Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

Posts Tagged ‘Donald Knuth

The unfinished lives

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Yesterday, the New York Times published a long profile of Donald Knuth, the legendary author of The Art of Computer Programming. Knuth is eighty now, and the article by Siobhan Roberts offers an evocative look at an intellectual giant in twilight:

Dr. Knuth usually dresses like the youthful geek he was when he embarked on this odyssey: long-sleeved T-shirt under a short-sleeved T-shirt, with jeans, at least at this time of year…Dr. Knuth lives in Stanford, and allowed for a Sunday visitor. That he spared an entire day was exceptional—usually his availability is “modulo nap time,” a sacred daily ritual from 1 p.m. to 4 p.m. He started early, at Palo Alto’s First Lutheran Church, where he delivered a Sunday school lesson to a standing-room-only crowd.

This year marks the fiftieth anniversary of the publication of the first volume of Knuth’s most famous work, which is still incomplete. Knuth is busy writing the fourth installment, one fascicle at a time, although its most recent piece has been delayed “because he keeps finding more and more irresistible problems that he wants to present.” As Roberts writes: “Dr. Knuth’s exacting standards, literary and otherwise, may explain why his life’s work is nowhere near done. He has a wager with Sergey Brin, the co-founder of Google and a former student…over whether Mr. Brin will finish his Ph.D. before Dr. Knuth concludes his opus…He figures it will take another twenty-five years to finish The Art of Computer Programming, although that time frame has been a constant since about 1980.”

Knuth is a prominent example, although far from the most famous, of a literary and actuarial phenomenon that has grown increasingly familiar—an older author with a projected work of multiple volumes, published one book at a time, that seems increasingly unlikely to ever see completion. On the fiction side, the most noteworthy case has to be that of George R.R. Martin, who has been fielding anxious inquiries from fans for most of the last decade. (In an article that appeared seven long years ago in The New Yorker, Laura Miller quotes Martin, who was only sixty-three at the time: “I’m still getting e-mail from assholes who call me lazy for not finishing the book sooner. They say, ‘You better not pull a Jordan.’”) Robert A. Caro is still laboring over what he hopes will be the final volume of his biography of Lyndon Johnson, and mortality has become an issue not just for him, but for his longtime editor, as we read in Charles McGrath’s classic profile in the Times:

Robert Gottlieb, who signed up Caro to do The Years of Lyndon Johnson when he was editor in chief of Knopf, has continued to edit all of Caro’s books, even after officially leaving the company. Not long ago he said he told Caro: “Let’s look at this situation actuarially. I’m now eighty, and you are seventy-five. The actuarial odds are that if you take however many more years you’re going to take, I’m not going to be here.”

That was six years ago, and both men are still working hard. But sometimes a writer has no choice but to face the inevitable. When asked about the concluding fifth volume of his life of Picasso, with the fourth one still on the way, the biographer John Richardson said candidly: “Listen, I’m ninety-one—I don’t think I have time for that.”

I don’t have the numbers to back this up, but such cases—or at least the public attention that they inspire—seem to be growing more common these days, on account of some combination of lengthening lifespans, increased media coverage of writers at work, and a greater willingness from publishers to agree to multiple volumes in the first place. The subjects of such extended commitments tend to be monumental in themselves, in order to justify the total investment of the writer’s own lifetime, and expanding ambitions are often to blame for blown deadlines. Martin, Caro, and Knuth all increased the prospective number of volumes after their projects were already underway, or as Roberts puts it: “When Dr. Knuth started out, he intended to write a single work. Soon after, computer science underwent its Big Bang, so he reimagined and recast the project in seven volumes.” And this “recasting” seems particularly common in the world of biographies, as the author discovers more material that he can’t bear to cut. The first few volumes may have been produced with relative ease, but as the years pass and anticipation rises, the length of time it takes to write the next installment grows, until it becomes theoretically infinite. Such a radical change of plans, which can involve extending the writing process for decades, or even beyond the author’s natural lifespan, requires an indulgent publisher, university, or other benefactor. (John Richardson’s book has been underwritten by nothing less than the John Richardson Fund for Picasso Research, which reminds me of what Homer Simpson said after being informed that he suffered from Homer Simpson syndrome: “Oh, why me?”) And it may not be an accident that many of the examples that first come to mind are white men, who have the cultural position and privilege to take their time.

It isn’t hard to understand a writer’s reluctance to let go of a subject, the pressures on a book being written in plain sight, or the tempting prospect of working on the same project forever. And the image of such authors confronting their mortality in the face of an unfinished book is often deeply moving. One of the most touching examples is that of Joseph Needham, whose Science and Civilization in China may have undergone the most dramatic expansion of them all, from an intended single volume to twenty-seven and counting. As Kenneth Girdwood Robinson writes in a concluding posthumous volume:

The Duke of Edinburgh, Chancellor of the University of Cambridge, visited The Needham Research Institute, and interested himself in the progress of the project. “And how long will it take to finish it?” he enquired. On being given a rather conservative answer, “At least ten years,” he exclaimed, “Good God, man, Joseph will be dead before you’ve finished,” a very true appreciation of the situation…In his closing years, though his mind remained lucid and his memory astonishing, Needham had great difficulty even in moving from one chair to another, and even more difficulty in speaking and in making himself understood, due to the effect of the medicines he took to control Parkinsonism. But a secretary, working closely with him day by day, could often understand what he had said, and could read what he had written, when others were baffled.

Needham’s decline eventually became impossible to ignore by those who knew him best, as his biographer Simon Winchester writes in The Man Who Loved China: “It was suggested that, for the first time in memory, he take the day off. It was a Friday, after all: he could make it a long weekend. He could charge his batteries for the week ahead. ‘All right,’ he said. ‘I’ll stay at home.’” He died later that day, with his book still unfinished. But it had been a good life.

Quote of the Day

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I’ll use dirty tricks [in coding] for two reasons. One is if it’s really going to give me a performance improvement and my application is one that the performance improvement is going to be appreciated. Or sometimes I’ll say, “This is tricky; I couldn’t resist being tricky today because it’s so cute.” So just for pure pleasure. In any case, I document it; I don’t just put it in there.

Donald Knuth, to Peter Seibel in Coders at Work

Written by nevalalee

March 29, 2018 at 7:30 am

Science and civilization

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Over the last week, I picked up two books—at the annual Newberry Library and Oak Park Public Library book sales, which are always a high point of my year—that I’d been hoping to find for a long time. One is a single volume, Civil Engineering and Nautics, of Joseph Needham’s landmark Science and Civilization in China, which currently consists of twenty-seven huge books that I all unreasonably hope to own one day. The other is a slim fascicle, or paperbound installment from a work in progress, from Donald Knuth’s The Art of Computer Programming, which, if we’re lucky, will release its fourth volume sometime in the next decade. These two projects are rather different in scale, but remarkably similar in their conception and incubation. Needham worked on his book for close to half a century without finishing it, and Knuth has been laboring on his for even longer, with no obvious end in sight. I’ve been intrigued by such grand projects for most of my life, but I’ve become even more interested after embarking on my own venture into nonfiction. Replace “computer programming” with “science fiction” and “discovered” with “written,” and what Knuth once said in an interview gets very close to my attitude two years ago when I started writing Astounding:

At the time, everybody I knew who could write a book summarizing what was known about computer programming had discovered quite a lot of the ideas themselves…By contrast, I hadn’t really discovered anything new by myself at that point. I was just a good writer…I had this half-conceited and half-unconceited view that I could explain it more satisfactorily than the others because of my lack of bias. I didn’t have any axes to grind but my own.

Knuth concludes: “Then, of course, as I started to write things I naturally discovered one or two new things as I went, and now I am just as biased as anybody.” Which pretty sums up my experience, too.

And what really fascinates me about both projects is how monstrously these tomes grew past their projected dimensions, both in space and in time. Both Needham and Knuth thought at first that their work would fit within a single volume, and although they each expanded it to the magic number of seven, neither seems to have grasped just how long it would take. Knuth recalls:

My original motivation was to write a text about how to write compilers, so I began drafting chapters. I was seriously planning to finish the book before my son was born…In June 1965, I had finally finished the first draft of the twelve chapters. It amounted to three thousand handwritten pages of manuscript…I figured about five pages of my handwriting would be about one page of a book.

As it turned out, he was a little off: the real proportion was one and a half handwritten pages to a single page in type, which meant that he had already written two thousand pages without even getting past the subject of compilers. Needham had a similar moment of clarity. As Simon Winchester writes in his biography The Man Who Loved China:

Needham had decreed early on in the process, as he watched each volume begin to swell and threaten to burst out of its covers, that no one volume should be “too big for a man to read comfortably in his bath.” But it was happening nonetheless…One book became two, three, or four. Volume V, a special case, became not five, but thirteen formal subsidiary parts, each one of them big and complicated enough to be made into a separate, self-standing, and equally enormous new volume of its own.

It’s frankly hard to imagine reading any of these expensive books in the tub, but Needham says elsewhere, more realistically, that critics found the volumes “too heavy and bulky for meditative evening reading,” which led to the work being repeatedly subdivided.

The Art of Computer Programming was released by a commercial educational publisher, Addison-Wesley, but it isn’t surprising that most such books tend to appear at academic presses, which are the only institutions capable of sustaining a project that lasts for decades. (Their sole competition here might be the Catholic Church, which has been underwriting a critical edition of the works of St. Thomas Aquinas since 1879. They’re about halfway through.) Winchester refers in passing to “the beleaguered Cambridge University Press, which was obliged to tolerate the constant expansion of the project,” and for the full picture, you can turn to the book A Skeptic Among Scholars, by August Frugé, the director of the University of California Press. He writes of The Plan of St. Gall, a three-volume monument of scholarship that is probably the most beautiful book I own:

The St. Gall manuscript…was said in 1960 to be in semifinal draft, about one hundred and fifty pages in length. When approved by the Editorial Committee and accepted by me in 1967, it came to several hundred typed pages, about right for a single quarto volume. As the work moved through the production process during the next twelve years, we paused every now and then to call for new estimates of size and cost, and each time discovered that new sections had been added, along with a few dozen new diagrams and drawings.

At one point, concerns about cost threatened to derail the whole enterprise, and Frugé retired before the three huge folios were published. James H. Clark, his successor, saw it to completion, writing later: “But what is a university press for if not to take these kinds of risks, make these investments, and publish books that make a difference?” Aside from Knuth, one of the few comparable examples on the commercial side must be Robert Caro’s The Years of Lyndon Johnson, which was originally planned as three volumes to be written over about six years. Forty years and four books later, Caro still isn’t done, and the fact that he has been allowed to keep working at the same methodical pace is a tribute to his longtime editor Robert Gottlieb at Knopf.

And if there’s one key takeaway from the examples I’ve mentioned, it’s that none of these authors set out to devote their lives to these projects—they all thought at first that they could finish it within a few years. Knuth recalls:

It gradually dawned on me how large a project this was going to be. If I had realized that at the beginning, I wouldn’t have been foolish enough to start; I wouldn’t have dared to tackle such a thing…[But] I had collected so much material that I felt it was my duty to continue with the project even though it would take a lot longer than I had originally expected.

You also realize that you can’t explain the subject at hand without covering a lot of other material first. Caro treats his books on Johnson as windows onto such vistas as local politics, Texas, and the Senate, which is a big part of their appeal. (The equivalent in my case would be deciding that I couldn’t write the life of John W. Campbell in a comprehensible form without telling the entire history of science fiction, too, which might well be true.) Frugé, perhaps to his credit, ventures a more cynical reading:

In my skeptical and perhaps scatterbrained way, I sometimes wonder how a research scholar can work on the same project decade after decade and retain faith in its intellectual importance. Perhaps some do not, and that is why their books are never completed. But we can also observe an opposite phenomenon. As the years go by the object or document for study may swell and expand in importance until—until, for example, “The Plan of St. Gall is…one of the most fascinating creations of the human mind.”

He makes a good point. The cycle feeds on itself, with the work expanding in scope to justify the amount of time it takes. It’s human nature, and there’s something a little absurd about it. But it’s also the only way we get art, science, or civilization.

Quote of the Day

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For simplicity, let me say that people like me are “geeks,” and that geeks comprise about two percent of the world’s population. I know of no explanation for the rapid rise of academic computer science departments—which went from zero to one at virtually every college and university between 1965 and 1975—except that they provided a long-needed home where geeks could work together.

Donald Knuth, to InformIT

Written by nevalalee

May 2, 2017 at 7:30 am

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Our fearful symmetry

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Yesterday, I spent an hour fixing my garage door, which got stuck halfway up and refused to budge. I went about it in the way I usually approach such household tasks: I took a flashlight and a pair of vise-grips and stared at it for a while. In this case, for once, it worked, even if I’m only postponing the inevitable service call. But it wouldn’t have occurred to me to tackle it myself in the first place—when I probably wouldn’t have tried to fix, say, my own car by trial and error—if it hadn’t been for two factors. The first is that the workings were all pretty visible. On each side, there’s basically just a torsion spring, a steel cable, and two pulleys, all of it exposed to plain sight. The second point, which was even more crucial, is that a garage door is symmetrical, and only one side was giving me trouble. Whenever I wasn’t sure how the result should look, I just had to look at the other half and mentally reflect it to its mirror image. It reminded me of how useful symmetry can be in addressing many problems, as George Pólya notes in How to Solve It:

Symmetry, in a general sense, is important for our subject. If a problem is symmetric in some ways we may derive some profit from noticing its interchangeable parts and it often pays to treat those parts which play the same role in the same fashion…Symmetry may also be useful in checking results.

And if I hadn’t been able to check my work along the way using the other side of the door, I doubt I would have attempted to fix it at all.

But it also points at a subtle bias in the way we pick our problems. There’s no question that symmetry plays an important role in the world around us, and it provides a solid foundation for the notion that we can use beauty or elegance as an investigative tool. “It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has a really sound insight, one is on a sure line of progress,” Paul Dirac famously said, and Murray Gell-Mann gave the best explanation I’ve ever found of why this might be true:

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.

Gell-Mann concludes: “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.”

He’s right, of course, and there are plenty of fields in which symmetry and self-similarity are valuable criteria. Yet there’s also a sense in which we’re drawn to problems in which such structures appear, while neglecting those that aren’t as amenable to symmetrical thinking. Just as I was willing to take apart my garage door when I wouldn’t have done the same with my car—which, after all, has a perfectly logical design—it’s natural for us to prefer problems that are obviously symmetrical or that hold out the promise of elegance, much as we’re attracted to the same qualities in the human face. But there are plenty of important questions that aren’t elegant at all. I’m reminded of what Max Perutz, who described the structure of hemoglobin, said about the work of his more famous colleague James Watson:

I sometimes envied Jim. My own problem took thousands of hours of hard work, measurements, calculations. I often thought that there must be some way to cut through it—that there must be, if only I could see it, an elegant solution. There wasn’t any. For Jim’s there was an elegant solution, which is what I admired. He found it partly because he never made the mistake of confusing hard work with hard thinking; he always refused to substitute one for the other.

In The Eighth Day of Creation, Horace Freehand Judson calls this “the most exact yet generous compliment I have ever heard from one scientist to another.” But there’s also a wistful acknowledgement of the luck of the draw. Both Perutz and Watson were working on problems of enormous importance, but only one of them had an elegant solution, and there was no way of knowing in advance which one it would be.

Given the choice, I suspect that most of us would prefer to work on problems that exhibit some degree of symmetry: they’re elegant, intuitive, and satisfying. In the absence of that kind of order, we’re left with what Perutz calls “thousands of hours of hard work, measurements, calculations,” and it isn’t pretty. (As Donald Knuth says in a somewhat different context: “Without any underlying symmetry properties, the job of proving interesting results becomes extremely unpleasant.”) When we extrapolate this preference to the culture as a whole, it leads to two troubling tendencies. One is to prioritize problems that lend themselves to this sort of attack, while overlooking whole fields of messier, asymmetrical phenomena that resist elegant analysis—to the point where we might even deny that they’re worth studying at all. The other is to invent a symmetry that isn’t there. You can see both impulses at work in the social sciences, which tend to deal with problems that can’t be reduced to a series of equations, and they’re particularly insidious in economics, which is uniquely vulnerable to elegant models that confirm what existing interest groups want to hear. From there, it’s only a small step to more frightening forms of fake symmetry, as Borges writes in “Tlön, Uqbar, Orbis Tertius”: “Any symmetry with a resemblance of order—dialectical materialism, anti-Semitism, Nazism—was sufficient to entrance the minds of men.” And the first habit has a way of leading to the second. The more we seek out problems with symmetry while passing over those that lack it, the more likely we become to attribute false symmetries to the world around us. Symmetry, by definition, is a beautiful thing. But it can also turn us into suckers for a pretty face.

Quote of the Day

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Donald Knuth

If you find that you’re spending almost all your time on theory, start turning some attention to practical things; it will improve your theories. If you find that you’re spending almost all your time on practice, start turning some attention to theoretical things; it will improve your practice.

—Attributed to Donald Knuth

Written by nevalalee

December 26, 2012 at 7:30 am

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Quote of the Day

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November 7, 2011 at 7:48 am

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