Are you confident about that?

The impulse to use statistics to forecast doomsday is an old one. But can we believe the numbers, asks Philip Ball?

Statistics challenge our intuition even when they concern rolls of the dice. When our own destruction is at issue, they become almost mystically ungraspable.

This aura of intangibility surrounds the latest calculation of doomsday probabilities by Max Tegmark of the Massachusetts Institute of Technology, Cambridge, and Nick Bostrom of the University of Oxford, UK¹. They derive upper and lower limits on the chances of an exogenous catastrophe - one that we do not bring on ourselves -exterminating humankind.

The researchers were originally motivated by the possibility that exotic physics, unleashed in the laboratory, might pose a threat. Could high-energy collisions at Brookhaven's Relativistic Heavy Ion Collider, or the Large Hadron Collider being built at CERN in Switzerland, create a black hole, or a growing nucleus of 'strange matter'? A study in 2000² suggested that such far-out catastrophes are more likely to happen naturally - through cosmic-ray collisions, for example - if at all.

In the face of such threats, Tegmark and Bostrom say that we cannot simply take heart from the fact that life on Earth has been just fine for nearly 4 billion years. They point out that cosmic catastrophes could regularly zap civilizations elsewhere in the Universe. The lucky handful that survive would be naïve to conclude that their existence is proof that such apocalypses never happen.

The two researchers propose a way of getting around this selection effect. Because we know how long it takes for planets like ours to form after the Big Bang, we can estimate our chances of still being here if planet-destroying catastrophes happen every few billion years. This calculation leads Tegmark and Bostrom to conclude that one habitable planet is sterilized every 1.1 billion years, with 99.9% probability.

So that's all right then. But what does it really mean?

Copernican gambit

The unsettling fact is that even experts cannot agree on the status of such estimates. They are even divided over whether statistics have anything meaningful to say about questions such as this.

Twelve years ago, Princeton astrophysicist J. Richard Gott analysed the "implications of the Copernican principle for our future prospects"³. The Copernican principle is the assumption that there is nothing special about our place in space and time. We are highly unlikely to be living very close to either the end or the beginning of a chronological list of all humans who will ever exist.

On the basis of that assumption alone, Gott argued that we can be 95% confident that our species will live for between 0.2 and 8 million years. This means that we are unlikely to colonize the galaxy: it would take so many people that you and me would be among the first minuscule fraction of humans that will ever exist. The Copernican principle would conversely dictate that we occupy an unprivileged position around the middle period of our species' history.

Logical alchemy

Gott's paper excited furious debate, and many of the criticisms looked formidable. Freeman Dyson argued that Gott had simply misapplied statistical reasoning⁴. He pointed out how the original statistical doomsday, predicted in 1798 by Thomas Malthus on the basis that population grows more quickly than food production, was similarly based on faulty premises - in this case, a failure to account for technological change.

Others felt that Gott had spun phantom knowledge from complete ignorance. Biostatistician Steven Goodman pointed out how John Maynard Keynes had dubbed such fallacious reasoning the principle of indifference, saying "no other formula in the alchemy of logic has exerted more astonishing powers... it has established the existence of God from total ignorance, and has measured with numerical precision the probability that the Sun will rise tomorrow."⁵ The basic flaw, said Goodman, lies in assigning equal probabilities to events about which we know nothing⁶.

Have Tegmark and Bostrom performed the same trick? Some will argue as much. Certainly, their analysis seems redolent of the doomsday argument developed by astrophysicist Brandon Carter and elaborated by Gott and the philosopher John Leslie⁷, because it uses the mere fact of our existence to pronounce on effects and events about which we know nothing.

But if nothing else, it shows that we are as eager as ever to imprison the future behind error bars of 95% probability.