CA As Models of The Fundamental Physical Reality
As Andrew Ilachinski points out in his Cellular Automata, many scholars have raised the question of whether the universe is a cellular automaton. Ilachinski argues that the importance of this question may be better appreciated with a simple observation, which can be stated as follows. Consider the evolution of rule 110: if it were some kind of "alien physics", what would be a reasonable description of the observed patterns? If you didn't know how the images were generated, you might end up conjecturing about the movement of some particle-like objects (indeed, physicist James Crutchfield made a rigorous mathematical theory out of this idea proving the statistical emergence of "particles" from CA). Then, as the argument goes, one might wonder if our world, which is currently well described by physics with particle-like objects, could be a CA at its most fundamental level.
While a complete theory along this line is still to be developed, entertaining and developing this hypothesis led scholars to interesting speculation and fruitful intuitions on how can we make sense of our world within a discrete framework. Marvin Minsky, the AI pioneer, investigated how to understand particle interaction with a four-dimensional CA lattice; Konrad Zuse—the inventor of the first working computer, the Z3—developed an irregularly organized lattice to address the question of the information content of particles. More recently, Edward Fredkin exposed what he terms the "finite nature hypothesis", i.e., the idea that "ultimately every quantity of physics, including space and time, will turn out to be discrete and finite." Fredkin and Wolfram are strong proponents of a CA-based physics.
In recent years, other suggestions along these lines have emerged from literature in non-standard computation. Wolfram's A New Kind of Science considers CA to be the key to understanding a variety of subjects, physics included. The Mathematics Of the Models of Reference—created by iLabs founder Gabriele Rossi and developed with Francesco Berto and Jacopo Tagliabue—features an original 2D/3D universe based on a new "rhombic dodecahedron-based" lattice and a unique rule. This model satisfies universality (it is equivalent to a Turing Machine) and perfect reversibility (a desideratum if one wants to conserve various quantities easily and never lose information), and it comes embedded in a first-order theory, allowing computable, qualitative statements on the universe evolution.
Read more about this topic: Cellular Automaton
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