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Home , The Road to Reality

BOOKSHELF A man is known by the books he reads. —Emerson

New and Noteworthy Titles on Our BookShelf Fashion, Faith, and Fantasy in the New of the December 2016 Universe, by (Princeton University Press, August 2016). Roger Penrose is world famous The Joy of SET: The Many Math- for his work in mathematical phys- ematical Dimensions of a Seemingly ics, for which he earned the 1988 Simple Card Game, by Liz McMahon, Wolf Prize (together with Stephen Gary Gordon, Hannah Gordon, and Hawking). Penrose has written several Rebecca Gordon (Princeton Univer- popular books, of which the Notices sity Press, November 2016). has reviewed: : SET is a game played with a deck A Search for the Missing Science of of eighty-one cards on which are Consciousness (1994), reviewed by printed some shapes. The cards William Faris, February 1996; and have four characteristics: number The Road to Reality: A Complete Guide to the Laws of of shapes (one, two, or three), type the Universe (2004), reviewed by Brian Blank, June/July of shape (oval, diamond, or squiggle), shading (open, 2006. Penrose’s latest popular book, Fashion, Faith, and hatched, or solid), and color (red, green, or purple). A “set” Fantasy in the New Physics of the Universe, was published is a collection of three cards such that, for each of the four in time for his eighty-fifth birthday. Don’t fashion, faith, characteristics, the cards are all the same or are all differ- and fantasy have a negative effect on physics research? ent. Facing a matrix of cards laid out on a table, players Not entirely, Penrose notes. Fashionable areas of phys- race each other to identify sets, and the player identifying ics are fashionable for sound scientific reasons, not for the most sets wins. SET is a game even very young children purely sociological ones. Faith in a time-tested theory like can play, and watch out—they are sometimes uncannily Newton’s theory of gravitation is very much warranted, good at it. Finding the patterns among the cards feels “provided that its limitations are kept appropriately under very much like a mathematical activity, and, as The Joy of firm consideration.” And fantasy? That has a role to play Set shows, the game has many mathematical aspects. The too: Some aspects of the universe are so odd “that if we do book discusses connections between SET and geometry, not indulge in what may appear to be outrageous flights modular arithmetic, combinatorics, probability, linear of fantasy, we shall have no chance at all of coming to algebra, and computer simulations. It also shows how terms with what may well be an extraordinary fantastical- the game can be used as a springboard to mathematical seeming underlying truth.” The book devotes one chapter exploration. The writing of the book was a family affair: each to (fashion), (faith), Liz McMahon and Gary Gordon are mathematics profes- and big bang cosmology (fantasy). Then, in the fourth sors at Lafayette College, and Hannah and Rebecca are and final chapter, Penrose describes some of his own their daughters. Hannah is currently the world champion ideas for alternative routes that could be taken in these of SET and a student of nutrition and health policy at New areas, including his and his ideas that come York University; Rebecca is a middle-school teacher. Han- under the name “conformal cyclic cosmology.” The book nah joined her parents at the MAA MathFest in Columbus ends with an appendix that sketches some of the main in August this year, where they gave a talk titled‚ “Tricks mathematical ideas needed to understand the exposition. with SET.”

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We try to feature items of broad interest. Appearance of a book in the Notices BookShelf does not represent an endorsement by the Notices or by the AMS. For more, visit the AMS Reviews webpage www.ams.org/news/math-in- the-media/reviews.

1286 NOTICES OF THE AMS VOLUME 63, NUMBER 11