Since Edward Abbott penned his original Flatland at the tail end of the 19th century, many modern mathematicians have found themselves unable to resist the urge to put pen to paper in various forms of imitation most notably includiing Ian Stewarts Flatterland, Dewdney's Plainiverse and this entry by Rudy Rucker.
And contrary to some other reviewers who thought that Rucker's Fourth Dimensional treatment paled in comparison to his underlying story, I must confess that I thought the reverse.
In this story, Rucker chose as his protagonist a dot commer named Joe Cube whose comely wife Jena was at various points in the book leaving him, cheating on him and ultimately, well, that would give away the ending. However the point is that Rucker wrote such a complete and convincing portrait of his Jena that you couldn't help yourself but eagerly turning the pages past all the Four D stuff to find out whether Joe would be able to save his marriage and in the end I found myself much more concerned about that than...well...even the fate of the 3D universe which we supposedly inhabit.
The reason I say we supposedly inhabit the 3D universe is because we actually are fourth dimensional creatures. And while viewed from a full fourth dimensional perspective it's true that we would probably more resemble a centipede with a baby at the one end and a (if we're lucky) vibrant geriatric at the other end and while it's also true that we see only slices of this fourth dimensional perspective, I nonetheless still consider it a misnomer to refer to us a "merely" existing in 3D.
Now that being said, Rucker found some exciting and stimulating ways in which to move his story along and to graphically depict the look and feel of 3D. For those alone, he deserves a five star rating (particularly when he retours all the dimensions in a fashion reminiscent of the original Abbott himself).
But for those who like story with their plot, read and it and see if you too get caught up for Cube and join me in rooting for him to save something even more precious than mathematical reality...his marriage.
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