You are here

The Fourth Dimension: Toward a Geometry of Higher Reality

Rudy Rucker
Dover Publications
Publication Date: 
Number of Pages: 
BLL Rating: 

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

[Reviewed by
Peter T. Olszewski
, on

If one wants a book on what the fourth dimension is from a variety of different viewpoints, The Fourth Dimension: Toward a Geometry of Higher Reality by Rudy Rucker might be the one. First published in 1984, the book takes the reader on a mystical and wonderful journey to what the fourth dimension is and how one can think about it. Rucker pulls in the reader from the first page of the book. “The fourth dimension is a direction different from all the directions in normal space. Some say that time is the fourth dimension… And this is, in a sense, true. Others say that the fourth dimension is a hyperspace direction quite different from time… This is also true. The book also contains over 200 illustrations and many puzzles that make the reader think about the fourth dimension.

One of the first examples Rucker uses is Etch-A-Sketch. Other examples of particular interest are the famous Plato’s Cave and the Spacetime Diary in Chapter 9. Rucker really brings out the human aspect in these examples, conveying to us how we can relate to the fourth dimension in our day-to-day lives. For example, in the Spacetime Diary, Rucker offers us to think about our world as a block universe and goes on to give his example of working in your office on pages 135–136. Such examples make the reader rethink the world and have a new perspective on life in general. Rucker also bases a lot of his examples on Flatland, by Edwin Abbott Abbott. These adventures of a square begin in Chapter 2 of the book and continue throughout the book.

One of the most interesting chapters of the book is Chapter 5: Ghosts from Hyperspace? The main question in this chapter is, how can we conceive of spirits living outside space? There have been many theories on this issue but Rucker points out that “spirits live in the fourth dimension” is the best theory. He goes on to talk about Henry More (1614–1687), who opposed the idea that spirits, angels, and Platonic forms could exists as insubstantial abstractions. He tells us about Johann Carl Friederick Zöllner (1834–1882) and his 1875 visit to England, where he got his interest in spiritualism from William Crooks. This is the part of the text where one starts to understand what the fourth dimension is on a spiritual level.

Chapter 11, “What is Reality?” is the climax of the book. Rucker starts out with the question: What is the most reasonable model of the world? Rucker talks about the Irish philosopher George Berkeley (1685–1753) who advocated an idealistic philosophy called immaterialism. He then goes on to talk about Lineland, fact-space, and infinite-dimensional Hilbert space. This final chapter makes us all realize that no one really knows why we are here or why we exist. Rucker argues, “Our ordinary notions of space and time are just a convenient fiction.”

This is the best book on trying to wrap one’s head around the fourth dimension that I have read. Most of the examples are easy to understand, though one needs to step away from reading through and looking at the illustrations, think, and relook to fully understand the higher order reality. I highly recommend this book to all who want to think beyond the third dimension.

Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes.

The table of contents is not available.