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Tuesday, June 23, 2009

Imaginary Numbers

One mathematician argues that if four dinosaurs stand together in a prehistoric clearing, they number four even though no people are there to count them. In other words, numbers exist independent of human beings. But consider the counterexample (suggested by British mathematician Sir Michael Atiyah) that starts with the imaginary idea that intelligence resides not in people but in a "vast solitary and isolated jellyfish, buried deep in the depths of the Pacific Ocean" with "no experience of individual objects, only with the surrounding water." In this thought experiment, argues Atiyah, "there would be nothing to count." It follows from this second example that numbers -- and all math -- arise from the way that humans perceive the world.

Who's right? That's [Mario] Livio's focus here. The question is mainly philosophical, but this book is mainly historical. That is, Livio traces the question of discovery versus invention by surveying the most fundamental and influential efforts in the Western tradition to understand the world mathematically. Is God a Mathematician? is a work of intellectual history -- the history of philosophy, logic, and especially math.

link: Book Review: Is God a Mathematician?, Mario Livio - B&N Review


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