non-computability

The idea that future states of a system may be determined but not algorithmically computable, implying limits on predictability and free will.

1 chapter across 1 book

The Emperor's New Mind (1989)Roger Penrose

part is not deterministic, and it introduces a completely random element into the time-evolution. Early on, various people leapt at the possibility that here might be a role for free will, the action of consciousness perhaps having some direct effect on the way that an individual quantum system might jump. But if R is really random, then it is not a great deal of help either, if we wish to do something positive with our free wills.

This chapter explores the limitations of determinism and computability in quantum mechanics, proposing that a new, non-algorithmic theory (CQG) may govern the quantum-classical boundary, allowing determinism without computability and potentially preserving free will. It also discusses the anthropic principle in both its weak and strong forms, evaluating its implications for consciousness and the universe. Finally, the chapter introduces quasi-crystals, highlighting their unusual fivefold symmetry that challenges classical crystallographic theorems and recounts their experimental discovery.