1.0.5: hyperbolic spaces and the Internet
One of the most mind-opening talks I've ever been to was Tamara Munzner's talk at SIGGRAPH '95. In hyperbolic space, as you get closer to an object, it gets larger. Not just appears larger, gets larger. This is incredibly useful for visualizing very large networks.
Tamara kind of dropped off my radar for a few years, but if you look at her software page, there is cool, related stuff there, including an SGI tool for managing web content.
Question for Bill and Suz: does anybody in network management use this stuff, or related ideas?
Question for Wook: can we use this somehow to visualize the state of a quantum computer? This would be highly non-representational, I think, but so is the Bloch sphere (see this text description from Mathworld and this GUI and animation).