That brings us to another interesting feature of topologies, and that is their variation with scale. A few years ago, the world was fascinated (quite rightly) with fractal patterns. For those of you too young to remember the fad :-), a fractal pattern is one like the shape of a fern, which when you look at it closer and closer rewards you with a similar level of interest through many orders of magnitude. It is like the tree outside my office window, but it is not like my office block, whose interesting features are limited to a rectangle maybe 100 meters long, windows around a meter wide, and rivets a few millimeters wide.
Is society fractal? Yes, it certainly is. There is structure at the highest levels and the lowest levels. There are great big links formed by organizations which themselves are made up of smaller links. You can simplify society on a number of levels. You look at a newspaper and it will perhaps have a few sorties of domestic bliss or otherwise in the neighborhood, a story on the town, a story at state level, and (even in Boston), usually some stories about world affairs. (For those not from the area, the Boston paper's typical foreign news headline is "Boston woman has twins in China".)
People need to be part of the fractal pattern. They need to be part of organisms at each scale. We appreciate that a person needs a balance between interest in self, family, town, state and planet. A person needs connections at each scale. People who lack connections at any given scale feel frustrated. The international jet-setter and the person who always stays at home share that frustration. Could it be that human beings are programmed with some microscopic rules which induce them to act so as to form a wholesome society? Will these rules still serve us when we are "empowered" by the web, or will evolution give us no clues how to continue?
Look at web "home pages". "Home pages" are representative of people, organizations, or concepts. Good ones tend to, just like people, have connections of widely varying "length". Perhaps as the web grows we will be able to see fractal structure emerge in its interconnections. Perhaps we ought to bear this in mind as we build our own webs.
One of the reasons that the web spread was that the hypertext model does not constrain the information it represents. This has allowed people to represent topologies they need. We have found that people love to use trees, but like to have more than one, sometimes overlapping. We have found they need structure and involvement at all scales.
