“Suppose you live in a place that has a constant chance of being struck by lightning at any time throughout the year. Suppose that the strikes are random: every day the chance of a strike is the same, and the rate works out to one strike a month. Your house is hit by lightning today, Monday. What is the most likely day for the next bolt to strike your house?
The answer is ‘tomorrow,’ Tuesday. That probability, to be sure, is not very high; let’s approximate it at 0.03 (about once a month). Now think about the chance that the next strike will be the day after tomorrow, Wednesday. For that to happen, two things have to take place. First lightning has to strike on Wednesday, a probability of 0.03. Second, lightning can’t have struck on Tuesday, or else Tuesday would have been the day of the next strike, not Wednesday. To calculate that probability, you have to multiply the chance that lightning will not strike on Tuesday (0.97, or 1 minus 0.03) by the chance that lightning will strike on Wednesday (0.03), which is 0.0291, a bit lower than Tuesday’s chances. What about Thursday? For that to be the day, lightning can’t have struck on Tuesday (0.97) or on Wednesday either (0.97) but it must strike on Thursday, so the chances are 0.97 x 0.97 x 0.03, which is 0.0282. What about Friday? It’s 0.97 x 0.97 x 0.97 x 0.03, 0.274 [sic]. With each day, the odds go down (0.0300…0.0291…0.0282…0.0274), because for a given day to be the next day that lightning strikes, all the previous days have to have been strike-free, and the more of these days there are, the lower the chances are that the streak will continue. To be exact, the probability goes down exponentially, accelerating at an accelerating rate. The chance that the next strike will be thirty days from today is 0.97 ^ 29 x 0.03, barely more than 1 percent.
Almost no one gets this right. I gave the question to a hundred Internet users, with the word next italicized so they couldn’t miss it. Sixty-seven picked the option ‘every day has the same chance.’ But that answer, though intuitively compelling, is wrong. If every day were equally likely to be the next one, then a day a thousand years from now would be just as likely as a day a month from now. That would mean that the house would be just as likely to go a thousand years without a strike as to suffer one next month. Of the remaining respondents, nineteen thought that the most likely day was a month from today. Only five of the hundred correctly guessed ‘tomorrow.’
Lightning strikes are an example of what statisticians call a Poisson process (pronounced pwah-sonh), named after the 19th-century mathematician and physicist Siméon-Denis Poisson. In a Poisson process, events occur continuously, randomly, and independently of one another. Every instant the lord of the sky, Jupiter, rolls the dice, and if the land snake eyes he hurls a thunderbolt. The next instant he rolls them again, with no memory of what happened the moment before. For reasons we have just seen, in a Poisson process the intervals between events are distributed exponentially: there are lots of short intervals and fewer and fewer of them as they get longer and longer. That implies that events that occur at random will seem to come in clusters, because it would take a nonrandom process to space them out.
The human mind has great difficulty appreciating this law of probability. When I was a graduate student, I worked in an auditory perception lab. In one experiment listeners had to press a key as quickly as possible every time they heard a beep. The beeps were timed at random, that is, according to a Poisson process. The listeners, graduate students themselves, knew this, but as soon as the experiment began they would run out of the booth and say, ‘Your random event generator is broken. The beeps are coming in bursts. They sound like this: “beepbeepbeepbeepbeep…beep…beepbeep…beepitybeepity-beepbeepbeep.”’ They didn’t appreciate that that’s what randomness sounds like.
This cognitive illusion was first noted in 1968 by the mathematician William Feller in his classic textbook on probability: ‘To the untrained eye, randomness appears as regularity or tendency to cluster.’ Here are a [couple] examples of the cluster illusion.
…The gambler’s fallacy. Many high rollers lose their fortunes because of the gambler’s fallacy: the belief that after a run of similar outcomes in a game of chance (red numbers in a roulette wheel, sevens in a game of dice), the next spin or toss is bound to go the other way. Tversky and Kahnemann showed that people think that genuine sequences of coin flips (like TTHHTHTTTT) are fixed, because they have more long runs of heads or of tails than their intuitions allow, and they think that sequences that were jiggered to avoid long runs (like HTHTTHTHHT) are fair.
…Constellations. My favorite example was discovered by biologist Stephen Jay Gould when he toured the famous glowworm caves in Waitomo, New Zealand. The worms’ pinpricks of light on the dark ceiling made the grotto look like a planetarium, but with one difference: there were no constellations. Gould deduced the reason. Glowworms are gluttonous and will eat anything that comes within snatching distance, so each worm gives the others a wide berth when it stakes out a patch of ceiling. As a result, they are more evenly spaced than stars, which from our vantage point are randomly spattered across the sky. Yet it is the stars that seem to fall into shapes, including the ram, bull, twins, and so on, that for millennia have served as portents to pattern-hungry brains. Gould’s colleague, the physicist Ed Purcell, confirmed Gould’s intuition by programming a computer to generate two arrays of random dots. The virtual stars were plonked on the page with no constraints. The virtual worms were given a random tiny patch around them in which no other worm could intrude. They are shown in [the picture above]; you can probably guess which is which. The one on the left, with the clumps, strands, voids, and filaments (and perhaps, depending on your obsessions, animals, nudes, or Virgin Marys) is the array that was plotted at random, like stars. The one on the right, which seems to be haphazard, is the array whose positions were nudged apart, like glowworms.”
“Witch hunts are always vulnerable to common sense. Objectively speaking, it is impossible for a woman to fly on a broomstick or to turn a man into a cat, and these facts are not too hard to demonstrate if enough people are allowed to compare notes and question popular beliefs. Throughout the Middle Ages there were scattered clerics and politicians who pointed out the obvious, namely that there is no such thing as a witch, and so persecuting someone for witchcraft was a moral abomination. (Unfortunately, some of these skeptics ended up in the torture chambers themselves.) These voices became more prominent during the Age of Reason, and included influential writers such as Erasmus, Montaigne, and Hobbes.
Some officials became infected with the scientific spirit and tested the witchcraft hypothesis for themselves. A Milanese judge killed his mule, accused his servant of committing the misdeed, and had him subjected to torture, whereupon the man confessed to the crime; he even refused to recant on the gallows for fear of being tortured again. (Today this experiment would not be approved by committees for the protection of human subjects in research.) The judge then abolished the use of torture in his court. The writer Daniel Mannix recounts another demonstration:
‘The Duke of Brunswick in Germany was so shocked by the methods used by Inquisitors in his duchy that he asked two famous Jesuit scholars to supervise the hearings. After a careful study the Jesuits told the Duke, “The Inquisitors are doing their duty. They are arresting only people who have been implicated by the confession of other witches.”
“Come with me to the torture chamber,” suggested the Duke. The priests followed him to where a wretched woman was being stretched on the rack. “Let me question her,” suggested the Duke. “Now woman, you are a confessed witch. I suspect these two men of being warlocks. What do you say? Another turn of the rack, executioners.”
“No, no!” screamed the woman. “You are quite right. I have often seen them at the Sabbat. They can turn themselves into goats, wolves, and other animals.”
“What else do you know about them?” demanded the Duke.
“Several witches have had children by them. One woman even had eight children whom these men fathered. The children had heads like toads and legs like spiders.”
The Duke turned to the astonished Jesuits. “Shall I put you to the torture until you confess, my friends?”‘
One of the Jesuits, Father Friedrich Spee, was so impressed that he wrote a book in 1631 that has been credited with ending witchcraft accusations in much of Germany. The persecution of witches began to subside during the 17th century, when several European states abolished it. The year 1716 was the last time a woman was hanged as a witch in England, and 1749 was the last year a woman was burned as a witch anywhere in Europe.
In most of the world, institutionalized superstitious killing, whether in human sacrifice, blood libel, or witch persecution, has succumbed to two pressures. One is intellectual: the realization that some events, even those with profound personal significance, must be attributed to impersonal physical forces and raw chance rather than the designs of other conscious beings. A great principle of moral advancement, on a par with ‘Love thy neighbor’ and ‘All men are created equal,’ is the one on the bumper sticker: ‘Shit happens.’ The other pressure is harder to explain but just as forceful: an increased valuation of human life and happiness.”
“Like the works of Homer, the Hebrew Bible (Old Testament) was set in the late 2nd millennium BCE but written more than five hundred years later. But unlike the works of Homer, the Bible is revered today by billions of people who call it the source of their moral values. The world’s bestselling publication, the Good Book has been translated into three thousand languages and has been placed in the nightstands of hotels all over the world. Orthodox Jews kiss it with their prayer shawls; witnesses in American courts bind their oaths by placing a hand on it. Even the president touches it when taking the oath of office. Yet for all this reverence, the Bible is one long celebration of violence.
In the beginning God created the heaven and the earth. And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. And the Lord God took one of Adam’s ribs, and made he a woman. And Adam called his wife’s name Eve; because she was the mother of all living. And Adam knew Eve his wife; and she conceived, and bare Cain. And she again bare his brother Abel. And Cain talked with Abel his brother: and it came to pass, when they were in the field, that Cain rose up against Abel his brother, and slew him. With a world population of exactly four, that works out to a homicide rate of 25 percent, which is about a thousand times higher than the equivalent rates in Western countries today.
No sooner do men and women begin to multiply than God decides they are sinful and that the suitable punishment is genocide. (In Bill Cosby’s comedy sketch, a neighbor begs Noah for a hint as to why he is building an ark. Noah replies, ‘How long can you tread water?’) When the flood recedes, God instructs Noah in its moral lesson, namely the code of vendetta: ‘Whoso sheddeth man’s blood, by man shall his blood be shed.’
The next major figure in the Bible is Abraham, the spiritual ancestor of Jews, Christians, and Muslims. Abraham has a nephew, Lot, who settles in Sodom. Because the residents engage in anal sex and comparable sins, God immolates every man, woman, and child in a divine napalm attack. Lot’s wife, for the crime of turning around to look at the inferno, is put to death as well.
Abraham undergoes a test of his moral values when God orders him to take his son Isaac to a mountaintop, tie him up, cut his throat, and burn his body as a gift to the Lord. Isaac is spared only because at the last moment an angel stays his father’s hand. For millennia readers have puzzled over why God insisted on this horrifying trial. One interpretation is that God intervened not because Abraham had passed the test but because he had failed it, but that is anachronistic: obedience to divine authority, not reverence for human life, was the cardinal virtue.
Isaac’s son Jacob has a daughter, Dinah. Dinah is kidnapped and raped — apparently a customary form of courtship at the time, since the rapist’s family then offers to purchase her from her own family as a wife for the rapist. Dinah’s brothers explain that an important moral principle stands in the way of this transaction: the rapist is uncircumcised. So they make a counteroffer: if all the men in the rapist’s hometown cut off their foreskins, Dinah will be theirs. While the men are incapacitated with bleeding penises, the brothers invade the city, plunder and destroy it, massacre the men, and carry off the women and children. When Jacob worries that neighboring tribes may attack them in revenge, his sons explain that it was worth the risk: Should our sister be treated like a whore?” Soon afterward they reiterate their commitment to family values by selling their brother Joseph into slavery.
Jacob’s descendants, the Israelites, find their way to Egypt and become too numerous for the Pharaoh’s liking, so he enslaves them and orders that all the boys be killed at birth. Moses escapes the mass infanticide and grows up to challenge the Pharaoh to let his people go. God, who is omnipotent, could have softened Pharaoh’s heart, but he hardens it instead, which gives him a reason to afflict every Egyptian with painful boils and other miseries before killing every one of their firstborn sons. (The word Passover alludes to the executioner angel’s passing over the households with Israelite firstborns.) God follows this massacre with another one when he drowns the Egyptian army as they pursue the Israelites across the Red Sea.
The Israelites assemble at Mount Sinai and hear the Ten Commandments, the great moral code that outlaws engraved images and the coveting of livestock but gives a pass to slavery, rape, torture, mutilation, and genocide of neighboring tribes. The Israelites become impatient while waiting for Moses to return with an expanded set of laws, which will prescribe the death penalty for blasphemy, homosexuality, adultery, talking back to parents, and working on the Sabbath. To pass the time, they worship a statue of a calf, for which the punishment turns out to be, you guessed it, death. Following orders from God, Moses and his brother Aaron kill three thousand of their companions.
God then spends seven chapters of Leviticus instructing the Israelites on how to slaughter the steady stream of animals he demands of them. Aaron and his two sons prepare the tabernacle for the first service, but the sons slip up and use the wrong incense. So God burns them to death.
As the Israelites proceed toward the promised land, they meet up with the Midianites. Following orders from God, they slay the males, burn their city, plunder the livestock, and take the women and children captive. When they return to Moses, he is enraged because they spared the women, some of whom had led the Israelites to worship rival gods. So he tells his soldiers to complete the genocide and to reward themselves with nubile sex slaves they may rape at their pleasure: ‘Now therefore kill every male among the little ones, and kill every woman that hath known man by lying with him. But all the women children, that have not known a man by lying with him, keep alive for yourselves.’
In Deuteronomy 20 and 21, God gives the Israelites a blanket policy for dealing with cities that don’t accept them as overlords: smite the males with the edge of the sword and abduct the cattle, women, and children. Of course, a man with a beautiful new captive faces a problem: since he has just murdered her parents and brothers, she may not be in the mood for love. God anticipates this nuisance and offers the following solution: the captor should shave her head, pare her nails, and imprison her in his house for a month while she cries her eyes out. Then he may go in and rape her.
With a designated list of other enemies (Hittites, Amorites, Canaanites, Perizzites, Hivites, and Jebusites), the genocide has to be total: ‘Thou shalt save alive nothing that breatheth: But thou shalt utterly destroy them…as the Lord thy God has commanded thee.’
Joshua puts this directive into practice when he invades Canaan and sacks the city of Jericho. After the walls come tumbling down, his soldiers ‘utterly destroyed all that was in the city, both man and woman, young and old, and ox, and sheep, and ass, with the edge of the sword.’ More earth is scorched as Joshua ‘smote all the country of the hills, and of the south, and of the vale, and of the springs, and all their kings: he left none remaining, but utterly destroyed all that breathed, as the Lord God of Israel commanded.’
The next stage in Israelite history is the era of the judges, or tribal chiefs. The most famous of them, Samson, establishes his reputation by killing thirty men during his wedding feast because he needs their clothing to pay off a bet. Then, to avenge the killing of his wife and her father, he slaughters a thousand Philistines and sets fire to their crops; after escaping capture, he kills another thousand with the jawbone of an ass. When he is finally captured and his eyes are burned out, God gives him the strength for a 9/11-like suicide attack in which he implodes a large building, crushing three thousand men and women who are worshipping inside it.
Israel’s first king, Saul, establishes a small empire, which gives him the opportunity to settle an old score. Centuries earlier, during the Israelites’ exodus from Egypt, the Amalekites had harassed them, and God commanded the Israelites to ‘wipe out the name of Amalek.’ So when the judge Samuel anoints Saul as king, he reminds Saul of the divine decree: ‘Now go and smite Amalek, and utterly destroy all that they have, and spare them not; but slay both man and woman, infant and suckling, ox and sheep, camel and ass.’ Saul carries out the order, but Samuel is furious to learn that he has spared their king, Agag. So Samuel ‘hewed Agag in pieces before the Lord.’
Saul is eventually overthrown by his son-in-law David, who absorbs the southern tribes of Judah, conquers Jerusalem, and makes it the capital of a kingdom that will last four centuries. David would come to be celebrated in story, song, and sculpture, and his six-pointed star would symbolize his people for three thousand years. Christians too would revere him as the forerunner of Jesus.
But in Hebrew scripture David is not just the ‘sweet singer of Israel,’ the chiseled poet who plays a harp and composes the Psalms. After he makes his name by killing Goliath, David recruits a gang of guerrillas, extorts wealth from his fellow citizens at swordpoint, and fights as a mercenary for the Philistines. These achievements make Saul jealous: the women in his court are singing, ‘Saul has killed by the thousands, but David by the tens of thousands.’ So Saul plots to have him assassinated. David narrowly escapes before staging a successful coup.
When David becomes king, he keeps his hard-earned reputation for killing by the tens of thousands. After his general Joab ‘wasted the country of the children of Ammon,’ David ‘brought out the people that were in it, and cut them with saws, and with harrows of iron, and with axes.’ Finally he manages to do something that God considers immoral: he orders a census. To punish David for this lapse, God kills seventy thousand of his citizens.
Within the royal family, sex and violence go hand in hand. While taking a walk on the palace roof one day, David peeping-toms a naked woman, Bathsheba, and likes what he sees, so he sends her husband to be killed in battle and adds her to his seraglio. Later one of David’s children rapes another one and is killed in revenge by a third. The avenger, Absalom, rounds up an army and tries to usurp David’s throne by having sex with ten of his concubines. (As usual, we are not told how the concubines felt about all this.) While fleeing David’s army, Absalom’s hair gets caught in a tree, and David’s general thrusts three spears into his heart. This does not put the family squabbles to an end. Bathsheba tricks a senile David into anointing their son Solomon as his successor. When the legitimate heir, David’s older son Adonijah, protests, Solomon has him killed.
King Solomon is credited with fewer homicides than his predecessors and is remembered instead for building the Temple in Jerusalem and for writing the books of Proverbs, Ecclesiastes, and the Song of Songs (though with a harem of seven hundred princesses and three hundred concubines, he clearly didn’t spend all his time writing). Most of all he is remembered for his eponymous virtue, ‘the wisdom of Solomon.’ Two prostitutes sharing a room give birth a few days apart. One of the babies dies, and each woman claims that the surviving boy is hers. The wise king adjudicates the dispute by pulling out a sword and threatening to butcher the baby and hand each woman a piece of the bloody corpse. One woman withdraws her claim, and Solomon awards the baby to her. ‘When all Israel heard of the verdict that the king had rendered, they stood in awe of the king, because they saw that he had divine wisdom in carrying out justice.’
The distancing effect of a good story can make us forget the brutality of the world in which it was set. Just imagine a judge in family court today adjudicating a maternity dispute by pulling out a chain saw and threatening to butcher the baby before the disputants’ eyes. Solomon was confident that the more humane woman (we are never told that she was the mother) would reveal herself, and that the other woman was so spiteful that she would allow a baby to be slaughtered in front of her — and he was right! And he must have been prepared, in the event he was wrong, to carry out the butchery or else forfeit all credibility. The women, for their part, must have believed that their wise king was capable of carrying out this grisly murder.
The Bible depicts a world that, seen through modern eyes, is staggering in its savagery. People enslave, rape, and murder members of their immediate families. Warlords slaughter civilians indiscriminately, including the children. Women are bought, sold, and plundered like sex toys. And Yahweh tortures and massacres people by the hundreds of thousands for trivial disobedience or for no reason at all. These atrocities are neither isolated nor obscure. They implicate all the major characters of the Old Testament, the ones that Sunday-school children draw with crayons. And they fall into a continuous plotline that stretches for millennia, from Adam and Eve through Noah, the patriarchs, Moses, Joshua, the judges, Saul, David, Solomon, and beyond. According to the biblical scholar Raymund Schwager, the Hebrew Bible ‘contains over six hundred passages that explicitly talk about nations, kings, or individuals attacking, destroying, and killing others…Aside from the approximately one thousand verses in which Yahweh himself appears as the direct executioner of violent punishments, and the many texts in which the Lord delivers the criminal to the punisher’s sword, in over one hundred other passages Yahweh expressly gives the command to kill people.’ Matthew White, a self-described atrocitologist who keeps a database with the estimated death tolls of history’s major wars, massacres, and genocides, counts about 1.2 million deaths from mass killing that are specifically enumerated in the Bible. (He excludes the half million casualties in the war between Judah and Israel described in 2 Chronicles 13 because he considers the body count historically implausible.) The victims of the Noachian flood would add another 20 million or so to the total.
The good news, of course, is that most of it never happened. Not only is there no evidence that Yahweh inundated the planet and incinerated its cities, but the patriarchs, exodus, conquest, and Jewish empire are almost certainly fictions. Historians have found no mention in Egyptian writings of the departure of a million slaves (which could hardly have escaped the Egyptians’ notice); nor have archaeologists found evidence in the ruins of Jericho or neighboring cities of a sacking around 1200 BCE. And if there was a Davidic empire stretching from the Euphrates to the Red Sea around the turn of the 1st millennium BCE, no one else at the time seemed to have noticed it.
Modern biblical scholars have established that the Bible is a wiki. It was compiled over half a millennium from writers with different styles, dialects, character names, and conceptions of God, and it was subjected to haphazard editing that left it with many contradictions, duplications, and non sequiturs.
The oldest parts of the Hebrew Bible probably originated in the 10th century BCE. They included origin myths for the local tribes and ruins, and legal codes adapted from neighboring civilizations in the Near East. The texts probably served as a code of frontier justice for the Iron Age tribes that herded livestock and farmed hillsides in the southern periphery of Canaan. The tribes began to encroach on the valleys and cities, engaged in some marauding every now and again, and may even have destroyed a city or two. Eventually their myths were adopted by the entire population of Canaan, unifying them with a shared genealogy, a glorious history, a set of taboos to keep them from defecting to foreigners, and an invisible enforcer to keep them from each other’s throats. A first draft was rounded out with a continuous historical narrative around the late 7th to mid-6th century BCE, when the Babylonians conquered the Kingdom of Judah and forced its inhabitants into exile. The final edit was completed after their return to Judah in the 5th century BCE.
Though the historical accounts in the Old Testament are fictitious (or at best artistic reconstructions, like Shakespeare’s historical dramas), they offer a window into the lives and values of Near Eastern civilizations in the mid-1st millennium BCE. Whether or not the Israelites actually engaged in genocide, they certainly thought it was a good idea. The possibility that a woman had a legitimate interest in not being raped or acquired as sexual property did not seem to register in anyone’s mind. The writers of the Bible saw nothing wrong with slavery or with cruel punishments like blinding, stoning, and hacking someone to pieces. Human life held no value in comparison with unthinking obedience to custom and authority.
If you think that by reviewing the literal content of the Hebrew Bible I am trying to impugn the billions of people who revere it today, then you are missing the point. The overwhelming majority of observant Jews and Christians are, needless to say, thoroughly decent people who do not sanction genocide, rape, slavery, or stoning people for frivolous infractions. Their reverence for the Bible is purely talismanic. In recent millennia and centuries the Bible has been spin-doctored, allegorized, superseded by less violent texts (the Talmud among Jews and the New Testament among Christians), or discreetly ignored. And that is the point. Sensibilities toward violence have changed so much that religious people today compartmentalize their attitude to the Bible. They pay it lip service as a symbol of morality, while getting their actual morality from more modern principles.”
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