How to Predict Everything

The Formula Transforming What We Know About Life and the Universe

William Poundstone

• Publisher: Oneworld Publications
• Year: 2019
• eBook ISBN: 9781786075727
• Topic: Mathematics
• Subtopic: Business Mathematics
• Index: Mathematics

How do you predict something that has never happened before?

There's a useful calculation being employed by Wall Street, Silicon Valley and maths professors all over the world, and it predicts that the human species will become extinct in 760 years. Unfortunately, there is disagreement over how to apply the formula, and some argue that we might only have twenty years left.

Originally devised by British clergyman Thomas Bayes, the theorem languished in obscurity for two hundred years before being resurrected as the lynchpin of the digital economy. With brief detours into archaeology, philology, and overdue library books, William Poundstone explains how we can use it to predict pretty much anything. What is the chance that there are multiple universes? How long will Hamilton run? Will the US stock market continue to perform as well this century as it has for the last hundred years? And are we really all doomed?

Part I

Consider the Lemming

The end is near. Or not. The following chapters explore the doomsday argument, a simple line of reasoning that leads headlong to the conclusion that humanity does not have much time left. We meet the doomsayers and their critics and encounter such topics as the runs of Broadway plays, the populations of lemmings, and the riddle of Sleeping Beauty. We find that at least some doomsday calculations deserve to be taken seriously, and we assess our prospects.

How to Predict Everything

Six-year-old Helen Gregg, her nine-year-old sister, Frances, and their nine-year-old cousin, Ella Davies, never saw the atomic bomb that hit their playhouse. They were about six hundred feet away, in the South Carolina woods, on that bright spring day of March 11, 1958. The bomb was egg-shaped with stabilizing fins, a near-twin of the “Fat Man” bomb that struck Nagasaki. It annihilated the playhouse that Helen and Frances’s father had built for the girls, leaving a crater seventy-five feet across and thirty feet deep.

All the tons of earth thrown up in the air came back down in a hellish rain. It was that that injured the three girls, parents Walter and Effie Gregg, and their son Walter Jr. There were no deaths aside from a few chickens. The Greggs lived in a town called Mars Bluff. Today, sixty summers later, the crater is still visible.

Albert Madansky was a young statistics PhD from the University of Chicago, recruited by the RAND Corporation, a Santa Monica think tank contracting to the Pentagon. RAND wanted Madansky to tackle a problem that was easy to state but difficult to answer: What is the probability of a nuclear weapon detonating by accident?

The Mars Bluff incident, occurring the year after Madansky began work at RAND, was a prime topic of discussion. Madansky learned what the public had not. A B-47 Stratojet had left Hunter Air Force Base, Georgia, as part of a drill in handling atomic weapons. Early in the flight a red warning light came on in the cockpit, indicating that the bomb wasn’t properly secured.

Copilot Bruce Kulka banged the warning light with the butt of his service revolver. The light went off. Later it came back on. Kulka went to the bomb bay to fix the problem. He reached around the bomb to engage a lock, hitting the wrong button. The weapon came loose, crashing through the bomb bay doors and plummeting fifteen thousand feet.

A fission bomb contains chemical explosives, TNT in this case, surrounding a core of uranium or plutonium. Unspeakable tragedy was avoided only because the bomb was unarmed, without any fissile material. The ground impact detonated the TNT, however, creating a massive conventional explosion.

Accidents like Mars Bluff had been happening for some time. Madansky was allowed to see a top secret list of sixteen “dramatic incidents” that had occurred between 1950 and 1958.

RAND’s people worried about other scenarios. What if a bomb was lost and a civilian found it? What if an angry or unstable officer launched an atomic bomb without authorization? There were no statistics on such events because they had never happened.

In conventional statistical thinking, you can’t assign a probability to something that has never happened. Whereof one has no data, one must remain silent. . . . But Madansky had studied statistics at Chicago with Leonard “Jimmie” Savage. Savage had been born with the name Ogashevitz, though it was generally agreed that Savage fit him better. He was brutally critical of anyone he judged less brilliant than himself, a group that seemed to cover just about everyone in the fields of mathematics and economics. Savage was a contrarian by nature. One of his most contrary pet ideas was Bayes’s theorem—an obscure formula, named for an obscure minister of eighteenth-century England. Madansky was able to see that Bayes’s theorem offered exactly what RAND needed: a way to assign a probability to doomsday.

RAND’s 1958 report (authored by Madansky and colleagues Fred Charles Iklé and Gerald J. Aronson, and declassified in 2000) noted that the US atomic arsenal was growing rapidly, multiplying the opportunities for an accident. At the height of the Cold War, the Strategic Air Command intended to keep about 270 B-52 bombers in the air at all times, ready to launch a nuclear attack on word from the president.

“A probability that is very small for a single operation, say one in a million, can become significant if this operation will occur 10,000 times in the next five years,” the RAND report warned. With more bombs being transported more miles, the authors computed that a major catastrophe was near-inevitable in just a few years.

The report sketched countermeasures, ranging from the mundane to the bizarre. It proposed electrifying the bomb’s arming switches, so that anyone touching them would get a mild shock, lessening the chance of accidentally hitting the wrong button. As to the Dr. Strangelove scenario of a deranged individual starting World War III, the report argued for psychological screening of all who worked with the bombs. The most practical ideas were to put combination locks on bombs and to arrange that two individuals must act simultaneously to arm a bomb.

The RAND group was reporting to General Curtis LeMay, a no-nonsense war hero who fretted about American leadership being too politically correct to use its nuclear weapons. To Madansky’s relief, LeMay immediately grasped the seriousness of the problem. The general ordered the combination locks and the two-person system.

In folk wisdom, lightning never strikes the same place twice. Yet on January 24, 1961, the Carolina low country had another nuclear close call. One of LeMay’s B-52s developed a fuel leak and began to break up in midair near Goldsboro, North Carolina. As the tail sheared off, two bombs slid out of the bomb bay and plunged to earth. Three crew members died, and five parachuted to safety.

There wouldn’t have been any safety had the bombs gone off. This B-52 was carrying hydrogen bombs. Had either of them detonated, the fallout plume would have reached Philadelphia, 400 miles away.

One of the bombs was discovered suspended from a tree by its parachute. It had barely kissed the earth. The “arm/safe” switch was still on “safe.”

The other bomb’s parachute failed to deploy. This bomb broke apart, and the fragments fell into a swampy area with enough water to soften the impact and spare the conventional explosives.

Bomb disposal expert Lieutenant Jack ReVelle was called in to find the pieces. “Until my death,” ReVelle said, “I will never forget hearing my sergeant say, ‘Lieutenant, we found the arm/safe switch.’ And I said, ‘Great.’ He said, ‘Not great. It’s on “arm.” ’ ”

“You’re the Product”

Thomas Bayes, the nonconformist minister of Tunbridge Wells, drew his last breath on April 17, 1761. For reasons not clear he left his life’s greatest achievement filed away, unpublished and unread. It was another mathematically inclined minister, Richard Price, who found Bayes’s manuscript after his death and recognized its importance. Price counted among his acquaintances a notorious group: the American revolutionaries Thomas Paine, Thomas Jefferson, and Benjamin Franklin, as well as Mary Wollstonecraft, the feminist who married an anarchist and gave birth to the author of Frankenstein.

Price sent the Royal Society of London “an essay which I have found among the papers of our deceased friend Mr. Bayes, and which, in my opinion, has great merit.”

This essay described what we now call Bayes’s theorem (or rule or law). It addresses a fundamental question of the Enlightenment worldview: How do we adjust our beliefs to account for new evidence?

To put it in modern terms, you start with a prior probability (“prior,” for short). This is an estimate of the likelihood of something happening, based on everything already known. This estimate is then adjusted up or down for new data, according to a simple formula.

Price praised Bayes’s ingenuity but offered this warning: “Some of the calculations . . . no one can make without a good deal of labour.”

Partly for that reason Bayes’s theorem was neglected. Repeated calculations were tedious to do by hand — but that changed in the twentieth century with the invention of the computer. Bayes’s theorem was adopted by insurance companies, the military, and the technology industry. It is no exaggeration to say that the Reverend Bayes’s long-forgotten rule is behind much of Silicon Valley’s wealth.

“If you’re not paying for it, you’re the product being sold.” This is a maxim of our digital economy. Google, Facebook, Instagram, Twitter, YouTube — all our entrancing and addictive apps — are free products that come with a Faustian bargain. To use these services we allow their providers to collect so-called personal information — information that is valuable because of Bayes’s theorem. In the aggregate, as “big data,” personal information allows marketers to predict what you will buy, how much you will pay, and whom you will vote for. These Bayesian predictions, updated with every click, swipe, post, or GPS coordinate, are the secret sauce of many a tech company.

This success story is, however, only the prologue to the stranger one that concerns us. In recent years it has been recognized that Bayesian methods can shed light on deep mysteries of existence, including the future of the human race itself.

Ozymandias

I met a traveller from an antique land

Who said — “Two vast and trunkless legs of stone

Stand in the desert. . . Near them, on the sand,

Half sunk a shattered visage lies, whose frown,

And wrinkled lip, and sneer of cold command,

Tell that its sculptor well those passions read

Which yet survive, stamped on these lifeless things,

The hand that mocked them and the heart that fed;

And on the pedestal these words appear:

My name is Ozymandias, King of Kings;

Look on my Works, ye Mighty, and despair!

Nothing beside remains. Round the decay

Of that colossal Wreck, boundless and bare

The lone and level sands stretch far away.”

This is the sonnet “Ozymandias” (1818) by Romantic poet Percy Bysshe Shelley, husband of Frankenstein author Mary Shelley, daughter of feminist Mary Wollstonecraft, friend of minister Richard Price, promoter of the intellectual property of Thomas Bayes. The theme of “Ozymandias” is that glory is fleeting. Nothing lasts.

In the summer of 1969, J. Richard Gott III celebrated his Harvard graduation with a tour of Europe. He visited the supreme monument of Cold War anxiety, the Berlin Wall. Standing in the shadow of the landmark, he contemplated its history and future. Would this symbol of totalitarian power one day lie in ruins?

This was a matter discussed by diplomats, historians, op-ed writers, TV pundits, and spy novelists. Opinions varied. Gott, who was planning postgraduate work in astrophysics, brought a different perspective. He devised a simple trick for estimating how long the Berlin Wall would stand. He did the maths in his head and announced his prediction to a friend, Chuck Allen. The wall would stand at least two and two-thirds more years but no more than twenty-four more years, he said.

Gott went back to America. In 1987 President Ronald Reagan demanded, “Mr. Gorbachev, tear down this wall!” From 1990 to 1992 the wall was demolished. That was twenty-one to twenty-three years after Gott’s prediction and within the range he announced.

Gott called his secret the “delta t argument.” “Delta t” means change in time. It’s also known as the Copernican method, after Nicolaus Copernicus, the great Polish astronomer of the Renaissance. Copernicus’s leap of imagination was that the Earth is not the center of the universe. It is only one of a number of planets circling the sun. This thinking led to a simpler model of the solar system, one that agreed better with observation.

To astronomers, Copernicus’s insight has been a gift that keeps on giving. Over the past five centuries it has been established again and again that humanity does not occupy a central or special place in the scheme of things. Our sun is an ordinary star in an ordinary galaxy. It is not at the center of the galaxy but well off to the margins. Our galaxy does not occupy a special place in the cluster of galaxies to which it belongs, and this cluster has no special place in the universe as we know it. Even the whole of the observable universe is now widely believed to be an insignificant speck in a yet-greater multiverse. The cosmic “you are here” dot says we’re smack in the middle of nowhere.

The Copernican principle is generally applied to an observer’s location in space, but the delta t argument applies it to an observer’s location in time. Gott began with the assumption that his visit to the Berlin Wall had not taken place at any special moment in the wall’s history. That premi...

Table of contents

• Cover
• Title Page
• Dedication
• Contents
• Diana and Charles
• Part I: Consider the Lemming
• Part II: Life, Mind, Universe
• Acknowledgments
• Notes
• Sources
• Index
• Copyright Page
• About the Author