Computation as Organisation

TL;DR

Problem: conventional definitions separate symbolic computation from physical dynamics, which is inadequate for living systems. Approach: redefine computation as the temporal enactment of organised matter constrained by relations, with information as relational invariance. Key contributions: a formal criterion set—persistence, recovery, and structural failure—plus an experimentally actionable perturbation framework and a generalization of computational limits across scales; demonstration via a chemotaxis example and cross-domain applicability. Significance: enables substrate-agnostic assessment of computation in biology and engineered systems, linking memory, processing, and execution under constraint and revealing intrinsic limits imposed by organisation.

Abstract

Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation becomes problematic when applied to living systems, where persistence, adaptation, and failure occur without symbolic instruction or central control. Here, computation is reformulated as a structural property of organised matter. Organisation is defined as the persistence of relational constraints that delimit admissible state transitions. Information is not encoded content but relational invariance: differences that influence future behaviour by reshaping what transitions remain possible. Computation is identified with the ongoing enactment of such organisation, integrating memory, processing, and execution as inseparable aspects of material dynamics. Within this framework, algorithms correspond to internally embedded regularities enabled by constraint, and computational limits arise from organisation itself. The account provides experimentally accessible criteria for computation based on persistence, recovery, and structural failure under perturbation.