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terms. And this has become all the more relevant as its replication with technology begins to seem realistic. But what the Principle of Computational Equivalence suggests is that abstract descriptions will never ultimately distinguish us from all sorts of other systems in nature and elsewhere. And what this means is that in a sense there can be no abstract basic science of the human condition—only something that involves all sorts of specific details of humans and their history.

So while we might have imagined that science would eventually show us how to rise above all our human details what we now see is that in fact these details are in effect the only important thing about us.

And indeed at some level it is the Principle of Computational Equivalence that allows these details to be significant. For this is what leads to the phenomenon of computational irreducibility. And this in turn is in effect what allows history to be significant—and what implies that something irreducible can be achieved by the evolution of a system.

Looking at the progress of science over the course of history one might assume that it would only be a matter of time before everything would somehow be predicted by science. But the Principle of Computational Equivalence—and the phenomenon of computational irreducibility—now shows that this will never happen.

There will always be details that can be reduced further—and that will allow science to continue to show progress. But we now know that there are some fundamental boundaries to science and knowledge.

And indeed in the end the Principle of Computational Equivalence encapsulates both the ultimate power and the ultimate weakness of science. For it implies that all the wonders of our universe can in effect be captured by simple rules, yet it shows that there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.

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