Whether one studies the farthest reaches of outer space or the inner space of elementary particles of matter, our understanding of the physical world is built upon that strange symbolic language we call mathematics. But what exactly is mathematics? And why does it work? Is it just an elaborate computer game? Or merely a human invention inspired by our practical needs? Or is it something larger than life? An immaterial 'pi in the sky' reality all of its own? Part of the mind of God? And how do the answers to these questions affect our quest to arrive at an understanding of the Universe?
John D. Barrow explores these tantalizing questions in this book, a lively and illuminating study of the origins, the meaning, and the mystery of mathematics. He takes us from primitive counting to computability, from the counting rituals of the ancients to logics that govern universes other than our own, from Egyptian hieroglyphics to logical friction, from number mysticism to Marxist mathematics. We learn of the origins of counting the world over, the propensities of the human mind for the numerical when in pursuit of the ineffable, and how the dethronement of Euclid's geometry ushered in a new world of philosophical relativism in which traditional truths were dissolved. We meet a host of peculiar individuals who have thought some of the deepest and strangest thoughts that human minds have ever thought. And in a extraordinary final chapter, the Platonic picture of mathematics is developed in a startling new way that challenges us to consider how the mathematics of the future may turn out to be radically different from that of the present, and how it impinges upon our efforts to create an artificial intelligence.
Full of the off-beat and the unexpected and quoting everyone from Lao-Tse to Robert Pirsig, to Charles Darwin and Stephen Leacock, Kurt Godel and Umberto Eco, Pi in the Sky is a profound - and profoundly different - exploration of the world of mathematics: where it comes from, what it is, and where it's going to take us if we follow it to the limit in our search for the ultimate meaning of the Universe.
Industry Reviews
The Sussex astronomer (Theories of Everything, 1991, etc.) has done it again - i.e., wrought a brilliant summation of ideas about mathematics that shows a depth of scholarship and an analysis that will leave the reader more than a little shaken. For example, Barrow traces the origins of counting and number systems in the Old and New Worlds (very much in parallel with John McLeish, reviewed below). His somewhat startling conclusion is that number systems do not arise like language, common to all human societies, but probably spread from one place to another. And thank God for the Indus culture, for without it - and without the Arabs who later spread the "word" about the decimal-place system and the zero - we might be stuck with Roman numerals. But Barrow's real point here is philosophical: Is mathematics a discovery or an invention; the ultimate description of reality or a form of abstract beauty in the eyes of the mathematician-logician beholder? Here, he points to the developments in the late-19th and early-20th centuries of the formalists like David Hilbert and the latter-day French descendants who called themselves the Bourbaki, eschewing all representations or models. Along came Godel to pull the rug out from under, declaring the incompleteness of math and the undecidability of statements in axiomatic arithmetical systems. Barrow contrasts the formalists with constructivist-empiricists and today's ultimate hackers to conclude that there remains a residue of Platonic religious mysticism in our feelings about mathematics. "All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics 'is'...why it works nor where it works; if it fails or how it fails." Heady stuff this, caviar for the connoisseur - but not for the innumerate. (Kirkus Reviews)
