Goodbye, Mr.Gardner
A few years ago, after I finished a presentation at an elementary school in Norman, Oklahoma, a boy came up to tell me that his great grandpa also liked to make math fun. “Who’s your great grandpa?” I asked. “Martin Gardner,” he said.
Martin Gardner! He might as well have told me that his great grandpa was God. No doubt about it, Martin Gardner, creator of the witty and mind-bending “Mathematical Games” column that ran for 24 years in Scientific American, could be called the God of recreational math. And Gardner was more than that. He wrote more than 70 books on subjects as diverse as philosophy, magic and literature — The Annotated Alice, his definitive guide to Lewis Carroll’s classic, was perhaps his best selling title. He was also a leading debunker of pseudoscience: after retiring from Sci Am, he sicked his penetrating logical powers on purveyors of quackery, ESP, UFOs and the like in a column called “Notes of a Fringe Watcher,” published for 19 years in The Skeptical Inquirer.
Poet W.H. Auden, sci fi author Arthur C.Clarke, evolutionary biologist Stephen Jay Gould and astronomer Carl Sagan were among his many admirers. Vladamir Nabokov named him in a novel. Astrophysicists named an asteroid after him.
Researching with Researchers
I always enjoy outdoor activities and meals with Tom and Ellen but I had an ulterior motive this time. Ellen, aka Prof. Simms, is a botanist in the Department of Integrative Biology at the University of California, Berkeley. I am writing a book on what happens to the jack-o’ lantern after Halloween — a Halloween book for November, you might say. My ulterior motive is that I wanted Ellen’s help in identifying some of the blotchy, fuzzy and moldy looking things growing on the pumpkin. Their portraits, captured by photographer Dwight Kuhn, were the perfect accompaniment to herb tea and ice cream.
When people think of what it means for a non-fiction author to do research, Read more »
To Be a Writer: Read, Read, Read. But…
Last week, I had the pleasure of working with Linda Sue Park and Ed Young at the American Embassy School of New Delhi, India. We were the featured authors at AES’s annual Authors’ Week. During one of our many dinners together, Linda Sue and I talked about the importance of reading children’s books as a prerequisite to writing children’s books. Linda Sue is a Newbury Award-winning novelist and picture book author. Although she is essentially a fiction writer, the crafts of writing fiction and non-fiction probably have more in common than they have differences, and the need for reading is surely a commonality.
The Importance of Reading
Read. That’s the single best thing an aspiring writer can do for his or her work. I once heard an editor say, “Read a thousand books of the genre you’re interested in. THEN write yours.”
I was astonished and pleased to hear her say this–because that’s exactly what I did. During the years when I had no thought of writing for children (see About the Author), I read and read and read. Middle-grade novels. Hundreds of them–easily more than a thousand. Then I wrote mine–and it sold on its first submission. Luck? Coincidence? Maybe…but I doubt it.
My personal reading list draws from a wide variety of genres. I love middle-grade novels best, but I also read Young Adult novels and picture books. I read adult literary fiction, mysteries and nonfiction. I read poetry. I love books on food and travel. Whether a wondrous story or a hilarious passage of dialogue or a beautiful sentence or a memorable image, every bit of reading I do helps my own writing. The rhythm of language and the way words combine to communicate more than their dictionary meanings infuse the serious reader’s mind and emerge transformed when that reader sits down to write.
That’s really the best possible advice I could give any writer–read. But I find that folks are often disappointed with this advice, so I’ll offer a few more basic tips.
Please do read Linda Sue’s valuable tips (www.lspark.com/writing.html) but that’s all I will quote here. I agree with absolutely everything she says on this subject and I would encourage any writer, whether previously published or not, to read extensively. But there is a “but.” The “but” has to do with my own early experience as a writer. Question: How many children’s books in the mathematical genre did I read before writing my first book, How Much Is a Million? Answer: none.
This is only in part because there weren’t many back in the late 70′s and early 80′s when I was working on the disorganized morass of handwritten and typed pages that eventually coalesced into that book. Mainly it is because I didn’t think of myself as a writer and I guess I didn’t take my project seriously. I had no idea if what I was working on would ever become a book. I simply had an idea that went back to my childhood fascination with big numbers, and I wondered if I could turn it into something anyone would want to read. In writing it, I just went with my instincts.
Perhaps — though I’m not really sure– this had something to do with the content of the telephone call I eventually got telling my that my manuscript was going to be published. “It’s so original,” said Barbara Lalicki, senior editor at Lothrop, Lee & Shepard Books. “We’ve seen plenty of number book manuscripts, but we’ve never seen one like this.”
Original. Would my manuscript have been considered so original if I had read a thousand books before reading it? Maybe. Maybe not. I don’t know but I have a hunch that my naivite had something to do with the ultimate product.
Yet I completey agree with Linda Sue. And here’s an irony. In preparing to write the 50 books since that one, I have always read as extensively as I could. But is any of these books as original as my first one? I have no idea. Please feel free to weigh in with your two rupees. I have to sign off because they’re about to close the internet cafe. Namaste.
Happy Pi Day
In case you missed it, March 14th was an important international holiday. Every year, math enthusiasts worldwide celebrate the date as Pi Day. March 14th. 3/14. 3.14. Pi. Get it? If you’d like a higher degree of accuracy, you can celebrate Pi Minute at 1:59 on that date (as in 3.14159). Or why not Pi Second at 26 seconds into the Pi Minute (3.1415926)?
“It’s crazy! It’s irrational!” crows the website of the Exploratorium, San Francisco’s famously quirky hands-on science museum. The Exploratorium invented the holiday twenty-one years ago. In a delightful coincidence, Pi Day coincides with Albert Einstein’s birthday. Exploratorium revelers circumambulate the “Pi Shrine” 3.14 times while singing Happy Birthday to Albert.
Pi Day celebrations have spread to schools. Just over a year ago, I visited Singapore American School to give a week’s worth of presentations and I found parent volunteers serving pie to appreciative students whose math teachers were trying to sweeten their understanding of the world’s most famous irrational number. Just as pi is endless, so is the list of activities, from memory challenges and problem solving to finding how pi is connected to hat size … and writing a new form of poetry called “pi-ku,” which uses a 3-1-4 syllable pattern instead of haiku’s 5-7-5.
Learn
math’s mysteries.
It is indeed the mysteriousness of pi that makes it so fascinating. For 3,500 years, according to David Blatner, author of The Joy of Pi, pi-lovers have tried to solve the “puzzle of pi” — calculating the exact ratio of a circle’s circumference to its diameter. But there is no such thing as “exact.” No matter how successful, pi can only be estimated.
A refresher course for the pi-challenged: The 16th letter of the Greek alphabet, ? or “pi,” is used to represent the number you get when you divide a circle’s circumference (the distance around) by its diameter (distance across, through the center). Try it on any circle with a ruler and string and you’ll get something a little over 3 1/8 or approximately 22/7 (some have therefore proposed the 22nd of July for Pi Day). Measured with a little more precision, the ratio comes out to 3.14. But don’t stop there. Pi is an irrational number, meaning that, expressed as a decimal, its digits go on forever without a repeating pattern. Hence the obsession of some with memorizing pi to 100, even 1,000 places. As a Pi Day gift from 5th graders at a school I visited this year on March 15th, I received a sheet of paper with pi written out to 10,000 digits. In 2002, a computer scientist found 1.24 trillion digits. Never mind that astrophysicists calculating the size of galaxies don’t seem to need an accuracy of pi any greater than 10 to 15 digits. Playing with pi offers endless hours of good, clean mathematical fun. So what if it’s irrational.
Happy (belated) Pi Day, everybody!
If They Had A Million Dollars
Remember the hit song by the Barenaked Ladies, a Canadian alternative rock band (whose members are neither ladies nor naked — it least in public)? Here’s how it starts:
If I had a million dollar
If I had a million dollars
Well I’d buy you a house
I would buy you a house
I’d buy you furniture for your house…
Hate to sound like a million dollar spoilsport, but I sure wouldn’t pay a million for those lyrics. Not even a hundred. Still, the tune is darn catchy, and the refrain is a bit touching:
If I had a million dollars,
I’d buy your love.
Whether or not that particular commodity can be purchased at any price will not be the subject of this post, although you may wish to pursue it elsewhere.
Since the 1989 publication of my second book, If You Made a Million, I have seen countless examples of student writing that begin with the prompt, “If I had a million dollars…” They fall into three categories of roughly equal size. I’ll call the them “fulfillment,” “greed” and “charity.”
Read more »
Math-Lit for the Older Set
I got an email the other day from a parent looking for good mathematical literature to interest and challenge older children. Is there any? Which books would I recommend?
Before I describe a few of my faves, I must point out, as I did at length in my INK post of May 28, 2008, that many educators have inspired intermediate grade, middle school and even high school students with picture books, using them as age-appropriate teaching tools. I believe my most successful mathematical picture books are those that can be used on many levels. In fact, when asked the target age for How Much is a Million?, I often say, “Preschool through high school.” Actually, it’s not true. I should say. “Preschool through college,” but that answer might sound overly smug. (I have twice met college professors who use my book when teaching about Avogadro’s number, a behemoth number critically important in understanding quantitative chemistry.) That said, I will mention a few books that probably wouldn’t make it into the 2nd grade math classroom but should be a staple of math classrooms or libraries serving upper elementary, middle school and high school students.
In The Number Devil by German author Hans Magnus Enzensberger, a middle school-age boy named Robert dreams of travels through the world of mathematics under the tutelage of an impish devil whom he at first finds annoying but gradually comes to enjoy and admire. At the start of the book, Robert is a mediocre and indifferent math student — no surprise, considering that his ho-hum teacher at school gives the students mathematical busywork without the least bit of mathematical inspiration. (His uncomprehending mother is no better: she believes a son who voluntarily speaks of mathematical concepts must be ill!) But Robert and the devil are on an irrepressible romp and together they challenge each other while developing plethora of mathematical concepts and meeting a pantheon of famous mathematicians. All names are whimsically disguised — Leonhard Euler becomes “Owl” (Eule in German translates to “owl” in English) and roots (as in square roots, cube roots, etc.) are called “rutabagas” (which are literal roots) — just two of many such examples. Figuring out the conventional words for the concepts at hand just adds to the devilish fun of this 1997 book which is well on its way to becoming a classic.
Flatland is not on its way to classic status: it’s already there. Like The Number Devil, it incorporates dreams but the concepts are geometrical rather than numerical. This novella, written in 1884 by English schoolmaster Edwin A. Abbott, is a pointed satire of closed-minded, hierarchical Victorian society but it is also, as Isaac Asimov put it, “The best introduction one can find into the manner of perceiving dimensions.” The story has been developed into several short films and a 2007 feature film; there have been TV episodes, a role-playing game and sequels by other authors.
The narrator of the original Flatland is a square named – ready? — A. Square. He lives in Read more »
The Play’s The Thing
The mother of a 7th grader in Oakland, CA, tells me that morning recess at her son’s middle school has been cut from twenty minutes to ten, and the entire recess, formerly held outdoors, is now limited to an indoor space. Even the theoretical 10 minutes is often whittled down to just a few minutes or none at all because teachers respond to the disruptive in-class behavior of a few students by holding the class through recess to make up for classroom delays.
This sorry state of affairs is not limited to the United States. I am just back from speaking at primary (elementary) schools in Australia. I had a few opportunities to interact with children on the playground and I was pleased to notice Read more »
On Googols and Google, Googolplex and Infinity: The Truth About Big Numbers
When I was in high school, I read a book called Infinity: Beyond the Beyond the Beyond. I don’t remember much about it, but I’ll never forget the title. The concept of infinity in its … well, infiniteness… can keep my mind occupied for a long time. And the idea of going “beyond the beyond” — and then beyond that! — provided more delicious food for thought. I sometimes think about that title and the mind-candy of endlessness when I’m speaking at a school, as I was last week in West Chester, PA, and someone asked, “What’s the biggest number?” It’s a question I often hear. The conversation usually goes something like this:
Child: What’s the biggest number in the whole wide world?
David: Do you think there is such a thing as the biggest number?
Audience: half “Yes,” half “No”
David: Will someone please tell me what you think the biggest number is.
Children, variously: billion, trillion, quadrillion, quintillion, googol, googolplex, etc.
David: Hang on. Let’s suppose you think “quintillion” is the biggest number. Then what about “quintillion-and-one”? Isn’t that bigger? And if that’s the biggest, what about “quintillion-and-two” — even bigger, right?
This usually leads to a triumphant retort about an enormous number familiar to many children (much less familiar to their parents and teachers):
Child: Googol has to be the biggest!
David: What’s a googol?
Many children know that “googol” is the name for a very large number — a one followed by a hundred zeros. This is an exciting concept. In my book G is for Googol: A Math Alphabet Book, I tell the story of how “googol” got its name from a nine-year old boy. Surely it is tempting to call googol “the biggest number,” but that’s a non-starter.
Me: If you think googol is the biggest number, then what about googol-and-one? Or two googol? Or a googol googol?
Almost inevitably, at this point someone proffers an even bigger number, “googolplex.” It is true that the word “googolplex” was coined Read more »
Messing About in Libraries: The Delectable Art of Browsing
To many of us, it’s almost unthinkable to imagine researching anything before the advent of the internet. Discovery of information before the era of google seems as onerous as hauling water out of a well. So seduced have we been by the simplicity and effectiveness of entering a few words into the rectangle at the top of the screen and — wowza! — dozens, hundreds or thousands of “hits” come up. If none is quite right, just change the search terms a bit and try again. For researchers, it’s like winning the lottery again and again.
But. . . you knew there would be a “but”. . . are we depriving ourselves of anything worthwhile when we boil the art of research down to finding 30,000 google hits in 18 microseconds? I would maintain that we are, for several reasons, and I am going to write about one of them: browsing. Sometimes there is both pleasure and success to be found by poking around in the shelves of libraries or bookstores, just to see what we might find.A few years ago, I wrote G is for Googol: A Math Alphabet Book, a potpourri of enjoyable mathematical ideas in an ABC format. Unlike the many alphabet books written for young children, this one is directed at readers in the intermediate and middle school grades (as is its sequel, Q is for Quark: A Science Alphabet Book). So how am I going to fill 26 slots with delightful math? Many entries popped into my mind right away. “A” is going to be for “abacus” because I love the fact that proficient abacus users can calculate lengthy addition or subtraction problems faster than the fastest calculator user. “Z” is going to be for “zillion” because it’s not a number at all but people often don’t realize that Read more »
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