Review | Biological Arrow of Time: Emergence of Tangled Information Hierarchies and Self-modelling Dynamics

Introduction

The concept of open-ended evolution has long been a cornerstone in understanding biological complexity. It refers to the continual production of novel forms and functions within evolving systems, a property that distinguishes biological evolution from mere adaptive change. Historically, this idea has roots in Darwinian natural selection but has since expanded with theoretical models from complex systems, artificial life, and computation theory.

A critical distinction in this discourse has been introduced by Pattee and Sayama in their work Evolved Open-Endedness, Not Open-Ended Evolution. They argue that open-endedness itself evolves rather than being a precondition for evolution. This view shifts the focus from searching for predefined mechanisms of open-ended evolution to understanding how the capacity for open-endedness emerges within evolving systems.

In their recent paper Biological Arrow of Time: Emergence of Tangled Information Hierarchies and Self-Modelling Dynamics, Prokopenko et al. present a computational-theoretic framework to describe biological complexification. They propose that biological evolution generates computational novelty in an open-ended manner within the Gödel–Turing–Post recursion-theoretic framework. In this review, I will examine the core arguments of this paper, tracing their connections with major evolutionary transitions and the computational limits of biological systems, which will be discussed in a future series of essays dedicated to relational biology.

Evolutionary Transitions

Section 2 of Biological Arrow of Time aligns with classical models of major evolutionary transitions. Building on Maynard Smith and Szathmáry’s framework, the authors explore how new information-processing structures emerge to support increased biological complexity. This perspective resonates with Kun’s insights in The Major Evolutionary Transitions and Codes of Life, which argue that information encoding systems (or “codes of life”) precede and facilitate such transitions.

The interplay between evolutionary transitions and codes of life reveals a fundamental characteristic of biological evolution: the emergence of new levels of individuality and inheritance systems. Prokopenko et al. argue that tangled information hierarchies—self-referential feedback loops between macro- and micro-scale biological structures—serve as the foundation for such transitions. This hypothesis suggests a computational scaffold for understanding the origin of novel biological organization.

Undecidability

Later the authors of Biological Arrow of Time advance a provocative claim: undecidability is a necessary feature of open-ended evolution. Drawing from formal methods in recursion theory, the authors frame biological complexification as an iterative expansion of problem-space, resolving tensions through meta-simulation. Such expansion of problem-space reminded me of the TAME’s framework proposed by Michael Levin.

This argument also aligns with Hernández-Orozco et al.’s Undecidability and Irreducibility Conditions for Open-Ended Evolution and Emergence, which asserts that systems capable of sustained complexity growth must be undecidable. Similarly, Abrahão et al.’s Learning the Undecidable from Networked Systems explores how biological and artificial systems may exploit networked computation to exceed the Turing limit.

Prokopenko et al. extend these ideas by conceptualizing evolutionary progress as a sequence of computational ‘jumps’ akin to oracle machines. Each evolutionary transition represents a resolution of prior computational inconsistencies, yet introduces new undecidable problems, ensuring the continuation of open-ended evolution.

Downward Causation

A central theme in the mid part of Biological Arrow of Time is the role of causality in biological complexification. The authors invoke downward causation—the idea that higher-level structures exert control over lower-level dynamics—to explain the persistence of tangled hierarchies. However, this perspective is controversial even today, in the mid 21st century.

Critically, Noble et al. in Biological Relativity Requires Circular Causality but Not Symmetry of Causation argue that downward causation is an observational artifact rather than an intrinsic feature of biological systems. They propose circular causality as a more robust explanatory framework, where interactions between levels are reciprocal but not necessarily hierarchical.

Rather than assuming that higher-level structures dictate lower-level behaviors, circular causality suggests that constraints emerge dynamically through bidirectional interactions. This model better accommodates the distributed nature of biological regulation and self-organization, making it a stronger alternative to downward causation in Prokopenko et al.’s framework.

Tangled Hierarchies

Towards the end of their paper, the authors introduce the concept of tangled information hierarchies, distinguishing between those with and without self-modelling capabilities. These hierarchies encode compressed representations of environmental patterns, enabling efficient information processing within biological systems.

A simple example drawn from the paper illustrates this idea: enzyme networks in metabolism. The feedback regulation of metabolic pathways allows cells to predict and preemptively adjust to environmental fluctuations, embodying a form of computational self-modelling. As tangled hierarchies become more complex, they facilitate increasingly sophisticated anticipatory mechanisms, driving major evolutionary innovations such as neural networks and cognitive systems.

Conclusion

The final section of Biological Arrow of Time synthesizes its computational perspective on biological evolution. The authors make strong assumptions about the universal applicability of recursion theory to biological systems, which warrants scrutiny. While their framework provides a compelling formalization of open-ended evolution, it risks oversimplifying the biochemical and ecological constraints that shape evolutionary dynamics. Is it true that the substrate does not matter? If so, why cannot we build complex artificial systems as those observed based on carbon?

And many other key questions remain open: How do tangled hierarchies interact with environmental selective pressures? To what extent can computational undecidability explain biological complexity without invoking extraneous metaphysical assumptions? Can circular causality (or causal spreading) fully replace downward causation in this framework?

Overall, Biological Arrow of Time presents a fascinating intersection of theoretical biology and computation. By integrating concepts from recursion theory, self-reference, and information processing, it offers a novel perspective on open-ended evolution. While certain aspects of its framework invite further refinement, its emphasis on computational novelty as a driver of biological complexity represents a significant contribution to evolutionary theory.