Search NKS | Online
121 - 130 of 200 for Implies
The existence of a fixed length scale at which such processes occur then almost inevitably implies that an embryo must develop in a somewhat hierarchical fashion.
But much more important is the fact that I do not believe in the distinction between space and its contents implied by the basic construction of a cellular automaton.
Following the discussion in the previous section , we know that whenever we find regularities, it implies that redundancy is present, and this in turn means that a shorter description can be given.
And in fact, as I mentioned in Chapter 7 , it essentially implies that no process based on definite rules can ever manage to generate randomness when there is no randomness before.
In a sense its most important consequence is that it implies that from a computational point of view a very wide variety of systems, with very different underlying structures, are at some level fundamentally equivalent.
It is truly remarkable that a system with such simple underlying rules should be able to perform what are in effect computations of arbitrary sophistication, but that is what its universality implies.
For it implies that even if in principle one has all the information one needs to work out how some particular system will behave, it can still take an irreducible amount of computational work actually to do this.
But what my discoveries about computational irreducibility now imply is that this is not in fact the case, and that instead there are many common systems whose behavior cannot in the end be determined at all except by something like an explicit simulation.
And now, what the Principle of Computational Equivalence implies is that in fact almost any system whose behavior is not obviously simple will tend to exhibit computational irreducibility.
But the existence of a compressed description does not on its own imply computational reducibility.