Author: David

On Googols and Google, Googolplex and Infinity: The Truth About Big Numbers

David

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 Continue reading →

Messing About in Libraries: The Delectable Art of Browsing

David

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 Continue reading →

The Truth — But Which Truth?

David


I’ve been working on What in the Wild? Secrets of Nature Concealed . . . and Revealed (a sequel to Where in the Wild? and the soon-to-be-released Where Else in the Wild?). One of nature’s secrets to be discussed is the nest holes of kingfishers, those handsome, crested birds of watery places who burrow into the riverbanks to make their nests. How deep? It turns out there is no clear answer to this question, as I discovered in my research, which led to some ruminations that will be the subject of this post.

The authors of Wildlife and Plants, 3rd edition (Marshall Cavendish Reference) write that the nest tunnels are “3-7 feet long.” In Water Birds of California, author Howard L. Cogswell says “3 to 6 feet (even 10),” while World Book Encyclopedia reports “4-15 feet.” So which is it?

Those who read non-fiction often seem to have the impression that facts are facts. Period. The writer of non-fiction must merely learn them and report them, and that’s that. I’ve gotten this attitude often from children, egged on by the adults in their lives. “You wrote X, but we read Y in another book. Who is right and who is wrong?” Cheers for the author of truth. Jeers for the liars. But in reality, the depth of kingfisher tunnels (and many other facts) are unknowable. It might be instructive to consider how the figures above have come to light.

Over 200 or so years of American ornithological research, what percentage of kingfisher nests have been measured? Continue reading →

A “Super” Find

David

Way back a few centuries ago in the mid-1980s, long before anyone had ever heard the word “internet,” I was assigned to write an article for Smithsonian magazine on the decline of a once-loved American institution, the drug store soda fountain. The research for my story led me to seek newspaper and magazine articles from the heyday of soda fountains in the early- and mid-20th century.

If you are of a certain age, you will understand what I mean when I say that this endeavor resulted in my spending many hours in a public library squinting through a gargantuan, eye-straining machine known as a microfilm reader. If you are younger than that, herewith a brief explanation: to make back issues of certain magazines and newspapers accessible for years to come, a few companies were in the business of photographing the publications, page by page, and printing them onto acetate film in a much reduced size.

The film was called microfilm and in order to actually read it, a researcher could put the film into a machine called a microfilm reader and turn a cranking device (later replaced by an electric motor) in order to scroll to the section being sought. Continue reading →

Paean to a Publisher

David

Today is Memorial Day and I am in the mood to memorialize a publisher. Not a publisher that has died, fortunately (though many worthy ones have), but a publisher that is in transition. I don’t know whether the transition will transform it, but I know what I like about the way it used to be and I’m going to celebrate that here.

Why would I use this forum to talk about a publisher? Because I often meet educators with a passionate interest in children’s literature and I have found that many want to understand the relationship between author and publisher. (Actually, I know plenty of authors who would like to understand the relationship between their publishers and themselves!) Whereas children ask authors, “Where do you get your ideas?” and “How old are you?” their teachers tend to ask, “Do you get to choose your illustrators?” or “How hard is it to get an editor to read your manuscript?”

My six publishers come in three sizes: small, medium and large. About two months ago, one of the small ones, Ten Speed Press of Berkeley, CA, was bought by one of the world’s largest media conglomerates. Ten Speed Press and its children’s book division, Tricycle Press, are now part of Random House of New York, a division of Bertelsmann AG of Germany. So, for those who are interested in the inside scoop Continue reading →

Raw Materials

David

“Where do you get your ideas?” This is a question I often hear from children, along with “How old are you?” and “How much money do you make?” I like to tell them that ideas are everywhere. “You just have to keep your eyes open, your ears open and your mind open.”


I’m just back from almost two months in Southeast Asia, with visits to four international schools (private schools with instruction conducted in English) in Indonesia, Singapore and Malaysia, along with a teacher conference in the exotically named city of Kota Kinabalu on the island of Borneo. I had many eye-, ear- and mind-opening experiences during my time in Asia, and I’ve been thinking about books that might come out of them.

The experiences alone would not be sufficient to create a book. I think it is a commonly held misconception that to write a non-fiction book you can simply do/see/hear/experience something interesting, write it up, and send it in. Books should be that easy! In reality, the experience alone provides just the rawest of raw materials for a book. It must then be augmented by a great deal of thinking to define an approach, followed by copious research before beginning to write. I haven’tgone beyond the first of those preliminary steps, but perhaps it would be interesting to lay out the raw materials from two of my experiences (one now and another in a future post). If either book ever gets written, you will be able to say, “I knew it when.”

When I was in college, I met an entomologist who was the world authority on fireflies and their flashing behavior. Continue reading →

Wondering Whether “Facts” are True

David

The opinions and questions of children often fascinate and delight me. 

As an author of non-fiction children’s books, I receive many letters from young readers. One that stands out came from a nine-year old girl named Lisa who wondered about the accuracy of various statements in my first book, How Much Is a Million? I was thrilled to receive her letter, for I am always happy to learn that my books are being read critically.

Lisa wondered about the truth of my book’s claim that counting from one to one billion (saying each number individually) would take 95 years. After questioning a few other statements in my book, she closed her letter:

“I had mixed up feelings about your book. That’s where the magic comes from the world of books. The magic of books is not knowing whether the facts are true or not.”

In my presentations at schools, I often tell children, “Wondering is wonderful.” Continue reading →

The Popcorn Factor

David

One Million Pieces of PopcornI know how to get kids really excited about math. Show them popcorn. Lots of popcorn. It’s one of my math props when I speak at schools. I pull out bags of popcorn that grow by powers of ten from one to ten to one hundred to one thousand and so on. Are you wondering how big the bags get? That’s exactly what the kids are wondering, and they’re at the edge of their figurative seats waiting to find out (I say “figurative” because they’re usually sitting on the floor). Their growing excitement is abated only momentarily when I tell them they won’t get to eat my popcorn (and wouldn’t want to eat it because I popped it in 1985). They groan but immediately go back to screaming with delight as a bag of popcorn ten times larger than the last one appears before their eyes. 

For years I’ve been using popcorn to demonstrate various math concepts as I act out the plot, if you can call it that, of On Beyond a Million, my powers-of-ten counting book. The popcorn almost never fails to excite children from grades K to 5 or 6, whether they are urban or rural, rich or poor, white or black, X or Y.  On several occasions I dropped the popcorn from my presentation, but I had to put it back because it’s so popular. 

The fact that 21st century children go wild over popcorn as a math prop encourages me wildly. Why? Continue reading →

Nature, Toddlers, Books: Connecting the Dots

David

This month I am still traveling in Southeast Asia visiting international schools and speaking at an education conference in exotically named Kota Kinabalu (in the Malaysian part of the island of Borneo), and I have asked my friend Nancy Raines Day — an environmental educator, bookseller and author of both fiction and non-fiction for children — to write a guest post for me. I will be back in April.
— David Schwartz

 

 

Thanks, David. I feel lucky to be in touch with this community! After spending the last couple of years working on California’s new environmental curriculum, I’ve been ruminating on how best to hook kids into nature right from the start, and how books might help do that.

 

 

Many of you know the book, The Last Child in the Woods: Saving Our Children from Nature-Deficit Disorder. In it,Richard Louv makes the point that children and nature are and must be connected for the health of our children and our planet.

 

 

It worries me that American children probably spend less time in touch with nature today than ever before. Especially city kids may have trouble relating to living things in environments they have no personal connection to. Of course, the more outdoor experiences—walks in the park, camping trips, or days at the beach—they can get, the better.

 

 

In between such opportunities, putting the right books in their hands can be a great way to connect kids with nature. As Louv wrote, “People who care about nature often mention nature books as important childhood influences.”

 

 

Many fine nature books are out there for school-age children. Nature books at the earliest (0 to 4-year-old) level can help build a base for later understanding. Rachel Carson has said, “It is not half so important to know as to feel when introducing a young child to the natural world.” Below, I’ve rounded up some books that help the youngest audience feel their connection to the natural world.

 

 

My favorite “young” books new for spring are In My Nest and In My Pond,written by Sara Gillingham and illustrated by Lorena Siminovitch (Chronicle Books, 2009). These tiny books are a tactile delight, allowing little fingers to delve through layers of thick pages while wiggling a baby bird–or fish–in the midst of its family. In My Nest shows the twigs, leaves, and feathers that go into building the nest. When a child later sees a real bird carrying a twig in its mouth, he or she will feel such satisfaction knowing why!

 



Also perfect for spring is Kevin Henkes’ Birds, a large book with appealing illustrations by Laura Dronzek (Greenwillow, 2009). Kids everywhere see birds in their daily life, so feathered friends are the perfect wildlife ambassador. The imaginative text engages all the senses. You have to see the illustrations to get a sense of the utter joy conveyed in this passage: If there are lots of birds in one tree and they all fly away at the same time, it looks like the tree yelled. . .

S U R P R I S E !

 

 


Another great intro to birds and other animals for toddlers is the whimsical, geometrical art in Charley Harper ABC’sand Charley Harper 123’s (Ammo Books, 2008). He captures each creature’s essence with warmth and humor. Harper said of his bird art, “I have never counted the feathers….I just count the wings.”

 

 

To introduce very young readers to environments they may not know firsthand, try Over in the Ocean in a Coral Reef by Marianne Berkes, illustrated by JeanetteCanyon, (Dawn Publications, 2004). Based on the traditional rhyme, “Over in the Meadow,” the bouncing, joyous text and colorful clay art will delight young listeners and lookers with the wonders of life on a coral reef. Likewise, Over in the Jungle (2007) enfolds young readers in the splendor of the rain forest. Both luckily come in board book editions.

 

 

 

I’d love to hear about your experiences with these or other books that strengthen young children’s nature connection!

Guessing Games

David

If you’re of a certain age, you will remember the one-word career advice given
to an ambitionless Benjamin (Dustin Hoffman) in the opening scene of the immortal 1967 film, The Graduate: “Plastics!” If an aspiring author of children’s non-fiction picture books asked for two words of advice, I might say “Guessing Games!”
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Children love to guess. The opportunity to figure out something or to find objects hidden in illustrations, combined with a chance to show off what they have already learned, gets kids jumping (sometimes literally) with knowledge and joy. If an author can present good factual material in an enjoyable format that allows to children to take guesses, the author might have a popular book on his or her hands. It’s happened to me 25 times, with number 26 on its way.

In the late ‘90s, I wrote two dozen science books in the series “Look Once, Look Again.” They came out in two batches of 12 – the first oriented around habitats and the second around anatomical features of animals and plants. The publisher, Creative Teaching Press, predicted they would be in print for five or six years but it’s now been almost a dozen since the first series came out, and the “LOLA” books (as photographer Dwight Kuhn and I fondly call them) are still going strong.

4There was nothing special about the idea, other than the interactive possibilities that come from children using both visual and textual clues to identify plants and animals. First they see a close-up photograph of an organism that gives a magnified view of part of its exterior (the plates of a turtle’s carapace, for example, or the kernels of an ear of corn). The text hints at the organism’s identity (“These are plates but you wouldn’t want to eat from them. What animal has hard plates on its back?” or “What has ears but cannot hear?”). And the child is on his or her way. Kids tear through these books and reach for more. With so many colorful covers, I long ago began to call them “book candy.” Unlike mouth candy, this kind of confection allows kids to think and have no-calorie fun at the same time, while expanding their knowledge of the natural world and, in a subtle way, encouraging them think like a naturalist — in terms of a creature’s characteristics.

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As an author who visits schools, I have had the most fun when I’ve seen class projects derived from my5books, including class-created books based on “Look Once, Look Again.” Typically, first or second graders have drawn close-ups of animal or plant parts and written clues about the identity, followed by drawings of the complete animal or plant and further explanation. In one school, the students went beyond modeling their work after the LOLA books. They invented fantastical animals that combined characteristics of various real creatures. It reminded me of one of my favoite Dr. Seuss books, On Beyond Zebra, which I first encountered on the shelf of one of my biology professors at Cornell.

1Late last year, I published (with co-author Yael Schy, who is also my wife) a book of poems that hint about the identity of well-camouflaged animals found (if you can spot them) in the photographs (also by Dwight Kuhn). The challenge is to find the animal hidden in the picture and identify it from the poem. We adopted a unique design element in which the gate-fold pages open up to reveal another version of the same photo; the difference is that now the background is faded (thanks to the miracle of PhotoShop) to allow the hidden animal to stand out. Then come prose “naturalist notes,” identifying the animal and offering more info about its life history, its use of camouflage, and a few more photos.

Many readers, both young and older, have suggested that Where In the Wild? reminds them of I Spy and Where’s Waldo?. Our book hasn’t yet enjoyed quite the success of those (their illustrations are not limited by the true arrangements of objects in the world), but it has captured the attention of many readers and reviewers (and, I’m pleased to say, award committees–most recently the Animal Behavior Society, which just honored it with its 2008 Outstanding Children’s Book Award). Again, I think the hook is the guessing game format.

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With great anticipation, I am waiting to see student projects based on Where In the Wild? Teachers and home schoolers: this is your chance to combine science with poetry. Please show me what you come up with by sending an email to (you know how to turn that into an email address). And all INK blog readers can post some of your favorite non-fiction books that use a guessing-game format. Why limit ourselves to science? How about history, geography, grammar, philosophy, math — there’s no limit! Aspiriing authors of non-fiction: it’s better than plastics.