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Tuesday, February 17, 2004

social software: representing relationships, part 3 

via d2r

From that follows that, if we represent n-dimensional data structures, we'll have to create projections. Projections are easy stuff, mathematically speaking (i.e., they involve fairly simple vector math). Visualizing them is not too difficult either. For example, consider hypercubes, which are one of the easiest cases because they're fully symmetrical graphs. For example this is what projections of hypercubes of dimensions n > 3 into 2D look like [source]:

hypercubes.gif

A 2D projection of a, say, 12D space might be pretty to look at, but I think most users would avoid that kind of complexity and its consequent cognitive overload.

This gets me thinking about hypercube projections of increasing dimensionality as backtrack-free generative sequences of morphological unfolding, talked about by Christopher Alexander

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