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universe, while as an abstract fact it could simply represent an incorrect deduction, and even as a definition it could prove not useful or relevant.

But as more and more evidence is accumulated for phenomena that would follow from the principle, so it becomes more and more reasonable to expect that at least in some formulation or another the principle itself must be valid.

As with many fundamental principles the most general statement of the Principle of Computational Equivalence may at first seem quite vague. But almost any specific application of the principle will tend to suggest more specific and precise statements.

Needless to say, it will always be possible to come up with statements that might seem related to the Principle of Computational Equivalence but are not in fact the same. And indeed I suspect this will happen many times over the years to come. For if one tries to use methods from traditional science and mathematics it is almost inevitable that one will be led to statements that are rather different from the actual Principle of Computational Equivalence.

Indeed, my guess is that there is basically no way to formulate an accurate statement of the principle except by using methods from the kind of science introduced in this book. And what this means is that almost any statement that can, for example, readily be investigated by the traditional methods of mathematical proof will tend to be largely irrelevant to the true Principle of Computational Equivalence.

In the course of this book I have made a variety of discoveries that can be interpreted as limited versions of the Principle of Computational Equivalence. And as the years and decades go by, it is my expectation that many more such discoveries will be made. And as these discoveries are absorbed, I suspect that general intuition in science will gradually shift, until in the end the Principle of Computational Equivalence will come to seem almost obvious.

But as of now the principle is far from obvious to most of those whose intuition is derived from traditional science. And as a result all sorts of objections to the principle will no doubt be raised. Some of them will presumably be based on believing that actual systems have

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