Biological arrow of time: Emergence of tangled information hierarchies and self-modelling dynamics (2409.12029v1)

Abstract: We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism's components, leading to self-modelling "tangled hierarchies". Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the G\"odel--Turing--Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

• The paper presents a computation-theoretic framework that models evolution as an open-ended meta-simulation driven by tangled information hierarchies.
• It distinguishes between hierarchies without self-modelling (TH-I) and those with self-modelling (TH-II) to explain major transitions in biological complexity.
• The study implies applications in AI by suggesting systems capable of recursive self-improvement and adaptive evolution.

Insights into the Emergence of Biological Complexity and the Arrow of Time

In addressing the phenomenon of increasing biological complexity, the paper "Biological arrow of time: Emergence of tangled information hierarchies and self-modelling dynamics" provides a compelling formal framework to understand open-ended evolution. The research pivots on the computational and information-processing dynamics that underpin major evolutionary transitions. By interpreting biological organisms as hierarchical dynamical systems, the paper advances a computation-theoretic hypothesis for biological complexification, leveraging the G\"odel--Turing--Post recursion-theoretic framework.

Key Concepts and Theoretical Foundation

Computational Dynamics Underpinning Evolution

The researchers posit that biological organisms generate regularities in their phase spaces through interactions with their environment. These emergent patterns, encoded within an organism's components, set the stage for what the authors term "tangled hierarchies." The encoded macro-scale patterns within micro-scale components foster computational inconsistencies unresolved within the current evolutionary scope. This tension underlies the driving force for major evolutionary transitions.

Tangled Hierarchies and Self-Reference

The study makes a critical distinction between two types of tangled hierarchies: those without and those with self-modelling capabilities. Type I hierarchies (TH-I) lack self-modelling and cannot compress or encode emergent macro-scale regularities, while Type II hierarchies (TH-II) incorporate self-modelling, encoding some of these regularities. This differentiation between TH-I and TH-II provides a nuanced understanding of how self-modelling dynamics contribute to biological complexity.

Open-Ended Meta-Simulation

A core argument is that biological evolution can be framed as an open-ended computational meta-simulation, analogous to Turing $\alpha$-oracle machines. These higher-order systems resolve lower-order computational inconsistencies, thus expanding the problem-space continually. This expansion is conceptualized as a biological arrow of time, characterized by an irreversible increase in complexity.

Practical and Theoretical Implications

Evolutionary Transitions and Coding Thresholds

The paper's interpretation of major evolutionary transitions asserts that encoded self-descriptions allow systems to innovate, underpinned by a balance of replicative accuracy and environmental adaptability. For instance, the transition from horizontal gene transfer (HGT) to vertical gene transfer (VGT) exemplifies the shift from imprecise replication to more robust encoded replication processes, contributing to genome complexity and stability.

Computational Novelty and Robust Replication

The emergence of encoded self-descriptions, a haLLMark of TH-II, facilitates robust replication by capturing and preserving beneficial regularities. These functional self-descriptions, akin to biological codes, allow organisms to handle environmental fluctuations more effectively. The conjecture is supported by comparing the efficiency of replicating optimal paths in TH-I with the genotype-phenotype relationship in TH-II.

Theoretical Synergies and Future Directions

Drawing connections between various schools of thought, such as DKS (Dynamic Kinetic Stability) and Assembly Theory, the paper grounds its hypotheses in well-established theoretical paradigms. These include the principles of collective behavior in non-equilibrium systems and the capacity for self-referential systems to generate complexity via recursive computation.

Speculations on the Future of AI

Applying these biological principles to AI, one might envisage AI systems capable of recursive self-improvement, navigating increasingly complex problem-spaces. Such systems could employ self-modelling algorithms that facilitate robust adaptation to novel environments, emulating the evolutionary transitions described in biological systems.

Conclusion

By framing biological evolution within the G\"odel--Turing--Post recursion-theoretic framework, the paper advances our understanding of complex adaptive systems. It underscores the central role of computational novelty and meta-simulation in driving biological complexity. This perspective not only enriches our theoretical grasp of evolution but also heralds new possibilities for designing AI systems that mirror the adaptive capacities of biological organisms.