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So does the notion of time that emerges actually have the familiar features of time as we know it? One might think for example that in a network there could be loops that would lead to a deviation from the linear progression of time that we appear to experience. But in fact, with a causal network constructed from an underlying evolution process in the way we have done it here no such loops can ever occur.

So what about traces of the sequential character of evolution in the original mobile automaton? One might imagine that with only a single active cell being updated at each step different parts of the system would inevitably be perceived to progress through time one after another. But what the pictures on page 489 demonstrate is that this need not be the case. Indeed, in the networks shown there all the nodes on each row are in effect connected in parallel to the nodes on the row below. So even though the underlying rules for the mobile automaton involve no global synchronization, it is nevertheless possible for an observer inside the mobile automaton to perceive time as progressing in a synchronized way.

Later in this chapter I will discuss how space works in the context of causal networks—and how ideas of relativity theory emerge. But for now one can just think of networks like those on page 489 as being laid out so that time goes down the page and space goes across. And one can then see that if one follows connections in the network, one is always forced to go progressively down the page, even though one is able to move both backwards and forwards across the page—thus agreeing with our everyday experience of being able to move in more or less any direction in space, but always being forced to move onward in time.

So what happens with other mobile automata?

The pictures on the next two pages [492, 493] show a few examples.

Rules (a) and (b) yield very simple repetitive networks in which there is in effect a notion of time but not of space. The underlying way any mobile automaton works forces time to continue forever. But with rules (a) and (b) only a limited number of points in space can ever be reached.

The other rules shown do not, however, suffer from this problem: in all of them progressively more points are reached in space as time goes on. Rules (c) and (d) yield networks that can be laid out in a quite

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