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Picture (e) shows the updating events and stripes from the top of picture (d), with the updating events now explicitly numbered. Pictures (f) and (g) then show how one can take the pattern of connectivity from picture (e) and lay out the updating events as nodes so as to produce an orderly network. And for the particular mobile automaton rule used here, the network one gets ends up being highly regular, as illustrated in pictures (h) and (i).

So what is the significance of this network? It turns out that it can be thought of as defining a structure for spacetime as perceived by an observer inside the mobile automaton—in much the same way as the networks we discussed two sections ago could be thought of as defining a structure for space. Each updating event, corresponding to each node in the network, can be imagined to take place at some point in spacetime. And the connections between nodes in the network can then be thought of as defining the pattern of neighbors for points in spacetime.

But unlike in the space networks that we discussed two sections ago, the connections in the causal networks we consider here always go only one way: each connection corresponds to a causal relationship in which one event leads to another, but not the other way around.

This kind of directionality, however, is exactly what is needed if a meaningful notion of time is to emerge. For the progress of time can be defined by saying that only those events that occur later in time than a particular event can be affected by that event.

And indeed the networks in pictures (g) through (i) on the previous page were specifically laid out so that successive rows of nodes going down the page would correspond, at least roughly, to events occurring at successively later times.

As the numbering in pictures (e) through (g) illustrates, there is no direct correspondence between this notion of time and the sequence of updating events that occur in the underlying evolution of the mobile automaton. For the point is that an observer who is part of the mobile automaton will never see all the individual steps in this evolution. The most they will be able to tell is that a certain network of causal relationships exists—and their perception of time must therefore derive purely from the properties of this network.

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