regardless of the path one chooses, the overall form of causal network will be essentially the same. And what this means is that on a sufficiently large scale, the universe will appear to have a unique history, even though at the level of individual events there will be considerable arbitrariness.

If there is not enough convergence in the multiway system it will still be possible to get stuck with different types of strings that never lead to each other. And if this happens, then it means that the history of the universe can in effect follow many truly separate branches. But whenever there is significant randomness produced by the evolution of the multiway system, this does not typically appear to occur.

So this suggests that in fact it is at some level not too difficult for multiway systems to reproduce our everyday perception that more or less definite things happen in the universe. But while this means that it might be possible for there to be arbitrariness in the causal network for the universe, it still tends to be my suspicion that there is not—and that in fact the particular rules followed by the universe do in the end have the property that they always yield the same causal network.

Evolution of Networks

Earlier in this chapter, I suggested that at the lowest level space might consist of a giant network of nodes. But how might such a network evolve?

The most straightforward possibility is that it could work much like the substitution systems that we have discussed in the past few sections [9, 10, 11]—and that at each step some piece or pieces of the network could be replaced by others according to some fixed rule.

The pictures at the top of the facing page show two very simple examples. Starting with a network whose connections are like the edges of a tetrahedron, both the rules shown work by replacing each node at each step by a certain fixed cluster of nodes.

This setup is very much similar to the neighbor-independent substitution systems that we discussed on pages 83 and 187. And just as in these systems, it is possible for intricate structures to be produced, but the structures always turn out to have a highly regular nested form.

From Stephen Wolfram: A New Kind of Science [citation]