Consider as an example a system defined by the string rewrite rules: […] Starting from A, the next state has to be BBB. But now there are two possible ways to apply the rules, one generating AB and the other BA. And if we trace both possibilities we get what I call a Multiway System — whose behavior we can represent using a multiway graph: […]
A typical way to think about what’s going on is to consider each possible underlying rule application as an “updating event”. And then the point is that even within a single string multiple updating events (shown here in yellow) may be possible—leading to multiple branches in the multiway graph: […]
At first, one might want to say that while many branches are in principle possible, the system must somehow in any particular case always choose (even if perhaps “non-deterministically”) a single branch, and therefore a particular history. But a key to the multicomputational paradigm is not to do this, and instead to say that “what the system does” is defined by the whole multiway graph, with all its branches.
In the ordinary computational paradigm, time in effect progresses in a linear way, corresponding to the successive computation of the next state of the system from the previous one. But in the multicomputational paradigm there is no longer just a single thread of time; instead one can think of every possible path through the multiway system as defining a different interwoven thread of time. If we look at the four paradigms for theoretical science that we’ve identified we can now see that they involve successively more complicated views of time. The structural paradigm doesn’t directly talk about time at all. The mathematical paradigm does consider time, but treats it as a mathematical variable whose value can in a sense be arbitrarily chosen. The computational paradigm treats time as reflecting the progression of a computation. And now the multicomputational paradigm treats time as something multithreaded, reflecting the interwoven progression of multiple threads of computation.
It’s not difficult to construct multiway system models. There are multiway Turing machines. There are multiway systems based on rewriting not only strings, but also trees, graphs or hypergraphs. **There are also multiway systems that work just with numbers.** It’s even possible (though not especially natural) to define multiway cellular automata. And in fact, whenever there’s a system where a single state can be updated in multiple ways, one’s led to a multiway system. (Examples include games where multiple moves are possible at each turn, and computer systems with asynchronous or distributed elements that operate independently.) And once one has the idea of multiway systems it’s amazing how often they end up being the most natural models for things. And indeed one can see them as minimal models pretty much whenever there’s no rigid built-in notion of time, and no predefined specification of “when things happen” in a system. But right now the “killer app” for multiway systems is our Physics Project. Because what we seem to be learning is that in fact our whole universe is operating as a giant multiway system. And it’s the limiting properties of that multiway system that give us space and time and relativity and quantum mechanics.
⇒ Observers, Reference Frames and Emergent Laws
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