And indeed this is true of any system. But as a practical matter we often end up describing what systems do in terms of purpose when this seems to us simpler than describing it in terms of mechanism.

And so for example if we can identify some simple constraint that a system always tries to satisfy it is not uncommon for us to talk of this as being the purpose of the system. And in fact we do this even in cases like minimization of energy in physical systems or natural selection for fitness in biological systems where nothing that we ordinarily think of as intelligence is involved.

So the fact that we may be able to interpret a system as achieving some purpose does not necessarily mean that the system was really created with that purpose in mind. And indeed just looking at the system we will never ultimately be able to tell for sure that it was.

But we can still often manage to guess. And given a particular supposed purpose one potential criterion to use is that the system in a sense not appear to do too much that is extraneous to that purpose.

And so, for example, in looking at the pictures below it would normally seem much more plausible that rule 254 might have been set up for the purpose of generating a uniformly expanding pattern than that rule 30 might have been. For while rule 30 does generate such a pattern, it also does a lot else that appears irrelevant to this purpose.

So what this might suggest is that perhaps one could tell that a system was set up for a given purpose if the system turns out to be in a sense the minimal one that achieves that purpose.

But an immediate issue is that in traditional engineering we normally do not come even close to getting systems that are minimal. Yet it seems reasonable to suppose that as technology becomes more advanced it should become more common that the systems it sets up for a given purpose are ones that are minimal.

So as an example of all this consider cellular automata that achieve the purpose of doubling the width of the pattern given in their input. Case (a) in the picture on the next page is a cellular automaton one might construct for this purpose by using ideas from traditional engineering.

But while this cellular automaton seems to have little extraneous going on, it operates in a slow and sequential way, and its underlying

If the purpose is to generate a uniformly expanding pattern it seems more plausible that the top cellular automaton should have been the one created for this purpose.

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