Overview... "Foolproof, and Other Mathematical Meditations"

"Mathematics is too important and too much fun to be left to the mathematicians." 

                             -- first sentence of Brian Hayes' Preface to his new volume

One of my favorite Murphy Law corollaries states, “Nothing can be made foolproof because fools are so damn ingenious”... while the quote doesn't pertain to Brian Hayes' new book, it was the first thing I thought of upon seeing his offering. ;) The quote, I think, does pertain to the world we live in, and Hayes is nothing, if not an astute observer of that world.  “Foolproof and Other Mathematical Meditations” is a compendium of 13 updated versions of previously-published Hayes' essays with the “Foolproof” essay actually being the last, and one of the most enjoyable, of the slim volume. But before I say more, let me digress further…

A common joke when I was growing up reading Scientific American, was that the magazine was just a wrapper for getting Martin Gardner’s monthly column into your mailbox. No doubt there literally were some readers who subscribed to the magazine just for Gardner's column. His writing was succinct, descriptive, intriguing, on topics that were unpredictable from month-to-month. Another reason I think many loved Gardner was that he was NOT a mathematician (if memory serves me right he never even took an academic math class after high school) — it gave some hope that non-professional math enthusiasts could still contribute to the field or at least communicate some math to others (in the sciences usually astronomy is often cited as one of the only areas where ‘amateurs’ have a fair chance of making a significant contribution).

Anyway, I mention all this now because Brian Hayes’ writing, to my sense, has the ring of Gardner’s popular writing. In fact, when I interviewed Hayes awhile back, I specifically asked if he consciously copied Gardner’s style (he overlapped with Gardner, working at Scientific American). He admitted, like so many, being a huge fan of Gardner, but said he never deliberately tried to mimic Gardner’s craft — but took my question as the compliment it was meant to be. Still, as I read these ‘Foolproof’ essays I could almost hear Gardner’s voice in the background. Martin’s writing was more “recreational,” perhaps even casual, while Hayes has a more technical or academic bent to it, but still the style and step-by-step presentation are similar. And the resemblance goes beyond their meticulous exposition, as Hayes too is not a professional mathematician, just a sort of dabbler in it, who like Gardner, is unpredictable in what topic may capture his interest next.

Enough about all that. Hayes' new book is a delight… with one shortcoming: at 200 pages and 13 essays it is too SHORT. I don’t know what the criteria was for essays that made it into this volume, but plenty of good Hayes material is left out.

Every offering here contains interesting little gems or tidbits that I suspect a math teacher could incorporate into a classroom discussion at the middle or high school level, while also containing many bits for the professional mathematician to mull over. Computer science is Hayes’ specialty, so several of the pieces are focused there. My own favorites, in addition to “Foolproof" though are the more mathematically-inclined pieces, including: “The Spectrum of Riemannium,” “Playing Ball in the nth Dimension,” and “Quasirandom Ramblings.” But your own favorites will depend on your own proclivities as Hayes jumps around from one wild, quirky musing to another, on biography, method, pure and applied math: Gauss, arithmetic, Sudoku, space-filling curves, statistics, Markov chains, pi, computer software, randomness, math history, the abc conjecture, and more are here… almost always dipping in deep enough at some point to make you slow down in order to grasp what he's positing.

This rich, mind-stretching book has come along at a time when I was feeling a bit frustrated by the lack of “generalist” popular math books showing up this year (plenty of books appealing to narrower niches), and will certainly be among my favorites from the last 12 months. Reading it reminds me a bit of what they say about Chinese meals… each essay here felt deep and satisfying while reading it, yet an hour later I was hungry for more! ;)

Finally, Hayes’ dedication for the book reads: “To the mathematics community that has taught me and charmed me.” He constantly returns that charm in spades.

Brian Hayes... Award-winning Science Writer

Math-Frolic Interview #38

“If you ever lie awake pondering the complexities of the universe, you may have a soul buddy in Brian Hayes.” 

― Justin Mullins, New Scientist

I read a LOT of math blog entries. In the last year-or-so though, two people, above all others, have consistently blown me away with their postings. The two (among so many solid writers), are James Propp and Brian Hayes. So after interviewing James in the last interview here, I'm especially thrilled today to present Brian, who's blog "Bit-player" is quirky (not limited to math), exceedingly well-written, wide-ranging, and always much anticipated.

I really knew very little about Brian, who has been called, "one of the most accomplished essayists active today," so I especially love how much new information there is for me in these answers.  And I'm glad to introduce him to any readers not already familiar with his work.

His fantastic blog, Bit-player, is here: http://bit-player.org/

He tweets as: @bit_player

...and many of his prior prolific essays/book-reviews are here:

http://www.americanscientist.org/authors/detail/brian-hayes

Without further adieu...:

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1) Your blog posts aren't frequent, but are always interesting, unpredictable, and thought-provoking. How do you choose your topics and how long does it take you to complete a typical post?

The world is chock full of stories I’d love to tell, but I can’t do them all. So I try to choose topics on which I feel I have something distrinctive to say, something to contribute to a wider conversation. I also try to choose stories that aren’t already getting a heap of attention from other writers.

As you point out (very tactfully!), I’m a mighty slow writer. American Scientist comes out every other month, so in all my years there I was on a 60-day schedule. I don’t recall ever finishing an article ahead of deadline. When I write for bit-player.org, I often spend a week or two on a piece, or more if there’s a substantial amount of programming needed, or elaborate illustrations.

2)  I didn't find much at all about your academic or personal past online; can you say a little about your path to becoming a popular writer on math/computer science?

In my youth I was seized by a fierce impatience. I couldn’t wait to get on with life, and so I skipped all the usual preparatory steps — like a college education — and plunged directly into a career as a writer and editor. (Advice to young people: Don’t be in such a hurry. The world will still be there waiting for you when you graduate.) 

While still in high school I began reviewing books for Saturday Review (a literary weekly, long defunct) and later for the New York Times Book Review. A couple years later I was the book review editor of the Baltimore Sunday Sun. I was also deeply interested in the sciences, technology, and mathematics, but I didn’t have much chance to connect my literary and scientific passions. Then a miracle happened: I was hired as an editor at Scientific American. The miracle worker was Dennis Flanagan, the editor in chief, who took a huge chance on a kid with very skimpy credentials. Dennis became my mentor and dearest friend. The dozen years I spent at Scientific American were my education, both in the craft of writing and in the fields I was writing about.

The staff editors in those days were not really supposed to specialize, but I did most of the high-energy physics for a few years, and a lot of molecular biology. There were also occasional pieces on mathematics and computer science, but my deepening interest in those subjects was something I pursued on my own time. This was in the late seventies and early eighties, the moment when personal computers first came into bloom. Eventually I got my hands on some hardware and learned how to do stuff with it. This was another transformative experience. I gradually came to understand that in computational science I could do more than just read about what other people were doing. I could repeat the experiment, or try one of my own. All the instruments I needed were sitting on my desk.

3)  You worked a dozen years at Scientific American, and your writing style is very reminiscent of Martin Gardner. I'm curious if you feel you have your own writing style, or have you consciously tried to emulate Gardner, who's writings were of course immensely popular?

Like so many mathy/nerdy folks of a certain age, I grew up devouring Martin Gardner’s Mathematical Games column. I was 13 or 14 when I started reading him regularly, in the early 1960s. I soon found a disreputable shop near the waterfront in Philadelphia where I could buy old issues of the magazine for 10 cents apiece, thereby catching up with some of the columns I had missed from earlier years.

When I met the man himself a few years later, it was an unsettling experience, like walking into a room and being told that the kindly, white-haired fellow in the far corner is Carl Friedrich Gauss. I was never Martin’s editor at Scientific American (he didn’t need much editing anyway), but I did have a chance to get to know him. He seldom came to the office, but for a few years I lived two blocks away from his home (on Euclid Avenue!) in Hastings-on-Hudson, New York. I was recruited as courier to carry manuscripts back and forth. Those visits always involved a glass of iced tea (Martin’s wife Charlotte would accept no refusals) and a puzzle or a magic trick or a bit of hot mathematical news from Martin.

Some years later, when Martin had retired and I began writing a column of my own, he became a generous advisor and guide, introducing me to his friends, suggesting topics, gently calling me out when I goofed. We remained in touch until shortly before his death in 2010.

I never consciously modeled my prose on Martin’s, but if you see a resemblance, I consider that a compliment. 

[Great to hear about this relationship, and I do think there's a similarity in the succinct precision of your prose and his.]

4)  If any of my readers aren't familiar with you could you point them to a few favorite (Web-accessible) mathematical essays they might enjoy?

All of my American Scientist columns and most of my other writings are freely available on the web. There’s a list with links at http://bit-player.org/publications-by-brian-hayes. (And of course the bit-player.org site itself is also open to everyone.)

Which pieces would I suggest as starting points? Here are a few that seem ripe today. Ask me tomorrow and I’ll have a different list.

• First Links in the Markov Chain. American Scientist, Vol. 101, No. 2, March-April 2013, pages 92-97. [On the centenary of A. A. Markov's probabilistic analysis of Eugene Onegin.] http://www.americanscientist.org/libraries/documents/201321152149545-2013-03Hayes.pdf
• An Adventure in the Nth Dimension. American Scientist, Vol. 99, No. 6, November-December 2011, pages 442-446. [On what happens to the volume of a ball in higher-dimensional spaces.] http://www.americanscientist.org/libraries/documents/201110101628308738-2011-11CompSciHayes.pdf
• The Spectrum of Reimannium. American Scientist, Vol. 91, No. 4, July-August 2003, pages 296-300. [On random-matrix theory and the Riemann zeta function.] http://bit-player.org/bph-publications/AmSci-2003-07-Hayes-Riemannium.pdf

5)  Are there certain current popular math writers you especially enjoy reading?

The community of mathematics writers is not large, and most of them are my friends. I can’t name favorites among them without snubbing the rest. So I’ll just mention one math writer I’ve never met: Sherman K. Stein. I particularly recommend his book How the Other Half Thinks (McGraw-Hill, 2001). 

[Totally new author to me... I'll have to check this out!]

6)  Any new books coming from you in the near future?

Yes! I’m working on a collection of essays that MIT Press will bring out next spring. Title: Foolproof, and Other Mathematical Meditations.

[This is super news to hear, and even without seeing the contents I love the title.]
[ADDENDUM: I've now reviewed this book HERE.]

7)  You're a bit of a polymath in your writings... is there some math/science subject though that you'd love to study more intensely and write about, but just haven't had the time or chance to cover yet?

Having missed my first chance at getting a proper education, I am highly susceptible to the daydream of going back to school. But I probably won’t do it. There’s too much on the agenda for my remaining years.

8)  You've worked at American Scientist magazine, which I always think of as one of the finest under-the-radar publications out there. But I know, like so many print publications these days, it's been through some rough times. Will just give you a chance to put in a promotional plug for the magazine if you care to tell folks anything about it….

Science writers often serve as intermediaries, standing between the scientist and the public, performing a sort of simultaneous translation. American Scientist has a different model: they foster direct communication between the scientist and a wider audience, helping the scientist tell his or her own story with the assistance of professional editors and illustrators. Both approaches have their virtues, but the direct channel of communication is becoming rare and thus all the more precious.

I no longer write for American Scientist on a regular basis, but I remain a consulting editor — and a huge fan. 

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Great answers Brian; I'm glad to know more about you, where you've come from, and to learn there is a new book on its way from you.

Brian's last book by the way, was "Group Theory In the Bedroom, and Other Mathematical Diversions," another superb collection of mathematical essays.