Principle of Computational Equivalence

The Principle of Computational Equivalence is the claim, formulated by Stephen Wolfram, that almost all computational processes that are not obviously simple can perform computations of equivalent sophistication. In other words, once a system crosses a minimal threshold of complexity, it is computationally universal — capable, in principle, of performing any computation that any other system can perform.

The principle dissolves the hierarchical picture in which some systems (human brains, digital computers) are "intelligent" while others (weather systems, chemical reactions) are merely physical. On this view, the difference is not computational capacity but computational history: what program the system is running, and what inputs it has received. The principle has been criticized for lacking formal proof and for conflating universal computation with interesting computation, but it remains a foundational claim in the computational universe program.