Things to Make and Do in the Fourth Dimension

  • By Matt Parker
  • Farrar, Straus and Giroux
  • 464 pp.
  • Reviewed by David Joyner
  • January 26, 2015

Hop on this mathematical tour bus for a fun look at numbers, formulas, and the occasional card trick.

There is a story, dating to well before the use of electricity in our daily lives, of Queen Victoria asking the scientist Faraday (or Maxwell, depending on which version of the story you believe), “What good is electricity?” He replied, “What good is a baby?” Without writers communicating the abstract results of working mathematicians in a way that is digestible by the everyday reader, the default mode is to believe mathematics is unimportant and nothing good comes from it.

But this assumption is not true. Mathematics is a rapidly evolving field, and writers such as Matt Parker are necessary to remind society of that truth. His book, Things to Make and Do in the Fourth Dimension, operates as a tour bus for readers who want to learn more about a wide variety of mathematical topics and how math can be fun.

For lovers of the YouTube channel Numberphile, Parker is a familiar figure. With an engaging Australian accent and an infectious smile, this stand-up comedian and mathematician discusses esoteric mathematical facts with an emphasis on fun.

If you imagine that all of Parker’s favorite mathematical objects come alive in a sort of math country, with the author’s tour bus roaring from one town to the next, then Things to Make and Do in the Fourth Dimension is a well-written, engaging book that tells about all the sights you saw and adventures you had, with breezy introductions to the more recreational side of this not-always-loved area of study.

The subtitle of Parker’s nearly 500-page book — A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More — gives readers a feeling for the variety of topics to be found within its covers. Parker wrote this book with the same light spirit found in his videos. He often pushes serious subjects aside to focus on fun recreational topics, which abound in the book.

In that vein, fans of Parker’s YouTube videos, Ball and Coxeter’s Mathematical Recreations and Essays, or Martin Gardner’s essays should enjoy this book.

On this mathematical tour, Parker provides readers with a brief overview of several topics, such as number systems (e.g., base 10, base 2, base 12, base 16). Many interesting topics arise from the digits of a number. Narcissistic numbers, which are k-digit numbers such that the sum of the digits raised to the k-th power gives you the original number (e.g., 153 or 8,208), and Munchhausen numbers, which allow you to raise each digit to the power of itself and add them all together to give you the original number (e.g., 3,435), are good examples.

Parker also discusses the honeycomb conjecture and Thomas Hales. The honeycomb conjecture asks to minimize the perimeter of a connected planar region, relative to its ability to cover the plane without overlap. For example, the circle has a minimum perimeter for a figure with a fixed area, so you might think the circle will work. But it doesn’t because when you try to cover the plane with circles (no overlapping allowed), the “holes” created are too large. The conjecture arises from the hexagonal structure of honeybee hives. This belief, which dates back thousands of years to the Romans and Greeks, was that honeybees naturally evolved the most efficient structure so they could maximize honey production. However, proving this belief mathematically took until 1999 via the work of Thomas Hales.

The book also takes on the “optimal” dating algorithm, which features three steps:

 Step 1: Estimate how many people you could date in your lifetime. Call it n.

 Step 2: Reject the first square root of (n) dates but use them to establish a benchmark for the best date.

 Step 3: After sqrt(n) dates are over, continue dating and settle down with the first person to exceed the benchmark set in Step 2.

Although Parker doesn’t actually recommend applying this algorithm to your love life, he does suggest it could work for buying a car!

From the field of geometry, Parker introduces a number of topics, including regular Platonic solids in three and four dimensions and the Wobbler. When it comes to number theory, his topics include Mersenne primes and the Riemann zeta function. On the algorithmic side, he surveys a less diverse but still impressive range of topics such as the Hilbert Hotel and Cantor’s diagonalization argument. He sometimes gives examples using the programming language Python.

If that’s not enough, this book also features mathematical card tricks (see Parker’s card trick videos on YouTube), the monster group, Hamiltonian cycles on graphs, the Champernowne constant and other transcendental numbers, at least two kinds of infinity, and much more.

Do you learn mathematics from such a book? That depends on the reader. How much do you really learn from taking a bus tour of, say, Annapolis, MD, from a tour guide who works as a comedian on the side? Sure, you will be amused and learn names and dates of important events. Moreover, it will probably raise your awareness of the significance of Annapolis in the history of the United States. But what you actually take from the tour is up to you.

Parker’s book is similar. Finishing this tome is like getting off a tour bus of several dozen carefully selected old and new cities. After reading it, you are probably more aware of the wide variety of topics mathematicians are investigating. However, to really learn more, you should become your own tour guide. Be adventurous, pick your own mathematical city to explore, and, like Matt Parker, be sure to have fun.

David Joyner is a mathematician who teaches in the Mathematics Department of the U.S. Naval Academy. He and his wife live near Annapolis with their cat and two dogs.

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