Safety cases and that room full of monkeys
Back in 1943, the French mathematician Émile Borel published a book titled Les probabilités et la vie, in which he stated what has come to be called Borel’s law which can be paraphrased as, “Events with a sufficiently small probability never occur.”
Borel’s law has also been called the infinite monkey theorem as Borel illustrated the theorem with the example of monkeys randomly hitting the keys of a typewriter and by chance producing the complete works of Shakespeare, to quote Borel for a moment:
Such is the sort of event which, though its impossibility may not be rationally demonstrable, is, however, so unlikely that no sensible person will hesitate to declare it actually impossible. If someone affirms having observed such an event we would be sure that he is deceiving us or has himself been the victim of fraud.
In essence to generate the works by monkey’s banging on the typewriter you’d either need more monkey’s than there are atomic particles in the universe, or you’d need to wait around for longer than the life of the universe for one monkey to wander in with the galley proofs under his arm.
When we see ridiculously enormous numbers in safety cases this is an argument based on Borel’s theorem, which I call the infinite monkey safety argument ©. Of course if you notice a small furry hand tugging on your jacket hem then you can reasonably assume that your infinite safety argument has been demonstrably proved false. Anyone want a bound slightly hairy copy of the works of Shakespeare?
See also magic numbers.