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A statement from Gilbert Keith Chesterton about the logic of randomness. Taken from The Innocence of Father Brown, “The Blue Cross”.

The only context needed is that the great detective Valentin is on the trail of the great criminal Flambeau, who has appeared in England but disappeared quite thoroughly. How is Valentin to find Flambeau?

The narrator says:

The most incredible thing about miracles is that they happen. A few clouds in heaven do come together into the staring shape of one human eye. A tree does stand up in the landscape of a doubtful journey in the exact and elaborate shape of a note of interrogation. I have seen both these things myself within the last few days. Nelson does die in the instant of victory; and a man named Williams does quite accidentally murder a man named Williamson; it sounds like a sort of infanticide. In short, there is in life an element of elfin coincidence which people reckoning on the prosaic may perpetually miss. As it has been well expressed in the paradox of Poe, wisdom should reckon on the unforeseen.

Aristide Valentin was unfathomably French; and the French intelligence is intelligence specially and solely. He was not “a thinking machine”; for that is a brainless phrase of modern fatalism and materialism. A machine only is a machine because it cannot think. But he was a thinking man, and a plain man at the same time. All his wonderful successes, that looked like conjuring, had been gained by plodding logic, by clear and commonplace French thought. The French electrify the world not by starting any paradox, they electrify it by carrying out a truism. They carry a truism so far–as in the French Revolution. But exactly because Valentin understood reason, he understood the limits of reason. Only a man who knows nothing of motors talks of motoring without petrol; only a man who knows nothing of reason talks of reasoning without strong, undisputed first principles. Here he had no strong first principles. Flambeau had been missed at Harwich; and if he was in London at all, he might be anything from a tall tramp on Wimbledon Common to a tall toast-master at the Hotel Metropole. In such a naked state of nescience, Valentin had a view and a method of his own.

In such cases he reckoned on the unforeseen. In such cases, when he could not follow the train of the reasonable, he coldly and carefully followed the train of the unreasonable. Instead of going to the right places–banks, police stations, rendezvous– he systematically went to the wrong places; knocked at every empty house, turned down every cul de sac, went up every lane blocked with rubbish, went round every crescent that led him uselessly out of the way. He defended this crazy course quite logically. He said that if one had a clue this was the worst way; but if one had no clue at all it was the best, because there was just the chance that any oddity that caught the eye of the pursuer might be the same that had caught the eye of the pursued. Somewhere a man must begin, and it had better be just where another man might stop.