Reproducing quantum phenomena Given molecular dynamics it is much easier to see how to reproduce fluid mechanics than rigid-body mechanics—since to get rigid bodies with only a few degrees of freedom requires taking all sorts of limits of correlations between underlying molecules.

For it shows that all sorts of sophisticated characteristics can emerge from the very same kinds of simple components. … In addition, the Principle of Computational Equivalence implies that all sorts of systems in nature and elsewhere will inevitably exhibit features that in the past have been considered unique to intelligence—and this has consequences for the mind-body problem, the question of free will, and recognition of other minds.

And in the end there are then all sorts of substitution systems which have the property that the causal networks they generate are always independent of the order in which their rules are applied.

Free from any effects of terrestrial biological evolution might it have developed all sorts of higher forms of perception and analysis?

But in the fifty or so years since the phenomenon of universality was first identified, all sorts of types of systems have been found to be able to exhibit universality.

And certainly there are all sorts of pictures in this book that lend support to this idea.

It is a little like what happens in thermodynamics, where all sorts of complicated microscopic motions are identified as corresponding in some uniform way to a notion of heat.

And as a result all sorts of objections to the principle will no doubt be raised.

And if there was some common higher form of regularity its discovery would no doubt lead to all sorts of important new advances in science and mathematics.

But in fact, in the fifteen years or so since I first emphasized the importance of cellular automata all sorts of traditional mathematical work has actually been done on them.