A hyperbolic space is a two-dimensional representation of relationships between objects -- perhaps, documents -- in which the object under examination is in the center of the screen. Documents related strongly to the central document appear in proximity to central document. Those that are less strongly related appear smaller in size and move closer and closer towards the edge of the space. They do not, however, "fall" off the edge of the space.
As a user "navigates" in the space, changing focus from document to document, the documents would shift size and position correspondingly.
I suppose the definition of "related" documents is also variable. Documents may be related by author, by subject, by citation, by size, by location, and so forth.
PARC's Experiments on the Future of Reading exhibit shows a hyperbolic reader for a comic book: www.parc.xerox.com/xfr.
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