Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

Posts Tagged ‘Albert Einstein

Quote of the Day

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It may perhaps seem to you as though our theories are a kind of mythology and, in the present case, not even an agreeable one. But does not every science come in the end to a kind of mythology like this?

Sigmund Freud, in an open letter to Albert Einstein

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February 21, 2018 at 7:30 am

Quote of the Day

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September 21, 2016 at 7:30 am

Quote of the Day

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Herbert A. Simon

Einstein was only twenty-six when he invented spatial relativity in 1905, but do you know how old he was when he wrote his first paper on the speed of light? Fifteen or sixteen. That’s the magic ten years. It turns out that the time separating people’s first in-depth exposure to a field and their first world-class achievement in that field is ten years, neither more nor less by much. Einstein knew a hell of a lot about light rays and all sorts of odd information related to them by the time he turned twenty-six.

Herbert A. Simon, to Omni

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November 13, 2015 at 7:30 am

Solving for X

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W.H. Auden

According to the poet Robert Earl Hayden, W.H. Auden once said: “Writing a poem is like solving for X in an equation.” More recently, a similar analogy was employed by the journalist and podcaster Alex Blumberg, who explains:

I’ve developed a mathematical test to tell whether you’re on the right track. It’s called the “and what’s interesting” test. You simply tell someone about the story you’re doing, adhering to a very strict formula: “I’m doing a story about X. And what’s interesting about it is Y.” So for example, again, taking the homeless story, “I’m doing a story about a homeless guy who lived on the streets for 10 years, and what’s interesting is, he didn’t get off the streets until he got into a treatment program.” Wrong track. Solve for a different Y.

And while this might seem to make the art of poetry or storytelling feel unbearably dry, it’s really quite the opposite. As Jakob Einstein famously told his nephew Albert: “[Algebra is] a merry science. When the animal that we are hunting cannot be caught, we call it X temporarily and continue to hunt until it is bagged.”

Thinking of writing, or any creative endeavor, as a subcategory of this “merry science” clarifies many of the issues that confront the aspiring solver. The typical problem in mathematics or geometry consists of an unknown, some data, and a condition, and the same can be said of many of the narrative issues that a writer is compelled to address. When you’re first plotting out a story, particularly a novel, the number of individual decisions you have to make can seem overwhelming, but you usually have more information than you realize. Once you’ve spent even a modicum of time mulling over an idea, you wind up with at least an initial premise, a location, some primary characters, and a few of the major story beats—although, as I’ve noted before, many of these seemingly fundamental units are also the result of working backward from an earlier problem. When you line them all up, you generally find that they also imply other scenes or ideas: to get your characters from point A to point C, it doesn’t take a genius to see that you should pass through point B first, at least in your initial outline. (Point B often ends up being omitted in the rewrite, but it helps to lay it out blandly at first, if only in hopes that it generates some useful material.) And by the time you’ve laid all the obvious scenes from end to end, along with the connective tissue that they suggest, you often discover that you’ve got most of what you need. The hard part is solving for the remaining unknowns.

George Pólya

And you can’t do this until you’ve suitably arranged the pieces that you have, which can be easier said than done. Just as the first step in solving a linear equation is to get the variable by itself on one side, the unknown in any story can only be found once you’ve isolated it as much as possible from the surrounding elements. Hence the charts, graphs, and lists that writers produce in such quantities: once you’ve got everything down on paper in some kind of rough order, you start to see where the gaps exist. George Pólya, in his classic book How to Solve It, advises:

If there is a figure connected with the problem [the student] should draw a figure and point out on it the unknown and the data. If it is necessary to give names to these objects he should introduce suitable notation; devoting some attention to the appropriate choice of signs, he is obliged to consider the objects for which the signs have to be chosen.

And this last point is crucial. The outline isn’t the story, any more than an equation is the physical object that it represents, but by giving names or signs to the component parts, you can see through to the reality beneath for the first time.

In On Directing Film, David Mamet says much the same about identifying the beats of a story: “Here is a tool—choose your shots, beats, scenes, objectives, and always refer to them by the names you chose.” Once you’ve named the unknown, you can start to hunt for it more systematically, using some of the methods that Polya describes:

Look at the unknown. This is old advice; the corresponding Latin saying is: “respice finem.” That is, look at the end. Remember your aim…Focusing our attention on our aim and concentrating our will on our purpose, we think of ways and means to attain it. What are the means to this end? How can you attain your aim? How can you obtain a result of this kind? What causes could produce such a result? Where have you seen such a result produced? What do people usually do to obtain such a result? And try to think of a familiar problem having the same or a similar unknown. And try to think of a familiar theorem having the same or a similar conclusion.

Pólya compares this “same or similar unknown” to a stepping stone, and he adds drily: “The new unknown should be both accessible and useful but, in practice, we must often content ourselves with less.” It’s a system of successive approximations, or good hunches, converging at last on an answer that fits. And if we’re lucky, we’ll find that X, for once, marks the spot.

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October 14, 2015 at 9:40 am

The art of guessing

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Jacob Bronowski

How does the outstanding scientist come to propose such a decisive axiom, while less imaginative minds go on tinkering with the old system? How did Gregor Mendel leap to conceive the statistical axioms of genetics? What moved Albert Einstein to make the constancy of the speed of light not a consequence but an axiom in the construction of relativity?

An obvious answer is that the great mind, like the small, experiments with different alternatives, works out their consequences for some distance, and thereupon guesses (much like a chess player) that one move will generate richer possibilities than the rest. But this answer only shifts the question from one foot to the other. It still remains to ask how the great mind comes to guess better than another, and to make leaps that turn out to lead further and deeper than yours or mine.

We do not know; and there is no logical way in which can know, or can formalize the pregnant decision. The step by which a new axiom is added cannot itself be mechanized. It is a free play of the mind, an invention outside the logical processes. This is the central act of imagination in science, and it is in all respects like any similar act in literature. In this respect, science and literature are alike: in both of them, the mind decides to enrich the system as it stands by an addition which is made by an unmechanical act of free choice.

Jacob Bronowski

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March 28, 2015 at 7:30 am

What is intuition?

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Robert Graves

One can have memory of the future as well as of the past. Memory of the future is usually called instinct in animals, intuition in human beings.

Robert Graves

Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it opens to us a thousand different ways on which we can embark in all confidence; we are assured of meeting there no obstacles; but of all these ways, which will lead us most promptly to our goal? Who shall tell us which to choose? We need a faculty which makes us see the end from afar, and intuition is this faculty. It is necessary to the explorer for choosing his route; it is not less so to the one following his trail who wants to know why he chose it…Logic, which alone can give certainty, is the instrument of demonstration; intuition is the instrument of invention.

Henri Poincaré

Intuition is a mode of gathering.

John Sallis

Kurt Gödel

Mathematical intuition need not be conceived of as a facility giving an immediate knowledge of the objects concerned. Rather it seems that, as in the case of physical experience, we form our ideas also of those objects on the basis of something else which is immediately given.

Kurt Gödel

[Intuition] grasps a succession which is not juxtaposition, a growth from within, the uninterrupted prolongation of the past into a present which is already blending into the future. It is the direct vision of the mind by the mind.

Henri Bergson

Intuition is the ability not to construct solutions to problems in a rational manner, but rather to produce them spontaneously (holistically) according to situational demands…Intuition is, we could perhaps say, a fire that lights itself.

Wolfram Wilss

Albert Einstein

My intuition made me work…Intuition makes us look at unrelated facts and then think about them until they can all be brought under one law.

Albert Einstein

By intuition I do not mean the fluctuating testimony of the senses or the deceptive judgment of the imagination as it botches things together, but the conception of a clear and attentive mind, which is so easy and distinct that there can be no room for doubt about what we are understanding…Intuition is the indubitable conception of a clear and attentive mind which proceeds solely from the light of reason.

René Descartes

Intuition [in Nobel laureates] is closely associated with a sense of direction; it is more often about finding a path than arriving at an answer or reaching a goal. The ascent of intuition is rooted in extended, varied experience of the object of research: although it may feel as if it comes out of the blue, it does not come out of the blue.

Ference Marton

Two of a kind

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Paul McCartney and John Lennon

Over the last few weeks, it’s been hard to avoid Joshua Wolf Shenk, an essayist and author whose new book, Powers of Two: Seeking the Essence of Innovation in Creative Pairs, has received prominent play in such outlets as The Atlantic and the New York Times. At first glance, Shenk’s argument is compelling, even seductive. Meaningful creative work, he says, isn’t the creation of solitary geniuses, but of interpersonal exchanges, either through explicit collaboration or more subtle dialogues often centering on pairs. Pointing to John Lennon and Paul McCartney, he reminds us that even if many of their greatest songs were written largely by one or the other, all were born out of a cycle of mutual competition and reaction: “Penny Lane” is part of a conversation with “Strawberry Fields Forever,” to the point where it’s hard to imagine either one without its counterpart on the flip side. As different as Paul and John may have been, neither was ever as good without the other, and their collaboration was greater than the sum of its parts. “The lone genius,” Shenk concludes in the Times, “is a myth that has outlived its usefulness.”

Well, maybe. Like many authors with a thesis—and a book—to sell, Shenk occasionally overstates his own argument, sometimes in ways that quietly undermine his most valuable points. He notes, correctly, that Shakespeare’s plays emerged from an atmosphere of collaboration: “Surviving records show three or four or even five playwrights receiving pay for a single production, according to the Columbia professor James Shaprio.” This is true enough, but it ignores the inconvenient fact that Shakespeare’s work still feels qualitatively different, to most thoughtful readers, from other works produced by an identical process. If collaboration was the most powerful factor involved, we’d find masterpieces on the level of Hamlet from the likes of John Ford, Thomas Middleton, and John Webster, all of whom worked in the exact same way. Instead, they gave us a body of plays that are remembered today, to the extent that they’re read at all, because of their proximity to Shakespeare. And when it comes to the origins of that Shakespearian difference, we’re left, frustratingly, with that “mythical” lone genius. (It’s unclear, incidentally, who is supposed to be promulgating that particular myth these days; if anything, modern critical theory and literary analysis is fixated to a fault on social and historical contexts.)

The Sanders portrait of William Shakespeare

Shenk muddies his case further by failing to distinguish—at least in the excerpts and articles I’ve read—between real creative pairs, like Lennon and McCartney, and instances in which an essentially solitary artist or thinker benefited from a confidant or trusted critic. He approvingly cites the example of Michele Besso, whom Einstein called “the best sounding board in Europe,” and laments the fact that “most Vera Nabokovs never get acknowledged.” But nobody seriously doubts that even the most idiosyncratic geniuses need to work their ideas out with others, or that many great works of art have been rooted in a productive friendship or marriage. We often don’t know what we think about something until we hear what we have to say about it, and it’s a blessing to find someone who pushes us to be more thoughtful or original than we’d be on our own. Yet this all comes down to saying that geniuses, like everybody else, are happier among friends than alone, and that truly original thinkers will seek out companions who bring out their best. It’s possible, as Shenk says, this fact deserves more emphasis. But in the end, it just boils down to the same mystery as before.

To be clear, I like a lot of what Shenk is saying. Creativity is about combinations, or the movement between extremes, and we often find fruitful pairings of ideas when we talk things out with those we trust. But while it might be tempting to champion the social spaces where such fertilization can take place, like “the crowd-sourced Wikipedia or the writer’s room at The Daily Show,” it’s only part of the story, and not even the most interesting part. No truly great novel has ever emerged from collaboration: it’s a process that makes considerable demands on an individual’s ability to tolerate solitude, introspection, and meticulous work in private. We’ve all known great talkers and dreamers who wove spellbinding patterns of ideas in conversation but seemed incapable of setting them down in a more permanent form, something that demands, alas, that we spend a lot of time alone. Collaboration has its place, and it certainly fascinates me, but it’s a mistake to call it “a more truthful model” than solitary genius, or to imply that we’ve all been willfully ignoring the context in which great work arises. It’s another promising approach to the central unknown of the creative life, but it only reminds us that creativity—together or alone—will do whatever it takes to live another day.

Quote of the Day

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July 10, 2013 at 7:30 am

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Kurt Gödel applies for citizenship

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Kurt Gödel and Albert Einstein

[W]hen Gödel decided to become a U.S. citizen in 1947…he took his preparation for the exam very seriously, studied the Constitution carefully, and (as might be expected by the formulator of the incompleteness theory) found what he believed was a logical flaw. There was an internal inconsistency, he insisted, that could allow the entire government to degenerate into tyranny.

Concerned, Einstein decided to accompany—or chaperone—Gödel on his visit to Trenton to take the citizenship test, which was to be administered by the same judge who had done so for Einstein. On the drive, he and a third friend tried to distract Gödel and dissuade him from mentioning this perceived flaw, but to no avail. When the judge asked him about the Constitution, Gödel launched into his proof that its internal inconsistency made a dictatorship possible. Fortunately, the judge, who by now cherished his connection to Einstein, cut Gödel off. “You needn’t go into all that,” he said, and Gödel’s citizenship was saved.

Walter Isaacson, Einstein

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May 4, 2013 at 9:50 am

Quote of the Day

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A new idea comes suddenly and in a rather intuitive way. But intuition is nothing but the outcome of earlier intellectual experience.

Albert Einstein, quoted by Walter Isaacson in Einstein: His Life and Universe

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May 9, 2012 at 7:50 am

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Albert Einstein on asking the right questions

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The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new problems, to regard old problems from a new angle, requires creative imagination and marks real advances in science.

Albert Einstein

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June 12, 2011 at 10:12 am

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The art of shaving

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A few days ago, I quoted the unnamed physicist who told Wolfgang Köhler that scientists in his profession speak of “the three B’s”—the bus, the bath, and the bed—as the places where ideas tend to unexpectedly emerge. In my own case, two other activities are especially conducive to serendipitous thinking. The first, as my hero Colin Fletcher knew, was walking. While I don’t often have a chance to go on long hikes of the kind Fletcher wrote about so unforgettably, even a short walk to the grocery store has a way of working out whatever story problem I’m trying to solve at the moment. (Although I’ve also found that if I have music playing on my headphones, as I usually do, it tends to drown out that inner voice, which is a reminder that it’s sometimes best to leave the iPod at home.)

My other favorite activity is shaving. I’m not quite sure what it is, but I’ve had more good ideas at the bathroom sink than at any other location in the house. And I’m not the only one. In The Origin of Consciousness in the Breakdown of the Bicameral Mind, Julian Jaynes writes: “A close friend of Einstein’s has told me that many of the physicist’s greatest ideas came to him so suddenly that he had to move the blade of the straight razor very carefully each morning, lest he cut himself with surprise.” And while I’ve never cut myself, at least not for that reason, I’ve certainly been startled by unexpected insights. The most stunning moment, by far, is when I realized the true identity and motive of the killer in The Icon Thief, for a murder that I had already described with an eye toward a different suspect entirely. It’s one of my favorite memories as a writer.

Not every profession lends itself to thinking while shaving. For poets, it can pose a problem, as A.E. Housman notes. I’ve quoted him on this before, but since it’s one of my favorite pieces of writing, I see no reason not to quote him again:

One of these symptoms [that poetry produces in us] was described in connexion with another object by Eliphaz the Temanite: “A spirit passed before my face: the hair of my flesh stood up.” Experience has taught me, when I am shaving of a morning, to keep watch over my thoughts, because, if a line of poetry strays into my memory, my skin bristles so that the razor ceases to act.

This is such an effective indicator of true poetry, by the way, that Robert Graves proposes it as the definitive test in The White Goddess, although authors seem divided on its consequences for a morning shave. In Pale Fire, Nabokov writes, in the voice of the poet John Shade:

                    …Better than any soap
Is the sensation for which poets hope
When inspiration and its icy blaze,
The sudden image, the immediate phrase
Over the skin a triple ripple send
Making the little hairs all stand on end
As in the enlarged animated scheme
Of whiskers moved when held up by Our Cream.

Later in the same novel, the mad commentator Charles Kinbote points out the inconsistency between Shade and Housman’s accounts, and notes that since Housman “certainly used an Ordinary Razor, and John Shade an ancient Gillette, the discrepancy may have been due to the use of different instruments.” Clearly, a controlled experiment is required, perhaps with a side investigation into Douglas R. Hofstadter’s self-referential number P :

P is, for each individual, the number of minutes per month that that person spends thinking about the number P. For me, the value of P seems to average out at about 2. I certainly wouldn’t want it to go much above that! I find that it crosses my mind most often when I’m shaving.

After years of experimentation, my own routine has settled, rather surprisingly, on an old-fashioned shaving brush and cake of shaving soap. I was partially inspired by Updike’s description of Harry’s shaving regimen in Rabbit is Rich (“He still uses a rusty old two-edge safety razor he bought for $1.99 about seven years ago, and lathers himself with an old imitation badger-bristle on whatever bar of soap is handy”) but mostly from simple frugality: a cake of shaving soap is cheap and lasts close to a year, at least the way I use it. My razor, at the moment, is a Gillette Sensor, the blade’s lifetime extended by occasional stropping on a pair of jeans. (It really seems to work, although reports of blades lasting for half a year or more are probably atypical. Two weeks is a good number for me.)

All in all, it’s a modest routine, but shaving, I’ve increasingly come to understand, is one of life’s joys, even with the simplest of tools. And it’s in those unassuming moments, when one’s mind is free to wander, that the best ideas often arrive. I think I’m going to try it right now.

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