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It turns out that the basic structure of the cellular automata discussed here implies that the maximum speed of any such motion must be one cell per step.
And if there is a fixed such scheme, then this implies that while certain similarities between pieces of data will immediately be recognized, others will not.
So knowing that a particular system is universal thus immediately implies that the system can produce behavior that is in a sense arbitrarily complex.
But the phenomenon of universality implies that this is not the case, and that as soon as one has passed the threshold of universality, nothing more can in a sense ever be gained.
less computational sophistication than is implied by the principle, while others will be based on believing that they have more.
And , Or , Not , and Implies are widely used in traditional logic.
And indeed the Principle of Computational Equivalence implies that a vast range of systems—even ones with very simple underlying rules—should be equivalent in the sophistication of the computations they perform.
For my discoveries imply that whether the underlying system is a human brain, a turbulent fluid, or a cellular automaton, the behavior it exhibits will correspond to a computation of equivalent sophistication.
Two-operator logic [axioms]
If one allows two operators then one can get standard logic if one of these operators is forced to be Not and the other is forced to be And , Or or Implies —or in fact any of operators 1, 2, 4, 7, 8, 11, 13, 14 from page 806 .
At every step in the procedure, regularities are tested for that would imply the possibility of an infinite repetitive pattern.