Life on the Infinite Farm

People who know me well know that my wife and I have a fairly large family with six children, spanning ages two to twelve (as of late 2018). As a mathematician with many children it is not surprising that the picture books by Richard Schwartz have gradually made their way into our house. I believe we own the complete set: You Can Count on Monsters, Really Big Numbers, Gallery of the Infinite, and now Life on the Infinite Farm.

Schwartz’s infinite farm contains a host of silly-looking but mathematically interesting animals, including Gracie the infinite cow who has a fondness for trying on new shoes but never wants to remove old ones, Bill the owl with his infinite eye like the Poincare disk, and Delores the infinite squid who can share an infinite amount of her jewelry with a friend but still have all of her tentacles decorated. We learn about their special traits and some of their problems. Later, questions from the audience are addressed, including how the infinite animals pass by each other, how the water animals with infinite tentacles or infinitely wide mouths all fit in what appears to be a finitely bounded pond, and how day and night work. The answers are imaginatively answered and illustrated. Some of the questions and answers reminded me of issues that arose in A. K. Dewdney’s novel The Planiverse, which discussed the possible realities of living in a two-dimensional world.

As with all of Schwartz’s picture books, the illustrations are engaging, very boldly colored, cute, and silly. In other words, they are well-designed to draw in an audience young and old, which is why I have collected his books and shared them with my kids over the years. The pictures are fun enough to amuse my kids, and the mathematics deep enough to entertain me but illustrated and narrated well enough to make sense to my older kids. In this book, Schwartz adds a twist by including a book within a book that addresses deeper ideas that can be easily skipped if too much for the younger reader. Just make sure you read the “Note to the reader” at the start and look carefully at the page borders if you want the simpler version of the book.

While these books are never going to be as popular with my kids as those by Rowling, Snicket, or Tolkien, I know my kids have read and enjoyed each of them (as evidenced by the broken binding on one that occurred when an unnamed child accidentally dropped it down the stairs after finishing reading it), and I am happy they have a place on our family bookshelf. The infinite farm is a very welcome addition to that collection.

Now, I am just going to wait until Schwartz and the team at Art of Problem Solving write a crossover where the students of the Beast Academy visit the infinite Farm. (Not holding my breath on that one though.)

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Geoffrey Dietz is a Professor of Mathematics at Gannon University in Erie, PA. He is married and has six children.