A Review of Infinity and Me by Kate Hosford, illustrated by Gabi Swiatkowska

Up until now, David M. Schwartz and Steven Kellogg had cornered the market on really big numbers with their classic How Much Is a Million? Their examples make the concept as clear as it’s going to get for human brains. (Did you know that four is the highest number of objects humans can count at a glance?) Now Kate Hosford tackles an even bigger number, or rather concept: infinity. She uses examples, too, but they tend to be more philosophical than Schwartz’s, along the lines of Albert Einstein’s thought experiments or plain old metaphors.

Concept books tend to get slapped with the "quiet" label almost automatically, and this book certainly isn't loud. I can't picture a rowdy first grader of either gender sitting still for it. But a more thoughtful child in the 7 to 9 age range, yes.

Picture this: A girl named Uma is wearing her new red shoes and looking up at the stars. “How many stars were in the sky? A million? A billion? Maybe the number was as big as infinity.” Feeling very small in the face of infinity, Uma starts asking her friends and relations how they picture that endless idea. Her friend Charlie says, “It’s a giant number that keeps growing bigger and bigger forever.” Her friend Samantha thinks of the infinity symbol as a racetrack she could drive around and around forever. Her grandma thinks about a family with an endless procession of descendants.

Uma asks more people what they think, but she also begins to play with the idea for herself. It's starting to make her head hurt, yet it fascinates her, as well. Infinity and Me goes on with its barely-there narrative. Although, come to think of it, this is a quest tale—a quest for knowledge. The red shoes provide a minor secondary motif. The book ends on a note of love and a return to looking at the stars. Kate Hosford's approaches to infinity are poetic and thought-provoking. Her small narrative makes a humanizing frame for a concept as cold and vast as outer space, whose stars are what get Uma thinking in the first place.

Illustrator Gabi Swiatkowska has an unusual style. The textures, floral patterns, and clothing make me think of Europe in the 1940s—and I just looked at the back jacket flap to confirm that the illustrator is from France. That doesn’t mean anything necessarily, but perhaps you’ll see my point when you look at the book. In addition, while Uma and her friends and grandmother are fairly dimensional, other parts of the book have a flat, decorative look. So we get a combination of three-dimensional and two-dimensional effects, an essentially black-and-white palette touched with splashes of color, and odd decorative elements such as a few flowers, a bee, two lollipop-top looking designs, and several hanging loops like jungle vines on the infinity racetrack spread. The infinity symbol “track” itself is checkered black-and-white like a finish flag for racecars. Uma rides her green bike around the track, while her friend Samantha drives a green car. There’s also a white chicken running along behind Samantha’s car. (The chicken pops up often in the pages of the book.) Plus there are a few splashes of greenish turquoise and a little yellow. When you stop to think about it, the effect is surreal. Then again, so is the idea of infinity.

A couple of my favorite spreads show portraits of Uma’s ancestors: the people in the many frames have such different personalities! Thanks to the text, some of them seem to be interacting with Uma on the second spread. It’s on that spread that Uma expresses her disappointment that “not one person had noticed my new red shoes.” The fact that she says it there hints that none of the people in the portraits have noticed, even though Uma is actually talking about her current friends and family. This kind of subtle humor is apparent in both the text and the illustrations. One more example is the spread that shows a giant ice cream cone on its side, supported by a small, almost steampunk mechanism. The ice cream has melted enough to create a puddle at the bottom of the page, which rests in a “lawn” made of a black-and-white floral design. The chicken and what appears to be a rat are swimming in the puddle of ice cream in a possible homage to Alice as Uma exclaims, “Maybe I could lick an ice-cream cone forever, but what if my tongue started to hurt?”

I should mention the endpapers. They are covered with multi-digit hand-inked numbers that do not count up in order. We get an author’s note with some great information, as well. Did you know that the infinity symbol is called a lemniscate?

So. This is a strange book. It’s also a beautiful one, and an apt one, dealing with something so difficult as to be thoroughly unimaginable. Which means Infinity and Me is an ambitious book, too. Considering what infinity is (or is not) and that this is a picture book, not a math tome, I would argue that it achieves its goals—with style.

See the really great guest post by Kate Hosford about writing the book at Cynthia Leitich Smith’s Cynsations. 

BIG Numbers

Millionaire. Billionaire. Three hundred million dollars to make Spiderman 3 and $5 billion to clean up the BP oil spill. Nine million people living in Mexico City and 1.3 billion people living in China. More than 100 million homeless people in the world today... We throw these numbers around all the time, but they're so large that they're truly difficult to picture. Leave it to children's book makers to address that problem! A new book about the concept of a million just came out—so how does it stack up compared to earlier books on the same topic? Here's a look at the latest attempt to wrap our brains around big numbers, along with reviews of two its predecessors.

How Many Jelly Beans? A Giant Book of Giant Numbers! by Andrea Menotti, illustrated by Yancey Labat

Let me just start off by pointing out that the book, like the number it honors, is really big—I personally measured it (because this is a full-service book review blog, dontchaknow): we're talking 11 by 14 inches. Definitely going on the oversize shelf!

Where other authors have considered the question of large numbers using different objects and scenarios, Menotti keeps it simple; she merely considers jelly beans in bigger and bigger quantities. Which brings me to the framing plot, one that will appeal to just about any kid... two siblings are trying to decide how many jelly beans they want. Pretty soon they are imagining greater numbers, the question being, "Is there such a thing as too many jelly beans?" Emma and Aiden and their little dog, Murphy, mostly don't think so. Mostly.

How many jelly beans would you like, Emma?
TEN!
How about you, Aiden?
TWENTY!

And the jelly beans are shown in the children's hands. The kids and their dog are presented in strong, simple black lines on a white background, in contrast to the jelly beans, which are brightly colored and are not outlined. An occasional pool of blue and the use of contour in the ink lines add some depth to the rather flat scenes.

Of course, the kids start topping each other with bigger numbers. "He can have twenty? I'll have TWENTY-FIVE!" And we see bigger and bigger batches of jelly beans. "I changed my mind," Aiden says. "I'll have FIVE HUNDRED JELLY BEANS!" Whereupon Emma tells him, "That's too many. You can't eat five hundred jelly beans." Aiden replies that in a whole year he could eat a thousand jelly beans. Next we get a thousand jelly beans parsed out on a dozen calendar pages. As a teacher, I appreciated how Menotti made the number more accessible by breaking it down into pieces again, "two or three a day," as Emma realizes. And when Aiden says he can eat a hundred thousand jelly beans, we are shown the number first as one huge bunch and then divided into different batches by color—ranging from 50,000 grape jelly beans to an amusing "1 lemon."

In this way, Menotti keeps her progression of numbers and questions from becoming entirely predictable. She also throws in a single analogy, with Emma comparing 5,000 stacked jelly beans to the height of a building.

At last, in a feat of tiny computer-generated jelly beans on a REALLY big foldout spread, Menotti and Labat give us all 1 million pieces of candy—along with the punch line to Emma and Aiden's conversation.

I will just note that illustrator Labat's little dog Murphy quietly steals the show as his facial expressions and ears offer commentary on the kids' statements. Being a dog, he is of course interested in all things edible, and he is more than willing to partake in a jelly bean feast.

I suppose my only quibble with this book from a teaching standpoint is that not every number is given numerically. Some are presented only as words. I would have liked to see both forms for each number. Overall, however, this is a very nice addition to a special subgenre of math books for children, offering readers a clear, upbeat take on the big number question.


A Million Dots by Andrew Clements, illustrated by Mike Reed

Clements is best known for middle grade fare such as Frindle, but here he, too, tackles the concept of 1 million. This picture book doesn't include any particular narration or characters, but it does march kids right through a count that goes all the way up to 1,000,000 dots.

So how do the writer and illustrator add interest? On each counting page, we are given an interesting little factoid about just one of the numbers that appears along the way. Here are a few of the facts:

Dot Number 1,860—A person must climb 1,860 steps to walk to the top of the Empire State Building.

Dot Number 24,901—It is 24,901 miles around the Earth at the equator.

Dot Number 87,600—The sooty tern can fly nonstop for 87,600 hours after it leaves the nest—that's ten years on the wing!

Dot Number 134,000—A person blinks about 134,000 times each week.

Each page notes the spotlighted number, and additional signposts indicate how many dots have been counted so far. (I suspect these two numbers might be confusing for some young readers.)

The particular dots that accompany the facts are highlighted, though sometimes this is hard to see. To add visual interest, the background of the mass of ranked dots is rendered on each page as a fairly simple illustration. For example, the backgrounds of the facts mentioned above are the Empire State building, the planet Earth, a sooty tern wearing goggles and carrying a suitcase, and a goat winking in an airplane (we get mountain heights on that page, as well).

The so-so illustrations and the lack of characters and a narrative frame (however slim) make this one somewhat austere. However, the facts are compelling, as is the diligent build to 1 million.

I mean, come on: Did you know that "a queen-size bedsheet is woven from more than 153,000 feet of cotton thread?"

I will add that this book begins and ends on a page with just one dot—the first dot and the millionth one. I find this especially satisfying, both from the literary standpoint of a framing device and from the mathematical standpoint of recognizing that even a huge number like a million is made up of units, dot after dot after dot.


How Much Is a Million? by David M. Schwartz, illustrated by Steven Kellogg

This one is the gold standard for books on the topic of big numbers. I have read it, not only to first graders, but to third graders, sixth graders, and twelfth graders. So how does is stand up after 27 years? The answer is, really well.

The ambitious Schwartz gives us a series of analogies to help us envision, not only a million, but a billion and a trillion. Kellogg packages it all up using a group of exuberant kids and a mathematical magician, not to mention a dog, a cat, and a unicorn. The book begins:

If one million kids climbed onto one another's shoulders, they would be taller than the tallest buildings, higher than the highest mountains, and farther up than airplanes can fly.

The other analogies are how long it would take to count to each number, how big of a goldfish bowl you'd need to hold that many goldfish, and how many little stars would be needed to reach the number in question.

The stars section shows rows and rows of tiny stars for seven pages. The characters float across the pages in a hot air balloon, making funny little remarks. We're told we would have to take that same journey of seven pages ten times to pass a million. Later in the book, the star pages are referenced for other, larger numbers.

David Schwartz's genius lies, not only in making the idea of a million accessible, but in building a comparative understanding of a billion and even a trillion while he's at it. Steven Kellogg's genius lies, as always, in creating slightly nutsy, appealing characters to humanize the concepts.

I think my favorite pages are the depictions of the counting question: With counting to a million, we get our little cast under a tree and learn it would take about 23 days. But counting to a billion would take 95 years—and Kellogg shows the kids all elderly, with a gravestone for the mathematical magician. Counting to a trillion would take almost 200,000 years. Not surprising, Kellogg gives us gravestones for the entire group this time (after showing the alarmed kids faced with boxes and boxes of calendars.)

I'll admit I am book greedy, and I would want to own all three of these books about big numbers if I were you. If you really must choose, I still think Schwartz and Kellogg's book is the best. But I have to say—I do love those jelly beans. And Murphy!

On a related topic, I recommend Betsy Franco and Shino Arihara's poetic book on the concept of zero, Zero Is the Leaves on the Tree. (See my review from a few years back.)

Note: Chronicle Books sent me a copy of How Many Jelly Beans?