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In case (b), only the single network shown is allowed.
So the only thing that ultimately makes sense is to measure space and time taking each connection in the causal network to correspond to an identical elementary distance in space and elementary interval in time.
For the only way we end up actually being able to measure physical distances is in effect by looking at the propagation of photons or other particles.
And indeed I believe that it is only with the discoveries in this book that one is finally now in a position to develop a real understanding of what randomness is.
For it is rather common to see cases in which only a few features of a system may be difficult to describe—and depending on whether or not a given program happens to be sensitive to these features it can ascribe either a quite high or a quite low complexity to the system.
And indeed the only reliable strategy is usually just to look for cases in which there are huge differences between results for particular pieces of data and for typical sequences.
The basic idea is to translate the rule for a given cellular automaton into a formula that depends on three variables a 1 , a 2 and a 3 whose values correspond to the colors of the three initial cells. … They are set up so that only at most one term in each formula is ever relevant for any particular configuration of colors.
For in a standard database one tends to be able to find only data that meets some precise specification, such as containing an exact match to a particular string of text.
But the point is that with such a setup detailed changes in the input to the first layer of cells only rarely end up having an effect on output from the last layer of cells.
For among other things, whereas in the process of thinking we routinely manage to retrieve remarkable connections almost instantaneously from memory, we tend to be able to carry out logical reasoning only by laboriously going from one step to the next.