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Achilles in the Quantum Universe
by Richard Morris

The meaning and interpretation of 'infinity' has gone through many changes, as Richard Morris shows in this book (subtitled, "The Definitive History of Infinity"). From the early Greek days when Zeno's paradox was revealed (showing that it was impossible for Achilles to ever catch up with a tortoise in front of him, to how Aristotle viewed infinity ("Only potential infinities exist") to the Stoics (cyclical time) to the present, where scientists struggle to find out whether the universe is infinite or not.

Along the way, Morris covers how the infinite was encountered and interpreted by different people. One part that I found fascinating was the interpretation of 'infinitely small divisions' used in calculus. Despite being put forward by Sir Isaac Newton and Gottfried Wilhelm von Leibnitz in the 16th century, it was only in the 19th century that Augustin-Louis Cauchy put it on a solid foundation by basing it on the idea of limits. The topic fascinated me because I studied the idea of limits as applied to calculus (as opposed to just using calculus) during my undergraduate days and to say that I was very puzzled over the whole idea was an understatement. Morris also puts across the idea of instantaneous velocity in a manner easily understood and distinguished from average velocity.

The later half of the book delves into the infinitely small world of particles, quarks, virtual particles and into the infinitely large world of cosmology, relativity and the fate of the universe. Along the way, he manages to explain some ideas and describes how some aspects of the subatomic world and cosmology still puzzle the best scientific minds today as well as 'hedge his bets' on which theories may prove to be correct in the future.

One thing I found surprising in this book was the lack of a list of references or recommended reading material. Granted, most of us will be satisfied with just reading the book, but for the few who have become engrossed in parts of the book, having a way to look up further material would be welcome. Some puzzling ideas of infinity were glossed over (like why the infinity of points on a line is the same as the infinity of points in an area) in the book: a reference for further study would have been useful.

A nicely written book that starts off explaining about infinity in number systems (and introduces Cantor's work at the start), goes through various paradoxes introduced by the term infinity in ancient and modern times, and ends up showing how, even at the frontiers of science, the concept of infinity still stands as a barrier between science and understanding nature.

[Home Page][Index of Reviews][Previous][Aesthetics of Computing]

Achilles in the Quantum Universe by Richard Morris

Achilles in the Quantum Universe
by Richard Morris