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At some level, however, the basic problem has always been to understand how the seemingly simple components in a brain can lead to all the complexities of thinking.
Yet what the discoveries in this book now show is that there are all sorts of systems that have much simpler structures, but that can nevertheless perform very sophisticated tasks.
But in fact almost all the work—at least in one dimension—has concentrated on just the three specific equations on the facing page , together with a few others that are essentially equivalent to them.
For in one dimension it is possible to prove that any local set of constraints that can be satisfied at all can always be satisfied by some simple and purely repetitive arrangement of colors.
And since one certainly does not even know at any given time exactly where all these molecules are, the details of their effect on the motion of the grain will inevitably seem quite random.
But despite this, my strong suspicion is that of all the examples of complex behavior that we see in nature almost none can in the end best be explained in terms of constraints.
Then after an initial period where the models are often said to be too simplistic to be worth considering, there begin to be all sorts of extensions added that attempt to capture more effects and more details.
And indeed as one looks at more and more complex features of biological organisms—notably texture and pigmentation patterns—it becomes increasingly difficult to find any credible purpose at all that would be served by the details of what one sees.
But in most cases I strongly suspect that it is comparatively coarse features that tend to determine the success of an organism—not all the details of any complex behavior that may occur.
There are several reasons for this, all somewhat related.
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