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Wolfram Institute Bulletins

Games and Puzzles as Multicomputational Systems

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. 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. And I explore here what seems like a particularly good example: games and puzzles.

Multicomputational Irreducibility

Multicomputation is the cornerstone of much of the basic science that my teammates and I are doing with Stephen Wolfram. We see an opportunity to metamodel many areas of applied science using the multicomputational paradigm. In fact, the range of opportunities that we envisage is so wide that we are launching the Wolfram Institute in order to expand the effort beyond Wolfram Research. It’s a momentous period. But because multicomputation is still new, I feel a responsibility to help communicate in greater detail the aspects of multicomputation that I personally find to be compelling. And I have great reference material for doing so, because introducing a new paradigm of science is precisely what Stephen began to do in the 1980s with the computational paradigm. And I still refer to those works from the 1980s today because they cover then-novel concepts that have come to serve as guiding principles for the work that we do now. And a key concept, which distinguishes those papers from other theoretical literature on the study of computability, is that of computational irreducibility. So, now that we are developing a new paradigm that builds upon the one that Stephen pioneered decades ago, it seems appropriate to consider irreducibility in the multicomputational context.

Twenty Years Later: The Surprising Greater Implications of A New Kind of Science

When A New Kind of Science was published twenty years ago I thought what it had to say was important. But what’s become increasingly clear—particularly in the last few years—is that it’s actually even much more important than I ever imagined. My original goal in A New Kind of Science was to take a step beyond the mathematical paradigm that had defined the state of the art in science for three centuries—and to introduce a new paradigm based on computation and on the exploration of the computational universe of possible programs. And already in A New Kind of Science one can see that there’s immense richness to what can be done with this new paradigm.

On the Concept of Motion

It seems like the kind of question that might have been hotly debated by ancient philosophers, but would have been settled long ago: how is it that things can move? And indeed with the view of physical space that’s been almost universally adopted for the past two thousand years it’s basically a non-question. As crystallized by the likes of Euclid it’s been assumed that space is ultimately just a kind of “geometrical background” into which any physical thing can be put—and then moved around.

The Concept of the Ruliad

I call it the ruliad. Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways. It’s yet another surprising construct that’s arisen from our Physics Project. And it’s one that I think has extremely deep implications—both in science and beyond.

In many ways, the ruliad is a strange and profoundly abstract thing. But it’s something very universal—a kind of ultimate limit of all abstraction and generalization. And it encapsulates not only all formal possibilities but also everything about our physical universe—and everything we experience can be thought of as sampling that part of the ruliad that corresponds to our particular way of perceiving and interpreting the universe.

Multicomputation: A Fourth Paradigm for Theoretical Science

One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. But what I’ve increasingly been realizing is that actually it’s showing us something even bigger and deeper: a whole fundamentally new paradigm for making models and in general for doing theoretical science. And I fully expect that this new paradigm will give us ways to address a remarkable range of longstanding central problems in all sorts of areas of science—as well as suggesting whole new areas and new directions to pursue.
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