Functions, representations, and zombies: Information theoretic perspectives on three standard confusions in cognitive science (Q2776469)

Many areas, ranging from foundations of computing to philosophy to cognitive psychology, use the notions of interpretation or model. Traditionally, the intuitive notion that one system models another one has been formalized as the existence of a 1-1 correspondence between the original system (e.g., the computer or the human brain) and the system that it tries to simulate (e.g., a chemical reactor), a correspondence that preserves the desired functionality of the system. The author argues that this formalization does not adequately capture the intuitive meaning of the notion of interpretation. Indeed, the intuitive notion indicates that if we know how the model works, it helps us to predict how the original system works; however, in many cases, we can find a purely mathematical 1-1 correspondence in which the computational complexity of this correspondence is so high that it is faster to analyze the original system from scratch (without using the model's results at all) than to translate the model's results into predictions of the original system's behavior. To capture the requirement that an interpretation be useful in predicting the original system's behavior, the author proposes to use Kolmogorov complexity: a system \(b\) is a model of a system \(a\) if the Kolmogorov complexity \(K(A)\) of the results of the system \(a\) is larger than the conditional complexity \(K(A|B)\) provided that we know the results \(B\) of system \(b\). The author also argues that similar Kolmogorov complexity ideas can help in formalizing other intuitive notions about systems, e.g., when a system can be reasonably represented as a collection of subsystems.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00020].