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Geometry Relativity, and the Fourth Dimension

Rudolf Rucker
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
P. N. Ruane
, on

This slender volume is a reprint of the first Dover edition (1977). Within 130 pages, it reveals the basic concepts of both special and general relativity and introduces various underlying concepts from non-Euclidean geometry.

Having read this delightfully presented book, I can confirm the accuracy of the publisher’s blurb on back cover, which claims that it provides ‘a remarkable pictorial discussion of curved space-time’. The treatment is the antithesis of Hawking’s Brief History of Time, in which there are very few illustrations and no mathematical symbols. In this book, there is hardly a page without a diagram, but the use of mathematics is kept to a minimum and doesn’t proceed beyond matrix transformations and elementary calculus.

The main challenge in writing a book on this theme is to greatly extend the reader’s capacity for spatial thinking. The task of addressing that aim begins in the early chapters on the fourth dimension, non-Euclidean geometry and time as a higher dimension. It continues in remaining chapters, which cover special relativity, time travel the shape of space-time.

Most of the fundamental concepts are placed within a wider theoretical and cultural context whereby the reader becomes acquainted with the work of Feynman, Gödel, Minkowski and, of course, Einstein himself. Edwin Abbott’s Flatland is the main literary influence, but there is reference to various other writers whose thinking has been extended by some basic awareness of relativity. Foremost amongst these is Jorge Luis Borges whose essay ‘A New Refutation of Time’ examines the metaphysical idealism Berkeley and Hume.

Reader-friendly this book may be, but it is certainly not light reading, and it has to be approached in a studious state of mind. It has been written in a lively manner and with use of many real world analogies. There are also imaginatively constructed exercises at the end of each of the book’s five chapters, and the process of reading the book requires the thinking cap to remain firmly placed on one’s head. Another innovative feature of Rudy Rucker’s book is the annotated bibliography which provides an overview of the contents of each of the 32 books that form the recommended further reading.

Overall, this book is recommended as a source of pure enjoyment and/or as one of the core texts within a taught course on relativity. 

Peter Ruane has taught mathematics to people between the ages of 5 and 55 — that is, from basic school arithmetic to transfinite arithmetic.




The Fourth Dimension
2: Non-Euclidean Geometry
3: Curved Space
4: Time as a Higher Dimension
5: Special Relativity
6: Time Travel
7: The Shape of Space-Time
  Annotated Bibliography