Comment on "Inferring Statistical Complexity"

TL;DR

This paper critically examines the longstanding measures of time series complexity introduced by Crutchfield and Young, highlighting persistent issues and clarifying their relevance within computational mechanics over the past three decades.

Contribution

It provides a critical analysis of the original measures, addressing unresolved faults and clarifying their role in the development of computational mechanics.

Findings

Identifies unresolved issues in the original complexity measures

Clarifies the relationship between complexity measures and nonlinear dynamics

Highlights the need for revised approaches in computational mechanics

Abstract

Nearly 30 years ago, J.P. Crutchfield and K. Young proposed in Phys. Rev. Lett. {\bf 63}, 105 (1989) some supposedly novel measures of time series complexity, and their relations to existing concepts in nonlinear dynamical systems. At that time it seemed that the multiple faults of this paper would make it obsolete soon. Since this has not happened, and these faults still infest the literature on what is now called "computational mechanics", I want here to rectify the situation.