![]() ![]() And in turn understanding the relation to games and puzzles has the potential to provide a new level of intuition and familiarity about multiway graphs. But with the multicomputational paradigm there are now some more general concepts that can be applied to these constructs. The notion of making what we call a multiway graph has actually existed-usually under the name of “game graphs”-for games and puzzles for a bit more than a hundred years. ![]() But the point of the multicomputational paradigm is to look globally at the consequences of all possible choices-and to produce a multiway graph that represents them. In any particular instance of the game, they’ll make a particular choice. And where the idea of multicomputation comes in is that there are usually several choices that they can make. Given a particular state of a game or puzzle, a player must typically decide what to do next. And the point is that this is directly related to how one can think about typical games and puzzles. ![]() But in a multicomputational system the key idea is that states can have multiple successors-and tracing their behavior defines a whole multiway graph of branching and merging threads of time. In an ordinary computational system each state of the system has a unique successor, and ultimately there is a single thread of time that defines a process of computation. ![]() And indeed one can view the very possibility of being able to have “interesting” games and puzzles as being related to a core phenomenon of multicomputation: multicomputational irreducibility. But the idea of multicomputation provides a link. One might not imagine that something as everyday as well-known games and puzzles would have any connection to the formalism for something like quantum mechanics. And I explore here what seems like a particularly good example: games and puzzles. But how can one get an intuition for what is initially the rather abstract idea of multicomputation? A good approach, I believe, is to see it in action in familiar systems and situations. Multicomputation is one of the core ideas of the Wolfram Physics Project-and in particular is at the heart of our emerging understanding of quantum mechanics. ![]()
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