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My strong belief—as I will argue in Chapter 12—is that at least in complete generality this will never be possible. But that does not mean that there cannot exist higher forms of perception and analysis that succeed in recognizing at least some regularities that our existing methods do not.

The results of this chapter, however, might seem to provide some circumstantial evidence that in practice even this might not be possible. For in the course of the chapter we have discussed a whole range of different kinds of perception and analysis, yet in essentially all cases we have found that the overall capabilities they exhibit are rather similar. Most of them, for example, recognize repetition, and some also recognize nesting. But almost none recognize anything more complex.

So what this perhaps suggests is that in the end there might be only certain specific capabilities that can be realized in practical methods of perception and analysis. And certainly it seems not inconceivable that there could be a fundamental result that the only kinds of regularities that both occur frequently in actual systems and can be recognized quickly enough to provide a basis for practical methods of perception and analysis are ones like repetition and nesting.

But there is another possible explanation for what we have seen in this chapter: perhaps it is just that we, as humans, are always very narrow in the methods of perception and analysis that we use. For certainly it is remarkable that none of the methods that we normally use ever in the end seem to manage to get much further than we can already get with our own built-in powers of perception. And what this perhaps suggests is that we choose the methods we use to be essentially those that pick out only regularities with which we are somehow already very familiar from our own built-in powers of perception.

For there is no difficulty in principle in constructing procedures that have capabilities very different from those of our standard methods of perception and analysis. Indeed, as one example, one could imagine just enumerating all possible simple descriptions of some particular type, and then testing in each case to see whether what one gets matches a piece of data that one has.

And in some specific cases, this might well succeed in finding extremely simple descriptions for the data. But to use such a method in

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From Stephen Wolfram: A New Kind of Science [citation]