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But my discussion of history is inevitably less precise.
Shells where successive whorls do not touch (as in the first picture on row (c) of page 415 ) appear to be significantly less common than others, perhaps because they have lower mechanical rigidity.
But as one looks at smaller molecules they become less specific to living systems.
In ontology (theory of being) the Principle of Computational Equivalence implies that special components are vastly less necessary than might have been thought.
Small galaxies such as globular clusters that contain less than a million stars seem to exhibit a certain uniformity which suggests a kind of equilibrium.
Other less spectacular examples include Exp[ π ]- π and 163/Log[163] .
… For any irrational number this quantity cannot be less than 2, while for algebraic irrationals Klaus Roth showed in 1955 that it can only have finitely many peaks that reach above any specified level.
In general, such approximations tend to work better for systems in larger numbers of dimensions, where correlations tend to be less important.
In fact, for a system involving k colors the pattern produced will always be essentially just one of the patterns obtained from an additive rule with k or less colors.
If one considers all 2 n possible sequences (say of 0's and 1's) of length n then it is straightforward to see that most of them must be more or less algorithmically random.
And in 1891 Giuseppe Peano gave essentially the Peano axioms listed here (they were also given slightly less formally by Richard Dedekind in 1888)—which have been used unchanged ever since.