Idolatry and Infinity: Of Art, Math, and God by David R. Topper (review)

The first thing to say about this book is that it is not an easy read; it is really an extended essay rather than a book. It is very scholarly and full of interesting facts. The layout of the book is almost chronological, but not quite. The first few chapters concentrate on religious notions of infinity—not a great surprise as the Bible and the Qu’ran are rich sources in a field where there are few rivals. The author discusses the Greeks’ intolerance of Zeno’s paradox and the infinite decimal representation of the square root of two. There follows an account that includes the geometry of tessellations and the attempts to represent God and link this representation to the infinite. His thesis also spills into architecture, with discussions on the Alhambra Palace with its geometrical designs, gothic fan vaulting in Wells Cathedral and the art of M.C. Escher. It is at this point one begins to ponder where the book is going. Is it actually going to talk about the meaning of infinity or just tell tales? We then land on firmer ground, with the Renaissance covering perspective in art as well as the Scientific Revolution. Copernicus, Galileo and Isaac Newton get a mention. The calculus is explained, rather naïvely, and Newton’s ideas on gravitation are contrasted with Einstein’s 20th-century space-time notions of gravity. This leads to a discussion of modern astronomy and theories of how the universe began. The idea of an infinite but bounded universe and the Steady State and Big Bang theories all get more than a mention. There’s no deep philosophical discussion, no complex mathematics. We are informed about many things, but rather like a tourist, the reader is shown around and then led on. Finally, after 100 pages, transfinite numbers are covered. I had been waiting for this, as it is a central idea in the meaning of infinity, and the treatment is accurate but limited. It is this part of the book that best demonstrates the difficulty presenting a coffee table book on a subject that does get rather technical. To go through Georg Cantor’s rigorous definitions of transfinite numbers is outside the scope of the book (as Topper confesses on page 106) but not to do so makes the explanation incomplete and frustrates the reader—maybe I should say, frustrates this reader. The book finishes with a short history of Cantor and his attempts to relate transfinite numbers to the theories of the “size” of the universe, to theology and to God. Finally the lack of transfinite numbers when describing the physical world, despite their use in the descriptions of computability, is covered. Altogether it is a very worthy, serious book, and a book that has my admiration.