there will be an additional source of randomness: the arbitrariness of the path corresponding to the history that we have experienced.

In many respects this randomness is similar to the randomness from the environment that we discussed at the beginning of Chapter 7. But an important difference is that it would occur even if one could in effect perfectly isolate a system from the rest of the universe. If in the past one had seen apparent randomness in such a system there might have seemed to be no choice but to assume something like an underlying multiway system. But one of the discoveries of this book is that it is actually quite possible to generate what appears to be almost perfect randomness just by following definite underlying rules.

And indeed I would not expect that observations of randomness could ever reasonably be used to show that our universe is part of a multiway system. And in fact my guess is that the only way to show this with any certainty would be actually to find a specific set of multiway system rules with the property that regardless of the path that gets followed these rules would always yield behavior that agrees with the various observed features of our universe.

At some level it might seem surprising that a multiway system could ever consistently exhibit any particular form of behavior. For one might imagine that with so many different paths to choose from it would often be the case that almost any behavior would be able to occur on some path or another. And indeed, as the picture below shows, it is not difficult to construct multiway systems in which all possible strings of a particular kind are produced.

But if one looks not just at individual strings but rather at the sequences of strings that exist along paths in the multiway system, then one finds that these can no longer be so arbitrary. And indeed, in any multiway system with a limited set of rules, such sequences must necessarily be subject to all sorts of constraints.

In general, each path in a multiway system can be thought of as being defined by a possible sequence of ways in which the replacements specified by a multiway system rule can be applied. And each such path in turn then defines a causal network of the kind we discussed in the previous section. But as we saw there, certain underlying rules have the

A multiway system in which strings of any length can be generated—but in which only specific sequences of lengths actually occur on any path.

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