2.6 The Principle of Computational Equivalence

summary

The Principle of Computational Equivalence, along with the Principle of Computational Irreducibility (covered in Lesson 2.2), are the two main ideas proposed by Stephen Wolfram and described in his book, A New Kind of Science (2002).
The Principle of Computational Equivalence is the more general of the two principles and implies the Principle of Computational Irreducibility.
The Principle of Computational Equivalence states that once a system can perform behavior that is complex, that system is as complex as any other system found in the universe and is computationally equivalent in its sophistication.
Following this principle, cellular automata programs like Rule 110 Cellular Automaton, the human brain, and even the evolution of weather systems, are computationally equivalent.
Observing how rules progress in cellular automata like rule 30 and rule 110 (simple programs with very complex behavior) can explain how rules govern systems in nature.
The computer revolution was launched after the discovery of a universal computer when it was shown that just by changing the software in a piece of hardware, you could run any computation you wanted.
Computational irreducibility can be looked at as a way to reconcile determinism and free will in that there are fixed underlying rules, but you can’t know the outcomes of those rules unless you watch them unfold.