INDEX

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