The blocks needed to represent each cell are now larger, since they must include all 32 cases in the rule.

When this line is gray, it then absorbs all other lines coming from the left until the next dashed line arrives.

But when one examines the known examples of such systems—all of which have very intricate underlying rules—one finds that even though the particular part of their behavior that is identified as output is sufficiently restricted to avoid universality, almost every other part of their behavior nevertheless does exhibit universality—just as one would expect from the Principle of Computational Equivalence.

For even though all the components of our brains presumably follow definite laws, I strongly suspect that their overall behavior corresponds to an irreducible computation whose outcome can never in effect be found by reasonable laws.

And certainly if one allows no more than 4-state 2-color Turing machines I have been able to establish by explicitly searching all 4 billion or so possible rules that there is absolutely no way to speed up the computations in pictures (i) through (l).

And one might think that if all such pathways could be found then this would immediately show that no intelligence was involved.

Practical arguments [about exterrestrials] If extraterrestrials exist at all an obvious question—notably asked by Enrico Fermi in the 1940s—is why we have not encountered them. … (It is notable that just a couple of decades ago, it was usually assumed that extraterrestrials would inevitably want to use large amounts of energy, and so would eventually for example tap all the output of a star.

In the 1960s there was also interest in so-called lattice gases in which—by analogy with spin systems like the Ising model—discrete particles were placed in all possible configurations on a lattice subject to certain local constraints, and average equilibrium properties were computed. … Yet despite all the work that has been done, the fundamental issues about the origins of turbulence that I had originally planned to investigate in cellular automaton fluids have remained largely untouched.

(Note that given explicit coordinates, one can check whether one is in d or more dimensions by asking for all possible points Det[Table[(x[i] - x[j]) . … Still another related approach is to consider coloring the edges of a network: if there are d + 1 possible colors, all of which appear at every node, then it follows that d coordinates can consistently be assigned to each node.)

And the hypothesis was then suggested that all these particles might actually be composed of just three more fundamental particles that became known as quarks. An alternative so-called democratic or bootstrap hypothesis was also suggested: that somehow any particle could just be viewed as a composite of all others with the same overall properties—with everything being determined by consistency in the web of interactions between particles, and no particles in a sense being more fundamental than others. … And indeed—apart from few rare suggestions to the contrary—the same is now assumed throughout mainstream practical particle physics for all of the basic particles that appear in the Standard Model.