Charles Darwin and Alan Turing, in their different ways, both homed in on the same idea: the existence of competence without comprehension.

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Some of the greatest, most revolutionary advances in science have been given their initial expression in attractively modest terms, with no fanfare.

Charles Darwin managed to compress his entire theory into a single summary paragraph that a layperson can readily follow.

Francis Crick and James Watson closed their epoch-making paper on the structure of DNA with a single deliciously diffident sentence. (“It has not escaped our notice that the specific pairings we have postulated immediately suggests a possible copying mechanism for the replicating unit of life.”)

And Alan Turing created a new world of science and technology, setting the stage for solving one of the most baffling puzzles remaining to science, the mind-body problem, with an even shorter declarative sentence in the middle of his 1936 paper on computable numbers:

It is possible to invent a single machine which can be used to compute any computable sequence.

Turing didn’t just intuit that this remarkable feat was possible; he showed exactly how to make such a machine. With that demonstration the computer age was born. It is important to remember that there were entities called computers before Turing came up with his idea, but they were people, clerical workers with enough mathematical skill, patience, and pride in their work to generate reliable results of hours and hours of computation, day in and day out. Many of them were women.

Early “computers” at work. (NASA)

Thousands of them were employed in engineering and commerce, and in the armed forces and elsewhere, calculating tables for use in navigation, gunnery and other such technical endeavors. A good way of understanding Turing’s revolutionary idea about computation is to put it in juxtaposition with Darwin’s about evolution. The pre-darwinian world was held together not by science but by tradition: All things in the universe, from the most exalted (“man”) to the most humble (the ant, the pebble, the raindrop) were creations of a still more exalted thing, God, an omnipotent and omniscient intelligent creator — who bore a striking resemblance to the second-most exalted thing. Call this the trickle-down theory of creation. Darwin replaced it with the bubble-up theory of creation. One of Darwin’s nineteenth-century critics, Robert Beverly MacKenzie, put it vividly:

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