A journey through birdsong

In Listening to a Continent Sing, Donald Kroodsma details a cross-country cycling trip he took with his son, David, in order to, literally, listen to the continent sing. Throughout, he describes in lyrical prose all of the birds he heard as they pedaled west along the TransAmerica Route—established in 1976 for the “Bikecentennial” of our country—and all of the adventures that he and his son experienced along the way. They began their journey in Yorktown, Virginia on May 4. Read on for a behind-the scenes glimpse of the symphony that is the Virginian countryside in mid-spring. Be sure to use the QR codes, found in the book, to hear the birds for yourself!

On May 4, day 1 of the journey, Kroodsma describes listening to the world wake up around him from inside the tent, his son sleeping beside him (“Best not to get up before the sun,” he says.).

A robin begins to sing, 5:34 a.m. according to my watch, about half an hour before sunrise. His low, sweet carols drop from above one by one, cheerily, cheer-up, cheerio, cheerily, and I am soon silently singing with him, three to five carols over a few seconds, then a brief pause. I feel his tempo, counting the number of carols in the next package and pausing, counting and pausing, his initial measured pace calming. I try to stretch each quarter-second carol into a second or more, slowing his performance, relishing the varying patterns in pitch and rhythm, listening and watching as miniature musical scores float through my mind.

American Robin
Day 2 brings a trip to Malvern Hill, sight of a bloody Civil War battle nearly 150 years before. In memory of that battle, the intrepid duo is subdued as they listen to the sweet call of a field sparrow.

Emerging from the insanity of this scene is the requiem now offered by a field sparrow nearby. His gentle whistles accelerate, sliding down the scale, each whistle a little shorter and lower than the one before, a two-second lament for all who suffered here. Ever few seconds he repeats his mournful song, over and over, never-ending. In the distance I hear two others, each with a unique cadence, each offering his own comment on the scene that his ancestors some hundred generations ago would have witnessed here.

Field Sparrows
On the road between Afton and Lexington Virginia, day 6, an early morning ride is accompanied by the Eastern towhee.

Still, silence … until a single, tentative chewink of an eastern towhee pierces the quiet. With my right hand, I fumble beneath the sleeves over my left wrist to punch the light button on my watch, leaning over the left handlebar to catch a glimpse 5:25 a.m., 45 minutes before sunrise. The call is contagious, as chewinks now erupt from seemingly every roadside bush. In less than a minute I hear a feeble song, then a louder one, and soon the bushes sing, drink-your-teeeeeee, two strongly enunciated introductory notes followed by a rapid series of repeated notes. The birds ease into it, at first repeating one song several times, much as they do later in the morning, but then the warm-up is over and no holds are barred.

Eastern towhee
For the next two months, father and son cycled across the United States listening to hundreds of birds, meeting new people, and enjoying the great outdoors together. Read Listening to a Continent Sing and let Kroodsma take you along for the ride.


Stephen Heard: Write like a scientist

the scientist's guide to writing heardScientific writing should be as clear and impactful as other styles, but the process of producing such writing has its own unique challenges. Stephen Heard, scientist, graduate advisor, and editor speaks from personal experience in his book The Scientist’s Guide to Writing: How to Write More Easily and Effectively Throughout Your Scientific Career. Heard’s focus on the writing process emphasizes the pursuit of clarity, and his tips on submissions, coauthorship, citations, and peer reviews are crucial for those starting to seek publication. Recently, Heard agreed to answer a few questions about his book.

What made you decide to write a book about scientific writing?

SH: I think the first spark was when I realized I give the same writing advice to all my students, over and over, and caught myself thinking it would be easier to just write it all down once. That was foolish, of course: writing the book wasn’t easy at all! But before long, my rationale shifted. The book became less about stuff I wanted to tell everyone else, and more about stuff I wished somebody had told me. A lot of us get into science without much writing experience, and without thinking much about how important a role scientific writing plays – and when we start doing it, we discover that doing it well isn’t easy. It took me many years to become a reasonably competent scientific writer, and the book includes a lot of the things I discovered along the way. I was surprised to discover that writing the book made me a better writer. I think reading it can help too.

Surely there a bunch of other scientific-writing books out there? What do you do differently?

SH: Yes – and some of them are quite good! But I wanted to write something different. I’m not sure my book says anything that no one else knows about outlining or paragraph structure or citation formatting (for example). But I thought there was a lot of value in a book that pays attention to the writer as much as the writing: to the way writers behave as they write, and to ways in which some deliberate and scientific attention to our behavior might help us write faster and better. I’ve also discovered that knowing a bit about the history and culture of scientific writing can help us understand the way we write (and why). Just as one example: knowing something about the history of the Methods section, and how it’s changed over the last 350 years as scientists have struggled with the question of how scientific studies gain authority, can help us decide how to write our own Methods sections. I also tackle the question of whether there’s a place in scientific writing for beauty or for humor – something that gets discussed so rarely that it seems almost like a taboo.

Finally, I wanted to write a book that was really engaging: to show that thinking about writing (as we all need to) needn’t be dry and pedantic. So readers might be surprised, in a book about scientific writing, to find mentions of Voltaire’s lover, SpongeBob SquarePants, and the etymology of the word fart. But I hope they’ll also find that there are lessons in all those things – and more – for scientists who want to write better and more quickly.

You also go into a lot of depth about the review and publication process. Why are these things important to cover alongside the writing process?

SH: Well, maybe that isn’t “writing”, strictly speaking – but it’s an essential part of getting one’s scientific writing in the hands of readers. All of us want our scientific writing to be read, and to be cited, and to help move our fields forward. So it’s not enough to write a good manuscript; we have to be able to shepherd it through the process of submission, review, revision, and eventual acceptance. Early in my own career I found this process especially mysterious. Since then, I’ve learned a lot about it – by publishing quite a few papers myself, but also by reviewing hundreds of manuscripts and acting as an Associate Editor for hundreds more. So I have a pretty good overview of the publishing process, from both the writer’s and the journal’s perspective. There’s no particular reason that process has to be mysterious, and I thought it would be helpful to draw back the curtain.

Is scientific writing really that different from other kinds of writing?

SH: Both yes and no! Of course, there are technical issues that matter in scientific writing, like ways of handling text dense with numbers, or ways we handle citations. There are also more cultural ways in which scientific writing is its own thing. One of them is that we’ve developed a writing form that efficiently conveys material to other people who are familiar with that form. Our conventional division of papers into Abstract, Introduction, Methods, Results, and Discussion is a piece of that. Our writing (and our publication process) have evolved in many other ways that aren’t quite the same as you’d find in the humanities, or in writing about science for the public. That’s why there are books about scientific writing, not just about writing. But on another level, good scientific writing is like most other good writing: clear, concise, engaging whenever possible, and did I mention clear? Nothing is more important than clarity! As a result of this similarity, people who learn good scientific writing are well positioned for any career that involves writing – which is to say, pretty much any career.

Do you think of yourself as a good writer?

SH: No! And to loop back to the first question, that’s a big part of why I wrote the book. There are a very few natural writers out there – geniuses – for whom good writing just seems to come naturally. But these are rare. I’m like nearly everyone else: writing is hard work for me. It’s a craft I’ve learned over the years by practicing, by thinking deliberately about how I do it, and by reading advice from books that have gone before mine. It’s still hard work, but that’s OK: I’m willing to put in the effort for my writing product to seem pretty good, even if my writing process is laborious. If I’d understood earlier in my career that most writers are just like me, I would have been less crushed by the discovery that my papers didn’t just write themselves! Every scientific writer can do what I’ve done: practice the craft and improve at it. I hope my book can help.

Stephen B. Heard is professor of biology at the University of New Brunswick in Canada and associate editor of the journal American Naturalist. His most recent book is The Scientist’s Guide to Writing: How to Write More Easily and Effectively Throughout Your Scientific Career.

Christopher Kutz on drone warfare: The real moral debate


By Christopher Kutz

Despite all the sound and fury of the Presidential primary campaign, the candidates have been effectively silent on one issue: our use of drone strikes as the central tool of security policy. Perhaps they could watch Eye on the Sky, by director Gavin Hood. The film vividly imagines two nations’ officials confronting a classic military dilemma, whether to kill an enemy at the risk of civilian life. In the movie, British officials, using drone-based cameras, have identified the home of two al-Shabbab terrorist leaders (one of whom is a British woman) in Kenya as they prepare young militants for a suicide terrorist mission. Given al-Shabbab’s history, which includes the attack on a Tanzanian shopping mall, the British officials have good reason to suspect an attack against large numbers of civilians. Because local forces are unable to storm the compound, the officials request support from an American drone with a Reaper missile.

The movie’s theme is that while drone technology appears to make war ethically easier, by reducing risks to civilians and soldiers, it mainly shifts the scene of responsibility, from the battlefield to the conference room and control center. The movie gains its dramatic power by reintroducing the dilemma, in the form of a little girl who comes to sell bread outside the compound during the crucial moments. The British and American officials and drone operators must now decide how to weigh the likely death of this concrete and identified girl against the unidentifiable civilians who might be killed in a terrorist attack. The film very effectively personalizes this debate by foregrounding a few of the officials and soldiers with clear views, for and against the strike, against the majority of officials who seek only to refer judgment to other layers and departments in government. (The movie indulges in a – perhaps accurate – stereotype of Americans as callously decisive and Brits as hand-wringingly nuanced and unsure.)

Eye on the Sky is right to remind us that the ethical dilemmas of war survive the shift to drone warfare. But I believe it makes a dangerous mistake about the real ethical problem with drones. The real problem is not that officials are too rarely courageous or principled. The problem is that we citizens have given up our own responsibility for the choices of war. What ought to be a wrenching decision for a democracy, about when to kill foreigners in pursuit of its interests, has been confined within the consciences of a few.

Few doubt that a state can use lethal force in the classic circumstances of national self-defense, with an invader at the border or missiles and bombs raining in. But drone campaigns are not like this: they involve decisions made through national security bureaucracies about killing people (or categories of people) identified through disparate intelligence as members of hostile networks, whose hostilities are often directed not at the US but at local and temporary allies of US security policy. According to public information, far from strapping suicide vests onto would-be martyrs or assembling dirty bombs, most of the targets identified in intelligence or surveillance reports are, essentially, young men with rifles. What used to be a strategic decision to go to war, with Congress involved and citizens rallied, has become a matter of executive decision making at the tactical level, made by the President and his security team, and the director of the CIA.

The personalization of the decision to kill is not unique to the drone program: special forces killing teams have been part of US security policy for decades. But the emergence of drone warfare has both let the policy of secret killing come out of the shadows on the one hand, while keeping it even more deeply in the shadows in another respect, placing it largely within the confines of the CIA, with White House oversight. While even former CIA Director Michael Hayden acknowledges the myth of the surgical strike, since inevitably non-combatants, including women and children are killed, the lesson we citizens are asked to accept is that these are difficult but reasonable choices for the President, not for us.

We should fear the loss of our accountability as citizens more than the myth of the surgical strike. Presidents and CIA advisors, not to mention drone operators, may well agonize over the potential deaths of innocents. But I fear our own complacency, in wanting these dilemmas to be theirs, and theirs alone. The deaths of civilians and militants alike belong to us as citizens, and we must be prepared as citizens to deliberate about our killing policy, and accept its consequences. Instead, the complicity of the media in personalizing drone warfare keeps us citizens in a fraudulent innocence.

How can we stop the fraud we are perpetrating on ourselves? We must put ourselves in the imaginary position of the drone warriors, and come to think of ourselves as making the decision when to kill. President Obama has done little to make good on his promises of greater transparency in the drone program. To the extent the primary candidates have addressed the issue at all, Bernie Sanders has said only that he would seek to use drone strikes rarely, while Hillary Clinton has praised drone strikes as a critically effective counter-terrorism tool. Meanwhile, the rhetoric of Ted Cruz and Donald Trump, on “carpet bombing” and killing terrorist families, does not suggest much reticence on their parts. Only John Kasich has offered a specific position that moves in the right direction: to effectuate the transfer of the drone program from the CIA to the Pentagon — a shift that was promised two years ago by President Obama but later abandoned. Such a move would work to increase accountability for drone killings, and to locate decisions within an institution historically better suited to considering legal and ethical limitations on the use of force. (Recall that the use of torture in interrogation was much more firmly resisted by military than CIA officials.)

We need to force our candidates, and our media, to do better than this, to discuss what we citizens must know if we are to take honest responsibility for the deaths of the children and other bystanders in our security policy. While Eye on the Sky does a terrific job of provoking a debate on the way out of the movie theatre, we need a debate that extends all the way to the voting booth.

kutz on war and democracy jacketChristopher Kutz is the C. William Maxeiner Distinguished Professor of Law and director of the Kadish Center for Morality, Law, and Public Affairs at the University of California, Berkeley. He is the author of Complicity: Ethics and Law for a Collective Age.

National Poetry Month: Featured reading by Austin Smith

almanac smith jacketAustin Smith’s debut collection, Almanac, is a lyrical and narrative meditation on the loss of small family farms. Most of the poems are personal, set in the rural Midwest where Smith grew up. Though they are geographically specific, the greater themes such as death and perseverance are as universal as they are disquieting.

The collection is also a meditation on apprenticeship. Smith, the son of a poet, reflects on the responsibility of a young poet to mourn what is vanishing.

Listen to Austin Smith’s reading of his poem, “Coach Chance”.

austin smithAustin Smith was born in the rural Midwest. Most recently, he was a Wallace Stegner Fellow in fiction at Stanford University. He has written a collection of poems entitled Almanac: Poems.

An interview with Tonio Andrade, author of Gunpowder Age

To what degree do times of peace impact military power and precision? In his new book, Gunpowder Age, Tonio Andrade shows how throughout Chinese history, powerful enemies have inspired periods of intense military innovation and technological advancement. Andrade recently took the time to answer some questions about his book, China’s fascinating military past, and its potential emergence a modern day superpower.

Gunpowder AgeChina is fast becoming a military superpower now. Your book claims to find a “pattern to the Chinese military past.” How do current events fit into this pattern?

TA: China under its current leader, Xi Jinping, has become increasingly assertive, for example by building artificial islands in the South China Sea to buttress China’s claims to jurisdiction over the vast majority of the sea. These claims are disputed by many nations, including the USA, and analysts wonder whether China would really go to war to defend them. Some believe that it inevitably will, because rising powers tend to use their muscle to overturn the status quo, while existing powers tend to defend the status quo. Others, however, argue that China has traditionally maintained a defensive perspective on military power and is typically uninterested in waging aggressive wars. If we look at China’s deep history, however, we find numerous occasions when China used its overwhelming military power for aggressive warfare. Intriguingly, many of those occasions occurred at times analogous to today, when the dynasty in question had consolidated power after a difficult period, often spanning generations, and had reached a position of overwhelming regional power.

So you believe that China will likely use military force to assert itself over surrounding areas?

TA: China will use the most effective means to achieve its ends and maintain its security. Xi Jinping has said that war between the USA and China would be disastrous at present for both countries, and I believe China will try to avoid direct confrontation. Typically, in the past, when China has waged aggressive war, its power was overwhelming (or perceived as such) vis-à-vis its enemies. Today, however, China is in a situation less like the early Ming Dynasty (1368–1644) or Qing Dynasty (1644–1911), in which China was far more powerful than any surrounding country, than like the Song Dynasty (960-1279), which faced enemies that matched it in power, or, indeed, outmatched it. The Song fought many wars, but usually these were defensive wars, not wars of expansion.

You argue that when China faces powerful enemies it tends to be stronger and more innovative, and when it is overwhelmingly powerful its military power tends to atrophy. Is its current military power due to the fact that China faces an unusually strong rival in the USA?

TA: China’s military past seems to follow distinct patterns. We have to be careful to distinguish what we mean by “China,” however, because much Chinese warfare has typically been against other Chinese, and/or against other states occupying parts of what is today China. In any case, for much of its history, China has shuddered between periods of intense warfare and periods of relative peace, and during times of frequent warfare it has tended to have state-of-the-art military technology, techniques, and organization. During periods of extended peace, on the other hand, it has tended to fall behind, simply because it had fewer reasons to invest in military innovation. China’s current military power has been stimulated by more than a century of war and geopolitical insecurity, and there’s no doubt that China’s current military innovation and expansion is stimulated by competition with powerful rivals, most importantly the USA.

What were other periods of strength and weakness in China’s history?

TA: Probably the most significant period of relative weakness was the nineteenth century, when China found itself spectacularly vulnerable to western power, as first made clear in its humiliating loss to Great Britain in the Opium War (1839-42). Many Westerners explained China’s stunning weakness at that time by recourse to its cultural conservatism, to what they felt was a deep resistance to new ways or foreign ideas. These sorts of ideas are still very much around. But in fact, China’s resistance to innovation was a pretty short-lived phenomenon, and it can be explained by looking at the incidence of warfare experienced by China. Starting in the mid-eighteenth century, China’s Qing Dynasty had a position of such overwhelming strength and authority both within and beyond its borders that for nearly a century its inhabitants faced fewer wars (both external and internal) than ever before in the historical records. China was, in a sense, too strong for its own good, because this overwhelming power removed the stimulus for military improvement. Meanwhile, the British and their neighbors were fighting huge wars and innovating furiously. When China and Britain went to war in 1839, the British had military capacities that were far beyond those of China: Congreve rockets; light and powerful cannons; light, mobile howitzers; percussion cap muskets; explosive shells of unprecedented precision; and artillery tables that allowed the calculation of trajectories with extraordinary accuracy.

After the Opium War, why did it take so long for China to catch up with the west?

TA: Actually, Chinese officials, military and civil, carried out quite a bit of innovation right after the Opium War, studying Western guns, steamships, and sailing ships, and that innovation sped up during the intense military conflagrations that beset China starting in the 1850s. Many historians (I am one) now believe that from a technical standpoint the Qing were catching up quite effectively by the late 1860s and early 1870s. Indeed, it seems likely that up to that point their modernization attempts were even more effective than than those of Japan. But by the late 1880s, the trajectory changed, with Japan’s innovations becoming more effective. The reason is not technological or cultural but political. Japan’s old regime fell in 1867, replaced by a newer, centralized government that modernized its political structures. The Qing, however, held on, and its political structures failed to adapt. In fact, it’s a curious coincidence of history that the Qing and Japan’s old regime lasted exactly the same number of years. It’s just that the Japanese regime, which was founded first, also fell first. Japan had a clean slate and could sweep away old, unproductive aspects of its old regime. China couldn’t, so the Qing, although it effectively added new military structures – huge factories, innovative new armies, powerful new navies – couldn’t get rid of old ones, and so it was burdened and inflexible.

Your book starts with the invention of gunpowder and traces the evolution of the gun in the period 900-1280 or so, but one of the great questions of world history is why, if the Chinese invented the gun, they didn’t use it as effectively as the West?

TA: Most people know next to nothing about early gunpowder weapons, and I was no different when I started writing the book. In fact, even experts in China’s military history knew very little about early guns until recently, but what we’re learning is causing us to question some deep narratives in world history. Guns were tremendously important in China, used highly effectively. By the mid- to late-1300s, some 10% or so of Chinese infantry soldiers were armed with guns, meaning there were probably more gunners in Chinese armies than there were troops of all kinds in Western Europe (excluding Iberia). By the mid-1400s, the proportion of gunners in China had reached 30% or so of infantry forces, a level Europeans didn’t reach until the mid-1500s. And Chinese soldiers used guns more effectively as well, deploying them in advanced and highly-disciplined formations by the mid-1300s. Similar disciplinary techniques and formations didn’t spread in Europe until the 1500s. So you can see that Chinese gunners were highly effective, more effective than westerners during this period. This early history of Chinese gunnery is almost entirely unknown, but it is a key part of world history.

That’s very interesting, but of course Europeans did eventually get better at gunpowder technology. When and why did this happen?

TA: During the early gunpowder Age, from around 900 or so (when the first gunpowder weapons were used in battle) to around 1450, East Asians led the world in gunpowder warfare. Starting around 1450, however, Europeans pulled ahead. Why? I believe the answer has to do with levels of warfare. From 1450 or so, the Ming dynasty entered into a period of relatively low warfare, which contrasted with the previous century of intense warfare. This period of relative peace (emphasis on the word relative) in China contrasted with a period of tremendous warfare in Europe. So Europeans, fighting frequently, developed new types of guns – longer, thinner, lighter, and more accurate – whereas Chinese guncraft stagnated. This period lasted only a short time, however. By the early 1500s, Chinese were innovating furiously again, and the period from 1550 to 1700 or so was a time of tremendous warfare in China. China stayed caught up with the west from a military perspective – ahead in certain respects, behind in others – until the mid-1700s when, as I said before, it entered into a great period of relative peace (again, emphasis on the word relative), during which it fell behind, a situation that lasted until the Opium War.

Tonio Andrade is professor of history at Emory University and the author of Lost Colony: The Untold Story of China’s First Great Victory over the West (Princeton) and How Taiwan Became Chinese. His most recent book is Gunpowder Age.

National Poetry Month: Featured reading by Anthony Carelli

carelli jacket carnations Throughout April, Princeton University Press has enjoyed featuring audio readings from an array of poets. Today, Anthony Carelli presents “The Brooklyn Heavens”, a poem selected from his debut collection, Carnations. Throughout the book, Carelli injects new life into metaphors as old as writing itself. The poems themselves are his carnations, wilting even as they are being written and being renewed with new writing and voice. Carelli transforms the most ordinary of images, such as a walk home from work or a game of Frisbee in a winter park.

An exclusive reading from Carnations:

Anthony Carelli’s poems have appeared in various magazines including The New Yorker, Columbia, and Commonweal, and on various websites including theparisreview.org, AGNI online, and Memorious. His first book, Carnations (Princeton University Press, 2011) was a finalist for the 2011 Levis Reading Prize. Recipient of a Hodder fellowship and a Whiting Writers’ Award, he currently lives in Brooklyn, New York and teaches at New York University.

Bird Fact Friday – Is the Mute Swan silent?

From page 284 of Waterfowl of North America, Europe & Asia:

The Mute Swan is not mute at all. Its most frequent call is a wee-rrrr or wiingrr-iew with a high-pitched second syllable. It will also make an in-rrr sound accompanied with strong hissing in aggression. In flight, the wings produce a whistling sound, typical of the species.

Waterfowl of North America, Europe, and Asia: An Identification Guide 
Sébastien Reeber

ReeberThis is the ultimate guide for anyone who wants to identify the ducks, geese, and swans of North America, Europe, and Asia. With 72 stunning color plates (that include more than 920 drawings), over 650 superb photos, and in-depth descriptions, this book brings together the most current information on 84 species of Eurasian and North American waterfowl, and on more than 100 hybrids. The guide delves into taxonomy, identification features, determination of age and sex, geographic variations, measurements, voice, molt, and hybridization. In addition, the status of each species is treated with up-to-date details on distribution, population size, habitats, and life cycle. Color plates and photos are accompanied by informative captions and 85 distribution maps are also provided. Taken together, this is an unrivaled, must-have reference for any birder with an interest in the world’s waterfowl.

National Poetry Month: Featured reading by Fiona Sze-Lorrain

The Ruined Elegance jacketTo celebrate National Poetry Month, Princeton University Press has been proud to present audio readings from our poets throughout the month of April.

Fiona Sze-Lorrain embraces influences from America, France, and Asia throughout her latest collection of poetry, The Ruined Elegance. The poetry is inspired by an array of sources, from concentration camps to sketches, photographs to musical pieces. With lyrical language and imagery, Sze-Lorrain’s work offers hope and elegance to offset devastation and ruin.

Below, listen to Sze-Lorrain read “Transparent” from The Ruined Elegance. 

Fiona Sze-Lorrain is a poet, literary translator, editor, and zheng harpist. The author of two previous books of poetry in English, My Funeral Gondola and Water the Moon, she also writes and translates in French and Chinese. She lives in Paris. Her most recent book is The Ruined Elegance: Poems.


Even celebrities misquote Albert Einstein

Calaprice_QuotableEinstein_pb_cvrAlice Calaprice is the editor of The Ultimate Quotable Einstein, a tome mentioned time and again in the media because famous folks continue to attribute words to Einstein that, realistically, he never actually said. Presidential candidates, reality stars, and more have used social media make erroneous references to Einstein’s words, perhaps hoping to give their own a bit more credibility. From the Grapevine recently compiled the most recent misquotes of Albert Einstein by public figures and demonstrated how easy it is to use The Ultimate Quotable Einstein to refute those citations:

Albert Einstein was a wise man, even outside the science laboratory. He has inspired painters, young students and comic book creators. Even budding romantics take advice from him.

So it should come as no surprise, then, that so many people today quote Einstein. Or, to be more precise, misquote Einstein.

“I believe they quote Einstein because of his iconic image as a genius,” Alice Calaprice, an Einstein expert, tells From The Grapevine. “Who would know better and be a better authority than the alleged smartest person in the world?”

Read more here.


Nicholas J. Higham: The Top 10 Algorithms in Applied Mathematics


From “Computational Science” by David E. Keyes in Princeton Companion to Applied Mathematics

In the January/February 2000 issue of Computing in Science and Engineering, Jack Dongarra and Francis Sullivan chose the “10
algorithms with the greatest influence on the development and practice of science and engineering in the 20th century” and presented a group of articles on them that they had commissioned and edited. (A SIAM News article by Barry Cipra gives a summary for anyone who does not have access to the original articles). This top ten list has attracted a lot of interest.

Sixteen years later, I though it would be interesting to produce such a list in a different way and see how it compares with the original top ten. My unscientific—but well defined— way of doing so is to determine which algorithms have the most page locators in the index of The Princeton Companion to Applied Mathematics (PCAM). This is a flawed measure for several reasons. First, the book focuses on applied mathematics, so some algorithms included in the original list may be outside its scope, though the book takes a broad view of the subject and includes many articles about applications and about topics on the interface with other areas. Second, the content is selective and the book does not attempt to cover all of applied mathematics. Third, the number of page locators is not necessarily a good measure of importance. However, the index was prepared by a professional indexer, so it should reflect the content of the book fairly objectively.

A problem facing anyone who compiles such a list is to define what is meant by “algorithm”. Where does one draw the line between an algorithm and a technique? For a simple example, is putting a rational function in partial fraction form an algorithm? In compiling the following list I have erred on the side of inclusion. This top ten list is in decreasing order of the number of page locators.

  1. Newton and quasi-Newton methods
  2. Matrix factorizations (LU, Cholesky, QR)
  3. Singular value decomposition, QR and QZ algorithms
  4. Monte-Carlo methods
  5. Fast Fourier transform
  6. Krylov subspace methods (conjugate gradients, Lanczos, GMRES,
  7. JPEG
  8. PageRank
  9. Simplex algorithm
  10. Kalman filter

Note that JPEG (1992) and PageRank (1998) were youngsters in 2000, but all the other algorithms date back at least to the 1960s.

By comparison, the 2000 list is, in chronological order (no other ordering was given)

  • Metropolis algorithm for Monte Carlo
  • Simplex method for linear programming
  • Krylov subspace iteration methods
  • The decompositional approach to matrix computations
  • The Fortran optimizing compiler
  • QR algorithm for computing eigenvalues
  • Quicksort algorithm for sorting
  • Fast Fourier transform
  • Integer relation detection
  • Fast multipole method

The two lists agree in 7 of their entries. The differences are:

PCAM list 2000 list
Newton and quasi-Newton methods The Fortran Optimizing Compiler
Jpeg Quicksort algorithm for sorting
PageRank Integer relation detection
Kalman filter Fast multipole method

Of those in the right-hand column, Fortran is in the index of PCAM and would have made the list, but so would C, MATLAB, etc., and I draw the line at including languages and compilers; the fast multipole method nearly made the PCAM table; and quicksort and integer relation detection both have one page locator in the PCAM index.

There is a remarkable agreement between the two lists! Dongarra and Sullivan say they knew that “whatever we came up with in the end, it would be controversial”. Their top ten has certainly stimulated some debate, but I don’t think it has been too controversial. This comparison suggests that Dongarra and Sullivan did a pretty good job, and one that has stood the test of time well.

Finally, I point readers to a talk Who invented the great numerical algorithms? by Nick Trefethen for a historical perspective on algorithms, including most of those mentioned above.

This post originally appeared on Higham’s popular website.

Higham jacketNicholas J. Higham is the Richardson Professor of Applied Mathematics at The University of Manchester. He most recently edited The Princeton Companion to Applied Mathematics.