A mother lode of lore and learning about the digits.
Hodges (Mathematics/Oxford Univ.; Alan Turing: The Enigma, 1983) has much to say about logic, computers, binary (and other base) notational systems, encryption and randomness. As is typical of books on numbers, the chapters proceed from one to nine, exploring characteristics of each number, but they are also (as is typical of Hodges) jumping-off points for loftier concepts. Chapter “One” duly discusses unity, but before long we are introduced to zero, primes and why their number is infinite, set theory and Kurt Gödel’s cunning theorems on undecidability in mathematics. Two themes are also introduced: Sudoku puzzles (including the fiendish “Killer” Sudoku) and the antipathy between English scholars G.H. Hardy, who gloried in the uselessness of pure math, and Lancelot Hogben, who saw it as an important tool in all human commerce and industry. As later chapters reveal, discoveries involving pure number theory turn out to have surprising utility. Thus “quaternion” multiplication (don’t ask) is “vital to quantum mechanics” and has applications in computer games and in controlling roll, pitch and yaw in spacecraft. And so it goes, as Hodges relates findings about the geometry of curved spaces to general relativity or the Fibonacci series to the growth of flowers. No book on numbers would be complete without a discussion of magic squares, the golden mean, probability theory and various formulations of the natural logarithm base e. To this add Hodges’s prodigious knowledge of music (harmonics), physics and cosmology (the Higgs boson, string theory, multiverses), plus developments in modern math, and you have a formidable mix that dazzles but will likely overtax most readers. This highbrow fare is packaged in airy, witty prose, complete with Anglo-American cultural references and the occasional political dig.
Not for the math-phobic reader, but a treat for those who like challenges.