*An open letter.*

Dear Professor Rindler,

I write to thank you for writing *Relativity: Special, General and Cosmological*. I picked it up by chance at a university bookstore several years ago, and I've found it to be very enlightening and well readable.

I'm what one might call a physics amateur – not quite a physics student, certainly nothing resembling a researcher, but possibly a step up from the "educated layman" level. I like to extend my understanding of modern physics, for my own amusement and a sense of moral duty for a thinking being to at least try to understand the world he finds himself in. Here, by "understanding" I mean something deeper than memorizing some popularizer's free-floating qualitative assertions and analogies. Luckily, as a computer scientist with a B.S. in mathematics, I am no stranger to formulae – a mathematics-free *understanding* of any area of physics appears to be an oxymoron.

It is not easy to find good literature for a project such as mine. There are, of course, many books that purport to explain modern physics to laymen, but they all studiously *avoid* presenting any mathematical content of the theories they speak of. (The only exception I have encountered is Roger Penrose's *The Emperor's New Mind*, which however covers so much ground that its treatment of any particular subject is very brief). Even when they manage correct qualitative descriptions of a theory, they cannot, lacking formulae, convey a good sense of the predictive character of the theory. As for general relativity, popular works tend to stop at the rubber-sheet analogy, usually without even developing it enough to make it clear whether they try to depict spatial curvature or graph gravitational potential.

On the other hand, actual university textbooks tend to be too dry for the amateur. They often dive straight into formalism, with much time spent on methods of concrete calculation and little emphasis on intuition and perspective. The amateur (meaning I) tends to have little patience with problem-solving tricks; he wants to understand the structure of the theory more than he wants to apply it in practice (though, of course, one person's clever computational shortcut can become a basic feature of another's theory – as I understand it to have been the case for quantum electrodynamics). And above all, he needs hints about intuition and perspective. Intuition without mathematics is for cocktail-party philosophers, but mathematics without intuition is for robots. Apparently most textbook authors rely on the instructor for supplying students with the big picture, which is not unreasonable but does not help for self-study.

Your book, however, is a rare gem: A text that both teaches the formalism of the theory and explains what it means intuitively. In reading some of the sections, I have followed the mathematics carefully, checking derivations and doing exercises. This gives me a solid sense of knowing what goes on. In other sections I have skipped most details of the formulae but still got a general picture from the connecting text. This general picture is, in a sense, second-hand knowledge, but feels more secure than that, because the mathematical details are *right there* should I ever want to check them.

It is very wonderful that the book is capable of being read both ways.

I'm convinced that this book has made me smarter. It has enabled me, in many discussions with fellow amateurs, to correct (I hope!) misconceptions and confusions caused by fuzzy and imprecise popularizations of GR and black holes. I have been recommending it left and right. I'm very happy that it exists, and that I discovered it.

Sincerely yours,

Henning Makholm

* * *

*Respectfully recommended for your reading pleasure: Relativity: Special, General and Cosmological by Wolfgang Rindler (Oxford University Press, 2001; 2nd ed. 2006). This book will teach you everything you want to know about special relativity (saw the Lorentz transform in high school and thought it was all there is to it? Think again), general relativity, black holes, as well as a fair overview of cosmology and tensor calculus. The preface promises: "Anyone who knows the calculus up to partial differentiation, ordinary vectors to the point of differentiating them, and the most useful method of approximation, the binomial theorem, should be able to read this book." As far as I can tell, that is what it delivers.*

They frequently jump right into formalism, devoting a lot of time to concrete computation methods and putting little emphasis on intuition and perspective. The amateur (me) has little patience with problem-solving tricks; he wants to understand the structure of the theory more than he wants to apply it in practice (though, of course, one person's clever computational shortcut can become a basic feature of another's theory - as I understand quantum electrodynamics to be the case). Above all, he requires guidance on intuition and perspective. Mathematics without intuition is for cocktail-party philosophers, but intuition without mathematics is for robots.Continue your excellent work! I look forward to seeing more intriguing factoids from your perspective in the future.

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