The Chronicle has a story based on the talks at Hyperlinked Society. It ends with:
“In the physical world, it’s a matter of taking the three-dimensional world and making it two-dimensional,” said Mr. Dodge. But on the Internet, he said, there are more dimensions to consider.
With all deference to Dodge, who is a genius, of course, I’m pretty sure that quote was from me. In fact, Matthew Hurst came back and noted that my comment (that there were tens or hundreds of thousands of dimensions) was an under-estimate, since there were as many dimensions as vertices.
In practice, since I rarely deal with data sets the size Hurst deals with, I am working in tens or hundreds of thousands of dimensions. Moreover, although I didn’t respond to his critique, the number of vertices represents an upper limit of the number of dimensions present, and given the sparse linkages on the web, it is an upper limit that is rarely approached, I suspect.
What that large number of dimensions means in practical terms is that maps like those on the Chronicle site, while they may get the “big picture” right (in terms of clustering, for example), are in some large part arbitrary. That is to say, there are millions of other maps that would represent the space equally as well.