But if one has a system that yields the same causal network independent of the scheme used to apply its underlying rules, then the situation is different. And in this case any slice that consistently divides the causal network into a past and a future must correspond to a possible state of the underlying system—and any non-overlapping sequence of such slices must represent a possible evolution history for the system.

If we could explicitly see the particular underlying evolution history for the system that corresponds to our universe then this would in a sense immediately provide absolute information about space and time in the universe. But if we can observe only the causal network for the universe then our information about space and time must inevitably be deduced indirectly from looking at slices of causal networks.

And indeed only some causal networks even yield a reasonable notion of space at all. For one can think of successive slices through a causal network as corresponding to states at successive moments in time. But for there to be something one can reasonably think of as space one has to be able to identify some background features that stay more or less the same—which means that the causal network must yield consistent similarities between states it generates at successive moments in time.

One might have thought that if one just had an underlying system which did not change on successive steps then this would immediately yield a fixed structure for space. But in fact, without updating events, no causal network at all gets built up. And so a system like the one at the top of the next page is about the simplest that can yield something even vaguely reminiscent of ordinary space.

In practice I certainly do not expect that even parts of our universe where nothing much seems to be going on will actually have causal networks as simple as at the top of the next page. And in fact, as I mentioned at the end of the previous section, what I expect instead is that there will always tend to be all sorts of complicated and seemingly random behavior at small scales—though at larger scales this will typically get washed out to yield the kind of consistent average properties that we ordinarily associate with space.

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