Search NKS | Online
91 - 100 of 200 for Implies
But the Principle of Computational Equivalence implies that this is not the case.
For the picture implies that both
and its negation can be proved to be true statements.
But the universality of rule 110 implies that such statements must in general be undecidable.
simple programs to brains to our whole universe, the principle implies that there is a basic equivalence that makes the same fundamental phenomena occur, and allows the same basic scientific ideas and methods to be used.
For it is what implies that
But it has never been at all clear just why this theory should imply that complexity is generated.
From experience with traditional mathematical models, however, one might then assume that this would inevitably imply that all plants and animals would have forms that look quite similar.
What one sees in these pictures is that after event 4, different choices of replacements are made in the two cases, and the causal relationships implied by these replacements are different.
And the point is that causal invariance then implies that the same underlying rules can be used to update the network in all such cases.
But such a reduction is exactly what is needed to correspond to positive curvature of the kind implied by the Einstein equations in the presence of ordinary matter.