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The Equations: Icons of Knowledge

Sander Bais
Harvard University Press
Publication Date: 
Number of Pages: 
[Reviewed by
David M. Bressoud
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The world is awash is popularizations of modern physics. Here is one more. The author writes clearly and incisively about the physical ideas, but so have other good popularizers. Bais has chosen an original means of setting himself apart. Most books of this genre take it as axiomatic that they must avoid equations. Bais embraces them, building his book around the equations of physics and using them as the vehicle for describing the counter-intuitive world of relativity theory, quantum mechanics, and string theory.

This book is structured around a comprehensive collection of important equations, starting with the logistic equation and continuing through the equations of Newtonian mechanics, electricity and magnetism, the Korteweg-De Vries and Navier-Stokes equations, the Boltzmann equation, equations of special and general relativity, the Schrödinger and Dirac equations, and ending with the equations of quantum chromodynamics, the Glashow-Weinberg-Salam model for electro-weak interactions, and super-string action. Quite an impressive list, especially when one considers that his audience really is the neophyte, witnessed by the need to begin this book with explanations of the concepts of function, vector, and derivative.

The equations provide useful hooks on which to hang a discussion of the big ideas of physics. Each equation (or collection of equations) gets its own page in which it is displayed in all its incomprehensible glory. In that sense, the equations serve their role as icons, mystical pointers to a meaning beyond what is visible to the uninitiated.

Bais is trying to do more than this. He would like the reader to gain an appreciation for the meaning of these equations. He does attempt an explanation of the significance of each of the symbols and operators, more diligently and successfully in the earlier equations than the latter. Ultimately, he fails. To someone with familiarity with the language of mathematics and with some of the physics, there is too little here. To the person who really is unfamiliar with such equations, too much comes too quickly. Once Bais has moved to partial differential equations and Lagrangian operators, the mathematics is treated perfunctorily and cryptically. I cannot fault him for this. Bais is trying to communicate an important physical principle in a few pages. There is neither time nor space for the mathematics.

The result is that the title of this book is something of a cheat. This is really about the physics, not the equations. The best that might be hoped for the general reader is an increased appreciation that equations play an important role in our understanding of physical universe.

Yet when all is said and done, this is a pretty book that is well-written, and I would not hesitate to give it as stocking-stuffer to a young person who is just beginning to discover the wonder of our physical universe and to appreciate the power of mathematics as the language in which we express our understanding of this universe.

David M. Bressoud is DeWitt Wallace Professor Mathematics at Macalester College in St. Paul, Minnesota.


Rise and fall
The logistic equation

Mechanics and gravity
Newton's dynamical equations and universal law of gravity

The electromagnetic force on a charge
The Lorentz force law

A local conservation law
The continuity equation

The Maxwell equations

Electromagnetic waves
The wave equations

Solitary waves
The Korteweg - De Vries equation

The three laws of thermodynamics

Kinetic theory
The Bolzmann equation

The Navier-Stokes equations

Special relativity
Relativistic kinematics

General relativity
The Einstein equations

Quantum mechanics
The Schrödinger equation

The relativistic electron
The Dirac equation

The strong force
Quantum chromodynamics

Electro-weak Interactions
The Gashow-Weinberg-Salam model

String theory
The superstring action

Back to the future
A final perspective