emerges from the same underlying network—or in effect from the structure of space. And indeed even in traditional general relativity one can try avoiding introducing matter explicitly—for example by imagining that everything we call matter is actually made up of pure gravitational energy, or of something like gravitational waves.

But so far as one can tell, the details of this do not work out—so that at the level of general relativity there is no choice but to introduce matter explicitly. Yet I suspect that this is in effect just a sign of limitations in the Einstein equations and general relativity.

For while at a large scale these may provide a reasonable description of average behavior in a network, it is almost inevitable that closer to the scale of individual connections they will have to be modified. Yet presumably one can still use the Einstein equations on large scales if one introduces matter with appropriate properties as a way to represent small-scale effects in the network.

In the previous section I suggested that energy and momentum might in effect be associated with the presence of excess nodes in a network. And this now potentially seems to fit quite well with what we have seen in this section. For if the underlying rule for a network is going to maintain to a certain approximation the same average number of nodes as flat space, then it follows that wherever there are more nodes corresponding to energy and momentum, this must be balanced by something reducing the number of nodes. But such a reduction is exactly what is needed to correspond to positive curvature of the kind implied by the Einstein equations in the presence of ordinary matter.

Quantum Phenomena

From our everyday experience with objects that we can see and touch we develop a certain intuition about how things work. But nearly a century ago it became clear that when it comes to things like electrons some of this intuition is no longer correct. Yet there has developed an elaborate mathematical formalism in quantum theory that successfully reproduces much of what is observed. And while some aspects of this