How did life begin? Why are amino acids left-handed (homochiral) in living organisms? This paper suggests that these questions can be approached by analysing computational constraints in complex dynamical systems (chemical or not) that are not in equilibrium. I will propose a model based on the behavior of dynamic billiards on billiard tables shaped like asymmetry graphs (A-graphs) constructed from Wolfram random cellular automaton #30 and Wolfram complex cellular automaton #110. The model entails an abstract geometrical illustration of the co-emergence of left-homochirality and complexity.
It is proposed that complexity and homochirality are co-emergent phenomena based on the formulation asymmetriy and entropy leads to complexity.
Consequently, life may not necessarily depend on carbon-water chemistry on worlds in the 'Goldilocks' zone.
Table of Contents
1. Introduction
2. Millers 1952 Experiment and Thermodynamic Equilibrium
3. Franks Amplification Theory
4. Geometric Chemistry and Dynamical Billiards
5. Covalent Bond Formation and Information Flow
6. Computation in A-Graphs of Wolfram Cellular Automata
7. Autocatalytic Sets as Emergent Phenomena
8. Universal Implications of Complexity
Research Objectives and Core Themes
This paper investigates the fundamental origins of biological homochirality by analyzing computational constraints within complex dynamical systems. It proposes that complexity and homochirality are co-emergent phenomena, moving beyond traditional chemical models to suggest that life may be a universal outcome of specific computational conditions far from thermodynamic equilibrium.
- Analysis of dynamical billiards and Wolfram cellular automata (#30 and #110) as models for computational complexity.
- The role of non-equilibrium thermodynamics in the emergence of symmetry breaking.
- The relationship between information flow, redox potential, and the formation of homochiral molecules.
- Evaluation of autocatalytic sets as self-organizing systems that mimic early life processes.
- Exploration of life and consciousness as universal computational consequences rather than results of specific local chemistries.
Excerpt from the Book
COVALENT BOND FORMATION—REDOX POTENTIAL-information flow
Figure 4 illustrates A-graph #110. It is a rational, concave polygon. Its internal angles are π/n, where n is a rational number. Note the V-notch which forms a partial obstruction to a dynamic billiard ball passing either way from H1 to H2 or from H2 to H1. A-graph #30 is also shown to illustrate the differences between the two graphs. A-graph #30 is also a rational polygon, and mainly convex, thereby allowing, by contrast, free movement of a dynamic billiard ball from one side of the polygon to the other. It is because of this difference in billiard ball freedom of movement that the random dynamics of A-graph #30 computes equal clockwise and counterclockwise (racemic) tetrahedral structures, while the computational consequence of the partial obstruction in the complex A-graph #110 means Left-handed tetrahedral structures are sequestered in H2, and separated from racemic structures in H1. Thus, Left-homochirality is a computational consequence of complexity, and generally independent of any particular chemistry. The numbers and primed numbers represent relative atomic numbers; the ordinate represents information flow and covalent bond formation. The computational model is based on Figure 4.
Summary of Chapters
Introduction: Presents the central question of why life uses left-handed amino acids and suggests an approach via computational constraints in non-equilibrium dynamical systems.
Millers 1952 Experiment and Thermodynamic Equilibrium: Reviews the classic abiotic synthesis experiment and explains why thermodynamic equilibrium inevitably leads to racemic mixtures rather than homochirality.
Franks Amplification Theory: Critiques the limitations of traditional amplification theories regarding the speed of racemization versus the development of life.
Geometric Chemistry and Dynamical Billiards: Introduces an abstract geometric theory based on billiard paths on asymmetry graphs derived from Wolfram cellular automata to model chemical systems.
Covalent Bond Formation and Information Flow: Details the computational model where energy decay during billiard ball collisions mimics the energy requirements for covalent bond formation.
Computation in A-Graphs of Wolfram Cellular Automata: Compares A-graph #30 and #110 to demonstrate how structural complexity in the graph leads to the sequestration of left-handed enantiomers.
Autocatalytic Sets as Emergent Phenomena: Discusses how random networks transform into complex small-world networks through the exponential increase in catalytic probability as molecular weight grows.
Universal Implications of Complexity: Speculates on the universality of life and consciousness as potential emergent properties of computational constraints throughout the universe.
Keywords
Homochirality, Complexity, Dynamical Billiards, Wolfram Cellular Automata, Autocatalytic Sets, Non-equilibrium Thermodynamics, Asymmetry Graphs, Information Flow, Symmetry Breaking, Abiotic Synthesis, Computational Equivalence, Enantiomers, Small-World Networks, Emergence, Geometric Chemistry
Frequently Asked Questions
What is the fundamental research question of this work?
The paper explores the origin of life and asks why amino acids in living organisms are exclusively left-handed (homochiral).
What are the primary thematic fields covered?
The work bridges computational theory, non-equilibrium thermodynamics, chemical geometry, and origin-of-life research.
What is the main hypothesis regarding homochirality?
The author proposes that homochirality is a co-emergent phenomenon resulting from computational complexity in far-from-equilibrium systems, rather than being determined by specific local chemistries.
Which scientific method is utilized in the study?
The study uses computational modeling based on dynamic billiards on asymmetry graphs derived from Wolfram cellular automata (#30 and #110).
What does the main body of the text focus on?
The core of the paper describes how structural constraints in A-graphs create "bottlenecks" that sequester specific molecular chiralities, effectively modeling the emergence of homochirality.
What are the most significant keywords characterizing this research?
Key terms include Homochirality, Computational Complexity, Dynamical Billiards, Autocatalytic Sets, and Symmetry Breaking.
How does A-graph #110 differ from A-graph #30 in this model?
A-graph #30 is an open, convex system that computes racemic mixtures, whereas A-graph #110 is a concave polygon with a V-notch that acts as a partial barrier, causing the sequestration of left-handed molecules.
Why is the "protein-first" vs "RNA-first" debate considered potentially pointless by the author?
The author suggests that if life is a result of universal computational constraints, both models could be valid or secondary to the underlying computation, making the distinction less critical.
- Citar trabajo
- Marshall Goldberg (Autor), 2019, Are complexity and homochirality co-emergent phenomena?, Múnich, GRIN Verlag, https://www.grin.com/document/458984
