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Wolfram holds that his principle is a stronger claim than the Church-Turing thesis because it is about the natural world rather than abstract models of computation. But saying that natural processes “can be viewed as computations” strikes me as a statement about theory choice more than a hypothesis about the natural world.
Also, with qualifications like “almost” and undefined terms like “obviously simple”, his hypothesis may be unfalsifiable. Falsifiability is an idea from the philosophy of science, proposed by Karl Popper as a demarcation between scientific hypotheses and pseudoscience. A hypothesis is falsifiable if there is an experiment, at least in the realm of practicality, that would contradict the hypothesis if it were false.
For example, the claim that all life on earth is descended from a common ancestor is falsifiable because it makes specific predictions about similarities in the genetics of modern species (among other things). If we discovered a new species whose DNA was almost entirely different from ours, that would contradict (or at least bring into question) the theory of universal common descent.
On the other hand, “special creation”, the claim that all species were created in their current form by a supernatural agent, is unfalsifiable because there is nothing that we could observe about the natural world that would contradict it. Any outcome of any experiment could be attributed to the will of the creator.
Unfalsifiable hypotheses can be appealing because they are impossible to refute. If your goal is never to be proved wrong, you should choose hypotheses that are as unfalsifiable as possible.
But if your goal is to make reliable predictions about the world — and this is at least one of the goals of science — unfalsifiable hypotheses are useless. The problem is that they have no consequences (if they had consequences, they would be falsifiable).
For example, if the theory of special creation were true, what good would it do me to know it? It wouldn’t tell me anything about the creator except that he has an “inordinate fondness for beetles” (attributed to J. B. S. Haldane). And unlike the theory of common descent, which informs many areas of science and bioengineering, it would be of no use for understanding the world or acting in it.