2.2 The Principle of Computational Irreducibility

summary

In the computational universe, there are computationally irreducible systems that exist that can be useful, for example being able to generate random numbers.
The Principle of Computational Irreducibility is one of two main ideas proposed by Stephen Wolfram and described in his book, A New Kind of Science. The other, the Principle of Computational Equivalence, is covered in Lesson 2.6.
The Principle of Computational Irreducibility states that the only way to determine the answer to a computationally irreducible question is to perform or simulate the computation.
Some cellular automata systems highlighted in A New Kind of Science, like rule 110*, show repetitive patterns alongside random and more complex ones.
Rule 30 Cellular Automaton is another example highlighted in A New Kind of Science that demonstrates the limitation of predictive science and is one example that helps to visualize the Principle of Computational Irreducibility.
Computational irreducibility is the phenomena that simple rules can cause complicated behavior and impedes our ability to make predictions or apply mathematical equations to understand what will happen.
*Note: A full list of cellular automaton rules appear in Chapter 3, “The World of Simple Programs”, in Wolfram’s book, A New Kind of Science.