Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

Posts Tagged ‘Isaac Newton

Quote of the Day

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Newton could not admit that there was any difference between him and other men, except in the possession of such habits as…perseverance and vigilance. When he was asked how he made his discoveries, he answered, “By always thinking about them.”

William Whewell, History of the Inductive Sciences

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November 29, 2018 at 7:30 am

Quote of the Day

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It is not that science is free from legends, witchcraft, miracles, biographic boostings of quacks as heroes and saints, and of barren scoundrels as explorers and discoverers. On the contrary, the iconography and hagiology of Scientism are as copious as they are mostly squalid. But no student of science has yet been taught that specific gravity consists in the belief that Archimedes jumped out of his bath and ran naked through the streets of Syracuse shouting Eureka, Eureka, or that the law of inverse squares must be discarded if anyone can prove that Newton was never in an orchard in his life.

George Bernard Shaw, in the preface to Back to Methuselah

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March 13, 2018 at 7:30 am

Quote of the Day

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There is the story of how [Isaac Newton] informed Halley of one of his most fundamental discoveries of planetary motion. “Yes,” replied Halley, “but how do you know that? Have you proved it?” Newton was taken aback. “Why, I’ve known it for years,” he replied. “If you’ll give me a few days, I’ll certainly find you a proof of it.” As in due course he did.

John Maynard Keynes, “Newton the Man”

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February 19, 2018 at 7:30 am

The intensity of the wish

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To work on an idea does not mean intellectual concentration of the usual kind. No sweating here will do. A prayerful solitude with a dash of austerity in the daily routine is necessary; then, what Tyndall, describing the production of inventions, called “brooding,” and what Newton called “thinking of it all the time.” It seems as if the earnest wish to get at the whole thing should be the chief thing, acting, of course, on our subconsciousness. The experience of most artists is that the quality of their production is in keeping with the intensity of their wish. As I said before, Sir Walter Scott reading books with no relevance whatever to his subjects, or Charles Dickens rambling through the deserted streets at night, was trying to retard rather than hasten what we call clear thought, but which ought to be called final thought. Real work, real brooding consist in peopling the mind with congenial images, sometimes called in by our desire, sometimes-conjured up from our memories gone over at random rather than methodically. When the light comes at last, as full as we can expect it ever to be, whatever we do, do not let us map out what we have discovered in the shape of a synopsis. Numbering and brackets are too unlike thought ever to revive its first appearance.

Ernest Dimnet, The Art of Thinking

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May 14, 2017 at 7:30 am

The Bob Hope rule

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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.

The law of elegance

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Murray Gell-Mann

There’s a quotation from Newton, I don’t remember the exact words but lots of other physicists have made the same remark since—that nature seems to have a remarkable property of self-similarity. The laws—the fundamental laws—at different levels seem to resemble one another. And that’s probably what accounts for the possibility of using elegance as a criterion [in science]. We develop a mathematical formula, say, for describing something at a particular level, and then we go to a deeper level and find that in terms of mathematics, the equations at the deeper level are beautifully equivalent. Which means that we’ve found an appropriate formula.

And that takes the human being, human judgment, out of it a little. You might object that after all we are the ones who say what elegance is. But I don’t think that’s the point.

Murray Gell-Mann

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March 8, 2014 at 9:00 am

The last of the magicians

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Portrait of Isaac Newton by Godfrey Kneller

Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. Isaac Newton, a posthumous child born with no father on Christmas Day, 1642, was the last wonder-child to whom the Magi could do sincere and appropriate homage…

His peculiar gift was the power of continuously holding in his mind a purely mental problem until he had seen straight through it. I fancy his preeminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one’s mind and apply all one’s powers of concentrating to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition which was preeminently extraordinary—”so happy in his conjectures,” said 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.

John Maynard Keynes

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October 19, 2013 at 9:00 am

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