In a tribute to Edwin Abbott's Flatland, a classic mathematical fantasy about a 2-dimensional being (A. Square) who receives a surprise visit from a higher-dimensional sphere, Rudy Rucker's Spaceland describes the life of Joe Cube, an average, modern-day Silicon Valley hotshot who one day discovers the fourth dimension from an unexpected visitation.
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Joe Cube is a high tech executive waiting for his company's IPO. On the New Year's Eve before the new millennium, trying to impress his wife Jena, he brings home a prototype of his company's new product (a TV screen that turns standard television broadcasting into a 3D image). It brings no warmth to their cooling marriage, but it does attract the attention of somebody else. Joe is suddenly contacted by a Momo, a woman from the fourth dimension she calls the All, of which our entire world (which she calls Spaceland) is like nothing but the thin surface of a rug.
Momo has a business proposition for Joe that she won't let him refuse. She is bent on making him start a company that will create a specific product that she will supply. The upside potential becomes much clearer for Joe once Momo "augments" him, by helping him grow a new eye on a 4D stalk, giving him the power to see in four dimensional directions, as well as the ability to see into our dimension using a four dimension perspective.
After that, it's a wild ride through a million-dollar night in Las Vegas, a budding addiction to a tasty purple fruit from the All, a troubled marriage, eye-popping voyages into Momo's universe and strange encounters with Momo's sworn enemies (who are another race of 4D beings), rubbery red creatures called the Wackles, who steal money, speak in unusual words, offer sage advice, and sometimes messily explode when shot at themselves. The plot gets complicated when the Wackles kill Momo, and Joe discovers the startling revelation about Momo's business scheme. Suddenly, the fate of all beings in our world Spaceland is at stake and Joe must do something about it fast before it is too late.