Flatland, by Edwin A. Abbot, is the must-read for anyone interested
in getting a feel for higher dimensions. The book is
extraordinarily readable and succeeds even with people that are
afraid of mathematics. Abbott's charm lies in his ability to write
simply and clearly about a topic that has its share of very
unreachable, esoteric books. You fall into the story (whose plot is
by no means secondary to the mathematical ideas), and before you
know it you find yourself in contemplation of things like the
fourth and fifth dimensions. The visual image that this book
provides is a necessary step to envisioning and then understanding
the idea of higher dimensions, even for those already versed in the
mathematics of it. You never know, after you read this, you might
even be willing to try your hand at things like Einstein's
relativity. A little on the social aspects of the book: keep in
mind that it was written in the very late 1800's. Hidden within the
philosophical and mathematical ideas is a satire of the social
climate of the times: how women, the military, the upper echelons
of society, and just about everyone else were viewed. Flatland
makes you think, and think deeply, on many different and sometimes
unexpected levels.
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