Posts Tagged ‘Alan Turing’
Quote of the Day
The survival of the fittest is a slow method for measuring advantages. The experimenter, by the exercise of intelligence, should be able to speed it up. Equally important is the fact that he is not restricted to random mutations. If he can trace a cause for some weakness he can probably think of the kind of mutation which will improve it.
The Bob Hope rule
A bank is a place that will lend you money if you can prove that you don’t need it.
—Attributed to Bob Hope
These days, there seem to be two categories of professionals in whom we expect to see intuitive thinking at work. One is the poet, whom we like to imagine as a creature of inspiration, to the point where we might even be a little disappointed to discover how much the finished product depends on craft, logic, and revision. The other, surprisingly, is the physicist or mathematician, who used to be regarded as a figure of pure reason, but whom we’ve started to romanticize as someone whose flashes of insight are supported by hard work after the fact. John Maynard Keynes set the tone seventy years ago in a lecture on Isaac Newton:
It was his intuition which was preeminently extraordinary—”so happy in his conjectures,” said [Augustus] de Morgan, “as to seem to know more than he could possibly have any means of proving.” The proofs, for what they are worth, were, as I have said, dressed up afterwards—they were not the instrument of discovery.
And if we’re comfortable with attributing such methods to poets and physicists, it’s because they seem to occupy opposite ends of the spectrum. Poets get to use intuition because they can’t possibly do any harm with it, while scientists can talk about their intuitive leaps because we trust that they’ll back it up later. Science and mathematics are structured in such a way that practitioners have to present their results in a certain form if they want to be published, and as long as they show their work, it doesn’t matter in which order it came. Consequently, we aren’t likely to think twice when Carl Gauss says: “I have had my results for a long time: but I do not yet know how I am to arrive at them.”
Imagine a social scientist making the same statement, however, and it feels vastly more problematic. Between poetry and physics, there’s an uncharted region of psychology, sociology, economics, history, and biography in which the admitted use of intuition would raise troubling questions. The reasoning, it seems, is that these disciplines are already filled with uncertainties, and intuition only muddies the waters. It’s easier to twist the facts to suit the theory in the “soft” sciences than it is in physics or math, so even if researchers happen to derive valid results from a lucky hunch, they can’t very well admit to this if they want to be taken seriously. In The White Goddess, Robert Graves writes that he couldn’t have arrived at his conclusions—which, to be fair, are often pretty questionable—if he hadn’t known the answers beforehand “by poetic intuition,” and he adds perceptively:
The proleptic or analeptic method of thought, though necessary to poets, physicians, historians and the rest, is so easily confused with mere guessing, or deduction from insufficient data, that few of them own to using it. However securely I buttress the argument of this book with quotations, citations, and footnotes, the admission that I have made here of how it first came to me will debar it from consideration by orthodox scholars: though they cannot refute it, they dare not accept it.
That’s true of most academic fields. The dirty secret, of course, is that it’s impossible to work on any major project for an extended period without intuition coming into play, and before publication, the scholar has to diligently scrub the result of all traces of intuitive thinking, like a murderer wiping down the scene of a crime.
Occasionally, you’ll see scholars acknowledge the role of intuition, particularly when it comes to structuring an argument. In an interview with The Paris Review, Leon Edel says of his famous biography of Henry James:
In the first volume I’d intuitively planted all my themes in the first four chapters; like Chekhov, I placed my pistols in the first act, knowing the audience would expect me to produce them in the third. Having James’s last dictation about Napoleon, I planted the Napoleonic theme, then the “museum world” theme, the relationship with his brother, and so on, and my structure took its form from my themes. Expediency, you see, made me artful.
That last sentence is one of the best things ever written about craft. But what Edel doesn’t mention, or leaves implicit, is the fact that these intuitive decisions about structure inevitably influence matters of emphasis, presentation, and interpretation, and even the research that the writer conducts along the way. Many works of reputable scholarship secretly follow the process that the cartographer Arthur H. Robinson said of his most famous map: “I decided to go about it backwards. I started with a kind of artistic approach. I visualized the best-looking shapes and sizes. I worked with the variables until it got to the point where, if I changed one of them, it didn’t get any better. Then I figured out the mathematical formula to produce that effect.”
But it’s hard for social scientists, or biographers, to admit to this. In the end, Bob Hope’s quip about the bank is equally true of intuition in academia: you’re allowed to use it, as long as you can prove that you don’t need it. It’s an acceptable part of the oral tradition in disciplines in which it doesn’t seem necessary, while the ones that truly depend on it do their best to hush it up. To some extent, these are valid correctives: emphasizing intuition in the hard sciences rightly reminds us that science is something more than data collection, while deemphasizing it in the social sciences sounds a useful note of caution in fields that run the risk of falling back on untested assumptions. But it’s misleading to pretend that it doesn’t enter into the process at all, even if, ideally, you should be able to remove it and have the entire structure still stand. (As Alan Turing once put it: “The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings. It is intended that when these are really well arranged the validity of the intuitive steps which are required cannot seriously be doubted.” And you could say precisely the same thing of history and biography.) The educational psychologist Ference Marton refers to intuition in Nobel laureates as providing “a sense of direction,” and that may be its most indispensable role in all forms of scholarship. Choosing any avenue of exploration over another often comes down to a hunch, and it’s possible that this intuition occurs so early on that it becomes invisible—those who lack it are weeded out of the field altogether. Like any powerful tool, it has to be handled with caution. But we still need it, even if we sometimes have to act as if we don’t.
Quote of the Day
Machines take me by surprise with great frequency. This is largely because I do not do sufficient calculation to decide what to expect them to do, or rather because, although I do a calculation, I do it in a hurried, slipshod fashion, taking risks. Perhaps I say to myself, “I suppose the voltage here ought to be the same as there: anyway let’s assume it is.” Naturally I am often wrong, and the result is a surprise to me, for by the time the experiment is done these assumptions have been forgotten. These admissions lay me open to lectures on the subject of my vicious ways, but do not throw any doubt on my credibility when I testify to the surprises I experience.
Quote of the Day
[Alan Turing] would set me a piece of work and when I had completed it he would not deign to look at my solution but would embark on the problem himself; only after having a preliminary trial on his own was he prepared to read my work. I soon came to see the advantage of this approach…He would frequently come up with some original approach which had escaped me and might well have eluded him, had he read my account immediately.
—James H. Wilkinson, in his Turing Award lecture
Alan Turing on intuition and ingenuity
Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. These judgments are often but by no means invariably correct…
The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings. It is intended that when these are really well arranged the validity of the intuitive steps which are required cannot seriously be doubted.
Quote of the Day
A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.
Alec Nevala-Lee 