Assembly theory (referred to in prior works as pathway assembly) has been developed to explore the extrinsic information required to distinguish a given object from a random ensemble.
In prior work, we explored the key concepts relating to deconstructing an object into its irreducible parts and then evaluating the minimum number of steps required to rebuild it, allowing for the reuse of constructed sub-objects. We have also explored the application of this approach to molecules, as molecular assembly, and how molecular assembly can be inferred experimentally and used for life detection.
In this article, we formalise the core assembly concepts mathematically in terms of assembly spaces and related concepts and determine bounds on the assembly index. We explore examples of constructing assembly spaces for mathematical and physical objects and propose that objects with a high assembly index can be uniquely identified as those that must have been produced using directed biological or technological processes rather than purely random processes, thereby defining a new scale of aliveness.
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.
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MARSHALL, Stuart M., MOORE, Douglas G., MURRAY, Alastair R. G., WALKER, Sara I. and CRONIN, Leroy, 2022. Formalising the Pathways to Life Using Assembly Spaces. Entropy. Online. July 2022. Vol. 24, no. 7, p. 884. [Accessed 15 July 2022]. DOI 10.3390/e24070884.
[…] This argument implies that information external to the object itself is necessary to construct an object if it is of sufficiently high complexity [4,5]. ⇒ Constructor Theory
Deutsch, D. Constructor theory. Synthese 2013, 190, 4331–4359.
Marletto, C. Constructor theory of life. J. R. Soc. Interface 2015, 12, 20141226.
In biology, the requisite information partly comes from DNA, the sequence of which has been acquired through progressive rounds of evolution.