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As the picture below shows, there are 16 different possible operators that take two arguments and allow two values, say true and false.
And with traditional intuition it has always seemed perfectly reasonable that it should take a system as complicated as a human to exhibit such capabilities—and that the whole elaborate history of life on Earth should have been needed to generate such a system.
It takes the fewest steps of any 3-color rule to generate its result.
There will be new questions formulated, but it will take time before it becomes clear when general theories are possible, and when one must instead inevitably rely on the details of judgement for specific cases.
Certainly it would be wonderful if one could just take the ideas and results in this book and somehow immediately use them to create models for all sorts of systems.
An alternative kind of model, somewhat analogous to the ones based on constraints on page 483 , is to take the pattern of evolution of a multiway system to define directly a complete spacetime network.
The effective mass for massive particles increases by a factor 1/Sqrt[1 - v 2 /c 2 ] at speed v , making it take progressively more energy to increase v .
Predicate logic on the other hand takes into account how such statements are built up from other constructs—like those in mathematics. … Monadic pure predicate logic—in which predicates always take only a single argument—reduces in effect to basic logic and is not universal.
[Computing] square roots
A standard way to compute √ n is Newton's method (actually used already in 2000 BC by the Babylonians), in which one takes an estimate of the value x and then successively applies the rule x 1/2 (x + n/x) .
Definitions of distance
Any measure of distance—whether in ordinary continuous space or elsewhere—takes a pair of points and yields a number.