Sometimes you want to learn a "new" multiplication algorithm from a general interest math book, sometimes you want to learn why voting systems are doomed to imperfection, and sometimes you just want to play with numbers, patterns, and pictures. Things to Make and Do in the Fourth Dimension by Matt Parker is the third kind of book. Parker, who is both a mathematician and a stand-up comedian, isn’t trying to convince you that math is useful, but that it’s fun.
Parker’s commitment to wacky ideas and demonstrations really makes the book sparkle. For some people, it would be enough to know that you can build a computer out of dominoes. Parker actually does it. In 2012, he gathered 10,000 dominoes and some friends and built a giant circuit in the main hall of the Museum of Science and Industry in Manchester. As he writes in the book, “Given the six hours of set-up time, this is possibly the most inefficient way ever to add 6 and 4 and get an answer of 10. Or, as some mischievous onlookers pointed out, we managed to take an entire day to show that 6+4=2+8.” You can watch the domino computer in action below. I am confident that this is the most suspense you will ever feel while watching someone add 9 and 3.
Parker's book covers some well-worn popular math topics: the optimal dating algorithm, Möbius strips, and Cantor’s diagonalization argument. But he also tackles some more complicated ideas: Seifert surfaces, the Riemann zeta function, and the intricacies of tiling three-dimensional space. Along the way, he gives us a taste of the passion, and sometimes obsession, mathematicians have for their work. For example, in 1994, two physicists found three-dimensional polyhedra that tiled three-space 0.3% more efficiently than the tiling that the great Lord Kelvin had conjectured was ideal a century before. The gain is minuscule in an objective sense, but Parker shows us why it's so exciting to the mathematicians who are still trying to determine whether they've found the most efficient tiling. It illustrates the difference between intuition and proof and the importance of both of them to mathematics. Without intuition, we wouldn't be able to come up with these tilings in the first place. Without proof, we'd probably decide that the tiling that was good enough for Lord Kelvin is good enough for us.
As promised in the title, the book gives us some things to make and do. After reading the chapter on graph theory, you can cut out a template for your own Perfect-Herschel polyhedron, and the first foray into the fourth dimension has instructions for building a tesseract out of pipe cleaners and drinking straws. (I'm personally a bit more excited to try another drinking straw structure: the aforementioned tiling of three-space that just edges out Lord Kelvin's in efficiency.) There are also some fun ideas for knitted and crocheted mathematics. I've crocheted some hyperbolic planes, but I've never tried to knit a Seifert surface or an error-correcting scarf like the one Parker's mother made for him for Christmas one year. Many of the puzzles and creations are also available on the book's website if you don't want to cut up your book.
The book starts small with integers and the many ways to represent them. Anyone who can count can get on the train at this station, and the rest of the trip is at a friendly pace with plenty of time to take in the landscape of anecdotes, party tricks, and stories of what life might be like for "hyperthetical" beings who live in four dimensions. If you already like math, Parker will probably give you some fun new nuggets to haul out at parties. If you're a bit hesitant around math, Parker has enough enthusiasm for both of you, and it is contagious.