This science fiction novel is about a dysfunctional family of superbeings (aliens? mutants? humans from the future?) in modern America. It reminds me a bit of the writings of Stanislaw Lem, which is not very surprising since the author is probably best known for his English translations of Lem's work. Of interest to this website is the role played by Penrose Tilings and the Golden Ratio in the grandfather's ability to travel in time and space as well as to other universes. The nonperiodic tiling built of kites and darts is described in great detail. In fact, we learn how to construct the golden ratio using a compass and straightedge and how the grandfather is able to replicate the tiling using nothing other than toilet paper and liquid soap! Unfortunately, the name "Penrose" is never mentioned, so someone reading this book who does not already know about this mathematical construction will have difficulty finding out more from other sources.
Other mathematical ideas discussed in less detail include the number e as applied to compound interest, and the mathematical structure of the pattern of sunflower seeds (which incorporates aspects of the Fibonacci sequence and hence are also connected to the golden ratio). However, the main focus of the book is not mathematical but rather on the violence enabled by this family's extraordinary abilities and the many universes interpretation of quantum physics. (The emphasis on the latter actually made it difficult for me to enjoy the book since if we know that every possible outcome occurs in infinitely many universes then it is not clear to me why I should be interested only in the particular sequence of results that the author chooses to present for us.)
In some ways, the book seems like a children's book since it focuses on the adventures, misfortunes and comingofage of a fifth grader. However, the existentialist mood of the book along with the explicit violence and implicit sexuality make it inappropriate for most young audiences (IMHO).
Thanks to Rob Milson for bringing this work of Mathematical Fiction to our attention!
