Rubin and Crucifix (2021, Entropy 23:915) argued that the Earth's complexity lies not in the nonlinear, chaotic, power-law dynamics that general circulation models simulate, but in the planet instantiating life at planetary scale — an autopoietic, metabolic-repair (M,R) organization closed to efficient causation — and concluded that such complexity cannot be surrogated by any algorithmic simulation. They left open how to turn this view into science: what would constitute a 'critical' perturbation (fatal to the self-producing organization, as opposed to a non-fatal structural change), whether the planetary-boundary thresholds are critical in this organizational sense, how to build concrete testable formal Earth-system models capturing closure to efficient causation and anticipation, how autonomy and anticipation figure in Earth-system dynamics, and what geoengineering would mean under the Earth system's autonomy. Later work by the authors and the adjacent literature through 2026 leaves the core open: the authors' own program supplies proof-of-concept formalizations — chemical-organization-theory reaction networks and a Markov-blanket/active-inference climate formalization — and adjacent threads (closure of constraints, free-energy-principle Gaia, Organic Gaia, Gaia 2.0) continue, but no testable organization-based Earth-system model, no fatal-versus-non-fatal criticality criterion, and no characterization of the role of anticipation in Earth-system dynamics exists.

Background

Earth system science studies the planet as a coupled system of atmosphere, oceans, cryosphere, land, lithosphere and biosphere, and its main quantitative instrument is the general circulation model (GCM): a deterministic numerical algorithm that simulates the evolution of these components from physical and biogeochemical equations. The Gaia hypothesis — introduced by Lovelock and Margulis in the 1970s and since developed into a family of research programs (Lenton & Latour 2018; Lenton & Dutreuil 2026) — proposes that the biosphere and its material environment form a single entity whose long-term habitability is maintained by life itself.

Rubin and Crucifix (2021) advance a radical version of this view. They hold that what makes the Earth genuinely complex, rather than merely complicated, is not the properties usually invoked — a large range of spatial scales, nonlinear chaotic response, turbulence, power-law scaling, all of which are algorithmically simulable and shared with lifeless planets such as Mars or Jupiter — but the fact that the Earth instantiates life at planetary scale. The relevant notion of life comes from theoretical biology. Autopoiesis denotes a system whose organization is a network of processes of production such that these processes recursively regenerate the very components that realize the network. The (M,R)-system is Rosen's relational model of the living organization, in which a metabolism is coupled to repair and replication components so that every function acting as an efficient cause within the system is itself entailed by other functions of the system; this self-entailment is called closure to efficient causation. A result of Louie (2007), extending Rosen's arguments, asserts that any material realization of an (M,R)-system has noncomputable models, i.e. its causal entailment structure cannot be embedded in a Turing machine; Rubin and Crucifix conclude that the Earth's complexity is non-computable and cannot be surrogated by GCMs or any algorithmic simulation, which they compare to early cartographers mapping a sphere with pieces of tangent planes. An anticipatory system, in Rosen's sense, is one carrying an internal predictive model of itself and its environment and acting on that model's prediction — energetically cheaper than correcting deviations by feedback; the authors argue anticipation is inherent to closure-based organization, so Earth-system behavior should be autonomous and anticipatory rather than input–output regulated.

From this standpoint the paper distinguishes structural change from organizational loss: the climate 'tipping points' of mainstream Earth-system research — abrupt transitions of state variables in a dynamical model — correspond, in Earth history, to non-fatal structural changes that the self-producing organization survived (for example the transition to an oxidative atmosphere or mass extinctions); but a perturbation could in principle destroy the organization itself ('autopoietic oscillator death'). The planetary boundaries framework (Rockström et al. 2009) proposes quantitative thresholds for human perturbation of the Earth system, yet whether those thresholds are critical in the organizational sense — fatal to autopoiesis rather than merely to a dynamical regime — is exactly what the paper leaves unresolved. The framework is contested: Cárdenas, Letelier, Gutierrez, Cornish-Bowden and Soto-Andrade (2010) analyze the leap from closure to efficient causation to non-computability and find it far weaker than Rosen's followers assert; the modeling questions below survive either reading.

The authors and collaborators have begun translating the program into formal tools: a proof-of-concept applying chemical organization theory (an algebraic theory of self-maintaining reaction networks) with the zero-deficiency theorem (a classical structural criterion guaranteeing, for reaction networks without a certain 'deficiency', that their equilibria are unique and stable) to a simplified Earth molecular reaction network (Rubin, Veloz and Maldonado 2021), and a Markov-blanket/active-inference formalization in which the climate system minimizes variational free energy — a bound on the discrepancy between an internal generative model's predictions and its inputs, whose minimization makes a system behave as if it anticipated its environment (Rubin, Parr, Da Costa and Friston 2020) — the Markov blanket being the partition separating a system's internal states from external states through sensory and active states. Both remain abstract. What is missing — the open problem — is stated below.

Problem Statement

The problem, as posed by Rubin and Crucifix (2021), is to convert the organization-based view of Earth's complexity into a scientific research program with concrete, testable content. Its components share one objective — giving the Earth's planetary autopoietic organization a formal representation against which questions can be asked, answered, and falsified — and are jointly the following.

(1) Formal, testable Earth-system models of closure. Develop formal models of the Earth system, based on the (M,R)-system or related frameworks that capture closure to efficient causation and anticipation, translating the abstract categorical/relational structure into concrete, testable Earth-system representations, in deliberate contrast to GCM-style algorithmic simulation of the whole Earth system.

(2) Critical perturbations of the autopoietic organization. Determine what constitutes a 'critical' perturbation that would break the Earth's autopoietic organization (a fatal tipping point) as opposed to a non-fatal structural change; in particular, whether the thresholds of the planetary boundaries are critical for the planetary self-producing organization.

(3) Biospheric anticipation. Characterize the role of anticipation in the Earth system's dynamics — how the biosphere builds predictive models of its environment — in a way distinguishable from reactive feedback.

(4) Management under autonomy. As an application of (1)-(3), determine whether geoengineering and management strategies can be devised that respect the Earth system's autonomy and anticipate its autonomous responses.

Components (1)-(3) are the scientifically linked core: (2) and (3) are precisely the questions an organization-based model of type (1) is meant to address, and (4) applies the resulting understanding.

All four components are jointly required: the task is complete only when (1)-(4) are each resolved, and a deliverable that settles a single component leaves the remaining questions open. Component (2) is itself two determinations — a general criterion for a 'critical' perturbation fatal to the self-producing organization, and the specific verdict of whether the thresholds of the planetary boundaries are critical in that organizational sense — and both are required for (2).

References

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