Notes

Chapter 12: The Principle of Computational Equivalence

Section 3: The Content of the Principle


Criteria for universality [in systems]

To be universal a system must in effect be able to emulate any feature of any system. So at some level any feature can be thought of as a criterion for universality. Some features—like the possibility of information transmission—may be more obvious than others, but despite occasional assertions to the contrary in the scientific literature none is ever the whole story. Since any given universal system must be able to emulate any other universal system it follows that within any such system it must in a sense be possible to find any known universal system. But inevitably the encoding will sometimes be very complicated. And in practice if there are many simple rules that are universal they cannot all be related by simple encodings. (See also the end of Chapter 11.)

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