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Among s = 3 , k = 2 machines there are 314 machines that do the same computation as 1507, but none any faster.
The axioms given can prove most of the results in an elementary geometry textbook—indeed all results that are about geometrical figures such as triangles and circles specified by a fixed finite number of points, but which do not involve concepts like area.
Existence and uniqueness [in PDEs]
Unlike systems such as cellular automata, PDEs do not have a built-in notion of "evolution" or "time".
Systems based on constraints do not have initial conditions.
When I started doing particle physics in the mid-1970s I assumed—like most theoretical scientists—that the results of experiments could somehow always be treated as rigid constraints on models.
And I also made some efforts to do actual biological experiments, but I gave up when it seemed that the species of molluscs I wanted to study were difficult, if not impossible, to keep in captivity.
Much as in the previous section, even if paths do not converge for every possible string, it can still be true that paths converge for all strings that are actually generated from a particular initial string.
But it turns out that very little is normally gained by doing this.
So how does all of this relate to class 2 behavior?
And indeed to assume that it does is effectively just to ignore the fundamental question of where randomness in nature comes from.