Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

Posts Tagged ‘Memorabilia Mathematica

The art of skimming

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[Arthur] Schopenhauer wrote that life and dreams were pages from the same book, and that to read them in their proper order was to live, but to leaf through them was to dream,” Jorge Luis Borges writes in the lovely short essay “Time and J.W. Dunne.” As far as I can tell, he was referring to this passage from The World as Will and Representation:

Life and dreams are the pages of one and the same book. In real life we read the pages in coherent order. But when the hour appointed for reading (i.e. the day) is done, and the time for rest has come, then we often leaf idly through the book, turning now to this page and now to another, in no particular order or sequence. Sometimes we turn to a page that we have already read, and sometimes to an unknown one, but they are always from the same book. So a page read separately is indeed out of sequence in comparison to the pages that have been read in order: but it is not so much the worse for that, especially when we bear in mind that a whole consecutive reading starts and finishes just as arbitrarily. In fact it should really be seen as itself only a single, separate, although larger, page.

Or as Borges puts it a few lines earlier: “To dream is to orchestrate the objects we viewed while awake and to weave from them a story, or a series of stories. We see the image of a sphinx and the image of a drugstore, and then we invent a drugstore that turns into a sphinx.”

Comparing a dream to the act of leafing through a book sheds a revealing light on the nature of dreaming, but I think that it also validates the undervalued art of skimming. We tend to see skimming as a degraded form of reading that dishonors the text, and when we approach it as if we’re cramming for a final exam, it can be. But there’s also a form of skimming as a creative tool that deserves to be celebrated. A few weeks ago, I quoted a description from the book Ladies and Gentlemen—Lenny Bruce of the comedian Mort Sahl at work:

Wherever he was, at home or on the road, he would have his room lined with magazines and books. He never read anything. A voracious skimmer. By flipping through this and staring at that, reading a sentence here and picking up a word there, he got a very good idea of where everything was. When he went into his monologue, you would swear that he had digested the whole world for that week.

At the time, I was making a point about the superficiality of this method of digesting the news. But you could come up with an equally persuasive case that for someone like Sahl, whose genius lay in making connections, this approach was actually more productive than a close reading, since it forced him to fill in the blanks with the twist that turned an idea into a joke.

And this applies to more than just comedy. In the collection Memorabilia Mathematica, there’s a reminiscence by the mathematician Andrew Forsyth of his colleague Arthur Cayley:

Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.

The italics are mine. The image of Cayley reading “only so much as would enable him to grasp the meaning of the symbols and understand its scope” is remarkably similar to Sahl “reading a sentence here and picking up a word there [so that] he got a very good idea of where everything was.” And while this shouldn’t be the only way in which we read, it’s indispensable for the referees and advisers who save the rest of us the trouble of keeping track of everything ourselves. (You can even compare it to the role of a good magazine editor, who sifts through the slush pile and picks out the best material for publication—a professional ability that appears to be inseparable from the ability to skim.)

Which brings us back to skimming as a way of dreaming. If creativity often consists of finding connections between existing ideas, it can be helpful read in a way that naturally encourages such combinations. More systematic reading has its place, and you could argue that skimming only results in anything useful when combined with a foundation of knowledge that has been built up in more conventional ways. (Much of the art of skimming lies in the instinctive ability to recognize when a piece of information is actually interesting, which only works when you can compare it to something else of known value.) But for truly creative types, a willingness to learn something thoroughly—which we find in abundance in every graduate department in the world—is conjoined with something more superficial, mystical, and even frivolous. It has affinities both with dreaming and with divination, and it can be deeply pleasurable. I also think that it requires a physical book, newspaper, or magazine, which limits the act of skimming in a way that allows it, paradoxically, to become the most free. In How to Talk About Books You Haven’t Read, which I haven’t read, Pierre Bayard asks: “Who, we may wonder, is the better reader—the person who reads a work in depth without being able to situate it, or the person who enters no book in depth, but circulates through them all?” And he answers his own question in terms that serve as a justification for skimming itself:

For a true reader, one who cares about being able to reflect on literature, it is not any specific book that counts, but the totality of all books…In our quest for this perspective, we must guard against getting lost in any individual passage, for it is only by maintaining a reasonable distance from the book that we may be able to appreciate its true meaning.

Checking your work

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As soon as human thought attempts long chains of conclusions, or difficult matters generally, there arises not only the danger of error but also the suspicion of error, because since all details cannot be surveyed with clearness at the same instant one must in the end be satisfied with a belief that nothing has been overlooked since the beginning. Everyone knows how much this is the case even in arithmetic, the most elementary use of mathematics. No one would imagine that the higher parts of mathematics fare better in this respect; on the contrary, in more complicated conclusions the uncertainty and suspicion of hidden errors increases in rapid progression.

How does mathematics manage to rid itself of this inconvenience which attaches to it in the highest degree? By making proofs more rigorous? By giving new rules according to which the old rules shall be applied? Not in the least. A very great uncertainty continues to attach to the result of each single computation. But there are checks. In the realm of mathematics each point may be reached by a hundred different ways; and if each of a hundred ways leads to the same point, one may be sure that the right point has been reached. A calculation without a check is as good as none.

Johann Friedrich Herbart, quoted in Memorabilia Mathematica

Written by nevalalee

November 19, 2017 at 7:30 am

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