→ August 16, 2010
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Prime Obsession.

I admit it: I am not afraid of math.

And if you’re not afraid of math either – in this case, some fairly heavy math – you might enjoy Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics as much as I did. It’s a book about an obscure question in the field of number theory, one that remains unsolved after 150 years and probably has little to no practical application, but John Derbyshire manages to give the subject some real personality while doing his best to make it accessible to readers who haven’t taken a lot of advanced math classes or who, like me, are a good 13 years removed from their last one.

The subject of Prime Obsession is the Riemann Hypothesis, which states that the non-trivial zeros of Riemann’s zeta function are half part real. “Non-trivial zeros,” in this case at least, are complex numbers (a + bi, where i is the imaginary number defined as the square root of negative 1 and b is nonzero) that give the result of 0 when plugged into the zeta function. “Half part real” means that a in that complex number is equal to ½.

The zeta function is the crux of the matter, the sum of the following infinite series:

That is:

Riemann posed his hypothesis when studying the Prime Number Theorem, which states that for any random number N, the probability of N being prime (and thus the frequency of primes around N) is roughly equal to the reciprocal of the natural logarithm of N, that is, 1/ln(N). In his one paper on the subject, he hypothesized that the frequency of primes and the differences between the actual frequency and the predicted frequency in the Prime Number Theorem was connected to the zeros of this zeta function. He couldn’t prove it at the time, and even though David Hilbert declared it one of the great mathematical problems of the 20th century in 1900, one of a list that has seen all but two of its number* solved, and in 2000 the Riemann Hypothesis was named one of the Millennium Prize Problems by the Clay Mathematics Institute, it remains unsolved. Prove or disprove it and you’ll get a cool million bucks for your trouble.

As you might imagine, solving the problem isn’t easy; indeed, it stands unsolved more than a decade after Sir Andrew Wiles’ solution of the equally perplexing problem of Fermat’s Last Theorem, one that required the development of an entire new field of mathematics (topology) unknown to Fermat at the time that he wrote that he had a “truly marvelous proof” to the problem. (Current thought is that whatever proof he had was incomplete.) The difficulty of proving or disproving the Riemann Hypothesis has led many of the major figures in mathematics, particularly in number theory, to attempt to tackle all or part of the problem or to work on further theorems and conjectures that build on the assumption that the “RH” is true. (And it has at least held true so far for very large numbers, which is not a proof but is weak evidence in its favor.)

Derbyshire’s main difficulty, beyond the lack of a clear resolution to the story, is making the solution of a potentially useless mathematical conundrum interesting; Wiles’ proof of Fermat’s Last Theorem was momentous and newsworthy, but the practical applications have been nil – it’s merely interesting to people who like numbers. Proving the Riemann Hypothesis would likely have a similar lack of real-world effects, and the hypothesis itself is a lot harder to grasp than Fermat’s Last Theorem was; the latter problem had an incredibly complex solution, but the question itself was easy for anyone who’d taken algebra to understand. Derbyshire does a masterful job of walking through the history of the Riemann Hypothesis, from earlier work on prime numbers, including the PNT, through Riemann’s brief life and career in mathematics to the major developments in the 151 years since his seminal paper appeared.

The book alternates between chapters walking through the math and chapters on the history and personalities involved in the hypothesis’ history. Carl Friedrich Gauss has a starring role early, while G.H. Hardy, Leonhard Euler, J.E. Littlewood, Jacques Hadamard, and Hilbert appear at some length later on. Derbyshire sprinkles stories of their peculiarities, senses of humor, and non-mathematical interests to keep the text lighter while also highlighting the chance occurrences that made some of the progress on the proof possible and regularly pointing out the remarkable longevity of most of the major mathematicians he mentions.

His math writing, while clearly geared to a lay audience, still got fuzzy for me when he got deeper into the zeta function as he tried to map it to the complex plane. Derbyshire relies on these “visual” interpretations that don’t correspond to any sort of plane or graphs that I’ve seen elsewhere, and I felt it was the one time he presupposed some familiarity with higher math on the part of the reader. But to his credit, he relies largely on algebra and gives a brief (re-)introduction to differentiation and integration for the short periods where calculus is necessary to move the math story forward. He also hits many major touchstones that will unlock memories for those of you who took and enjoyed lots of math classes, from the Sieve of Eratosthenes to the amazing Euler’s Identity, the latter of which states that

And if you look at that formula and are amused, fascinated, or just generally intrigued, Prime Obsession is a book for you.

I also recommend a book about one of the mathematicians who makes a cameo appearance in Derbyshire’s book, The Man Who Loved Only Numbers: The Story of Paul Erd?s and the Search for Mathematical Truth. Erd?s was a Hungarian-born savant who lived most of his life out of a suitcase, traveling the world, arriving at the doors of mathematicians he knew and announcing that “my brain is open,” after which he’d settle in for a few days or weeks and embark with his host on a streak of problem-solving and paper-writing. He had his own peculiar vocabulary, consumed large quantities of caffeine and later amphetamines, and combined brilliance and prolificacy (that’s peak and longevity for you Hall of Fame watchers) to the point where other mathematicians are referred to by their “Erd?s number,” where a person who co-authored a paper with Erd?s has an Erd?s number of one, while others are marked by how many papers you must go through to create the shortest possible chain back to Erd?s.

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→ December 28, 2008
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The Riddle of the Compass.

Amir Aczel’s The Riddle of the Compass: The Invention that Changed the World isn’t as strong as his first two books, Fermat’s Last Theorem (a very math-heavy book but one that relies on the centuries-long efforts to solve that problem for narrative greed) and God’s Equation (a more accessible work about great “blunder” by Albert Einstein that turned out to be correct). Although the story within Compass is mildly interesting, the book – just 159 pages in paperback, including diagrams and a few blank pages between chapters – is so superficial that we get neither story nor an interesting character. In fact, the predominant character in the book probably never existed.

Aczel argues that the compass was, at the time it was invented, the most important invention since the wheel, and produces a reasonable case for the argument while splitting time between the western “invention” of the compass and the evidence for a much earlier invention in China, where the device was used in medicine and by magicians but seldom if ever used for navigation in a country that rarely took to the sea. He takes a detour into Italian history, including an interesting chapter on Amalfi (now known as a tourist mecca, but briefly a maritime power and a flourishing city-state) that is itself a digression from the early inquiry into the alleged inventor of the compass, Flavio Gioia. It seems likely that Gioia himself never existed, and while it’s amusing to see how a missing comma could lead to the creation of a historical personage, it’s not much of a basis for a book.

Aczel accentutates the problem by himself glossing over details that, even if tangential, would add color to the book. While bemoaning both the west’s dismissive and patronizing treatment of Chinese culture during for most of the last millennium and China’s refusal (under multiple regimes) to reveal many scientific and medical secrets, he mentions the very recent discovery that an herb that Chinese doctors have long used as a treatment for malaria has had promising results in tests in western studies. He never mentions the plant’s name (it’s a type of wormwood known by the Latin name Artemisia annua) and lets the matter drop after the one-paragraph teaser.

Next up: A little Wodehouse for the holidays, with a trip to Blandings Castle in Summer Lightning , available only in the compilation Life at Blandings.

Filed Under: Nonfiction Tagged With: , , ,
→ October 22, 2007
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Top 25 non-fiction books.

Since this is probably going to be my lone post of the week, I figured it should be a long one. I started out planning to offer a list of the ten best nonfiction books I’ve read, and then found I’d written down thirty titles. I trimmed a few and settled on twenty-five. I’ve omitted self-help/instruction books (like books on cooking) and stuck to more serious topics, although some are lightly treated.

25. Seabiscuit, by Laura Hillenbrand. Heard the movie was terrible, which is a shame because the book was great. It’s a classic underdog story – horse thought to be too small, jockey blind in one eye, trainer with unorthodox methods, and so on – with Seabiscuit’s rise punctuated by several high moments and an almost too-good-to-be-true shot at redemption when he gets one last chance to win the race that has always eluded him.

24. The Catholic Church: A Short History, by Hans Küng. I’ll admit that this book may have a narrow appeal, but I think it’s a solid read even for those with no direct interest in the Catholic Church. Küng is the Church’s greatest internal critic, a Catholic priest and theologian who underwent an excommunication proceeding for his teachings. He rejects or questions several doctrines of the mundane Church, pointing out that such concepts as papal infallibility and the celibacy requirement for clergy are man-made, not divinely granted. The Catholic Church serves as a summary of many of his major works to date within the context of a Catholic’s history of the Church itself, dating back to its early days as a small-c catholic church hewing much more closely to the teachings of Christ than the bloated and often corrupt bureaucracy we see today.

23. The Prize Game, by Donald Petrie. A bit short and a bit slow, The Prize Game still has a fascinating and improbable story at its core: Piracy was once a government-sanctioned business with clear rules of engagement. Captured ships were known as “prizes” and there were strict guidelines for how captured cargo and sailors were to be treated. This style of privateering was all but ended after 1815, although the book does go briefly into privateering during the U.S. Civil War. If you’ve read any Patrick O’Brian books or perhaps played the Sid Meier game Pirates!, this book’s right up your alley.

22. The Invention of Clouds, by Richard Hamblyn. Reviewed briefly here. Hamblyn tells an interesting story about the amateur meteorologist who came up with the system of nomenclature and descriptions for clouds that is still more or less in use today. The only hitch here is that there wasn’t a lot of drama in the book – not that Hamblyn should have made any up – so the book just sort of flows along without the tension that tends to drive successful history of science books forward. There are some interesting asides, and it’s amazing to think that there was a time when science presentations to the public resulted in packed houses.

21. Kitchen Confidential, by Anthony Bourdain. Hilarious and cutting and explosive in its revelations of kitchen culture, Kitchen Confidential will make you think twice when deciding where to eat when eating out. And I would hope that it would teach all of you to head in the other direction when you see a sign that says “Discount Sushi.”

20. Catch Me If You Can, by Frank Abagnale. The movie sucked, but the book was great, and it’ll make you wonder why the movie’s producers felt the need to alter anything given how outrageous Abagnale’s life of deception was. He pioneered a new type of check-kiting and is one of the greatest social engineers the world has ever seen – all because he wanted to impress the ladies. And if his tale is to be believed, impress them he did.

19. The Power of Babel, by John McWhorter. Reviewed in depth here, Power offers us a history of human languages with a good dose of McWhorter’s own opinions, including his view that language is a dynamic, living entity that can only be constrained through fiat. He also takes the view that all “languages” are merely dialects, and explains why some languages still have nasty features like noun declensions and the subjunctive mood while others have lost them over time.

18. The Island of Lost Maps, by Miles Harvey. The Island of Lost Maps tells the story of one of the boldest and for a time most successful thieves of whom you’ve never heard, a milquetoast man – appropriately named Bland – who cut antique maps out of rare books in university libraries and sell them to collectors. Bland made about a half-million dollars in the early 1990s before he was caught. Harvey weaves Bland’s story in with a few other narratives, including a description of the map-collecting industry, the history of this sort of maps, and his own obsession with the story and with learning about the map world. That last thread is the one major negative of Island, as I’m firmly in the camp that says that a nonfiction book’s author doesn’t belong in the book unless he’s the subject as well.

17. God’s Equation, by Amir Aczel. Aczel’s first book was Fermat’s Last Theorem, a history of that famous equation and the math that led up to the ultimate solution by Andrew Wiles. The book started with a riveting description of Wiles’ first presentation of his solution – I’m serious, you’ll be caught up in it too – but the rest of the book was dry and very mathy, with only the occasional bit of real-life drama (like the suicide of one of the Japanese mathematicians whose work was invaluable to Wiles) to keep it moving. For his second book, however, Aczel chose a broader topic and crafted a much stronger narrative, describing how Albert Einstein’s greatest “mistake,” that of the cosmological constant (a sort of high-physics fudge factor) turned out, in the end, to be correct.

16. The Lighthouse Stevensons, by Bella Bathurst. The family of Robert Louis Stevenson is known for something very non-literary: constructing a series of lighthouses around the dangerous coastlines of the British Isles. Not only were these projects dangerous and very difficult, they also disenfranchised the various communities of wreckers who thrived on the proceeds of shipwrecks off their shores, often killing survivors to ensure their hauls. (Bathurst, also a journalist and the author of one novel, started to lose her hearing a few years ago after a head trauma suffered in a car crash, and wrote a column on how the loss is not entirely without compensations.)

15. The Tummy Trilogy/Feeding a Yen, both by Calvin Trillin. A series of four books that are more collections of stories of the quest for good eats across America and eventually the world. The Tummy Trilogy’s stories are more folksy, while Feeding a Yen seemed more focused on the food, although the disappearance of Trillin’s wife Alice midway through that tome is a sad reminder of her early death in 2001.

14. All the President’s Men , by Bob Woodward and Carl Bernstein. Still riveting thirty-plus years later, the book is more about the reporters’ gradual uncovering of the Watergate scandal than it is about the scandal itself. Loses a bit of its romance now that we know who “Deep Throat” was.

13. Brunelleschi’s Dome, by Ross King. The story of the construction of the cupola on the duomo of Florence, Brunelleschi’s Dome focuses on the technological advances that Brunelleschi had to drive to be able to construct such a large dome without internal supports or risk of collapse. The story offers a surprising intensity because of the deadlines, the pressure from the Church, and various other external factors that make the project’s completion seem uncertain, although I can assure you from firsthand experience that it all worked out in the end. If you enjoyed this one, you might like the similar but fluffier Tilt, by Nicholas Shrady, about that crooked tower an hour down the A11 in Pisa.

12. Nathaniel’s Nutmeg, by Giles Milton. I picked this one up in the remainders room of a local independent bookstore for no other reason than the inclusion of my favorite spice in the book’s title. It turns out that it’s a riveting and thorough history of the Indonesian spice trade, which has not a little to do with the fact that we in the United States are speaking English today and not Dutch. Black pepper, mace (the aril covering the nutmeg seed itself), and cinnamon all make appearances, but nutmeg was the spice that drove the markets and led to fierce battles and even torture over the control of the Spice Islands, particularly the tiny nutmeg-producing island of Run.

11. Millionaire, by Janet Gleeson. I may be biased on this one, as the subject of Millionaire is the inventor of paper money, a manor-born English ne’er-do-well named John Law. Law’s financial genius (just sounds right, doesn’t it?) led to the development of modern currency systems and credit markets, but also created one of the biggest speculative booms and crashes in history, and led to the need for a new word to describe those who had amassed so much wealth: “millionaire.”

10. The Island at the Center of the World, by Russell Shorto. The story of the Dutch colony New Amsterdam, the early history of Manhattan (starting with the arrival of the Europeans, that is), and the enduring influence of the Dutch culture, language, and society on New York, both city and state, and the United States in general. Shorto had access to a recently-unearthed trove of over 12,000 pages of documents from the Dutch colonial government, and the result is a fascinating story with two heroes, the idealistic Adriaen van der Donck and the better-known but half-villian Peter Stuyvesant, some serious villains in the English, the Swedes’ short-lived foray into colonization, and early experiments in things like democracy, tolerance, and free trade.

9. Living to Tell the Tale, by Gabriel García Marquéz. I’m not big on memoirs, but this book has a lot of the feel of a Marquez novel, and if you’ve read One Hundred Years of Solitude, then Living to Tell the Tale will give you a lot of insight into where the amazing stories from that novel originated. He’s lived a fascinating life, and his role as a journalist in the midst of revolutions and strife provides some incredible and often darkly comic stories.

8. Lords of the Realm, by John Helyar. Still the best book about Major League Baseball I’ve ever read, although it’s somewhat out of date. Helyar looks at MLB as a business and delves into a lot of the self-dealing and corruption that have shaped the monolithic monopoly we see today. And indeed, the self-dealing hasn’t stopped since the book’s publication.

7. Freakonomics, by Steven Levitt and Stephen Dubner. The book responsible for the -onomics nomenclature scourge does do wonders to lift the image of the dismal science, showing how we can use data to learn things about human behavior and how we respond to changes in our economic world. Freakonomics includes a highly-controversial study of the connection between the legalization of abortion and the drop in crime in the 1990s, but also includes an interesting chapter on the life cycles of baby names, a chapter on why realtors – excuse me, Realtors® – are running a bit of a scam, and an ever more relevant chapter on cheating.

6. The Professor and the Madman/The Meaning of Everything, both by Simon Winchester. These two books, not strictly original/sequel but still inextricably linked, revolve around the production of the Oxford English Dictionary, a 70-year project that outlived all of its original heads and contributors. Professor is the better-known and more successful of the two books, telling the story of the asylum-bound murderer who proved to be one of the most prolific contributors of example sentences to the OED project, but I found it lacked the sort of narrative greed that propels Meaning, which tells the story of the OED’s history from genesis through publication, forward. I don’t see why you’d read one and not jump to read the other, though, since each offers a built-in teaser for its partner book.

5. Liar’s Poker, by Michael Lewis. I’ve got some serious issues with Moneyball, where Lewis put the narrative ahead of strict adherence to the facts, fabricating the anecdote that includes a mention of me towards the end of the book (and declining to correct it between the hardcover and paperback editions when I pointed out that it wasn’t true). As a result, I look at Liar’s Poker with a slightly jaundiced eye, because I’m not sure if the same accuracy problems infect Lewis’ other books. But I can’t deny that Lewis is a master of prose and storycraft, and Liar’s Poker is a cracking good read, with hilarious stories and comical characters and the intensity you’d expect to see in scenes set in a bond-trading room in the wild boom leading up to the 1987 crash.

4. Longitude, by Dava Sobel. I’ve always seen Longitude as the book that started the whole history-of-science book craze, by taking an esoteric story around a forgotten hero and crafting it as a novel, complete with villains, setbacks, and a linear plot that leads to a big climax. And as it turns out with so many of the best books in the genre, the invention at the heart of Longitude made the world as we know it possible: Transoceanic voyages were not safe until the invention of the chronometer, a device that allowed a ship in the middle of the ocean to determine its longitudinal location and thus its distance from Europe or the Americas. Longitude remains one of the kings in this field because the trials and tribulations faced by its hero, clockmaker John Harrison, were so severe.

3. Mauve, by Simon Garfield. The remarkable story of a teenaged chemist named William Perkin who in effect invented a color while trying to create a synthetic form of the anti-malarial compound quinine. Perkin’s mistake left him with a strong dye he called mauveine and an industrial process that would allow for easy, large-scale production. Perkin became a global celebrity, and his visit to the United States in 1906 was front-page news in the New York Times. He’s all but forgotten today outside of an award named after him that is given to a leading scientist in the field of applied chemistry.

2. Charlie Wilson’s War, by George Crile. Reviewed at length here, and soon to be a major feature film adapted by Aaron Sorkin and starring Tom Hanks. The book revolves around two amazing characters and their successful launching of the largest covert military operation in history, the U.S. funding and arming of the Afghan mujahideen, whose guerrilla warfare against Russian invaders was a major factor in the collapse of the Soviet Union.

1. Barbarians at the Gate, by Brian Burrough and John Helyar. Still, for my money, the most novelesque non-fiction book I’ve ever read. Helyar and Burrough couldn’t have created better characters if they tried. The superficial story here is the takeover battle for RJR Nabisco, but the real story is how some very wealthy and intelligent men managed to act like teenaged boys when winning became more important than maximizing profits. The leveraged buyout of RJR Nabisco, until 2007 the largest LBO in history, ended up costing the victors in the battle nearly 50% more per share than the original offer due to the bidding war between multiple suitors, with the primary players being a management-led group that includes Shearson-Lehman, the buyout firm Kohlberg Kravis Roberts, and rival buyout firm Forstman Little. One entertaining subplot is RJR’s then-failing effort to introduce a smokeless cigarette without admitting that cigarette smoke itself was a health hazard. Good luck with that.

Filed Under: Languages, Nonfiction Tagged With: , , , , , , ,