The puzzlement is nothing new—after all, polished surfaces have been in use for thousands of years. The problem has left many philosophers scratching their heads. According to Plato, “all such appearances are necessary consequences of the combination of the internal and external fire, which forms a unity at the reflecting surfaces.” Lucretius believed that the image “turns inside out.” And Kant reasoned that these objects were merely “sensuous intuitions, that is, appearances whose possibility rests upon the relation of certain things unknown in themselves to something else, namely to our sensibility.” (You probably have questions about these explanations. Can I get back to you?)

In modern times, the problem has not gone away. In the opinion of Martin Gardner in The Ambidextrous Universe (1964), it is all due to a “mental rotation,” and “the mirror has not reversed left and right at all, it has reversed front and back!”

Then in June 1987, there was a renewed flurry of interest when the subject cropped up in the letters section of New Scientist. The result of all this was that I happened to become involved in a three-way correspondence on the subject with Lewis Wolpert (currently emeritus professor of biology as applied to medicine at University College, London) and Richard Gregory (currently emeritus professor of neuropsychology at Bristol University).

By now a subsidiary problem had developed: why do mirrors switch left for right but not top for bottom? Was there some way a mirror could express a preference?

Lewis Wolpert insisted that left and right hands were really inverted. “I still think the real problem with mirrors,” he told me, “is about rotations, and the key thing one needs to explain is why clockwise looks anticlockwise.” What’s more, he maintained that if you rotate a book around its horizontal axis, its mirror image will be not only upside-down but also reversed left-right. To see that this is untrue, try the experiment yourself with this page.

Richard Gregory commented, “[Wolpert] is used to observing embryological, etc., structures, and evidently images are not in his or many other people’s cognitive maps of how things should be.”

Arthur C. Clarke opined that this all had something to do with gravity. Gregory told me, “Whether Arthur Clarke put this thing forward as a joke I am not sure: it was complete nonsense.” He wrote to Clarke, enclosing a typescript of the essay on mirror reversals in his book “Odd Perceptions” but received no reply.

So when you hold a book up to a mirror, what is it that causes the left-right transposition? The answer is . . . you do. What do you do when you want to show the mirror the page? You rotate the book around a vertical axis, switching left for right. And the mirror obligingly displays the result of your rotation. The text in the image reads from right to left.

Why can’t the mirror show an upside-down image? But it can. And once again you are the cause. Beginning with the page facing you, rotate the book around a horizontal axis, switching top and bottom. Once again, the mirror faithfully shows you an upside-down image. And you will notice that the text is not additionally switched left for right. Why should it be?

In case you are confused by the fact that a book is opaque and doesn’t allow you to see the printed page and its mirror image at the same time, imagine that you have written a single lower-case letter b on a sheet of glass. While the letter is still facing you, look at its mirror image: you will see that the letter and its mirror image are exactly the same—b. The mirror has altered nothing. Rotate the sheet of glass around a vertical axis, switching left and right. The letter on the glass has reversed and now looks like a lower-case letter d. And so does its mirror image—again, the mirror has not changed it in any way.

Go back to your starting position showing b, and this time, rotate the sheet of glass around a horizontal axis, switching top and bottom. The letter on the glass now looks like a capital P—and so does its image.

There is a final possibility. Begin with your starting position showing b and rotate the glass twice—once vertically and once horizontally. The glass will now show you what looks like a backwards capital letter P—and so does the mirror, so the letter and its image are still identical. In other words, it is your physical movement of the object that causes any reversals of the image.

Doubters have one further shot in their locker. “Stand in front of a mirror,” they say, “and wave your left hand. The image will wave back with its right hand. So the mirror does cause reversals after all.”

But this is mere word play. Get rid of the words “left” and “right,” and the problem disappears. Wear a wrist watch on your left hand and call this hand the wrist-watch hand. Wave your wrist-watch hand, and the image waves back at you with its wrist-watch hand. Nothing has crossed over. Richard Gregory wrote, “It is amusing that many extremely bright people—Kant, Plato, Martin Gardner, and more immediately some of my cleverest colleagues and students—have got this wrong in various ways.” And the final sentence in his letter to me was the one word: “Amazing.”

Nor was the voice of science silent on the matter: “I have heard from the lips of three witnesses to the most striking occurrences of this kind—The Earl of Dunraven, Lord Lindsay and Captain C. Wynne—their own most minute accounts of what took place. To reject the recorded evidence on this subject is to reject all testimony whatever, for no fact in sacred or profane history is supported by a stronger array of proofs.” So wrote Sir William Crookes, discoverer of the element thallium, inventor of the radiometer, and a pioneer in the study of electrical discharge in a vacuum.

This case has become an object lesson in the fallacy of trusting the reports of “people of standing” rather than the evidence. It concerned the thirty-five-year-old medium Daniel Home (rhymes with fume rather than foam), who, in December 1868, allegedly floated out a window at Ashley House in London, then back through the window of the next room. There were three witnesses: Viscount Adare (later the Earl of Dunraven) was twenty-seven years old; Lord Lindsay (twenty-one) was an astronomer, who later became a fellow of the Royal Society; and Captain Wynne (thirty-three) was an army officer stationed at the Tower of London.

Adare was the first to describe the event in print. He said: “Lindsay and Charlie (Wynne) saw tongues or jets of flame proceeding from Home’s head. We then all distinctly heard, as it were, a bird flying round the room, whistling and chirping.”

Two spirit voices spoke through Home to Wynne. Then Home got up, was “elongated” and raised into the air, and said: “On no account leave your places.” Adare heard Home go into the next room, “heard the window thrown up, and presently Home appeared standing upright outside our window.” Adare was baffled, and Home took him to the window in the next room and invited him to watch: “he told me to stand a little distance off; he then went through the open space, head first, quite rapidly, his body being nearly horizontal and apparently rigid. He came in again, feet foremost, and we returned to the other room.”

From that point on, in the words of the investigator Trevor H. Hall, “it is hard to understand why the witnesses, believing that they had been present at a miracle, were quite incapable afterwards of giving a coherent account of what occurred.”

Even the title of Adare’s account was wrong: “Séance at 5 Buckingham Gate, Wednesday 16th.” But Ashley House was not in Buckingham Gate: it was in Ashley Place. And the séance was held not on a Wednesday but on a Sunday. And the date was not the 16th, but the 13th. Lindsay introduced further confusion when he wrote: “I saw the levitations in Victoria Street.”

Adare wrote: “Outside each window is a small balcony or ledge, 19 inches deep, bounded by stone balustrades, 18 inches high. The balustrades of the two windows are 7 feet 4 inches apart. . . .”

Ashley House is no more, but there still exist photographs of it, and Trevor Hall arranged for his architect friend Peter Bond to calculate all the necessary measurements. The distance between the two windows was about four feet, two inches.

Lindsay said the window was eighty-five feet above the street. The true height was about thirty-two feet. He also said there were no balconies at all, but they are clearly visible in the photographs. The word balcony suggests places where one could stroll outside and take the air, but to my eye, they appear to be more in the nature of large window boxes for plant pots.

It was also Lindsay who “saw two spirits on the sofa, and others in different places.” He wrote: “The moon was shining full into the room.” But on that date, the moon was new, and besides, Adare had written: “It was so dark I could not see clearly how he was supported outside.” There is also the awkward fact that Lindsay was sitting with his back to the window and also, in Trevor Hall’s words, “managing by some miracle to be in both rooms at the same time, saw Home floating outside the window in the next room.”

There were many other discrepancies, and at this late stage, there is no way of sorting out exactly what happened, though even at the time, there were speculations about the method. Some people thought that maybe Home didn’t go outside at all, but simply crept back quietly into the room he had just left.

Nor was everyone charmed by his charisma and his claims to be in touch with the spirit world. When Home had first arrived in London from the United States, the poet Robert Browning attended one of his séances, and said he had never seen so impudent an imposture. When Home called on him, Browning threatened to throw “this dungball” down the stairs. Later he wrote a sarcastic poem about Home, titled “Mr. Sludge, ‘The Medium.’” (“I cheated when I could, rapped with my toe-joints, set sham hands at work. . . .”)

Even Charles Darwin was intrigued with reports of Home’s abilities, but he was too shrewd to take them at face value. “I cannot disbelieve Mr. Crooke’s statement,” he wrote, “nor can I believe in his result.” Unfortunately, he was too ill to accept an invitation to attend a séance—but what a fascinating diary entry that could have given us.

After fourteen years, the players have now put away their darts. In the end, the pros came out ahead, with an average investment gain of 10.2 per cent, while the darts players only managed 3.5 per cent. The really surprising thing is that the stock pickers actually gained an edge over random odds (although there is a suspicion that the pros’ selections may have influenced other people to buy the same stocks, and thus pushed up the price). Not that the pros had things all their own way by any means: there was one wonderful six-month spell in which the darts won six times in a row.

Randomness is of course well known as the psychic’s friend. Persuade people that you have access to the secret pattern in some random sequence, then sit back and wait for the cash to roll in. This has been called the Jeane Dixon Effect, in which the odd hit receives maximum publicity and the thousands of misses are ignored. The recipe is simple: forecast often and don’t keep records. This is a particular favorite of those psychics who claim to help the police by locating the bodies of murder victims.

Random results are also the ally of scammers who offer worthless health remedies. It’s easy to be tempted into thinking that highly surprising results can’t possibly be the result of chance. That’s why random events have been called effects in search of causes. Take Evelyn Adams, the woman who won the New Jersey lottery in 1985 and again in 1986. Not quite the one-in-a-trillion chance claimed by the New York Times. Statisticians Persi Diaconis and Frederick Mosteller put the odds that this would happen to someone, somewhere in America at 1 in 30. This is roughly the same chance as my guessing the playing card you’re thinking of after you've told me it’s a red card.

Nassim Nicholas Taleb held senior trading positions in New York and London before founding his own trading firm, and now specializes in the risks of rare events. He writes: “Outside of textbooks and casinos, probability almost never presents itself as a mathematical problem . . . (in the real world, one has to guess the problem more than the solution).”

He confesses that he once joined the hunt for the secret of entrepreneurs who became millionaires. He found that success simply depended on taking risks (he called these people crisis hunters). Then he realized that if he had done the same study on bankrupts, he would have come up with the same answer. “The first counter-intuitive point is that a population entirely composed of bad managers will produce a small amount of great track records.”

Thus, “if a twenty-five-year-old played Russian roulette, say, once a year, there would be a very slim possibility of him surviving until his fiftieth birthday-but, if there are enough players, say thousands of twenty-five-year-old players, we can expect to see a handful of (extremely rich) survivors (and a very large cemetery).”

After all, if talent were only a matter of good results, firms would go out of their way to hire people who had won the lottery. After listening to the O.J. Simpson trial, Taleb confessed to being truly scared of being arrested for no discernible reason. And “having to fight some glib lawyer in front of a randomness illiterate jury.”

Unfortunately, you can always find some sort of pattern in a random series if you look hard enough. When Carl Sagan studied the cancer cures resulting from a visit to Lourdes, he found that the cure rate was, if anything, lower than the one for spontaneous remission. It was lower than the average for those who didn’t go to Lourdes at all. (So does your chance of survival diminish after you visit the place?)

Sometimes a miss is so egregious that you just can’t hide it: the stock market crash of 1987, the Gulf War, the fall of communist East Berlin. The forecasters missed every one.

The American Meteorological Society has admitted that the limit for weather forecasting is between ten and fourteen days. But as business forecasting consultant William A. Sherden has pointed out, “Any farmer who bets his ranch on weather forecasts going out more than one or two days could just as well use a roulette wheel.” And those who imagine that tinkering with a gas such as carbon dioxide can significantly affect the planet’s climate can have little understanding of the complexity of the random fluctuations of the huge atmospheric engine.

As for money matters, you may recall the old joke: “Why did God create economists? To make weather forecasters look good.”

Alvin Toffler made himself an impressive reputation with such books as Future Shock, but practically all of his predictions have been dead wrong. Herman Kahn, Director of the Hudson Institute, made himself famous for an entire slew of planetary predictions: between 75 and 85 percent have been shown wrong. Professor of Demography Paul Ehrlich (with such books as The Population Bomb) confidently predicted war, pestilence, and famine for the planet, and (as Boston Globe columnist Jeff Jacoby ruefully showed) has been “richly rewarded for his almost perfect record of getting things wrong.”

Why rake over this old ground? Let H.L. Mencken provide an answer: “It seems to me that one of the prime jobs of the educated man on this earth is to denounce charlatans. New ones are always popping up, and the common run of idiots are always succumbing to them.”

In the words of F.R. Rosenthal (The Classical Heritage of Islam): “Islamic rational scholarship, which we have mainly in mind when we speak of the greatness of Muslim civilization, depends in its entirety on classical antiquity . . . Islamic civilization as we know it would simply not have existed without the Greek heritage.”

Ibn Warraq, author of Why I Am Not a Muslim, points out: “Islamic science was founded on the works of the ancient Greeks, and the Muslims are important as the transmitters of Greek (and Hindu) learning that may well have been lost otherwise” (Aristotle, Plato, Galen, Hippocrates, Archimedes, Euclid, Ptolemy). And even so, “most of the translators were Christian.”

Warraq writes: “There is a persistent myth that Islam encouraged science. Adherents of this myth quote the Koran and hadith [traditional sayings of Muhammad] to prove their point . . . ‘Seek knowledge, in China if necessary'; ‘The search after knowledge is obligatory for every Muslim.’ This is nonsense, because the knowledge advocated in the previous quotes is religious knowledge. Orthodoxy has always been suspicious of ‘knowledge for its own sake,’ and unfettered inquiry is deemed dangerous to the faith. . . . All sciences are blameworthy that are useless for acting rightly toward God.”

“Those who kill do not think they are committing any crime,” said Girija Shankar Jaiswal (a lawyer who argues cases for victimized women). “They think they are becoming martyrs. They do not mind going to jail.”

Al-Hasan ibn al-Haytham was one of the greatest scientists of medieval Islam, and his “Optics” strongly influenced Kepler. The French philologist Ernest Renan wrote: “A disciple of Maimonides, the Jewish philosopher, relates that he was in Baghdad on business, when the library of a certain philosopher (who died in 1214) was burned there. The preacher, who conducted the execution of the sentence, threw into the flames, with his own hands, an astronomical work of Ibn al-Haitham, after he had pointed to a delineation therein given of the sphere of the earth, as an unhappy symbol of impious Atheism.”

One is reminded of the nineteenth century English politician John Morley, discussing the life of Voltaire: “Where it is a duty to worship the sun, it is pretty sure to be a crime to examine the laws of heat.”

In the twelfth century Averroes studied medicine and philosophy, and his work on Aristotle was responsible for the development of the inductive, empirical sciences. His reward was to be tried as a heretic, condemned, and exiled. Yet his name is often put forward as being at the forefront of the Islamic history of science.

Renan begged to differ: “To give Islam the credit of Averroes and so many other illustrious thinkers, who passed half their life in prison, in forced hiding, in disgrace, whose books were burned and whose writings almost suppressed by theological authority, are as if one were to ascribe to the Inquisition the discoveries of Galileo, and a whole scientific development which it was not able to prevent.”

There is also a current line of thought that assumes Islamic science has been "hijacked” by fundamentalists, and that all ills can be conveniently attributed to them. But shifting the burden of anti-science to an isolated hard-core fundamentalist group evades the central issue. Taslima Nasreen had a government warrant issued for her arrest in Bangladesh (for “outraging religious feelings”), and has some experience of official Muslim displeasure. “I don’t find any difference between Islam and Islamic fundamentalists,” she says. “. . . I need to say that, because some liberals always defend Islam and blame fundamentalists for creating problems.”

In New Scientist (15 December 2001), Ziauddin Sardar reported: “One particular study, sponsored by the International Federation of Institutes of Advanced Studies (IFIAS) in Stockholm brought together Muslim scientists and scholars worldwide in seminars held between 1980 and 1983. The IFIAS study, published as The Touch of Midas, concluded that the issue of science and values in Islam must be treated within a framework of concepts that shape the goals of a Muslim society.”

Sardar also reports that the early 1990s brought a shift into obscurantism by the defenders of Muslim science: “it began to be argued that all knowledge, including scientific knowledge, could be found in the Koran. This thesis received a tremendous boost from the well-funded Saudi project, Scientific Miracles in the Qur'an (Koran). The project spanned both empirical work, involving comparisons of those verses of the Koran that deal with astronomy and embryology with the latest discoveries, and popularizations through conferences and seminars. Relativity, quantum mechanics, big bang theory, embryology-practically everything was ‘discovered’ in the Koran.”

In summary: “science becomes not a problem-solving enterprise or objective enquiry, but a mystical quest to understand the Absolute. Conjecture and hypothesis have no real place; all enquiry must be subordinate to the mystical experience.”

Nor are there any visible prospects that there will even be open debate in print on the subject. It is a numbing thought that there does not exist a single secular Arabic periodical. In any case, debates that revolve around the concept of heresy are unlikely to lead anywhere worth reaching.

“The idea of the sacred is quite simply one of the most conservative notions in any culture, because it seeks to turn other ideas-uncertainty, progress, change-into crimes.” Those are the words of Salman Rushdie in his Herbert Reade Memorial lecture in February of 1990, while in hiding from a fatwa for blasphemy.

A villager in Karandih died of tuberculosis. Hours later, ten frenzied men, waving swords in the dark, battered at the frail wooden door of Manikui Goipai’s mud and thatch house. “Kill the witch,” they screamed. The attackers broke open the door, and hacked Goipai’s husband to death. They sliced through her son’s arm, but he escaped to summon police before bleeding to death. Then a sword came down on Goipai’s forehead, causing a grievous wound. The attackers fled. Goipai is one of only a few women to survive an attack after being branded a witch in Bihar, India’s most lawless state. According to the Free Legal Aid Committee, 536 women have been killed in the past ten years in just two districts of Bihar. Unofficial estimates say at least 200 women are killed as witches across India every year.

Accused women are dragged into the forest and hacked, hanged, or burned to death. Heads of children have been smashed on rocks. Women suffer smashed teeth, shaved heads, or chopped off breasts. Others have been forced to eat excrement, or to strip and walk naked through the village. Many of the killers are related to the victims, and attack out of fear of a witch’s powers, and the possibility of social rebuke for having a witch in the family.

“Those who kill do not think they are committing any crime,” said Girija Shankar Jaiswal (a lawyer who argues cases for victimized women). “They think they are becoming martyrs. They do not mind going to jail.”

In the village of Damaria, a young man chopped off his aunt’s head and took it to a police station to boast that he had killed a witch. But most such villages are located deep inside hilly and forest areas, and thus still inaccessible, so convictions are rare. By the time reports of the tortures and killings reach the police, all evidence leading to the culprits has been destroyed.

Witch killers are not interested in proof. A man who was merely suspected of practicing witchcraft was beaten to death by villagers at Kottkameta. In the village of Burrathogu, a woman, Korru Venkamma, died of ill health. Suspecting witchcraft, the villagers took her body to the house of Soyam Mutyalu, and searched for him. When they found him returning from the fields, they beat him to death with sticks.

But most of the victims are women. One of them was twenty-seven-year-old Chaibindia, a physically handicapped woman. About a dozen people, including one of her close relatives, raped her, then killed her and six members of her family, including her mother, father, and sister.

Most witch killings have their roots in sickness or death. In Bihar state, where only 52 percent of the men and 23 percent of the women are literate, there is only one primary care center for every 100,000 people. So the village exorcist doubles as a doctor. Ajitha George is doing research on witch killings for the Chicago-based MacArthur Foundation. “Traditionally,” she says, “ojhas used to give medicine using herbal potions, but now the tribal health system is falling apart. Now there are many new diseases, and they don’t know the cure.”

But when they fail to treat a sick person, they attribute their failure to some woman, usually a widow or a childless woman, preferably one with some property. They claim that such a woman can harm a person by just looking at them, or by throwing something like a piece of driftwood towards their victim. A woman is said to acquire this power by killing someone close to her. Then, by going through some rituals, she can inflict injury on anyone without being visible.

The torture and execution of witches are not impulsive actions taken in the heat of the moment. In a planned operation lasting four hours, the single phone connection to the village of Timmapur was cut, then the five victims were bound, battered, and tied to a tree. They were then doused in kerosene and burnt alive.

Nor is the credulity always connected with belief in witchcraft. In the Bidar district, construction workers found the arms and legs of a six-and-a-half-year-old victim sticking out of a pit. They found the head separately “with scratch marks on it.” His grandfather said the boy was killed to appease the gods before commencing the construction of the building.

At Newasa, three children were kidnapped, but not for ransom. Their blood was needed to propitiate the gods, to reveal the spot where a treasure trove was said to have been hidden. The police recovered a pitcher used for carrying the children’s blood.

Some people who do not have a male child think they can get one by sacrificing a young child. This is the reason given by Tara, a Punjab woman, who sacrificed the five-year-old son of a neighbor at the suggestion of a local tantrik or baba. In the words of a local policeman, “the neck was twisted to draw out the blood. Then the toes and fingers were also cut to draw more blood to fill a vessel, to adhere to the tantrik’s directions of drawing out maximum blood.” The tantrik, Om Parkash, unhesitatingly confessed to presiding over the entire procedure.

He explained without emotion that the boy cried a little before he was felled by a swoop of the sharp-edged fodder-cutter.

It might also help to explain why it was in ancient Greece that science had its one and only beginning on this planet. The ancient Greeks, you see, had no Sacred Book. There was no holy, indisputable, God-dictated Book to which you could refer to obtain a final ruling. There was no ultimate authority to consult if you wanted an answer to your questions about the world. If you wanted to know something, your only recourse was to sit down and figure it out. And if you wanted to convince others of the correctness of your solution, you had to set out your reasoning and see if they bought it.

There was almost no preoccupation with sin, since the very concept was a religious notion. Neither were there officials who forbade you to investigate certain taboo areas of knowledge. And since there was no Book, there were no authorities to insist on interpreting it for you.

There were priests who had duties in making sacrifices and keeping festivals and observing rituals, but these were ordinary citizens with normal lives to live and families to raise. There was no class or caste of priests. (Compare the power of priests in Babylonia, Egypt, Persia, Syria, and of the Druid-priests of Europe.) Since priests in ancient Greece were only laymen doing part-time jobs, they had no authority to demand blind submission from their fellow citizens. The Greeks took a poor view of such self-abasement, and would have looked down on it as dishonorable behavior.

They had no urge to go forth and convert heathens to the service of Greek gods. A Greek who claimed to have the one true religion, and who preached that other gods were false, would have been thought in need of a lesson in good manners. So there were no missions, and no missionaries. Seltman again:

“One emperor, Severus Alexander, wishing to venerate Christ, had a statue of Jesus put in the palace chapel upon the Palatine Hill in Rome. It was quite impossible for any sincere Christian to reciprocate with a like polite gesture without committing the sin of a ‘lapse'.”

As a result, there were no martyrs, and of course, no religious persecutions. There is no point in persecuting deviation from the Book if you don’t have a Book to deviate from.

In the words of biologist Lewis Wolpert: “Thales of Miletos, who lived in about 600 b.c., was the first we know of who tried to explain the world not in terms of myths but in more concrete terms, terms that might be subjected to verification.” Simply keeping a tally of events doesn't count as science. “There is thus nothing in the Egyptian cosmology which even tries to account for Ra’s journeys or their seasonal variations.” And Buddhist doctrines were of no help to cosmologists in ancient China: “Even though the Chinese were the most persistent and accurate observers of celestial phenomena before the Renaissance, they did not develop a planetary theory and they did not have access to a geometrical theory. There was no Chinese Euclid.” On the contrary, “the Chinese, often thought of as scientists, were expert engineers, but made negligible contributions to science.”

It would be nice to think that in these enlightened times we are at last free of the dead hand of the Book. But as Carl Sagan reminds us, “When the movie Jurassic Park was shown in Israel, it was condemned by some orthodox rabbis because it accepted evolution and because it taught that dinosaurs lived a hundred million years ago, when, as is plainly stated at every Rosh Hashanah and every Jewish wedding ceremony, the Universe is less than 6,000 years old.”

It is never long before the Book is claimed to contain everything that anyone could possibly want to know, and that to search further for knowledge is wicked. Ibn Warraq writes: “Every time there is a new scientific discovery in, say, physics, chemistry or biology, the Muslim apologists rush to the Koran to prove that the discovery in question was anticipated there; everything from electricity to the theory of relativity.” Ernest Renan maintained: “Science and philosophy flourished on Musalman soil during the first half of the Middle Ages; but it was not by reason of Islam, it was in spite of Islam. Not a Musalman philosopher or scholar escaped persecution.”

Stephen Hawking was one of the cosmologists invited to a conference at the Vatican. Later, he reported, “At the end of the conference, the participants were granted an audience with the pope. He told us that it was all right to study the evolution of the universe after the big bang, but we should not inquire into the big bang itself because that was the moment of creation and therefore the work of God.”

It is all sadly at odds with Isaac Asimov’s characterization of the Bible as “a collection of two-thousand-year-old writings by provincial tribesmen with little or no knowledge of biology, astronomy, and cosmogony.”

People often lay claim to a belief that in fact they cannot hold. A belief needs to be defensible. Anyone who claims to believe everything in the Bible, for example, only thinks he believes these things. Since parts of the Bible flatly contradict other parts, it just isn’t possible to believe all of it. This is true of many beliefs that come in packages. It is sometimes said that an opinion is what someone says he has when he is still willing to argue his case, and to be persuaded that he is wrong; or that faith is, as H. L. Mencken put it, “an illogical belief in the occurrence of the improbable.” But in fact there’s a whole spectrum of belief-words, and there’s no way of ranging opinions, claims, notions, views, tenets, gut reactions, and viewpoints into any kind of foolproof order from the most airy of hunches to the most passionate of convictions. Nor does firmness of belief equate with probability of truth. In the words of Friedrich Nietzsche: “a casual stroll through the lunatic asylum shows that faith does not prove anything.”

To avoid drowning in a sea of warring definitions, I propose to label them all opinions (of varying strengths). This allows one to extend the line of inquiry by asking another question: Does a man have a right to his opinions? In a democracy, the answer yes is often taken for granted, and is defended with arguments about personal freedom. But the thoughtful answer is: “not necessarily.” The square root of forty-nine is not a matter of opinion. To put it more strongly, no one has the right to believe that it is eight, since this is an opinion that cannot be defended.

Readers of this newsletter will not need reminding that the fourth letter of CSICOP stands for the word “claims.” Indeed that concern is itself a claim. And sometimes skeptics with a misguided notion of tolerance assert that any claim whatever ought to be fully investigated. The purveyors of quack medicine have always been quick to pick up this point of view, and agree that (in the name of the open mind) medical researchers should drop whatever they are doing and spend their time endlessly testing and retesting pyramid power or faith healing or prayer. It is a common assumption that for any given subject, people must have an opinion; and furthermore that people know what their own opinion is. Neither of these assumptions need be true.

A survey organization once asked the simple question: “Have you ever heard of the Taft-Johnson-Pepper Bill on veterans’ housing?” Fifty-three percent of the respondents said yes. It can hardly be denied that these people had no right to their opinion, since the bill in question does not exist, and was simply invented for the purpose of the survey. Pollsters know that “the good respondent answers yes.” (People have learned that the answer no is often followed by disagreeable requests for justification.) When Britain’s Consumers Association asked people what they thought of the complementary medicine they had tried, 51 percent of them claimed it had improved them, and 31 percent claimed it had cured them. Notice that these people were not just saying they felt better: they were specifically claiming that the treatment was the cause of their improvement or cure - an opinion they had no right to (and that the Consumers Association had no right to ask them). It was a neat illustration of the philosopher Wittgenstein’s comment: “If there were a verb meaning believe falsely, it would not have any significant first person, present indicative.”

Tiny changes in wording can affect people’s stated opinions. One survey wanted to find out whether people favored limiting the president to one term in office. When asked if they favored doing this by “adding to” the Constitution, 50 percent said no. When asked if they favored doing it by “changing” the Constitution, 65 percent said no. Answers without responsibility also give notoriously poor quality opinions. If asked, “Would you like a free Skeptical Briefs with your copy of The Times?” most people would say yes. This would not show that most people like Skeptical Briefs. (Those who hated it could give the copy to someone else, or just throw it away.) The mention of even a small fee would change the answers drastically.

Respondents can’t even be relied upon with plain facts. In an Australian census, one-third of respondents claimed to have no ethnic origin at all. In a repeat American census, more than a third gave a different ethnic origin between one survey year and the next. When asked what they valued about a job, people ranked “good pay” first when asked an open-ended question, but they ranked it last when asked to choose from a list.

Lists themselves can affect answers. The last item on a list attracts about 10 percent more responses than when placed as the first item. A response can be affected by the response to the previous item. People claim to be much happier with their marriage if the response follows a previous question about happiness with things in general. In an agree-disagree question, about 22 percent will shift to “don’t know” if they are given that added option. People tend to agree with what they imagine the interviewer is thinking, even this involves contradicting themselves. They will agree that when it comes to crime, social conditions are more to blame than individuals; and later in the same interview they will agree that individuals are more to blame than social conditions. It is a reminder that “being positive” about something is often, in the words of Ambrose Bierce, “being mistaken at the top of one’s voice.”

One television critic protested at the unveiling of a natural “mystery,” and complained that the series was an “intrusive delving into the sanctity of human life.”

The declared message is simply, “I don’t want to know.” But the wider implication is, “People in general should not be allowed to know these things.” Mystery equals fun, and by explaining mysteries you are taking all the fun out of life. Spoilsport!

I don’t know what answer these people would give if you asked them whose names should be on the priesthood list of those privileged to possess such forbidden knowledge. Would the mystifiers care to have an inflamed appendix removed by a surgeon who had kept himself uncorrupted by the sacred mysteries of the inner abdomen? Would they be happy to cross the Atlantic in a plane piloted by someone who thought the only qualification he needed was an appropriate sense of awe at the mysteries of flight?

I would guess that skeptics and scientists have been familiar with this kind of attitude for as long as there has been such a thing as science. The key phrase these days seems to be “a sense of wonder” — characterized as something you suddenly lose as soon as you learn something of the inner workings of some phenomenon.

Not even Nobel laureates are immune to these charges. A friend of physicist Richard Feynman once told him, “I, as an artist, can see how beautiful a flower is. But you, as a scientist, take it all apart and it becomes dull.” (Feynman’s comment: “I think he’s kind of nutty.”) Later, Feynman explained, “First of all, the beauty that he sees is available to other people — and to me too, I believe . . . But at the same time, I see much more in the flower than he sees. I can imagine the cells inside, which also have a beauty.”

On another occasion, he said, “For instance, the ancients believed that the earth was the back of an elephant that stood on a tortoise that swam in a bottomless sea. Of course, what held up the sea was another question . . . It was a poetic and beautiful idea. Look at the way we see it today. Is that a dull idea? The world is a spinning ball, and people are held on it on all sides, some of them upside down. And we turn like a spit in front of a great fire. We whirl around the sun. That is more romantic, more exciting . . . Or there are the atoms. Beautiful — mile upon mile of one ball after another ball in some repeating pattern in a crystal . . . What looks still to our crude eyes is a wild and dynamic dance.”

Richard Dawkins has made the point in another way: “I wish I could meet Keats or Blake to persuade them that mysteries don’t lose their poetry because they are solved. Quite the contrary. The solution often turns out more beautiful than the puzzle . . .” Let’s say you’re watching a ventriloquist and enjoying the amusing repartee, when someone turns to you and whispers: “The other guy is just a dummy, you know. Not a real person.” Do you now leave in disgust, because the illusion has been spoiled forever? Or do you still find yourself turning your head from one performer to the other as they talk? If you really think rational explanation destroys a good illusion, I have bad news for the next time you attend a film or a play: the people in it are all pretending. There. Now I've ruined your theatre-going experience for the rest of your life. Haven't I?

Magicians can get very jumpy on the subject of explaining illusions. They have a stock set of dire predictions. “Nobody will ever come to see magic shows.” “Nobody will employ magicians again.” Sure. And David Copperfield is back on the bread line.

One of the weakest lines of argument is that little children are being deprived of their “sense of wonder” (here we go again): “Are you saying you would destroy a child’s belief in Santa Claus?” This last is offered as a knock-down argument with which no one could disagree. I have never understood why. The appearance of presents on a child’s birthday is not attributed to a secret delivery by a Birthday Fairy, and I have never heard a child complain because the gifts were handed over by the giver in person. As Tom Flynn puts it (in The Trouble with Christmas): “There is something disturbing in the length to which parents will go to fabricate physical evidence to support the Santa Claus myth. It is popular to call such deceptions ‘cute,’ but don’t they really amount to laying traps for youngsters’ emerging capacities for critical thinking?”

Scott Kim is perhaps best known for his ”Inversions” — words that can be read “right side up, upside down and every which way.” He once wrote: “When I was a child, magic fascinated me. I learned very young just how powerfully people’s attention can be misdirected. The only problem was that I always wanted to explain how the tricks were done. I wanted everyone to see how they were being fooled.” He then added something that some will find very hard to understand, but that sums up the whole issue neatly: “To understand the mechanism and still be entranced — that to me is the greatest magic.”

These days, alternative therapies and claims of the paranormal are commonly defended by the same line of argument: “We don’t know the mechanism, but that doesn't matter as long as it works.” It seems like a call for simple tolerance in the face of incomplete knowledge. And in the case of aspirin, it was just that. It may seem curmudgeonly to insist that results alone are not enough, and that attention needs to be paid to the mechanism. Well, I guess that makes me a curmudgeon.

In the first place, it has always struck me as deeply suspicious that someone would herald the existence of a new and surprising phenomenon, and then just walk away from it, and claim to have no interest in how it works. If you had been the discoverer of the totally unexpected phenomenon of X-rays, would you have shrugged off the whole thing and washed your hands of any further involvement?

Would this not suggest that you not only had done little in the way of serious investigation yourself, but that you might have some curious disinclination to encourage investigation by others? As James Alcock reminded us in Parapsychology: Science or Magic? (Pergamon, 1981), “within two months of his discovery of X-rays, Roentgen had identified seventeen of their major properties.” Now that’s more like it.

It becomes impossible to take seriously any of the astrologers (including Gauquelin and his “astrobiology”) when you realize that not one of them appears to have the slightest interest in discovering a possible mechanism. The nearest thing we ever get is analogy, not theory. (“Gravity can act across space, can’t it? Well then.”)

“Events that ‘cannot happen’ according to received wisdom rarely gain respectability by a simple accumulation of evidence for their occurrence,” writes Stephen Jay Gould; “they require a mechanism to explain how they can happen.” The lack of any curiosity about mechanism alerts us to the likelihood that someone prefers grinding axes to grinding out experimental procedures. It increases our respect for the founder of evolution that in the early stages he was profoundly disturbed by his inability to answer the question how. In Gould’s words: “Darwin returned to London without an evolutionary theory. He suspected the truth of evolution, but had no mechanism to explain it.”

There is a general belief that until Wegener came along, scientists were compulsively blind to the obvious possibility of a fit between the continents of Africa and America. In fact, there was never any doubt about the shapes and what they might mean. What was lacking was any conceivable mechanism for pushing entire continents across the surface of the globe. But as soon as plate tectonics provided a causal mechanism, the theory of continental drift took off. As Philip Kitcher has pointed out, geologists “do not respond to a particular earthquake by stating some ‘principle of plates'.”

Faced with a firm believer in the existence of witches, you are unlikely to be offered a simple demonstration of a woman turning into a toad. But in view of the enormity of the claim, it would be fair to ask how. Since believers will never have personally witnessed this transformation either, they should at least be willing to explain why they find the mechanism plausible.

Notice that in practical matters of life and death, no one disputes that the question how is vital. If you were accused of murder, it would scarcely do for the prosecution to simply claim that you “obviously” did it. With no satisfactory answer to how, the case would be at an end.

On the night of September 27, this year, certain communities in various parts of the world beat gongs and tom-toms to restore the light of the moon after the eclipse. You may have noticed that this procedure was entirely successful. If you disagree, then you will have relied on asking yourself the simple but powerful question: How?

Those whose professional life revolves around the assessment of psychic events are especially prone to dismiss the importance of mechanism and to show little interest in searching for it. As statistician Chris Scott once wrote, this “encourages a further suspicion: that parapsychologists are, by motivation, not problem-solvers, but mystery-mongers.”

Psychoanalysts have a great deal to answer for in this regard. Psychologist Stuart Sutherland (in Breakdown) has reminded us of “all the poor wretches who have endured to no purpose the pain of analysis, and the fact that the mystique of analysis may have prevented psychologists from attempting to develop more effective procedures for dealing with mental illness . . . . Most hospitals in both Great Britain and North America can instance cases of women who were treated for frigidity by analysts, only to discover eventually that they had a vaginal lesion; or of men who underwent the pain and expense of an analysis to cure depression or agitation, only to discover that their thyroid glands were not functioning properly.”

I will concede only this much: if the claimed results really occur, then (and only then) might you be given a temporary benefit of the doubt; but even so, only on the assumption that you will waste no time in getting on with the task of finding out how the thing works. Only then, as in the case of aspirin, can you begin amending and refining and improving the outcome. In cases where there are no confirmed results of predictions in the first place, even the search for a mechanism is a waste of time.

Some cause-and-effect sequences are straightforward. Some are more complex. And some are misinterpreted by those who should know better. For a bizarre example of this last phenomenon, I offer you the health activists (variously known as health Leninists, health fascists, and other even less complimentary terms).

When coronary heart disease (CHD) became the latest media bogeyman, the alarmists were keen to tell us all what to do and what not to do. Unfortunately, they were aided by the epidemiologists, who were looking for something else to occupy their attention, now that infectious diseases were becoming so much less common. I say “unfortunately” because the epidemiological model is the wrong one to use. It is the clinician who pinpoints cause and effect by noting and manipulating changes in the individual. The epidemiologists set about comparing entire countries.

There are countless similarities and differences between one country and another, so it’s not surprising that the list of things held in common by CHD sufferers across the world quickly became a long one. By now, there are about 300 of these poorly named, so-called risk factors. They include snoring, baldness, not having siestas, extramarital sex, not keeping appointments, not eating mackerel, having English as a mother tongue, not being a Mormon, slow beard growth, no garlic, and having an intelligent wife. They also include the interesting pair: too much milk, and too little milk.

You might expect that any rational thinker would be able to distinguish between a correlation and a cause. Otherwise the possession of a driving license would have to count as a “risk factor” for a fatal car accident, and learning to swim would be a “risk factor” for drowning. Nevertheless, an entire health-alarm industry has fallen in love with the association game. The belief seems immune to disproof. James McCormick and Petr Skrabanek gathered together the results of all the major intervention trials, and published the resulting tables in the medical journal The Lancet (Oct. 8, 1988). The various interventions manipulated diet, smoking, blood pressure, exercise, and reducing weight, and covered 828,000 man-years. “This summary shows no experimental evidence to support the notion that intervention programs prevent coronary heart disease or reduce overall mortality. . . . Despite this considerable body of evidence, which shows no benefit for intervention, many have interpreted the results as supportive of their wishful thinking.” This review, they say “provides no data to justify the time, energy, and money which are being devoted to this crusade.”

One of the favorite villains right now is cholesterol. Most of the public had never heard of it before the present hit list was drawn up, but now many of them are altering their entire lifestyle and eating habits trying to avoid it. This is in spite of all the evidence showing the pointlessness of any such measures. The result produced by 115,176 man-years of observation was that “lowering cholesterol by drugs did no good and may have done harm.” The same applies to altering cholesterol by diet. In Sweden, for example, coronary deaths in middle-aged men were rising while the risk factors were falling. In a number of countries, death rates for men and women are moving in opposite directions, in spite of the fact that they eat the same foods. In fact, most people with heart disease have a normal cholesterol level.

Skrabanek summarizes evidence presented in the British Medical Journal and The Lancet: “Blood cholesterol for practical purposes has no predictive value for the risk of future heart attack in the individual, and manipulation of blood cholesterol with diet or drugs has no effect on overall mortality, though it may significantly increase the risk of cancer death.”

Do you really want to turn over your life to the heath zealots? G. S. Myers has put together this composite picture of someone with a low risk of CHD: “. . . an effeminate municipal worker or embalmer completely lacking in physical or mental alertness and without drive, ambition, or competitive spirit who has never attempted to meet a deadline of any kind; a man with poor appetite, subsisting on fruits and vegetables laced with corn and whale oil, detesting tobacco, spurning ownership of radio, television, or motorcar, with full head of hair but scrawny and unathletic appearance, yet constantly straining his puny muscles by exercise. Low in income, blood pressure, blood sugar, uric acid and cholesterol, he has taken nicotinic acid, pyridoxine, and long-term anti-coagulant therapy ever since his prophylactic castration.”

All this health advice is not the work of clinical or medical researchers, who know better, but is issued by “health committees,” who vote their list of recommendations into existence. Their unstated motto appears to be (in Skrabanek’s words): “If it is delicious, proscribe it; if it is bland, prescribe it.” K.A. Oster, in Medical Counterpoint, warned that these recommendations, “with wasteful neglect of nutritious foods, such as butter, eggs, whole milk, cheeses and beef, borders on irresponsibility and smacks of medical quackery.”

Another result of “riskfactormania” is that city streets are often littered with joggers, who seem unaware of the most common cause of death among joggers—coronary heart disease. The American cardiologist Henry Solomon estimates that every year about 40,000 Americans drop dead while exercising “for their health.”

Perhaps I should now confess that the Bell Prompt I mentioned in the beginning was the digital watch on my left wrist. In health committee terms, that makes the display on my watch a risk factor for the striking of Big Ben. I shouldn’t take that too seriously either if I were you.