Charles Darwin and Alan Turing, in their different ways, both homed in on the same idea: the existence of competence without comprehension.
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 pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.")
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.
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:
In the theory with which we have to deal, Absolute Ignorance is the artificer; so that we may enunciate as the fundamental principle of the whole system, that, in order to make a perfect and beautiful machine, it is not requisite to know how to make it. This proposition will be found, on careful examination, to express, in condensed form, the essential purport of the Theory, and to express in a few words all Mr. Darwin's meaning; who, by a strange inversion of reasoning, seems to think Absolute Ignorance fully qualified to take the place of Absolute Wisdom in all the achievements of creative skill.
It was, indeed, a strange inversion of reasoning. To this day many people cannot get their heads around the unsettling idea that a purposeless, mindless process can crank away through the eons, generating ever more subtle, efficient, and complex organisms without having the slightest whiff of understanding of what it is doing.
In order to be a perfect and beautiful computing machine, it is not requisite to know what arithmetic is.
Turing's idea was a similar -- in fact remarkably similar -- strange inversion of reasoning. The Pre-Turing world was one in which computers were people, who had to understand mathematics in order to do their jobs. Turing realized that this was just not necessary: you could take the tasks they performed and squeeze out the last tiny smidgens of understanding, leaving nothing but brute, mechanical actions. In order to be a perfect and beautiful computing machine, it is not requisite to know what arithmetic is.
What Darwin and Turing had both discovered, in their different ways, was the existence of competence without comprehension. This inverted the deeply plausible assumption that comprehension is in fact the source of all advanced competence. Why, after all, do we insist on sending our children to school, and why do we frown on the old-fashioned methods of rote learning? We expect our children's growing competence to flow from their growing comprehension. The motto of modern education might be: "Comprehend in order to be competent." For us members of H. sapiens, this is almost always the right way to look at, and strive for, competence. I suspect that this much-loved principle of education is one of the primary motivators of skepticism about both evolution and its cousin in Turing's world, artificial intelligence. The very idea that mindless mechanicity can generate human-level -- or divine level! -- competence strikes many as philistine, repugnant, an insult to our minds, and the mind of God.
Consider how Turing went about his proof. He took human computers as his model. There they sat at their desks, doing one simple and highly reliable step after another, checking their work, writing down the intermediate results instead of relying on their memories, consulting their recipes as often as they needed, turning what at first might appear a daunting task into a routine they could almost do in their sleep. Turing systematically broke down the simple steps into even simpler steps, removing all vestiges of discernment or comprehension. Did a human computer have difficulty telling the number 99999999999 from the number 9999999999? Then break down the perceptual problem of recognizing the number into simpler problems, distributing easier, stupider acts of discrimination over multiple steps. He thus prepared an inventory of basic building blocks from which to construct the universal algorithm that could execute any other algorithm. He showed how that algorithm would enable a (human) computer to compute any function, and noted that:
The behavior of the computer at any moment is determined by the symbols which he is observing and his "state of mind" at that moment. We may suppose that there is a bound B to the number of symbols or squares which the computer can observe at one moment. If he wishes to observe more, he must use successive observations. ... The operation actually performed is determined ... by the state of mind of the computer and the observed symbols. In particular, they determine the state of mind of the computer after the operation is carried out.
He then noted, calmly:
We may now construct a machine to do the work of this computer.
Right there we see the reduction of all possible computation to a mindless process. We can start with the simple building blocks Turing had isolated, and construct layer upon layer of more sophisticated computation, restoring, gradually, the intelligence Turing had so deftly laundered out of the practices of human computers.