from Cavendish Press Ann Arbor

On the need for algebra

The math-less and even the math-sparse books on a subject like relativity are necessarily weak on definition of terms. They use words, and while the author may understand what is meant by these words in relativity, the reader is left with the vague association that these words evoke from their usage in spoken English. This leaves the critical reader of the conceptual-only books on relativity constantly asking, "just what does this phrase mean?"
Only when terms are defined exactly, and this is what algebra is designed to do for a subject like relativity, can they be used beyond the particular sentences in which they appear.

How much math does the reader need?
    -- Just what is taught in first year high school algebra class."

Stephen Hawking reports being advised while writing his popular book about time, that "each equation included in the book would halve the sales."

Whole books on relativity have been written based on the advice given Hawking. No equations. If that is what you are looking for, there are many beautiful books to choose from that fit that description. But this isn't one of them.

We go rather with Anthony Leggett who responded this way to the advice Hawking received: "No doubt this may be so, but from any but a commercial perspective, a more interesting question is what effect each equation will have on the percentage of readers who will get out of the book the level of understanding intended." from a book review in Physics Today July 1999 p51


Lillian Lieber wrote a wonderful little book about relativity for the general reader in 1936. You won't find her book except in the dusty stacks of an occasional University library. It was called The Einstein Theory of Relativity published by Reinhart & Co. New York

I want to quote from its timeless preface: "... just enough mathematics to HELP and NOT to HINDER the lay reader."

Lieber's preface goes on, "Many 'popular' discussions of Relativity without any math at all have been written, but we doubt whether even the best of these can possibly give to a novice an adequate idea of what it is all about. ... One the other hand, there are many [relativity books] that are accessible to the experts only."

We call this the Lillian Lieber standard.


Here is how that standard has been applied in this book:

  1. Tell without math what can be told without math. The clash of giant principles that began the search for a solution, the detective story, Einstein's insights. These are in the first five chapters, which anyone can read easily and enjoyably.
  2. Go at the ideas that can't be adequately conveyed without some math, using basic algebra where it will do the job, use it sparingly, and use it to enlighten the discourse, not to substitute for it.
  3. Arrange the content of the book so that the mathematics and the more abstract concepts advance gradually, and with purpose. So as not to deny it to those who can handle it, don't omit the concepts that are abstract and require a heavier dose of math, but place them so that those who can't (or don't want to right now), can move as far in that direction as they choose, meeting the more comfortable parts before they encounter that which stops them.
  4. Use language and pictures to help tell the story, letting the math do what only the math can do.
  5. Use examples that will live in the minds of the readers forever as models for their consideration of the questions that their own minds will conjure.

For whom is this book intended? CLICK HERE

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