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On the Nature of Time
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

On the Nature of Time

Stephen Wolfram

Time is a central feature of human experience. But what actually is it? In traditional scientific accounts it’s often represented as some kind of coordinate much like space (though a coordinate that for some reason is always systematically increasing for us). But while this may be a useful mathematical description, it’s not telling us anything about what time in a sense “intrinsically is”.

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Observer Theory
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Observer Theory

Stephen Wolfram

We call it perception. We call it measurement. We call it analysis. But in the end it’s about how we take the world as it is, and derive from it the impression of it that we have in our minds.

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Games and Puzzles as Multicomputational Systems
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Games and Puzzles as Multicomputational Systems

Stephen Wolfram

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.

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On the Concept of Motion
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

On the Concept of Motion

Stephen Wolfram

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.

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Multicomputation with Numbers: The Case of Simple Multiway Systems
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Multicomputation with Numbers: The Case of Simple Multiway Systems

Stephen Wolfram

Multicomputation is an important new paradigm, but one that can be quite difficult to understand. Here my goal is to discuss a minimal example: multiway systems based on numbers. Many general multicomputational phenomena will show up here in simple forms (though others will not). And the involvement of numbers will often allow us to make immediate use of traditional mathematical methods.

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Multicomputation: A Fourth Paradigm for Theoretical Science
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Multicomputation: A Fourth Paradigm for Theoretical Science

Stephen Wolfram

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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The Problem of Distributed Consensus
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

The Problem of Distributed Consensus

Stephen Wolfram

In any decentralized system with computers, people, databases, measuring devices or anything else one can end up with different values or results at different “nodes”. But for all sorts of reasons one often wants to agree on a single “consensus” value, that one can for example use to “make a decision and go on to the next step”.

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Multiway Turing Machines
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Multiway Turing Machines

Stephen Wolfram

Over the years I’ve studied the simplest ordinary Turing machines quite a bit, but I’ve barely looked at multiway Turing machines (also known as nondeterministic Turing machines or NDTMs). Recently, though, I realized that multiway Turing machines can be thought of as “maximally minimal” models both of concurrent computing and of the way we think about quantum mechanics in our Physics Project. So now this piece is my attempt to “do the obvious explorations” of multiway Turing machines.

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