Models show limits on predicting free will using computer algorithms

Ontological free will as incompressible information adjunction: A noncomputability boundary beyond P versus NP

Logic in Computer Science

Summary

The paper explores a mathematical model of free will where before a decision, many outcomes are possible without highlighting one as the chosen future. The authors show that once a choice is made, the information revealing that choice is essentially incompressible—that is, it can’t be predicted or simplified by any algorithm using only past data. This suggests a boundary in computability about predicting choices, distinct from known problems about speed or efficiency in computing. However, the authors do not claim humans actually have this kind of free will or solve other famous computer science problems.

What this means in practice

  • For complexity theorists: Identify a conceptual boundary distinguishing computability from computational complexity in predicting choice events.
  • For philosophers of mind: Provide a formal model to discuss limits on deterministic prediction of free choice in philosophical debates.

A theory result. No direct application yet.

Authors

J{é}rome Clech

Abstract

We study a conditional model of ontological free will in which a pre-act state structures several coherent global continuations without intrinsically distinguishing one as the future actualisation. The topos-theoretic component is formalised by a choice sheaf and by the action of automorphisms preserving the pre-act data: the absence of a fixed point rules out any natural equivariant selection. An act changes an unpointed object into a pointed one and reduces its symmetry group to a stabiliser. Independently, a causal algorithmic incompressibility axiom imposes nearly maximal online description complexity on the actual choices. Uniformly observable post-act traces then allow their reconstruction. We prove a conditional transfer result: such traces must carry asymptotically all the singularisation information unavailable in the pre-act regime, and no uniform Turing predictor computes the choices from causal histories alone. The formalism proves neither that human beings satisfy the model nor a separation of P from NP; it identifies a boundary at which prediction concerns the existence of a computable function rather than its time complexity.
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