3rd Task

Notes on Computational Equivalence Principle

Can simple programs produce very rich and complicated behaviors? Could it be possible that all of the amazing things we see in the universe be the result of a simple program? That would be very exciting to have a program that is an ultimate precise model of our universe. If you run it long enough it would produce complex models. Stephen Wolfram asks how would this program be like.

The principle of computational equivalence says that “systems found in the natural world can perform computations up to a maximal ("universal") level of computational power, and that most systems do in fact attain this maximal level of computational power.” With Wolfram's own words "When it comes to computation—or intelligence—we are in the end no more sophisticated than all sorts of simple programs, and all sorts of systems in nature. But from the Principle of Computational Equivalence there emerges a new kind of unity: for across a vast range of systems, from simple programs to brains to our whole universe, the principle implies that there is a basic equivalence that makes the same fundamental phenomena occur, and allows the same basic scientific ideas and methods to be used."

The structure of a system need not be complicated for its behavior to be highly complex. Cellular Automata (e.g rule 30) or reaction-diffusion models that Alan Turing developed just before his death can provide an example to provide models for a wide variety of complex systems. Even Turing machine model with one cell updating would be a model for complex behaviors. It is easy to see the reflections of the Computational Equivalence Principle in Richard Dawkins Biomorphosis, Thomas Ray’s Tierra project, and Karl Sim’s virtual creatures.

Evolutionary biologist Thomas Ray makes a comparison as the genetic language consists of an alphabet of 20 letters and a computer language has many. He takes inspiration from natural science and uses computer science to solve problems. Not only algorithms, but he also distinguishes the inside of a computer as a physical system by making an analogy of the sun, the source of energy, as CPU and creatures living in the memory. This also supports Wolfram’s idea of a close correspondence between physical processes and computations. Like the Computational Equivalence principle says, Thomas Ray seems to build very complex ecological phenomena with his very simplified computer program.

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I always have an impression that everything in the universe is too complicated and doesn’t give too much chance to be computed. ---