Zenith Grant Awardee

Markus Mueller

IQOQI

Co-Investigators

Andrew Garner, IQOQI

Project Title

Where agents and algorithms meet: free will and computational irreducibility

Project Summary

Do humans have free will? If so, can machines have free will too? In more technical terms, how can there be agency in a world that evolves according to stringent physical laws? We are proposing this project because we believe that information theory opens up a fascinating new take on this old problem. Consider a simple physical system that evolves according to physical laws: our solar system. Suppose we want to predict the position of planet Jupiter on New Year?s Eve 2050. To do this, it is sufficient to use Kepler?s laws (that every planet orbits the sun in an ellipse). That is, we can do a simple and fast computation that reliably predicts Jupiter?s position. But there are many physical systems whose behaviour cannot be predicted in such a simple way ? for example, the weather, a powerful computer, or the human brain. Information theory tells us that we must simulate all their details to extreme accuracy to predict their behaviour reliably. This is the idea of computational irreducibility as proposed by Stephen Wolfram. Our project will explore the mathematical foundations and applications of computational irreducibility, and use this to argue that physics and free will are, surprisingly, fundamentally compatible.

Technical Abstract

Do humans have free will? If so, can machines have free will too? How can there be agency in a world that evolves according to stringent physical laws? In this project, we will address these questions by taking an information-theoretic approach to computational irreducibility ? a promising concept proposed by Stephan Wolfram. Computational irreducibility describes processes whose behaviour cannot be reliably predicted, save for direct perfect simulation of all their details. What if the constitution of a decision-making agent is not its physical substrate (e.g. brain) but rather an abstract algorithm and related information. If this agent was computationally irreducible, predicting its decision would require perfect simulation ? equivalent to directly asking the agent itself about the decision. Does this constitute agency? In this project, we will provide a formal definition of computational irreducibility that can be applied to deterministic and stochastic processes. We shall investigate how this applies to existing complexity theory (particularly computational mechanics), and which concepts and consequences change when quantum information processing is also allowed. From this rigorous mathematical base, we shall then provide a precise notion of agency in the physical world in terms of computational irreducibility and relate it to existing information-theoretic notions of free will.