*Atom Land: A Guided Tour Through the Strange (And Impossibly Small) World of Particle Physics* by Jon Butterworth. The Experiment. New York. 2018.

*A Mind at Play: How Claude Shannon Invented the Information Age* by Jimmy Soni and Rob Goodman. Simon & Schuster. New York. 2017.

*Genius at Play: The Curious Mind of John Horton Conway* by Siobhan Roberts. Bloomsbury USA. 2015.

These three books form a progression from the most concrete to the most abstract or, taking a different point of view, from the most serious to the most playful. At the same time all three are in different ways, highly imaginative.

The first is an account of particle physics, framed as a voyage into the unknown waters of the atomic and subatomic scales in the natural world, accompanied by charts at the beginning of each section that map physicists’ increasing knowledge as they probe matter at ever higher energies. The classes of particles recognized by current theory are shown as islands, while the forces that link them are shown as connections – electromagnetism as bridges traversed by cars, the strong force as sea lanes crossed by boats and the weak force as airplane routes. Butterworth describes the steps by which these waters were charted, from the development of the atomic theory of matter to the Standard Model, which culminated recently with the finding of the Higgs boson, using the Large Hadron Collider.

This model is a triumph of the partnership between theoretical and experimental physics, relying on both advanced mathematics and powerful machines, such as particle colliders for achieving high energy at incredibly tiny scales and sophisticated detectors for examining the resulting products. Both the mathematical calculations and the engineering are among the most challenging being carried out anywhere in the world, and it is an open question how much deeper we can push these explorations.

Butterworth concludes by describing some of the conjectures and hints of what lies beyond (at even higher energies) cast in the form of sailors’ tales of the prodigies and monsters found in uncharted waters, like dark matter and energy, super symmetry and string theories. His account spares his reader all but the most basic mathematics and yet provides a very helpful overview of the current theory of our physical universe as well as an enjoyable tale.

The second book is a biography of the pioneer of communications theory, Claude Shannon, mathematician and engineer, whose work helped provide the basis for today’s digital computers and the entire structure of information technology built on their power. Shannon is a man who loved both thinking and tinkering and who was fortunate to be brilliant enough to be allowed to make those activities his career, without having to worry too much about where it all led. His most influential work, A Mathematical Theory of Communication, changed the way communications engineers thought about their work by eliminating the focus on the mechanism (telegraph, telephone, radio, television) and instead considering the fundamental logic of information. Among his key contributions were a focus on probability and his demonstration that all messages can be reduced to simple binary codes, consisting of “bits.” His basic measure of information is familiar to me from my days as an ecology graduate student, because it can be repurposed as a way of measuring species diversity in samples of organisms. This was one of my first experiences with the idea that information is a property of more than just human communications. The authors discuss the way in which the concept of information ( especially its conceptualization as uncertainty or randomness) pervades many aspects of modern science. They warn that this may prove just another version of the old “clockwork universe,” an example of the tendency to imagine nature in terms of our own inventions. Still, there is no doubting the extent of Shannon’s influence.

Despite his reputation, and despite being associated with many of the greatest minds of the twentieth century at Bell Labs and MIT, Shannon preferred his private family life and his playful activities, from robot building to unicycle riding, over fame and influence. He and his mathematician wife, Betty, spent much time devising toys and games, some quite sophisticated, including one of the earliest chess playing computers. He could accomplish amazing results with erector sets and a few switches and relays, like a juggling robot, dressed to look like W.C. Fields. He had earned, in the eyes of his employers, the right to pursue these activities by his amazing early achievements. Perhaps as robots and IT gradually take away the need for so many to spend lives in repetitive toil, more of us will be able to enjoy such a playful existence.

The last book suggests what a life of pure play might look like. I heard and saw John Conway at my institution many years ago giving a talk and demonstration on knots. It was a virtuoso performance, culminating it a dance in which a group of volunteers from the audience followed his directions to turn themselves into an amazingly elaborate pattern while joined together by a web of pieces of rope. I don’t recall the final result except that it was quite astonishing. Conway is widely known as the inventor of Conway’s Game of Life and of surreal numbers, among the numerous mathematical subjects that have engaged his attention over the years. The game of life has become a staple among computer pastimes, both because of the fascinating and sometimes beautiful patterns it generates and because of the way it models self replication and the universal Turing machine (the mathematical essence of computers). Indeed, as the Wikipedia article on the game notes, with those two properties, it can be thought of as modeling life itself, at least as mathematically defined.

Conway is in Roberts’ account perpetually at play, and like a heedless child, he leaves messes everywhere he lights. His offices at various venerable centers of mathematical research have been famous for the nearly impenetrable heaps of toys, games and paper constructions he accumulates. Conway loves games (he sees every game as a number, indeed games for him seem to underlie numbers, and provide a basic way to conceive of his surreal numbers). His method of solving problems is frequently to construct something or use a game as a model. His play leads to real mathematical discoveries, however, and other mathematicians, including some far more serious in demeanor than Conway, have been eager to collaborate with him on major projects.

Roberts biography is interspersed with accounts of her interactions with Conway during the time she was gathering material from and about him. Someone referred to the book as “metabiography,” since its making is part of the story, and it certainly manages to convey some of the strangeness of a life so dedicated to play. Mathematics, like tinkering, is one of the most primal forms play can take. When our educators come to understand that learning is about how to live and not just how to earn a living, they will have new and even better reasons to be sure everyone learns the fundamentals. We all need math to open up the horizons of beauty and pleasure.

I know I’m going to keep rereading these books and also plunge into the colder waters of Wikipedia to try to better understand some of the concepts presented, but for now, I will post these impressions.