Space as a Network

In the last section I argued that if the ultimate model of physics is to be as simple as possible, then one should expect that all the features of our universe must at some level emerge purely from properties of space. But what should space be like if this is going to be the case?

The discussion in the section before last suggests that for the richest properties to emerge there should in a sense be as little rigid underlying structure built in as possible. And with this in mind I believe that what is by far the most likely is that at the lowest level space is in effect a giant network of nodes.

In an array of cells like in a cellular automaton each cell is always assigned some definite position. But in a network of nodes, the nodes are not intrinsically assigned any position. And indeed, the only thing that is defined about each node is what other nodes it is connected to.

Yet despite this rather abstract setup, we will see that with a sufficiently large number of nodes it is possible for the familiar properties of space to emerge—together with other phenomena seen in physics.

I already introduced in Chapter 5 a particular type of network in which each node has exactly two outgoing connections to other nodes, together with any number of incoming connections. The reason I chose this kind of network in Chapter 5 is that there happens to be a fairly easy way to set up evolution rules for such networks. But in trying to find an ultimate model of space, it seems best to start by considering networks that are somehow as simple as possible in basic structure—and it turns out that the networks of Chapter 5 are somewhat more complicated than is necessary.

For one thing, there is no need to distinguish between incoming and outgoing connections, or indeed to associate any direction with each connection. And in addition, nothing fundamental is lost by requiring that all the nodes in a network have exactly the same total number of connections to other nodes.

With two connections, only very trivial networks can ever be made. But if one uses three connections, a vast range of networks immediately become possible. One might think that one could get a