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Computational Irreducibility: Perspective, Nature, and Free Will
Computational Irreducibility is the principle that all intermediate computational steps must be performed to evolve a system from a state X to another state Y, with no shortcuts possible.
Although this is a simple concept, it has an exhilarating breadth, depth, and domain of applicability. I consider some here interesting ramifications starting from a very simple first principles formulation of a system that is used to consider philosophical issues.
1. Determinism vs. Non-Determinism is a Matter of Perspective
Are all events in the cosmos already predetermined? Or do events happen randomly? Do we really exercise free will, or is it an illusion? What is the nature of our agency over ourselves and our surroundings?
To more easily tackle and ponder these questions, let’s reduce this problem to a very simple system that we can think of intuitively with minimal formalism.
Let X be valid state of some system S.
This system could have a small space of states such as heads or tails in a coin, or a larger space such as the relative arrangement of water molecules in the ocean, or even larger such as the arrangements of all atoms in the universe including…
