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I actually disagree that humans don't think about problems algorithmically. Obviously we have reflexes that aren't quite what you'd call algorithmic, and we're capable of thinking irrationally, but a lot of what we do is done algorithmically. Driving a car is a process of taking in visual input about what's on the road, how fast you're going, etc. and adjusting how you drive accordingly. There's even an argument that multiplication is done algorithmically. Sure I remember that 6*8 is 48, but when I read a problem like that i first see the 6 and understand i can probably do the problem mentally, regardless of the second number. When I see the 8, I remember that this information is stored in such a way that I can immediately retrieve the answer, much like a computer could have hash tables of answers to mathematical problems and provide the answer by recognizing the problem.

I think the important question to consider when trying to determine if CA are so important they're worth studying almost to the exclusion of all else is this: Accepting the possibility that CA are the basis for everything that has developed since the big bang, do they necessarily produce structures which are themselves irreducible? To provide a similar example, when psychology entered its behaviorist phase sociology came under attack as studying phenomena which were fundamentally psychological. Sociology had to problematize this idea by showing that there were social phenomena not atomistically reducible to a collection of individuals behaving in the same way.

I talked some last week about Durkheim's collective conscience, and again it is a useful example. The collective conscience is born out of the shared values of individuals in a society. However, it takes on its own existence separate from these individuals when it becomes self-replicating across generations by means of social pressure which cannot be brought back down to the level of individuals. This may not have been the most cogent presentation of this argument, but hopefully my point is clear.

So are there parts of the world which originate in CA but are no longer reducible to such? I feel the obvious answer is yes, but find myself hard pressed to give a clear example. Human emotions may be an arguable example. Certainly we can imagine the patterns of neurons and the levels of chemicals that create emotion in a physical sense emerging from CA in a very early stage of evolution. But isn't it also possible that the modern experience of love is constituted not by its origins in CA but in the cultural achievements which have shaped our ideal of love? If this is the case, it seems unlikely to me that the emotion remains something reducible to CA.