The network is a prototype of the socio-politico-cultural organization of the future. For that reason, it is important to understand its functioning, and to avoid applying to it outdated or irrelevant procedures derived from other media, technologies or cultural habits. A mathematical model may help us in this. The network is spherical, and its dimension is fractal. Finding its dimension may help us to develop a model for it.

We reason as follows. We have a number of connections on the surface of the globe, A to B, B to C, A to C, etc. At first glance, a large number of connections would give us a geodesic globe, a la Fuller, but that implies connections with only immediate neighbors. In a network everyone is con- nected more-or-less directly with everyone else, on a one-to-one basis, without going through any other point. This multiplies the number of potential connections rapidly, and the addition of any new member increases enormously the number of those connections. As the number becomes larger, tending toward infinity, the pattern of connections slides away from that of a complex line on the surface of a sphere and approaches that of a spherical plane. An infinite numbers of connections contained in a finite space. My reasoning is similar to that of Koch)s curve. The dimension must be a spherical one, between one and two, thus a fractal. In using the geodesic sphere as a model, we stay within the realm of classical geometry and completely cut ourselves off from the actual description of the functioning of the network that we find when using a fractal approach. And then, there is its strange attractor.