A line has 1, a polygon has 2, a cube has 3. How does the concept of dimensions in an information space have meaning?
One can think of hyperlinks in an article (which link to other articles, which link to other articles…) as providing an extra dimension to the article. The Sesquiotica blog sets up these concepts nicely in an article on fractals.
The World Wide Web, with its hyperlinks in hyperlinks in hyperlinks, is also, in its way, fractal. That’s right. You are reading this on a fractal that exists (by the calculation of J.S. Kim et al., arXiv:cond-mat/0605324v1) in 4.1 dimensions.