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And indeed, within my company I have been able to build up a remarkable group of people—who have supported my efforts in all sorts of ways.
The idea was to have say n quantum spins (each representing a so-called qubit), then to do computations much like in the reversible logic systems of page 1097 or the sorting networks of page 1142 by applying some appropriate sequence of elementary operations.
But given an enumeration of primitive recursive functions (say ordered first by LeafCount , then with Sort ) in which the m th function is w[m] diagonalization (see page 1128 ) yields the function w[x][x] shown below which cannot be primitive recursive.
Just as for all sorts of other systems with complex behavior, some idea of overall properties of Diophantine equations can be found on the basis of an approximation of perfect randomness.
But cellular automata—and especially 1D ones—make the phenomena particularly clear, which is why even after investigating all sorts of other systems 1D cellular automata are still the most common examples that I use in this book.
In the 1940s, however, successes in the analysis of logistical and electronic systems led to discussion of the idea that it might be possible to set up some sort of general approach to complex systems—especially biological and social ones.
As mentioned in the main text, there were by the late 1950s already all sorts of general-purpose computers on which simulations of cellular automata would have been easy to perform.
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