in the 1950s, my main sources of esoteric information were mail-order paperbacks from Dover Books.
I devoured Dover’s volumes on mazes, the fourth dimension, infinity, and language games—all of these to become lifelong interests.
But without the tool of infinite-dimensional spaces, modern physics would be almost impossible.
Older books on quantum mechanics talk about how the measurement of particles and quantum systems “collapses the psi function.” More recent books prefer the language of a complex Hilbert space, an approach adopted by John von Neumann in his classic work on quantum theory.
The subtitle is the exact title of a paper by the eminent logician Kurt Gödel, with whom Rucker had the privilege of many stimulating conversations.
The Fourth Dimension: Toward a Geometry of Higher Reality will be eagerly read by writers and readers of science fiction, but anyone with even a minimal interest in mathematics and fantasy will find the book as informative and mind-dazzling as Rucker’s book on infinity.
When I got my first teaching job, at SUNY Geneseo, I began working out these connections in my lectures for a course on higher geometry. Philosophers and mystics meditate upon it; physicists and mathematicians calculate with it. One of these higher dimensions is time, another higher dimension is the direction m which space is curved, and still another higher dimension may lead toward some utterly different universes existing parallel to our own. By combining the three mutually perpendicular types of motion, one can trace out any possible curve in our space. This fact is illustrated in two dimensions by a toy that was popular a few years ago, the Etch-A-Sketch.
I’m very pleased that Dover is republishing it in paperback and ebook editions.
Here I am unable to go along with his “All is One” philosophy.
He seems to have inherited a genetic fondness for the Absolute from his great-great-great-grandfather, the famous philosopher Hegel.
In more recent times, several professional mathematicians have written science fiction with strong mathematical underpinnings.
Now along comes Rudolf von Bitter Rucker — mathematician, novelist, cartoonist, rock music buff, and a thinker with the courage to explore dark and unfamiliar territory in what he likes to call the mindscape.