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Guillen, Michael. Five Equations That Changed the World. New York: Hyperion, 1995. 277pp. $22.95
When Stephen Hawking wrote A Brief History of Time, his publisher said that each equation in the book would reduce sales by half. Five equations should thus reduce sales by two to the fifth power, or one thirty-second. Fortunately, Michael Guillen's publisher is not of a like mind.
Guillen, a Harvard instructor in physics and mathematics and a science editor for ABC TV, has a nice touch for the history of mathematics and physics and their impact on the world. He has taken five influential equations, each a precise expression of a foundational physical principle, and set the development of each in the intellectual context of its times and of the mind of the mathematician who devised it.
In 1680, Isaac Newton was the most celebrated natural philosopher in England. From his chair at Cambridge, he had done the differential calculus. Now his attention was drawn to the motion of the moon: why did it not fall?
By looking at the balance of forces involved, recognizing that the Earth also pulled on the Moon, and using Johannes Kepler's century-old data on the motion of heavenly bodies, Newton was able to reason that the gravitational pull between two bodies is given by the gravitational constant times...