[Paper Review] Quantifying the pathways to life using assembly spaces

Stuart M. Marshall, Douglas Moore+3 more|arXiv (Cornell University)|Jul 6, 2019

Earth Systems and Cosmic Evolution1 references7 citations

TL;DR

This paper introduces 'assembly spaces' to quantify the pathway assembly information (PA) required to construct complex objects, defining PA as the minimal steps to rebuild an object from irreducible parts. It proposes that objects with high PA values (above a threshold) are likely products of biological or technological processes rather than random assembly, offering a new framework to identify life-like complexity in the universe using information-theoretic measures.

ABSTRACT

We have developed the concept of pathway assembly to explore the amount of extrinsic information required to build an object. To quantify this information in an agnostic way, we present a method to determine the amount of pathway assembly information contained within such an object by deconstructing the object into its irreducible parts, and then evaluating the minimum number of steps to reconstruct the object along any pathway. The mathematical formalisation of this approach uses an assembly space. By finding the minimal number of steps contained in the route by which the objects can be assembled within that space, we can compare how much information (I) is gained from knowing this pathway assembly index (PA) according to I_PA=log (|N|)/(|N_PA |) where, for an end product with PA=x, N is the set of objects possible that can be created from the same irreducible parts within x steps regardless of PA, and NPA is the subset of those objects with the precise pathway assembly index PA=x. Applying this formalism to objects formed in 1D, 2D and 3D space allows us to identify objects in the world or wider Universe that have high assembly numbers. We propose that objects with PA greater than a threshold are important because these are uniquely identifiable as those that must have been produced by biological or technological processes, rather than the assembly occurring via unbiased random processes alone. We think this approach is needed to help identify the new physical and chemical laws needed to understand what life is, by quantifying what life does.

Motivation & Objective

• To develop a framework for quantifying the extrinsic information required to assemble complex objects.
• To identify objects in nature or the universe that are unlikely to arise via random processes alone.
• To distinguish biological or technological systems from those formed by unbiased physical processes using a formalized measure of assembly complexity.
• To provide a physical and information-theoretic basis for understanding what defines life.

Proposed method

• The method uses an 'assembly space' to represent all possible objects constructible from a given set of irreducible parts.
• It defines the pathway assembly index (PA) as the minimal number of steps required to reconstruct an object within that space.
• The pathway assembly information (I_PA) is calculated as I_PA = log(|N|) / |N_PA|, where |N| is the total number of objects possible in x steps and |N_PA| is the subset with PA = x.
• The formalism is applied to 1D, 2D, and 3D configurations to assess how PA values scale with dimensionality and complexity.
• Objects with high PA are identified as those requiring non-random, directed processes to form.
• The approach enables comparison of assembly pathways across different systems, identifying uniquely identifiable, high-information structures.

Experimental results

Research questions

• RQ1 What is the minimal number of steps required to reconstruct a given object from its irreducible components, and how does this vary across dimensions?
• RQ2 How can we distinguish between objects formed by random processes versus directed processes such as biology or technology?
• RQ3 What information content is encoded in the pathway to assemble a complex object, and how can it be quantified?
• RQ4 Which objects in 1D, 2D, and 3D space exhibit PA values that exceed a threshold indicating non-random origin?
• RQ5 Can the pathway assembly index serve as a universal metric to detect life-like complexity in physical systems?

Key findings

• Objects with high pathway assembly index (PA) values are uniquely identifiable as products of non-random processes, such as biological or technological systems.
• The pathway assembly information (I_PA) increases logarithmically with the total number of possible objects (|N|) and inversely with the number of objects sharing the same PA (|N_PA|).
• In 1D, 2D, and 3D spaces, the formalism successfully identifies structures with high PA as unlikely to form via unbiased random assembly.
• The method provides a quantitative threshold to distinguish life-like complexity from random configurations.
• The framework suggests that high-PA objects are candidates for being evidence of life or technology in the universe.
• The approach offers a new physical basis for identifying life by quantifying the information content of assembly pathways.