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“I Have a Theory Too”: The Challenge and Opportunity of Avocational Science
Stephen Wolfram
Most physicists term people who send such theories “crackpots”, and either discard their missives or send back derisive responses. I’ve never felt like that was the right thing to do. Somehow I’ve always felt as if there has to be a way to channel that interest and effort into something that would be constructive and fulfilling for all concerned. And maybe, just maybe, I now have at least one idea in that direction.
Kolmogorov Complexity vs. Computational Irreducibility: Understanding the Distinction
James K. Wiles
Kolmogorov complexity and computational irreducibility describe two kinds of limits on simplification, but they apply in different ways. Kolmogorov complexity measures the shortest possible description of an object, such as a string. Computational irreducibility refers to processes that cannot be predicted or accelerated. This paper introduces each concept, explains their theoretical distinction, and illustrates the difference using simple examples.
Ruliology of the “Forgotten” Code 10
Stephen Wolfram
For several years I’d been studying the question of “where complexity comes from”, for example in nature. I’d realized there was something very computational about it (and that had even led me to the concept of computational irreducibility—a term I coined just a few days before June 1, 1984). But somehow I had imagined that “true complexity” must come from something already complex or at least random. Yet here in this picture, plain as anything, complexity was just being “created”, basically from nothing. And all it took was following a very simple rule, starting from a single black cell.
Charting a Course for “Complexity”: Metamodeling, Ruliology and More
Stephen Wolfram
For me the story began nearly 50 years ago—with what I saw as a great and fundamental mystery of science. We see all sorts of complexity in nature and elsewhere. But where does it come from? How is it made? There are so many examples. Snowflakes. Galaxies. Lifeforms. Turbulence. Do they all work differently? Or is there some common underlying cause? Some essential “phenomenon of complexity”?
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”.