Apocalypse Not Just Now
The Doomsday Argument is a case-study in 'probabilistic illusion', for it rests on a web of insidious intuitions, hidden assumptions and seductive but imprecise analogies. The Argument claims that the observation that we are alive now increases the probability that Homo sapiens will become extinct in the relatively near future. It does not predict Doom at a specific time or with a specific probability. Its conclusion is more abstract and puzzling: whatever our best estimate would be (based on all available evidence, including the latest scientific, historical or other research) of the probability that our species is relatively close to extinction, it must be revised upwards. In reaching this conclusion, the Argument does not rely on evidence in the ordinary sense or, indeed, on anything peculiar to our present situation; it would yield the same conclusion at any point in human history.
It may seem preposterous that such a conclusion could be reached by armchair reasoning from the mere fact of our being alive now. Yet it would be wrong to rush to judgment. The counter-intuitive nature of probability is itself a reason for caution; moreover, the Doomsday Argument involves issues about time and existence, which are themselves notoriously resistant to intuition. Many who encounter it immediately conclude that it is unsound. Their objections tend not to hold up under scrutiny, however, and some of the initially sceptical join the ranks of the converted, which now include several eminent scientists and philosophers. The debate has endured for nearly two decades, resurfacing regularly in philosophical, mathematical and scientific journals. John Leslie, the Argument's foremost proponent, has responded indefatigably and ingeniously to a host of objections.
The widespread sense that something is wrong with it is, however, correct, and its failings illuminate a main source of our trouble with understanding probability: its close connection to randomness or unpredictability. Randomness seems to confound us. For example, we have a tendency to infer non-randomness from apparent patterns in random events (witness the incorrigible optimists who spot trends in the spins of a roulette wheel or the ups and downs of the FT Share Index); at the same time, the history of statistics suggests that, when random samples are required, we often mistake the merely haphazard - or whatever happens to be near at hand - for the truly random. As I will show, the Doomsday Argument's fundamental mistake is to rely on the intuitive but misguided notion that we can in general take ourselves to be typical humans, and thus, in effect, random samples of the species.