The Key to Everything

Johnny Miller/Unequal Scenes/Thomson Reuters Foundation
Ciudad Nezahualcóyotl, part of greater Mexico City, 2016

Geoffrey West spent most of his life as a research scientist and administrator at the Los Alamos National Laboratory, running programs concerned not with nuclear weapons but with peaceful physics. After retiring from Los Alamos, he became director of the nearby Santa Fe Institute, where he switched from physics to a broader interdisciplinary program known as complexity science. The Santa Fe Institute is leading the world in complexity science, with a mixed group of physicists, biologists, economists, political scientists, computer experts, and mathematicians working together. Their aim is to reach a deep understanding of the complexities of the natural environment and of human society, using the methods of science.

Scale is a progress report, summarizing the insights that West and his colleagues at Santa Fe have achieved. West does remarkably well as a writer, making a complicated world seem simple. He uses pictures and diagrams to explain the facts, with a leisurely text to put the facts into their proper setting, and no equations. There are many digressions, expressing personal opinions and telling stories that give a commonsense meaning to scientific conclusions. The text and the pictures could probably be understood and enjoyed by a bright ten-year-old or by a not-so-bright grandparent.

The title, Scale, needs some clarification. To explain what his book is about, West added the subtitle “The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies.” The title tells us that the universal laws the book lays down are scaling laws. The word “scale” is a verb meaning “vary together.” Each scaling law says that two measurable quantities vary together in a particular way.

We suppose that the variation of each quantity is expressed as a percentage rate of increase or decrease. The scaling law then says that the percentage rate for quantity A is a fixed number k times the percentage rate for quantity B. The number k is called the power of the scaling law. Since the percentage changes of A and B accumulate with compound interest, the scaling law says that A varies with the kth power of B, where now the word “power” has its usual mathematical meaning. For example, if a body is falling without air resistance, the scaling law between distance fallen and time has k=2. The distance varies with the square of time. You fall 16 feet in one second, 64 feet in two seconds, 144 feet in three seconds, and so on.

Another classic example of a scaling law is the third law of planetary motion, discovered by the astronomer Johannes Kepler in 1618. Kepler found by careful observation that the time it takes for a planet to orbit the sun scales with the three-halves power of the diameter of its orbit. That means that…


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