An infinite possibility of uncovering metaphorical monkey business

Were monkeys forever to tinker on typewriters, they would - it is casually said - eventually type the complete works of Shakespeare. But this overlooks the possibility that, in their eternal typing, they could continually miss the bard's particular wordy ways. Typing for an eternity offers no guarantee that everything which could get typed does get typed.

Typing monkeys, bizarre though it may seem, have become relevant to cosmology and to cosmological speculations about the nature of time. Professor Paul Davies, mathematician, physicist and this year's winner of the Templeton Prize for Progress in Religion, writes in The Last Three Minutes that, were the universe to have an infinite lifetime, "any physical process, however slow or improbable, would have to happen sometime" - including the aforementioned monkey business. If this is right and were the world temporally infinite, interesting conclusions flow: all lottery entrants would eventually enjoy top prize winnings; toast would occasionally fail to fall butter-side down; and one day, even government ministers would apologise. Fascinating though such speculations might be, the initial reasoning generating such curious conclusions may depend upon a simple mistake. People commonly mistake infinity for all.

If you could infinitely (endlessly, eternally) continue counting the number series 2, 4, 6 ... your counting would miss the infinite series of odd integers. The infinite number of even numbers fails to include all numbers and an infinite number of processes (states, events) may not capture all those which are possible.

However, if there is only a finite number of possible processes, must they not all eventually occur, given infinite time? Well, if the universe is deterministic, with a finite number of possible states, infinite time does not ensure that all such states would occur. The determinism could be such that the same cycle of states repeatedly roll, yet the cycle excludes some possible states - just as the "count even numbers only" rule excludes infinitely many other numbers. The endless deterministic cycle might just happen to shut out Michael Heseltine's ever becoming prime minister.

If the universe is indeterministic, must all possibilities occur? In About Time (the professor's most recent book), we learn that continual random card shuffling, because the number of cards is finite, must cause every card to turn up. At face value, this is a non-sequitur. It is logically possible, albeit unlikely, that an infinite random sequence should just happen to omit a given card. Some individuals head towards bankruptcy through acting on mistaken beliefs that the longer a particular number fails to show, the more likely it will next appear. Truly random roulette wheel spinnings lack regard for past winnings. An infinity of spins generates the possibility of infinite unluckiness.

Professor Davies, steering between determinism and complete randomness, might well defend his claim by saying that he was speaking only of states and processes which have some physical, non-zero probability of occurring - meaning that states with such a probability would have to occur given an infinite period of time. If so, we lose immediate eye-catching "popular science" conclusions of our lives repeating, government ministers ultimately having to apologise and apes' Shakespearean labours necessarily bearing fruit. None of these comes clearly tagged with the requisite probability. That such states are logically possible is doubtless the case, but this secures no guarantee of occurrence. The question moves to that of how you tell which possible states possess this kind of probability. To know whether they possess Professor Davies's probability, necessitating occurrence in infinite time, we need to examine his understanding of probability and possibility.

Spreading the scientific word through everyday language may result in misunderstandings and beguiling images; it just might also expose some metaphorical and metaphysical monkey business.

The author is visiting lecturer in philosophy, City University, and tutor in philosophy at The Open University.