paper:doi-10-1098-rsos-261059Open questions about time and self-reference in living systems
Methods (4)
- Computational ReflectionProgramming technique allowing a program to inspect and change its own contents, proposed for fully self-modifying systems.
- Genetic Programming (GP)Evolutionary technique that evolves computer programs, discussed as a route toward self-modifying models.
- Lambda CalculusChurch's formalization of computation via replacement operations on strings; one of multiple equivalent formalizations
- Self-Modifying Cartesian GPVariant of GP where operators can determine input dimensionality, enabling systems to solve general problem classes.
Frameworks (17)
- Anticipatory SystemsRosen's framework for systems with predictive models of their environment; relevant to understanding cognition in living systems.
- Automata ChemistriesArtificial Life research paradigm relying on self-modifying code (e.g., Tierra, Avida, Stringmol) to evolve digital organisms.
- AutopoiesisMaturana-Varela principle of self-maintaining systems that organize themselves through internal feedback; extended here to biological, technological, and hybrid systems.
- Calculus of Indications (Laws of Form)Spencer-Brown's formal system generating an 'imaginary value' from self-referential re-entry, extended by Varela to a three-valued autonomous state.
- Closure to Efficient CausationRosen's key concept making the (M,R)-system an irreducible cause of its own organization.
- Generate and TestAbstract iterative scheme underlying Darwinian evolution, GP, and Dennett's tower of learning.
- Integral Biomathics (IB)Programme seeking frameworks expressive enough for self-reference, emergence and evolving organizational structure.
- (M,R)-Systems (Metabolism-Repair Systems)Rosen's relational-biology model expressing self-reference and self-production mathematically.
- Memory Evolutive Systems (MES)Category-theoretic hierarchical framework allowing metamodels to evolve via 'complexification'.
- Multi Scale Competency ArchitectureProposed architecture enabling evolution of robust problem-solving across cellular collectives at multiple organizational scales.
- Natural TimeThe continuing present of physical processes, introduced/distinguished by this paper as the substrate of all dynamics.
- Representational TimeA new kind of time with past/present/future that co-originates with life, enabling memory, anticipation and learning.
- Second-order CyberneticsFramework folding the observer's act of distinction into the account of observed systems; underlies the paper's treatment of self-reference.
- Stack TheoryBennett's multi-level formal account of representation as a stack of abstraction layers, applied to representational time.
- Three-Level Novelty Framework (variation/innovation/transformation)Banzhaf et al.'s definition of open-endedness via level-0/1/2 novelty in systems, models and metamodels.
- Wandering Logic Intelligence (WLI)Non-axiomatic spatio-temporal logic for context-dependent reasoning, integrated with MES.
- WLIMESIntegration of MES and WLI enabling second-order reasoning about categorical structures themselves.
Findings (4)
- Moths trained as caterpillars retain learned memories after metamorphosis despite near-total destruction and rebuilding of the brain (Blackiston et al.).
Cited empirical result supporting the claim that memory persists through radical self-transformation.
- Scratching an embryonic blastoderm can produce multiple independent, viable embryos (conjoined twins, triplets, etc.) (McMillen & Levin).
Empirical support for the claim that the number of selves in an embryo is not genetically fixed.
- Planarian flatworms regenerate their entire brain and retain memories after head amputation (Shomrat & Levin and related work).
Cited empirical result supporting persistence of self/memory through structural regeneration.
- Stringmol has been shown to exhibit type-1 (innovation) and type-2 (transformation) novelty (Stepney & Hickinbotham).
Cited computational evidence that an automata-chemistry system realizes the paper's open-endedness novelty levels.
Claims (15)
- Representation as explanatory strategy and autonomy as constitutive process generate an apparent contradiction that may not need to be dissolved but confronted, opening a wider domain of understanding.
Final unresolved theoretical tension the paper leaves open regarding whether representation is foundational or founded on autonomy.
- The number of coherent selves in an embryonic blastoderm is not fixed by genetics but can range from zero to several, arising from the physiological process demarcating cooperating subsystems.
Supports the claim that selfhood boundaries are dynamically constructed rather than genetically predetermined.
- Memory Evolutive Systems currently use externally parametrized dynamics rather than endogenous, self-referential time, so the approach remains outside the constitutive dynamic it describes.
Critical assessment of MES/WLIMES as a formal tool.
- The body is a biological Ship of Theseus, remaining the 'same' object across decades of cellular turnover because of persistent bioelectric, biomechanical and biochemical pattern memories.
Central claim about self-maintenance through radical component replacement.
- Apparent paradoxes of self-reference are illusions produced by projecting a time-involving process into a timeless representation, and are resolved when natural time is made explicit.
Core theoretical move of the paper unwinding circular self-reference into a natural-time spiral.
- Living things model themselves as agents because tracking microstates is impractical for survival, committing organisms to an agency-first view of the world from the microbial stage.
Explains why selfhood/self-awareness emerges as a coarse-graining strategy.
- The non-set-theoretic nature of powerdomains in domain theory creates unresolved obstructions when lifting standard game-theoretic solution concepts to model rule-changing games.
Assessment of Vassilakis's domain-theoretic economic models.
- Coalgebra offers a promising and mathematically clear approach to self-referential systems but it is unclear how useful it will be for systems undergoing structural evolution.
Balanced assessment of coalgebra's promise and limits.
- Cancer represents a shrinking of the cognitive light cone in which defecting cells revert to ancient unicellular goals and treat the rest of the body as external environment.
Explains disease as a self/world boundary failure within the multi-scale competency architecture.
- Morphogenesis is self-referential in the deepest sense because the cell collective computing what to do next is the same medium being remodelled by those computations.
Key claim connecting embryogenesis to self-reference and strange loops.
Hypotheses (2)
- Many kinds of chemical pathways, not just cells or neurons, can exhibit six different types of learning, suggesting representational time is exploited broadly across living subsystems.
Supports the gradualist view of representational time's emergence.
- Representational time might be a non-binary, gradual concept that switches on incrementally as systems become more self-referential and more alive.
Proposed extension of the natural/representational time distinction to non-neural systems like gene-regulatory networks.
Questions (7)
- Whether representation can serve as a foundational principle, or whether it is itself founded on the autonomous organization that makes representation possible at all.
Final open question of the discussion, left genuinely unresolved.
- What are appropriate mathematical formalisms and computational tools for modelling a self-modifying system that changes its own rules, and is open to its environment?
Organizing question for §6 on tools for modelling self-referential systems.
- What are effective tools and modelling paradigms for implementing and running (simulations of) self-modifying open systems?
Organizing question for §6.2 on computational tools.
- Does the possibility of self-reference in a system require or imply the existence or use of natural time?
Organizing question of §4.2 linking self-reference and natural time.
- Are there non-iterative processes that can effectively explore a Vast state space of possibilities?
Open question about whether evolution/development are the only routes to exploring atypical possibility space.
- What are appropriate analysis tools for interrogating self-modifying, evolving, open systems?
Organizing question for §6.3 on analysis tools.
- Is there a new concept of time that comes into being with the origin/development of life?
Central organizing question of §2, motivating the natural time/representational time distinction.
Original abstract (expand)
Abstract Living systems exhibit a range of fundamental characteristics: they are active, self-referential, self-modifying systems. This paper explores how these characteristics create challenges for conventional scientific approaches and why they require new theoretical and formal frameworks. We introduce a distinction between ‘natural time’, the continuing present of physical processes, and ’representational time’, with its framework of past, present and future that emerges with life itself. Representational time enables memory, learning and prediction, functions of living systems essential for their survival. Through examples from evolution, embryogenesis and metamorphosis, we show how living systems navigate the apparent contradictions arising from self-reference as natural time unwinds self-referential loops into developmental spirals. Conventional mathematical and computational formalisms struggle to model self-referential and self-modifying systems without running into paradox. We identify promising new directions for modelling self-referential systems, including domain theory, coalgebra, genetic programming (GP) and self-modifying algorithms. There are broad implications for biology, cognitive science and social sciences, because self-reference and self-modification are not problems to be avoided but core features of living systems that must be modelled to understand life's open-ended creativity.
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