Networks
If a typical scale-free network looks like a series of connected stars, and a monopolistic network looks like one single, giant star, there must be other network topographies which have different shapes.What does the government network look like? Everyone in the country is connected to the government directly. That looks like the monopolistic star model. But everyone is also connected to provincial or state governments and to municipal governments. Both of these levels of government are also connected to the central government.
The shape we end up with looks something like this. The central node is the federal government. The nodes at the end of the spines emerging from it are the provincial or state governments, and the fuzzy mass of nodes at the end of the spines emerging from the provincial/state nodes are nodes representing municipalities. At the end of the spines emerging from the nodes representing municipal governments are supposed to be nodes representing individual citizens, but they are too numerous to depict, so I have used a fuzzy, uneven grey wash.
The grey areas throughout the diagram are attempts to represent nodes and connections which are too numerous to depict. Every single person in every province/state is connected to the central government, so the things that are shaped a bit like blades on a ceiling fan are an attempt to represent that. There are so few connections between an individual and more than one municipality (as far as government is concerned, not work or leisure) and so few between an individual and more than one province/state that the blade structure emerges.
In fact I haven’t even represented it properly, because every single person (with so few exceptions as to make no difference) is connected to each of the three levels. The only real nodes and connectors visible in this diagram are the three levels of government, represented by the central (federal) government in the middle, the provincial/state governments at the end of the blades coming out from the middle, and the municipal governments, already looking like not much more than fuzz, which are at the end of each of the spokes coming from the provincial/state nodes.
Even the grey wash, which represents the fuzziness produced by so many individual connections isn’t depicted accurately. It should encircle each one of the provincial/state nodes evenly.
I guess that network purists, mathematicians and topologists would criticize the diagram for using a grey wash to represent connectors and nodes which are too numerous to depict separately. The whole point of topology is to simplify such representations. However I think there might be something to be gained from using such a technique, as a kind of morphology rather than a topology is created. This morphology might recur in representations of other networks and we might learn from the similarities.
But here’s the interesting thing about this particular network: you can remove the whole central government (through a coup or something) and leave a ‘vacuum’ for a period of time, then install a new, completely different, central government and the connections will magically reappear as they were, which doesn’t make sense in network theory. In network theory, once a node is gone, all connections to it are gone too. They have no reason to exist. Therefore a new node should have to work from scratch (in fact at a huge disadvantage compared to the other nodes) to rebuild the connections.
The links themselves must therefore have ‘a life of their own’. They must be able to be sustained even without a node to link to.
This might relate to information theory too, but I’m not sure. For example, when I was maybe six years old I used to play hopscotch. I knew all the rules. Now I can’t remember them and wouldn’t be able to play a game of hopscotch without someone explaining them to me. In other words I have lost the information. This must happen to everyone. The vast majority of adults who ever played hopscotch must have a vague idea of how to play, but the information containing the exact rules has decayed to the point where it is useless.
However every year a new generation of children plays hopscotch and learns the rules from the previous generation (certainly not from a book called ‘The Official Rules of Hopscotch). So the information containing the rules remains intact, somehow ‘hovering’ around six year-olds, while the six year-olds themselves change and eventually lose it.
This is the same effect as with the composition of a living organism. I am made up of billions of cells, but none of them are the same cells as the ones I had when I was born. However the information contained in that cell network, which has its expression as my particular morphology, has been preserved.
Which refers back to the government network. The central node can be removed, time can pass, and it can be replaced, while losing only a tiny fraction of the connections to other nodes. This persistence can only be explained by assigning a larger role to the connections than is currently assumed. Similarly, the information containing the rules to hopscotch can be thought of as a network, whose topology is formed over time rather than geography. Or, actually, as well as geography. If networks can be represented graphically in two dimensions, this would be a 3-dimensional network, with an additional temporal dimension.
Is this how memory works? The brain is this immense network, with billions of nodes and zillions of connections. But even though the brain cells are replaced over time, the information contained in memories isn’t lost. Are the axons which connect neurons the real secret to persistence of memory, rather than the neurons themselves?
