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And this made informal definitions of complexity often include all sorts of detailed features of life (see page 1178 ). … In general it is possible to imagine setting up all sorts of definitions for quantities that one chooses to call complexity.
Nevertheless, starting in the 1970s many programs were written to simulate all sorts of scientific and technological systems, and often these programs in effect defined the models used.
One cannot for example sort n objects in less than about n steps since one must at least look at each object, and one cannot multiply two n -digit numbers in less than about n steps since one must at least look at each digit.
In practical trading, partly as an outgrowth of theories of business cycles, there had emerged all sorts of elaborate so-called technical analysis in which patterns of price movements were supposed—often on the basis of almost mystical theories—to be indicators of future behavior.
But the Principle of Computational Equivalence implies that in fact there are all sorts of statements that simply cannot be decided by any computational process in our universe.
History [of emergence of order]
The fact that despite initial randomness processes like friction can make systems settle down into definite configurations has been the basis for all sorts of engineering throughout history.
Note that the first example on page 507 has a canonical form consisting of a sorted string.
For if an ultimate model is going to be simple, then in a sense it cannot have room for all sorts of elements that are immediately recognizable in terms of everyday known physics.
But now that the book is out, all sorts of other people can begin to participate—adding their own personal achievements to the development of the intellectual structure that I have built in this book.
… And indeed from almost every page of this book there are all sorts of new questions that emerge.
And indeed in other situations it seems likely that there will be all sorts of other solutions to the classical equations that become important. … And Monte Carlo studies of such theories suggest all sorts of complex behavior, often similar in outline from what appears to occur in the corresponding classical field theories.