Microsoft Word Kurzweil, Ray The Singularity Is Near doc

Just how complex are the results of class automata?
Wolfram effectively sidesteps the issue of degrees of complexity. I agree that a degenerate pattern such 
as a chessboard has no complexity. Wolfram also acknowledges that mere randomness does not represent 
complexity either, because pure randomness becomes predictable in its pure lack of predictability. It is true 
that the interesting features of class 4 automata are neither repeating nor purely random, so I would agree 
that they are more complex than the results produced by other classes of automata. 
However
, there is nonetheless a distinct limit to the complexity produced by class 4 automata. The 
many images of such automata in Wolfram's book all have a similar look to them, and although they are 
nonrepeating, they are interesting (and intelligent) only to a degree. Moreover, they do not continue to 
evolve into anything complex, nor do they develop new types of features. One could run these for trillions or 
even trillions of trillions of iterations and the image would remain at the same limited level complexity. They 
do not evolve into, say, insects or humans or Chopin preludes or anything else that we might consider of a 
higher order of complexity than the streaks and intermingling triangles displayed in these images. 
Complexity is a continuum. Here I define "order" as "information that fits a purpose."
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A completely 
predictable process has zero order. A high level of information alone does not necessarily imply a high level 
of order either. A phone book has a lot of information, but the level of order of that information is quite low. A 
random sequence is essentially pure information (since it is not predictable) but has no order. The output of 
class 4 automata does possess a certain level of order, and it does survive like other persisting patterns. But 
the patterns represented by a human being has a far higher level of order, and of complexity. 
Human beings fulfill a highly demanding purpose: they survive in a challenging ecological niche. Human 
beings represent an extremely intricate and elaborate hierarchy of other patterns. Wolfram regards any 
patterns that combine some recognizable features and unpredictable elements to be effectively equivalent to 
on another. But he does not show how a class 4 automaton can ever increase it complexity, let alone 
become a pattern as complex as a human being. 
There is a missing link here, one that would account for how one gets from the interesting but ultimately 
routine patterns of a cellular automaton to the complexity of persisting structures that demonstrate higher 
levels of intelligence. For example, these class 4 patterns are not capable of solving interesting problems, 
and no amount of iteration moves them closer to doing so. Wolfram would counter than a rule 110 
automaton could be used as a "universal computer."
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However, by itself, a universal computer is not 
capable of solving intelligent programs without what I would call "software." It is the complexity of the 
software that runs on a universal computer that is precisely the issue. 
One might point out that class 4 patterns result from the simplest possible automata (one-dimensional, 
two-color, two-neighbor rules). What happens if we increase the dimensionality—for example, go to multiple 
colors or even generalize these discrete cellular automata to continuous function? Wolfram address all of 
this quite thoroughly. The results produced from more complex automata are essentially the same as those 
of the very simple ones. We get the same sorts of interesting by ultimately quite limited patterns. Wolfram 
makes the intriguing point that we do not need to use more complex rules to get complexity in the end result. 
But I would make the converse point that we are unable to increase the complexity of the end results 
through either more complex rules or further iteration. So cellular automata get us only so far.