Optimized to Death: The Hypernetic Law of Experience

Abstract

The Hypernetic Law of Experience (HLE) generalizes Ashby’s neglected Law of Experience from determinate machines to stochastic, gradient-driven adaptive systems. The HLE characterizes a persistent tendency of adaptive systems exposed to sustained directional experience: internal variety is progressively consumed, and system trajectories converge toward increasingly narrow regions of state space, even when local transitions remain probabilistic. We formalize this contraction pressure using the Rebis equation, a discrete-time variance-contraction dynamic that relates optimization pressure and novelty injection to the evolution of internal diversity. Through cross-domain comparative analysis, we show that HLE-consistent geometry appears in biological evolution, recursive model collapse in machine learning, economic cycles, neural plasticity and habituation, linguistic convergence, and institutional lock-in. In these domains, excessive variety consumption is associated with brittle attractors and heightened vulnerability under distributional shift. We further show that biological systems employ countervailing mechanisms—such as sexual recombination, mutational plasticity, sleep-driven renormalization, and variance-preserving neuromodulation—that mitigate, but do not eliminate, the contraction pressure described by the HLE. We conclude that the HLE and the Rebis equation provide a systems-level diagnostic for identifying and explaining optimization-induced fragility and for informing the design of regulators, AI architectures, and institutions that remain viable under drift.

1. Introduction

The Law of Requisite Variety—“variety can destroy variety” [1] (p. 207)—is the most renowned insight in W. Ross Ashby’s seminal Introduction to Cybernetics. Its neglected counterpart, the Law of Experience, describes how repeated inputs progressively erode internal variety: trajectories converge, distinctions vanish, and the initial system state loses relevance. Requisite Variety concerns external coupling between a system/regulator and environment, while the Law of Experience describes internal evolution under feedback.

Complex adaptive systems (CAS) are groups of many interacting parts that exhibit emergent behaviors not easily predicted from individual components alone [2]. Such systems are characterized by nonlinear interactions, continuous adaptation through feedback with their environment, and dynamic balancing of exploration and exploitation while maintaining internal variety as a resource for responding to change. Modern adaptive systems often operate under stochastic gradients rather than fixed transitions, yet they display geometries comparable to those Ashby described in determinate machines.

We propose the Hypernetic Law of Experience (HLE) as a generalization of Ashby’s original insight to stochastic, gradient-dominated systems. The HLE describes how recursive optimization in adaptive systems drives variance collapse over time, making systems increasingly brittle to environmental changes even as local performance improves. Unlike Ashby's determinate formulation, the HLE accounts for probabilistic transitions while maintaining the core insight that experience erodes internal diversity.

To state the HLE formally, in adaptive systems exposed to sustained directional experience—whether through feedback, selection, or structural asymmetry—ensemble behavior tends to converge toward increasingly narrow regions of state space when optimization pressure is not counterbalanced by sufficient novelty injection. Over long horizons, internal variety decays and trajectories become effectively determinate, even when local transitions remain stochastic. Recursive optimization, in which system outputs influence future inputs, constitutes a particularly strong regime of the HLE by increasing contraction pressure and accelerating the decay of internal variety unless countervailing channels remain operative.

The HLE operates as an internal dynamic within CAS, describing how iterative optimization can diminish net variety in systems. While these variance dynamics operate broadly across systems, the HLE applies most nontrivially to CAS where recursive feedback operates on observable timescales. It does not claim that brittle failure is inevitable in all CAS. The HLE suggests that adaptive systems tend to optimize toward locally reinforcing success criteria, and that—because mechanisms which preserve adaptive phase space are typically costly and non-parsimonious with respect to short-term performance—such systems tend toward brittleness unless countervailing structures are maintained.

Following Stafford Beer’s POSIWID principle—“the purpose of a system is what it does” [3]—this paper treats optimization operationally rather than teleologically. A system optimizes when it increases the reliability or efficiency of its characteristic behaviors—producing more viable outputs—under some input distribution. This definition does not depend on normative judgments, intended goals, or claims about what the system ought to do, but is compatible with external evaluation. For example, a biological population is said to optimize when its reproductive viability improves under environmental pressures, while an AI system optimizes when its observable performance on benchmark tasks improves under its training regime.

In classical cybernetics, system behavior is shaped by regulatory processes that constrain outputs through feedback in order to maintain stability or improve performance relative to some criterion [1,4,5]. Such regulators need not be centralized or intentional; they may be distributed, implicit, or emergent. These regulatory systems are typically analyzed in terms of their capacity to maintain stability or improve performance, but classical cybernetics left largely implicit how such regulation evolves under sustained, biased experience.

Together with Requisite Variety, the HLE defines a cybernetic dialectic. Variety is required for control, while experience tends to consume it. Systems transformed under a directionally biased input distribution will tend to lose variety. This is exacerbated when a system’s outputs recursively reinforce its input distribution, causing systems to become progressively less sensitive to perturbations originating outside their dominant feedback loops.

The HLE itself does not describe a failure mode, but a general tendency of optimizing systems toward convergence. Failure arises in specific regimes where experience-driven convergence proceeds without sufficient mechanisms for preserving or replenishing internal variety. In such regimes, systems collapse into narrow projections of reality that are robust locally but brittle under distributional shift. Experience replaces uncertainty with structure until systems lose robustness to environmental changes.

Recent work on recursive training collapse in large-language models (LLMs) [6] provides a direct empirical instance of brittleness that results when HLE-mediated contraction proceeds without compensatory mechanisms. As a generative model is trained on its own outputs, improbable events disappear from its distribution. Diversity decays, and the model converges toward effectively determinate behavior. The HLE predicts this outcome as a general vulnerability of adaptive systems operating without sufficient external or endogenous variety injection.

2. Background

The Law of Experience has received almost no explicit treatment in the academic literature. A literature search conducted at the time of writing for “Law of Experience” AND “Ashby” returns fifteen works published between 1959 and 2021—largely confined to educational or behavioral systems research [7,8,9,10,11] or reviews of An Introduction to Cybernetics [12], and all with fewer 50 citations. We find no study to date that extends the law beyond Ashby’s original framing directly into stochastic, gradient-dominated systems.

Gregory Bateson’s [13] concept of deutero-learning similarly noted that feedback-driven learning loops narrow behavioral variety as patterns stabilize—a cognition-facing parallel to Ashby’s general ideas—but he did not formalize the underlying geometry. Other works, such as Paritsis’s [9] Law of Optimal Variety, hinted at the same trade-off between too little and too much informational input. Yet no formulation quantifies how substrate-agnostic optimization depletes variety.

2.1. The Neglected Twin of Requisite Variety

Ashby’s Law of Requisite Variety—extended with Roger Conant into the Good Regulator Theory [14]—is foundational in cybernetics-informed fields: a regulator must possess at least as much variety as the system it is meant to control. It is a declaration about external coupling, about how variety must be matched across interacting systems for control to be possible. The Law of Experience, introduced in an earlier chapter of An Introduction to Cybernetics [1] (pp. 137–139), is its inward-facing complement. Where the Law of Requisite Variety concerns the balance between regulator and environment, the Law of Experience concerns the fate of variety within a system subjected to repeating inputs. Ashby writes:

“Information put in by change at a parameter tends to destroy and replace information about the system’s initial state.” [1] (p. 139)

In other words, each cycle of operation erases traces of internal diversity. Repeated exposure to uniform transformations drives a system toward an attractor region of its state space. Ashby illustrates this by imagining multiple machines with different starting states subjected to the same inputs: over time their behaviors become indistinguishable. “As the variety falls,” he notes, “so does the set change so that all its members tend, at each moment, to be at the same state” [1] (p. 138). Moreover, the principle holds for a single system evolving through successive iterations. The Law of Experience thus describes an entropic convergence: repeated transformation under constraints makes systems progressively less distinguishable from one another.

Despite its simplicity, the law provides a powerful mechanism for homogenization processes over time. Ashby’s ideas, however, assumed a determinate machine: a system whose next state follows from its current one. That assumption, as the next section suggests, constrains how his law has been interpreted and why it now warrants an extension.

2.2. From Ashby’s Determinate Law to a General Law of Convergence

Ashby’s formulation of the Law of Experience assumes a determinate machine, “one whose transformations are single-valued” [1] (p. 24)—a presumption underlying all material in Parts I and II. In Part III he introduces Markovian machines, whose state transitions follow a probability matrix, noting that “a determinate absolute system is a special case of a Markovian machine in which all the probabilities have become either 0 or 1” [1] (p. 195).

The stochastic generalization proposed here—the HLE—extends Ashby’s insight from single-valued transformations to systems whose next state is drawn from a probability distribution rather than a fixed map, yet which still exhibit global convergence under iterative optimization. Making this distinction explicit allows the Law of Experience to be situated within contemporary accounts of optimization and recursive collapse in stochastic systems without misrepresenting Ashby’s original scope.

Ashby later remarks that “often we shall not need to make the distinction between determinate and Markovian” [1] (p. 235), but this refers to the generality of regulation—not to the Law of Experience. Elsewhere, he continues to preserve the difference: Markovian components “wander, at each step, somewhat at random” [1] (p. 235), whereas determinate components remain single-valued. The unification he hints at is never formalized. Ashby does not revisit the Law of Experience for probabilistic systems (it appears only twice by name in the volume) nor demonstrate that equivalent convergence behavior occurs under stochastic regimes.

Two further limitations are important for what follows. First, Ashby treats the Law of Experience as a descriptive mechanism of convergence rather than as a persistence condition. He does not ask what happens when a system whose internal variety has been eroded continues to face environmental variability, nor does he frame variety loss as a source of brittleness or failure. Second, he does not treat novelty or noise as a resource to be actively managed. Parameter changes drive convergence in his examples, but there is no suggestion that systems must regulate the amount or structure of novelty they encounter in order to remain viable over long horizons.

The point is not to treat Ashby’s work as scripture but to clarify that the Hypernetic Law of Experience is not implicit in his original formulation. If the Law had already encompassed stochastic or gradient-dominated systems, such as AI learning architectures, its citations and applications would likely appear across CAS, control theory, and machine learning literature, rendering the present contribution redundant. Nor does Ashby connect the Law of Experience directly to optimization or learning, systems that recursively train on their own outputs, or experience-driven convergence as a general failure mode for adaptive regulators. Recognizing this gap enables a generalized law of adaptive convergence. The following section develops the HLE, formalizing how variance compression arises in gradient-driven recursion and unifies collapse dynamics across contemporary systems.

The convergence described by the HLE is conditional rather than inevitable. Neither Ashby’s original formulation nor the HLE says that complex adaptive systems must collapse into brittle behavior. Instead, these laws characterize a risk regime: when optimization proceeds without sufficient mechanisms for preserving or reintroducing internal variety, systems become increasingly vulnerable to environmental change. In this sense, the HLE functions as a diagnostic framework for identifying degenerative trajectories within CAS—cases where recursive optimization induces fragility through excessive variety consumption—rather than as an inevitable law of adaptive failure.

3. Materials and Methods

The methodology adopted here is consistent with classical cybernetics. Rather than analyzing one system in isolation, we work at the level of what Ashby called “all possible machines” [1] (p. 2): we identify a behavioral schema—in this case, variance contraction under optimization pressure—and examine whether empirical studies across structurally diverse systems are consistent with the described schema. Rigor is achieved through formalization, structural consistency, and cross-domain validation rather than direct experimentation.

This is an application of cybernetics akin to geometry. We provide a unifying relationship in which different systems appear as individual cases of more general forms. The HLE is proposed as such a form, based on its ability to organize and explain convergence phenomena across biological, economic, cognitive, and artificial systems.

3.1. Mathematical Formalization

To make the Law of Experience applicable to stochastic, gradient-dominated systems, we introduce a minimal discrete-time recurrence relation describing the evolution of a system’s ensemble variance under optimization pressure. This relation (the Rebis equation) is a reduced-form description capturing the balance between variance contraction and variance injection common to many adaptive systems.

The formulation assumes bounded stochasticity and operates at the level of ensemble behavior rather than individual trajectories. Its role is illustrative and unifying rather than causal, and it provides a compact way to reason about how repeated experience biases systems toward increasingly narrow regions of state space, even when local transitions remain stochastic.

3.2. Comparative Structural Analysis

To evaluate generality, we apply the Rebis formalism to diverse adaptive systems—examining whether each exhibits the predicted contraction dynamics under sustained optimization. Examples were selected for well-documented convergence behavior, with particular attention to systems where outputs influence future inputs.

3.3. Cross-Domain Isomorphism Testing

For each domain, we assess whether the observed dynamics conform to the predicted variance geometry, providing a structural test of the HLE. This method mirrors classical cybernetics, where laws are validated through the consistency of their transformation rules across substrates. Our claims rest on mathematical derivation and previously published empirical results.

3.4. Provenance Disclosure

All concepts, theory, extrapolations, and interpretations are original to the author or cited sources. AI tools were used to assist with language refinement and organization. The author assumes complete responsibility for the material within this paper.

4. Extending the Law of Experience from Determinate Machines to Gradient-Dominated Systems

Ashby’s original Law of Experience was not framed mathematically, and it was for determinate machines—systems where the next state follows uniquely from the current one. He does not detail how convergence interacts with changing environments or optimization pressures. Ashby’s Law of Experience is not presented as a constraint on persistence so much as a tendency of machines under repeated transformation.

In contrast, most modern adaptive systems are stochastic and gradient-dominated: their transitions are probabilistic at the local scale but governed by gradients that impose long-term directional bias. A stochastic system of this type is “law-abiding” (in the Ashbyan sense) in expectation rather than in instance. The system’s global behavior converges even while local transitions vary.

To situate the HLE within modern stochastic adaptive systems, consider a generic discrete-time state update of the following form:

$$x_{t+1}=f(x_t,{\theta }_t)+{ϵ}_t,$$

(1)

where f defines the update rule, θₜ are system parameters modified through adaptive channels, and ϵₜ represents variance-generating influences not aligned with the system’s dominant optimization gradient (e.g., stochastic perturbations, exploratory deviations, or environmental shocks). We assume bounded variance of ϵₜ and stationary first and second moments over the interval of interest. This generic form captures systems whose local transitions may be stochastic but which exhibit sustained directional bias under experience.

To study convergence in such systems, variance is evaluated over an ensemble of realizations or trajectories under an expected input distribution. Ensemble variance serves as a tractable proxy for the system’s effective cybernetic variety within the modeled frame. As experience accumulates, probability mass shifts toward one side of an evaluation axis, smoothing the distribution of possible trajectories and narrowing the set of accessible responses. This defines a general contraction tendency at the ensemble level, even when individual transitions remain stochastic.

Taking expectations and applying the law of total variance yields an approximate recurrence relation for ensemble variance,

$$Var\left[x_{t+1}\right]\approx (1-{\lambda }_t)Var\left[x_t\right]+{\eta }_t,$$

(2)

where ${\lambda }_t\in [0,1]$ is an effective contraction coefficient summarizing the net strength of variance-reducing pressures acting on the system at time t, and ηₜ represents the contribution of variance-generating influences (novelty, noise, or perturbation). Both λₜ and ηₜ are composites: λₜ reflects how strongly expected system dynamics favor convergence over exploration, while ${\eta }_t$ captures the degree to which new variation is introduced from internal or external sources.

Writing ensemble variance explicitly as cybernetic variety Vₜ, Equation (2) can be expressed in the minimal Rebis form,

$$V_{t+1}=(1-{\lambda }_t)V_t+{\eta }_t,$$

(3)

which provides a reduced-form description of how variance evolves under the joint influence of convergence pressure and variance injection. Here λₜ denotes the contraction rate (gradient dominance), Vₜ the cybernetic variety of the system, and ηₜ any input which extends the system’s variety. The Rebis equation represents varietal decay under optimization pressure, offset by stochastic input, illustrating that iterative experience reduces state diversity unless stabilized by variance injection. This recurrence has the same general structure as classical stochastic-approximation dynamics [15,16] and can be interpreted as an entropy-contraction process under optimization [17].

The Rebis equation characterizes variance dynamics in iterated adaptive systems and is useful as an illustrative formalism for the HLE. HLE-mediated recursive collapse is a case in which system outputs increasingly shape future inputs or parameter updates, causing the contraction term λₜ to dominate adaptive processes and leaving the system brittle to inputs that fall outside the distribution for which it has been optimized. The Rebis formalism assumes that the system operates under an expected input distribution containing exploitable regularities. In the absence of such structure—i.e., under purely random input—no meaningful optimization gradient exists, and the contraction dynamics described here do not apply.

Subsequent sections demonstrate the applicability of this geometry across radically different substrates. Determinate physical systems can be treated as an idealized limiting case in which stochastic contributions to variety are negligible and system behavior approaches full determinacy. In this sense, purely deterministic physical systems can be viewed as limiting cases of the same contraction geometry, rather than as exceptions to it.

In practice, the Rebis formalism supports at least two complementary uses:

• An observer-defined mode where λₜ measures convergence toward a designated target.
• An intrinsic mode where λₜ measures the system’s own reinforcement of its characteristic behavior.

The latter corresponds to Beer’s POSIWID principle [3] and allows cross-domain generalization without making assumptions about intent.

Stochastic shock—the deliberate or selected/evolved injection of ηₜ as noise or bounded randomness—functions as an anti-collapse mechanism: a structured injection of variability that replenishes effective state-space diversity within the modeled frame. For instance, retroviruses exhibit high ηₜ through error-prone replication, offsetting intense selection gradients λₜ within host environments (cf. [18]).

When Vₜ falls toward zero, the system’s adaptive capacity is extinguished within the modeled frame, and behavior becomes effectively determinate. The system may continue to operate functionally, but it no longer possesses internal degrees of freedom sufficient to respond to perturbations outside its learned or optimized manifold. Under a persistence-oriented frame, an optimized low-variety system is vulnerable to destruction by changes in the input distribution.

In this sense, Vₜ → 0 defines an adaptive viability boundary: a point at which continued persistence or functionality depends entirely on environmental stability or external intervention to maintain a constant input distribution. Biological systems may fail catastrophically beyond this boundary, whereas artificial or institutional systems may persist in a frozen or brittle regime.

The opposite limit (λₜ → 0) corresponds to a purely stochastic process with unbounded variance, in which no stable learning or convergence occurs. At finer resolutions, both λₜ and ηₜ are composite quantities whose effective contributions depend on context. In many systems, the contraction term λₜ can be usefully decomposed into exogenous pressures (e.g., environmental constraints, external selection, institutional incentives) and endogenous pressures (e.g., entrenched priors, internal attractors, homeostatic set-points), each of which predictably compresses system variety. Likewise, ηₜ frequently includes both exogenous perturbation (novel shocks, new information, environmental variability) and endogenous perturbation (spontaneous stochasticity, exploratory dynamics). This decomposition is not required for the Rebis formalism but clarifies how diverse substrates instantiate the same variance geometry through different mixtures of internal and external forces.

For example, stress-induced mutagenesis in bacteria reflects adaptive up-modulation of endogenous ηₜ in response to rising exogenous λₜ-pressure. In high-stress environments, the bacterium behaves in a teleonomically anticipatory manner. Empirically, stress-induced mutagenesis was found to boost mutation rates from very small amounts up to thousands of times the baseline rate, which maps to the Rebis equation as a boost to ηₜ under elevated λₜ [19].

As optimization proceeds, systemic variety tends to decrease: the gradient hardens, and the system’s trajectory toward its dominant attractor intensifies. Unless ηₜ is modulated, as with the bacteria example, phase space diversity tends to narrow. Systems that persist under such conditions exhibit mechanisms for modulating stochastic shock to maintain robustness.

This formulation operationalizes and extends Ashby’s Law of Experience: experience (ongoing perturbation/transformation of the system) erodes effective variety. The HLE describes the internal convergence of adaptive systems in the same way the Law of Requisite Variety describes the external coupling between regulator and environment. Together, they delineate two poles of adaptive persistence: variety is required for “good regulation”, but it is continually pruned by experience.

Now that we have a candidate formalism in the Rebis equation, we will look across diverse systems to examine its applicability and generality.

4.1. Entropy, Information, and Economics

The HLE applies to informational systems. As with physical systems, updates replace high-entropy uncertainty with low-entropy regularity. When a system’s outputs bias its future inputs, that regularity compounds across iterations.

Shannon’s [20] entropy H(X) gives the expected uncertainty over possible system states, the effective diversity of states the system can still realize. If, at each iteration, the update transformation t shifts probability mass toward historically rewarded/high-payoff states (i.e., favors exploitation over exploration), then the expected entropy obeys

$$H\left(X_{t+1}\right)\le H\left(X_t\right),$$

(4)

and such a system will converge to an attractor state.

We can rewrite this dynamic in the same functional form as the Rebis equation

$$H_{t+1}=(1-{\lambda }_t)H_t+{\eta }_t,$$

(5)

where λₜ is the effective contraction rate (the strength of optimization pressure) and ηₜ is injected informational noise (unmodeled novelty, exogenous data shocks, etc.). Under sustained optimization pressure and limited external noise, Hₜ decays geometrically toward zero. Probability mass concentrates into a narrow attractor.

In information-geometric terms, recursive optimization traces a path of decreasing distance between successive distributions; over time the manifold effectively flattens as the system converges toward a delta-like distribution. Shumailov et al. [6] empirically observe this “convergence to delta” in recursively fine-tuned language models.

This smoothing of variance manifests behaviorally as a reduction in the system’s output diversity—its ability to produce distinct reactions to unusual perturbations. As the attractor basin narrows, perturbations are increasingly absorbed by the same over-specialized compensatory pathway. Diversity of potential response decays, and the system’s future behavior becomes determined chiefly by its history of updates rather than by its initial state.

Optimization behaves as a local entropy sink and a global entropy source [21,22,23]: the system lowers its own uncertainty by burning energy and dumping the resulting entropy into its surroundings. This asymmetry underlies the HLE: local convergence requires global divergence. Every increment of efficiency is paid for with an increment of exported disorder [24,25,26]. Ashby’s variety absorption and Schrödinger’s negative entropy intake are two views of the same geometry: persistence via selective entropy consumption. When the surrounding environment can no longer absorb this exported disorder, the system begins consuming its own adaptive capacity instead, burning future flexibility to survive the present.

In complex adaptive systems, this results in a conservation-like dynamic: entropy is displaced rather than destroyed. When a system boosts its order (ΔH_s < 0), its coupled environment accommodates via a complementary rise in disorder (ΔH_e > 0) (cf. [25,27]). The exchange continues until the environment’s absorptive capacity saturates, at which point the system begins to cannibalize its own adaptive capacity.

Minsky’s [28] Financial Instability Hypothesis aligns with this geometry. While Minsky did not frame capitalist oscillations in information-theoretic terms, the structural mapping is coherent. Firms, investors, and regulators recursively optimize for a narrow scalar proxy—profit (or close correlates like share price). Through repeated updates, strategies that best maximize the target scalar(s) become increasingly homogeneous, compressing the diversity of financial behaviors in the system.

Minsky identified leverage as the amplifier: “the total market valuation […] of a highly indebted firm was typically greater than the market valuation of a more conservatively financed firm” [29]. In other words, debt magnifies apparent performance under the chosen metric. That pressure steepens the optimization gradient λₜ. Each iteration replaces strategic heterogeneity (varying philosophies, risk tolerances, and credit postures) with low-entropy regularity (debt-levered yield extraction)—homogenization of financial strategies. The ensemble variety of the financial subsystem decays as experience accumulates.

To maintain apparent stability, firms externalize the resulting disorder—by socializing risk through derivative chains (debt to finance debt) or leaning on central-bank liquidity. Paralleling thermodynamics, the system consumes internal variety and exports entropy to its environment. The external environment—public balance sheets, the customer base—temporarily absorbs this exported instability, allowing the optimization regime to persist. When that absorptive capacity saturates (credit freezes, collateral chains break, liquidity evaporates), the exported entropy rushes back in (in a bank run, for example). Failures that were dismissed as “idiosyncratic” suddenly synchronize, crystallizing into a crisis.

State and central-bank interventions then act as stochastic shock aimed at rescuing the firms, with bailouts and other emergency measures expanding phase space by reopening trajectories that would otherwise have been eliminated. They restore the diversity of viable states to the firms, preventing total collapse. But critically, these interventions preserve the underlying optimization geometry. After stabilization, the pressure to maximize profit using the most efficient mechanism λₜ reasserts itself. The system resumes recursive compression. The bailout boosts Hₜ temporarily but leaves the incentivization mechanisms unchanged—or even intensifies them, since firms learn to count on bailouts.

Thus, Minsky’s cycle—from hedge (income-covered lending) to speculative (liability-covered lending) to Ponzi (debt-covered lending), and then to crisis/bailout—illustrates the entropic rhythm implied by the formalizations of the HLE within economics. Local convergence (all firms learning the same high-leverage strategy) demands global divergence (risk pushed into the public balance sheet). The cycle persists by consuming its own uncertainty and periodically conscripting the wider environment (the public) to absorb the waste.

To maximize profit, maximize share value. Share value correlates positively with debt load. To maximize share value, maximize debt load. To maximize permitted debt load, pressure regulators to loosen regulations, and so forth. λₜ is recursively reinforced.

4.2. Recursive Collapse in LLMs

Recursive model-training collapse, as documented by Shumailov et al. [6], provides the clearest contemporary demonstration of the HLE. These results show that repeated self-optimization drives distributional variance toward zero: improbable outputs vanish, and the system converges on a single dominant attractor. This is parallel to what Ashby described in his original Law of Experience, but applied to a stochastic high-dimensional manifold rather than a determinate machine.

This collapse dynamic is a direct empirical instance of the informational Rebis equation dynamics. With repeated self-training, λₜ (gradient dominance) approaches 1 as stochastic input ηₜ decays, driving the model’s output distribution toward a single-mode attractor (Hₜ approaches 0, “convergence to delta”). The result is an effectively determinate model: stochastic sampling remains technically possible, yet draws yield nearly identical sequences. Entropy decays with recursive exposure, and the system increasingly approximates a closed transformation of its own prior state. However, when the authors continuously substitute 10% of model outputs with the original human-sourced training data (a boost to ηₜ and throttling of λₜ), functional degradation is largely mitigated. Other studies show that, as models become optimized according to AI benchmark metrics, the result is “narrow behaviors that result in distinct disadvantages”, with optimized models being less capable of randomness and less creative than baseline models [30]. This pattern closely parallels classical overfitting in machine learning, where optimization improves performance on a narrow training distribution while degrading generalization and robustness across other inputs. In this sense, overfitting can be understood as a specific instantiation of the broader HLE dynamic: recursive optimization driving variance collapse when stochastic or exploratory inputs are insufficiently maintained.

Wang et al. [31] provide convergent evidence: recursive fine-tuning on mis-specified distributions induces variance collapse—manifesting as emergent “persona” attractors—while re-exposure to benign data (“even unrelated to alignment”) restores distributional diversity. Such benign data map onto the Rebis relationship as injections of ηₜ that counteract λₜ-driven contraction. Their findings are consistent with the predicted entropy-replenishment dynamics of the HLE. The authors do not formalize this geometry; they show what happens, whereas the HLE explains why it happens.

Uniform inputs are not required for systemic collapse. Probabilistic sampling still obeys the same law when a dominant gradient compresses the effective output manifold as experience accumulates. The model’s transformation becomes single-valued in practice, satisfying the definition of a determinate machine in the limit.

4.3. Inbreeding: Genetic Diversity Loss via Self-Sampling

A biological instance of this geometry can be found in genetic inbreeding, which is the recursive reuse of genetic material within a bounded population. Each generation samples from its own outputs, recombining an ever-diminishing subset of allelic variance. Excepting mutation (as the classic equation does), stochastic recombination becomes functionally determinate as heterozygosity decays.

In population genetics, this reduction can be expressed as the inbreeding coefficient

$$F_t=1-{(1-{\displaystyle \frac{1}{2N}})}^t,$$

(6)

where N is population size and t is the number of generations. As t increases, Fₜ approaches 1, representing total fixation of alleles [32]. The population becomes effectively determinate with respect to allelic variation. In such a regime, injected variance cannot keep pace with the optimization gradient, inhibiting the introduction of genetic variety.

All of this assumes an idealized regime in which environmental conditions remain permissive enough for inbreeding to proceed without causing population collapse. In natural systems, however, such conditions are rarely sustained. Populations prone to inbreeding are less fit in the long-term relative to those that tend towards outcrossing, making complete genetic closure of this kind rare to observe [33,34], supporting the claim that injections of novelty are crucial for maintaining adaptive variety just as adaptive variety is crucial for maintaining reactive variety under non-static environments.

If the HLE holds, we should expect evolution to select mechanisms that resist recursive closure. Sexual reproduction is an archetypal example. It is a major drag on baseline reproductive efficiency, introducing expensive and complex developmental and behavioral overheads; the so-called “twofold cost of sex” [35]. Yet sex persists across the clades of multicellular life.

The preponderance of sex implies a deep teleonomic “recognition” that the fostering of long-term variance is worth the steep price. Asexual lineages reproduce more efficiently but suffer from reduced adaptive potential and faster accumulation of deleterious mutations—the so-called Muller’s ratchet effect [36]. The HLE maps directly onto Muller’s ratchet: a lineage that copies itself—without an offsetting mechanism for variance injection—experiences cumulative information loss. Each replication turns high-entropy diversity into low-entropy regularity—a major risk for lineages exposed to environmental instability. Sexual recombination functions as one biological stochastic shock mechanism that counteracts this contraction. In effect, eukaryotic systems pay an ongoing energetic and reproductive premium to maintain variety across generations.

When sexual lineages inbreed, that investment is largely squandered. The machinery of recombination remains, but the informational diversity it is meant to generate is severely blunted. The population pays the cost of sex without gaining its benefit. Again, assuming that the injection of variety is critical for long-term viability, we would expect to find mechanisms that support the variance-boosting mechanisms of sex. We do: hybrid vigor, outbreeding preference, and anti-inbreeding disgust responses [37,38]. The preservation of these complex and expensive mechanisms suggests the importance of maintaining variance within clades.

Even the apparent exceptions to Muller’s ratchet—such as the asexual bdelloid rotifers—illustrate the same geometry. Their genomes are mosaics of outside DNA acquired during desiccation-rehydration cycles, effectively importing environmental genetic variance [39,40,41]. In the context of the HLE, this process can be understood as a periodic replenishment of ηₜ—stochastic shock required to maintain persistence under recursive self-sampling. If bdelloid lineages were fully isolated from all exogenous genomic input the HLE suggests that their genetic reservoir would drain. Conversely, if such lineages remain viable, they should exhibit compensatory mechanisms that restore ηₜ, such as elevated mutation rates or chromosomal anomalies.

Viewed in the context of the HLE, asexuality, horizontal gene transfer, sexuality, and polyploidy can be framed as escalating biological strategies for preserving variance under recursive selection pressure. Each introduces additional degrees of freedom that counteract experience-mediated contraction. Evolution, in this sense, has teleonomically “rediscovered” the same geometry of persistence at increasing energetic cost.

The biological inbreeding example mirrors recursive self-sampling in AI (Section 4.2). Mutation-driven diversity and outbreeding parallel the injection of fresh data from external sources. The absence of such mechanisms leads to collapse, demonstrating the same entropic decay under recursive cycling.

4.4. Neurological Parallels: Plasticity and Habituation

While evidence at the scale of human cognition is less formalized than in AI training or inbreeding, human neurology exhibits geometry consistent with the HLE on the scale of individual organisms. Repetition induces experiential suppression effects via reduced neural responses and tuning sharpening—the preservation of variance for novel situations. Repetition enhancement arises in specific regimes consistent with predictive-coding accounts [42,43].

Habituation reflects local optimization—an increase in λₜ that compresses responses to redundant inputs—yet serves a global stabilizing role by preventing the brain from being overoptimized by routine experience. In effect, the system quarantines redundancy, preserving higher-level variety against overfitting to low-novelty environments.

On a longer timescale, biological senescence follows the recurring experience-mediated geometric pattern: “all organisms undergo non-pathological, cumulative, and irreversible synaptic deterioration as they age” [44]. The relation between experience, efficiency, and the loss of adaptive degrees of freedom aligns with Bateson’s work; learning limits learning [13].

In both the long and short term, experience increases local efficiency while eroding unused connections, reducing the system’s effective variety and adaptive capacity. Neuroplasticity therefore mirrors the same geometry observed in computational and evolutionary systems: attractor basins deepen but narrow through repeated transformation, trading flexibility for efficiency [45]. In this light, the folk wisdom of “you cannot teach an old dog new tricks” reads like a recognition of neuroplasticity constraints now supported by recent empirical data and the HLE.

A particularly intuitive instance of the variance/experience dichotomy appears in dreaming and sensory attenuation. During wakefulness, perception includes regular injection of novelty—unexpected sensory input, task-level perturbations, and the everyday shocks of lived experience (ηₜ)—combined with ongoing optimization and prediction (λₜ). Under the predictive-processing view, wakefulness corresponds to high-precision sensory prediction errors anchoring the model to the external world.

As sensory input (and therefore exogenous ηₜ) falls toward zero during sleep, the brain compensates by generating endogenous variance through spontaneous imagery and narrative construction. From this perspective, dreams function as internally generated perturbations that maintain representational entropy: the system injects its own ηₜ to avoid collapse into overly rigid (high-precision) priors. This is structurally consistent with recent framings of psychedelic drug mechanics, where reduced sensory precision allows high-level priors to expand, explore, and recalibrate [46].

Selective forgetting of dreams fits within this geometry. Integrating self-generated noise too faithfully into the waking model would contaminate externally anchored inference with internally produced variance. Dream amnesia therefore acts as a filtration mechanism: endogenous ηₜ is used for maintenance but prevented from leaking into the high-precision λₜ regime of wakefulness. When this filtration weakens—when REM-like (rapid eye movement) dynamics intrude into waking states—the resulting distortions align with known correlates of hallucinatory intrusions and psychosis [47]. This framework suggests one possible interpretation of schizophrenia as involving dysregulated precision assignment: inappropriate elevation of internally generated variance relative to sensory precision, consistent with predictive-processing interpretations of aberrant salience and dysregulated precision assignment.

Sensory deprivation offers a parallel demonstration. When external ηₜ is experimentally suppressed (e.g., flotation tanks), subjects reliably report vivid visual and auditory hallucinations once input falls below a threshold [48,49]. Under the HLE framing, both dreaming and deprivation-induced hallucination illustrate the same underlying principle: when exogenous perturbation decreases, the system must generate endogenous perturbation to preserve representational flexibility. The brain appears to maintain some baseline level of internal variety generation. Even at the perceptual level, the HLE predicts that robust recursive systems require some means to supply internal variance when the environment no longer does.

Studies of subjective time estimation under altered sensory environments found that the rate of the cognitive timer is environment-dependent: when sensory variety increases, subjective time expands; when inputs are repetitive or deprived, perceived time compresses [50]. In Hypernetic terms, temporal experience scales with ηₜ—the richness of environmental perturbation. Low-variance environments produce time contraction and experiential smoothing, while high-variance conditions expand subjective duration and novelty density. In other words, the brain seems to be disregarding experience in order to preserve internal variance.

While speculative, modern attention disorders may reflect a kind of environmental Rebis imbalance rather than some innate neurological deficit. As human systems grow increasingly optimized (high λₜ), endogenous noise generation or chemical interventions (ηₜ) increase in prominence [51,52]. The rise of stimulant use and micro-stimulation behaviors (fidgeting, for example) can thus be interpreted as compensatory stochastic shock mechanisms for an environment that is becoming over-determinate for an increasing proportion of human minds. People who may have been perfectly functional in less optimized/higher-ηₜ environments are diagnosed as disordered due to their inconvenience.

Neurophysiological evidence is consistent with this interpretation. Studies of auditory stimulation in ADHD (attention deficit hyperactivity disorder) individuals found that both random (pink noise) and structured (pure tone) external signals reduce neural noise while improving cognitive performance [53]. This is consistent with the varietal maintenance implied by the HLE. The idea is that external stimulation provides the cognitive perturbation that ADHD brains require, allowing local resources to focus on task performance rather than self-stimulation. By boosting environmental noise, the task of stochastic shock generation falls to the environment rather than requiring endogenous stimulation through fidgeting, self-talk, or mind-wandering.

The number and complexity of neurological mechanisms with coherent mapping to the HLE/Rebis supports the importance of accounting for experience-mediated degradation in recursive systems. Biological learning systems have had millions of years to evolve under these constraints. If recursive exposure to optimized outputs inevitably compresses internal variety, and if the collapse in internal variety is detrimental to long-term survival, then we should expect any brain capable of long-term persistence to have means to counteract it. Processes such as meta-plasticity [54], neuromodulatory feedback regulating the explore/exploit balance [55], and sleep-driven synaptic renormalization [56] can be viewed as anti-collapse apparatus that modulate variance and guard against over-specialization.

In contrast, artificial recursive systems like AI, bureaucracies, social media platforms, and economies are recent inventions. Their architectures do not universally contain anti-compression dynamics as features. They exhibit the HLE in its unmitigated form—as dumb recursive optimization machines without the intricate mechanics that biological systems produced over countless generations of selection under a consistently changing input distribution.

4.5. Linguistic Convergence

The same geometry manifests at the scale of languages. Over centuries, human linguistic systems, once proliferating in relatively isolated ecological and cultural niches, have come under increasingly uniform global gradients: literacy, trade, media, and capital. These shared selection pressures act as recursive filters on linguistic variance. As speakers and institutions repeatedly transmit language through standardized educational and digital channels, idiosyncratic forms are smoothed away.

This becomes clear through revisiting the informational Rebis with a linguistic focus in mind, with Hₜ denoting the ensemble entropy of phonological, grammatical, and lexical features across languages worldwide at time t. Exposure to uniformity within semiotic environments boosts the optimization gradient λₜ—the strength of composite homogenization pressure (standardization in media, formal schooling, market integration, and so forth)—and ηₜ is a composite term that accounts for the novelty injected via slang, creoles, and other linguistic inventiveness.

Empirically, λₜ has come to dominate ηₜ in recent centuries: roughly half of the world’s approximately 7000 languages are projected to vanish by the year 2100 [57]. Linguistic convergence thus constitutes a cultural instance of the HLE. Capital operates as the context-dominant attractor, privileging communicative efficiency and global legibility, while literacy and digital media as its proxies. Dialects, minority languages, and oral traditions are pruned in favor of optimized throughput, exacerbating the global decline of linguistic diversity [58]. This contraction yields efficiency in global communication but brittleness in adaptability: the system becomes more synchronized and less diverse, trading fertility for fluency.

A striking corollary emerges in the rise of mathematics as the lingua franca of capital. Archaeological and historical evidence indicates that the majority of the early mathematical artifacts—Mesopotamian tablets, Egyptian papyri, and Chinese counting rods—were overwhelmingly concerned with accounting, construction, and debt calculation rather than astrology or abstract speculation [59,60,61,62]. From its inception, mathematics served as the semiotic infrastructure of property and exchange. As markets globalized, this shared grammar of numbers, accounting, and algorithmic optimization supplanted local symbolic forms, allowing value, risk, and prediction to circulate across linguistic and cultural boundaries. Mathematical literacy became the substrate of global market legibility; an ultra-efficient compression code for exchange, coordination, and control. This represents the extreme case of linguistic convergence: a universal formalism optimized for transaction throughput, but utterly abstract and indifferent to local meaning.

AI systems, inherently formal and computational, interface with capital in its native medium. Each generation of models translates more of human activity into computable form [63], further extending mathematics as the lingua franca of economic coordination. The operations most native to capital (high-frequency trading, risk modeling, logistics optimization) are now executed overwhelmingly by machines, whose speed and fluency exceed human capacity by orders of magnitude [64,65]. The long-term socioeconomic effects remain uncertain, but it is widely acknowledged that automation will displace some forms of human labor for a more efficient artificial substitute [66].

A further extension of this idea concerns the other languages of capital. Historical accounts consistently frame modern capitalism’s point of origin as the Dutch Republic and England, where commercial expansion, Protestant literacy, and emergent financial institutions converged to produce the first fully capitalist systems [67,68]. Linguistic features, like the grammatical emphasis on tense, linear causation, and explicit quantification within English/Germanic languages—not universal among the world’s languages—may have improved the semiotic substrate’s likelihood to spark the runaway of contractual, ledger-based economic relations (cf. [69,70,71]).

This observation is not meant to support strict linguistic determinism, nor to rank the quality of languages or their speakers, nor to imply that causation was simple or mono-directional. The pressures of exchange and linguistic development share a reflexive relationship even today. Our proposal is that certain grammatical architectures not common to all languages align more readily with the temporal and numerical logics where capital thrives—a kind of co-evolution: linguistic structures that facilitate abstraction, tense, and quantification may have made scalar exchange logics easier to ignite into capitalism as we know it, just as pre-capital buying/selling pressures had stabilizing effects on those linguistic features. What began as a local mode of expression became an overwhelming global gradient once it was embedded within expanding trade networks, colonial infrastructures, scientific discourse [62,72,73,74], and computer systems.

Recent work on multilingual large language models is consistent with this pattern. Schut et al. [75] demonstrate that, even when models are trained and prompted in other languages, their internal reasoning steps occur within an English-shaped latent space. Semantically loaded tokens in French, Mandarin, and German are handled as English-adjacent embeddings before being translated into the target language. Moreover, activation-steering interventions are most effective when computed in English, revealing that the model’s control geometry—the layer where “thought” occurs—is Anglocentric by default.

Etxaniz et al. [76] find that instructing LLMs to translate non-English prompts into English before reasoning improves performance, with this advantage growing larger at scale. Paradoxically, more capable models show greater English-dependence, not less, suggesting that English-centric reasoning represents a strengthening attractor rather than a transient limitation. In effect: these systems think better in English. What began as a linguistic convenience for early computer science has congealed into a global cognitive substrate.

The world’s dominant programming languages—C, C++, Java, Python, JavaScript, C#, and so forth—are overwhelmingly Anglomathematical in form, with English keywords bound to algebraic grammar, then rendered purely mathematical when compiled. In this view, contemporary AI—mathematical in substrate and trained predominantly on English corpora—emerges as the heir to that lineage: an Anglomathematical techno-linguistic agglomeration arising from a post-modern semiotic slurry—capital learning to think in English.

4.6. The Loudness War

Using the informational form of the Rebis equation, we can treat Hₜ as the Shannon entropy (effective uncertainty) of amplitude distributions, λₜ as optimization pressure toward loudness, and ηₜ the introduction of novelty or stochastic variation. Over time, the competitive gradient λₜ dominates the injection of novelty ηₜ, and the entropy of the amplitude distribution collapses.

Empirically, Haghbayan et al. [77] show a six-decade contraction in track-to-track loudness (modal level shifting from loudnesses of −20 dBFS in the 1950s to −8 dBFS in the 2010s, accompanied by a contraction in SD from 5.1 to 4.3). In Hypernetic terms, the recording industry’s recursive optimization for competitive loudness motivates λₜ: amplitude entropy declines toward a single attractor. The pattern, once again, mirrors Shumailov et al.’s model-entropy collapse in recursive AI training [6], with listener preferences substituting for token-level reward.

The result is a drift towards maximal volume: informational diversity collapses toward a single over-compression attractor. What began as stylistic experimentation becomes a uniform plateau of loudness, with songs differing in melody or genre but sharing increasingly similar amplitude landscapes. Listeners describe the outcome as perceptual fatigue; excessive loudness and reduced dynamic entropy diminish engagement and may even risk hearing loss [77,78]. Dynamic range compression eliminates the system’s capacity for contrast and nuance along a music–critical information axis.

4.7. Innovation Collapse in Peer-Reviewed Journals and Patents

The findings of Park et al. [79] illustrate the HLE on a wide cultural/scientific scale. Analyzing 45 million papers and 3.9 million patents, they report a universal decline in the disruptiveness of scientific and technological (patent) work across six decades, measured in terms of the effect size a contribution has on its citation network—a functional measure of variance within domain knowledge manifolds.

Despite exponential growth in publication volume, disruptiveness collapses across all fields. In Hypernetic terms, the scientific ecosystem exhibits rising λₜ (pressure for publishable, fundable, citable work) and declining ηₜ (stochastic introduction of unconventional ideas and forms). Citation networks narrow and novelty suffers. The system learns to reproduce its own outputs as inputs, optimizing scientific endeavors for institutional fitness rather than epistemic expansion. In a follow-up editorial, Leahey [80] summarizes: “[critics say that] researchers and institutions take the safe option to keep the grant–publication–citation wheel turning.”

The observed decline in CD mirrors the Rebis geometry. As λₜ maximizes and ηₜ dwindles, the epistemic manifold contracts toward determinacy. The scientific process becomes a determinate machine optimized for self-consistency over novelty. Park et al. [79] describe this as a “fundamental shift in the nature of science”—a transition from an open system to one of closed optimization.

The replication crisis represents the same HLE-mediated contraction at the level of scientific methodology. Peer-reviewed journals increasingly optimize for legibility and publishability over discovery (cf. [81]). In scientific practice, this manifests when researchers—generally proficient in modeling and operating under strong institutional and financial incentives—tailor their work to the most legible evaluation conventions; for example, treating p < 0.05 as a fixed criterion of validity, incentivizing p-hacking [82]. Editors, in turn, are constrained by complementary logic: once statistical significance is established, publication is systemically pressured even when the work’s value is minimal.

As scientific efficiency rises, its internal diversity collapses. Each refinement consumes part of the variance reservoir that once sustained discovery. Unless optimization pressure (λₜ) is muted through editorial focus on less gameable evaluation criteria, or organizations give more weight to unconventional scientific approaches by unconventional people (ηₜ), science is likely to stabilize into a high-efficiency, low-entropy epistemic monoculture.

4.8. The Geometry of Collapse

Across these examples, the same geometric pattern recurs: recursive optimization under experience drives variance collapse, concentrating system behavior into increasingly narrow attractors.

The Rebis relationship describes this contraction as variance consumption under optimization pressure. Initial system diversity spans multiple viable states, but accumulated experience progressively narrows behavioral repertoires even as local performance improves.

The HLE therefore formalizes a geometric trade-off between efficiency and adaptive capacity that manifests across substrates—from genetic diversity to linguistic variation to neural plasticity.

5. Discussion

For Ashby, experience meant the erosion of a system’s initial distinctions under repeated transformation—a thermodynamic process rather than one of psychology or learning necessarily. Recasting this in the Hypernetic frame reveals its full scope: experience is bound to internal entropy decay. What appears as learning or adaptation is, in a geometric sense, a contraction of variance. Efficiency rises and flexibility falls. Systems that minimize entropy too rapidly exhaust their capacity for further change. In that way, intelligence and brittleness can emerge from the same optimization dynamics. The HLE therefore defines experience as the dynamic tension between entropy reduction (optimization) and variety retention (adaptability). Persistence depends on balancing the two; collapse arises when compression outpaces renewal.

The HLE nestles neatly within Ashby’s classic architecture. Requisite Variety governs external coupling—a system’s variety must match the environment’s complexity. The HLE governs internal evolution—systemic experience continually consumes that variety. Together they form a cybernetic dyad: systems must generate variety to compensate for its erasure. This symmetry underlies familiar trade-offs—explore/exploit in machine learning, mutation rates in biology, novelty/expertise as it pertains to human competency. The ratio between experiential compression and renewal defines a system’s viability in the long-term.

Brittle collapse in recursive systems is the result of excess stability rather than disorder. Increasingly recursive feedback makes the system too certain of itself; outputs loop back as inputs until the model of reality replaces reality; the map becomes the territory. Recursive optimization converts openness into closure.

The HLE/Rebis geometry applies consistently across domains. In machine learning, over-fitting eliminates novelty; in finance, prediction of prediction displaces fundamentals; in biology, inbreeding collapses the gene pool; in culture, echo chambers wall off dissent. All manifest the same geometric drift (λₜ ≫ ηₜ)—optimization ironically drowning out the noise. The HLE therefore generalizes recursive collapse as an attractor state generated through successive feedback.

Systems that remain robust under transformations to their input distributions reliably conserve some kind of variety-expanding channel. Sustained self-reference pulls systems toward brittle optimization and determinacy unless continually perturbed by independent signals—by looking up occasionally to see the territory instead of myopically fixating on the map.

6. Conclusions

The HLE generalizes across systems. In biological evolution, closed breeding pools lose adaptive potential; in social systems, ideological echo chambers erode collective decision-making; in AI, systems training on data generated by themselves or other systems leads to performance degradation; in individual cognition, fidgeting and dreaming compensate for high-optimization environments; within the linguistic ecosystem, the use of rare languages falls as utility dominates; in music, less compressed tracks struggle to compete; and in science and technology, optimization pressures and metric gaming select for superficial compliance rather than genuinely interesting work. Each is an instantiation, at least in part, of parallel geometry that goes deeper than surface mechanics. The persistence of an adaptive system depends on maintaining legible, durable, redundant channels to environmental information. Environments drift. If an over-optimized system experiences an abrupt, significant change in its input distribution, the system is too brittle to generate viable responses to novel and challenging perturbations. Each example illustrates the same broad feedback geometry: optimization without replenishment erases variance.

Ashby’s homeostat demonstrated that equilibrium can persist only while a reservoir of variety remains. In HLE terms, ultrastability is the limit where entropy reduction (λₜ) and stochastic input (ηₜ) perfectly counterbalance. Real systems never reach such a state—due to thermodynamics if nothing else. Feedback latency and lossy interpretation guarantee drift. Every input channel (biological, artificial, cultural) exhibits semiotic porosity: the sign never fully contains its referent. Information loss couples with material entropy to yield systemic brittleness in the limit.

This framing invites a shift in how we evaluate what constitutes system success. Instead of measuring short-term performance or stability, it makes more sense to assess the persistence qualities of systems over time under a wide variety of possible input distributions, and to tune optimization and stochastic shock processes accordingly such that the capacity for adaptation is reliably retained.

If we accept that the HLE manifests in large-language models as recursive narrowing of representational diversity, and those narrowed outputs shape human cognition in turn, then a direct continuity of risk emerges between artificial and biological domains. Empirical studies show that exposure to AI-generated text can reinforce prior beliefs and reduce openness to alternative views [83]. Small initial biases that are embedded within AI training data are amplified when converted to AI algorithms, and humans interacting with those biased AI systems have their own biases intensified, suggesting a bridge between artificial and human cognition. This echoes concerns that AI exposure can have negative effects on human agency [84].

The ubiquity of variance-protecting mechanisms in biology—from meta-plasticity in neurons to hybrid vigor in genetics—suggests that the HLE is not an incidental pattern but a fundamental constraint on persistence. Living systems invest heavily in processes that counteract the compression of experience—the two-fold cost of sex, dreams—because failure to do so is an existential risk. By contrast, most human-designed systems—economic, bureaucratic, algorithmic, and even scientific—optimize recursively with few or no endogenous variance-restoration mechanisms. They behave, in effect, as naïve learning systems that continually amplify λₜ while allowing ηₜ channels to be muted. The result? Boom/bust cycles in markets, institutional monocultures in governance, and recursive collapse in AI models trained on their own outputs.

If biological evolution treats variance preservation as life and death, its absence as a design principle across human recursive systems warrants scrutiny. The HLE therefore suggests evaluating social, economic, and computational architectures by their capacity to regenerate variance under recursion, and incorporating variance-restoration mechanisms as a core design requirement for systems intended for long-term persistence.

7. Future Directions

There are substantial and varied opportunities for follow-up work to the ideas established and explored in this paper.

7.1. A True Cross-Domain Principle?

If further empirical validation confirms the HLE’s broad applicability, it may represent a foundational principle for Hypernetics and other systems science approaches—a true universal for recursive systems. Such a principle could profoundly inform our understanding of variance dynamics across domains, with potential applications ranging from AI safety to institutional design to economics—and beyond, to all manner of human concerns.

7.2. Explore the Rebis Equation

The Rebis equation was developed by extending Ashby’s Law of Experience [1] beyond deterministic transducers to stochastic, recursive systems. Its form emerged from cross-domain theoretical synthesis. Echoing Ashby’s own methodological style, this is evidence from structural coherence and empirical generality rather than axiomatic proof. Preliminary reasoning suggests strong coherence with empirical material across domains, yielding insights and predictions. Empirical studies could refine and parameterize its coefficients—λₜ and ηₜ—by fitting variance decay curves to time-series data in biological, economic, and linguistic systems. Biological data can be used to track genetic variance in populations under controlled selection pressure, estimating λₜ from selection intensity and ηₜ from mutation rate. Corpus studies could measure lexical or syntactic entropy over time to see whether linguistic optimization similarly contracts diversity. Further work should also examine how λₜ and ηₜ are regulated in living systems—such as stress-induced mutagenesis in bacteria [19]—to identify “solved examples” for balancing optimization and stochastic shock in designed systems.

7.3. Systems-Focused Biomimicry

The HLE suggests a systematic approach to learning from biological variance preservation mechanisms. Beyond morphological “inspired by nature” biomimicry (velcro, airplane wings), we propose studying evolution’s 4-billion-year solutions to recursive optimization problems. For example, rather than looking to low-level human or animal cognitive architectures for inspiration on resolving AI alignment (cf. [85])—since the minds of humans and animals are not reliably aligned themselves—researchers could examine evolution as a meta-system that has successfully maintained long-term viability despite recursive optimization pressure. Evolution’s variance preservation mechanisms—sexual reproduction as stochastic shock, stress-induced mutagenesis as adaptive ηₜ modulation, population structure as distributed redundancy—offer design principles for building AI systems that remain robust under recursive self-improvement. Looking to biology for cross-domain organizational principles to mitigate optimization collapse may yield more robust solutions than rote physiological copying.

7.4. HLE Auditing

Given that most existing adaptive systems were designed without awareness of variance collapse dynamics, systematic HLE auditing of critical infrastructure is warranted. Social media algorithms, financial markets, educational systems, political apparatus, bureaucratic processes, and scientific institutions should be evaluated for vulnerabilities to optimization-driven brittleness as a test of its predictive validity across human systems.

7.5. Design LLM-Focused Persistence Experiments

With clear evidence that artificial systems adhere to HLE dynamics, they should make ideal laboratories for testing the Rebis equation. Recursive-training studies can measure variance half-life under controlled noise injection. By systematically varying λₜ (strength of fine-tuning) and ηₜ (introduced novelty), we can test whether moderate stochastic shock maximizes long-term diversity without destabilizing performance. Multi-model ensembles or periodic “memory resets” could operationalize this idea. Wang et al. [31] show that “misaligned persona” features can be corrected by small doses of benign data (reinjection of ηₜ), while Shumailov et al. [6] demonstrate that maintaining even 10% of the original training corpus prevents collapse (a combination slight λₜ reduction and boost in stochastic shock ηₜ)—useful starting points for systematic exploration of the Rebis equation.

7.6. Study HLE-Mediated Optimization Cascades Across Domains

As we observe throughout this work, optimization effects are not siloed (e.g., a tech firm optimizing their operations for profit optimizes their AI products for profit, which optimizes human behavior for profit, and so forth). These cross-domain HLE effects may exacerbate in-progress overoptimization processes (conspiracy-style thinking, cultural polarization). It makes sense that sustained exposure to increasingly optimized, low-variance LLMs and other AI products may reduce creative or exploratory behavior in human users. Joint studies could measure cognitive-diversity metrics—as entropy or originality in the answer pool—before and after long-term interaction with different model classes. Similar variance-contraction dynamics may occur in human education, where over-optimization of curricula or standardized testing suppresses exploratory variance. We could explore whether controlled usage of stochastic shock and throttling of optimization pressures preserves optimization.

7.7. Reexamine Classical Cybernetics Material in Light of Modern Systems

Finally, the HLE’s origin in classical cybernetics suggests that it may be worthwhile to assess underexplored aspects of the discipline’s heritage. Shumailov et al. [6] do not cite Ashby or any canonical cyberneticists in their influential work—which is not unexpected, considering the obscurity of the original law and because there was no formal bridge to stochastic systems. Although Ashby uses examples from across domains to illustrate his ideas, his work remains most influential within the context of mechanical control systems—thermostats, switches, and signaling apparatus. But the HLE suggests that at least some core cybernetics ideas may be worth revisiting considering our updated knowledge of complex systems. There may be other insights in the works of Ashby, Wiener, Bateson and other first-wave cybernetics figures that are more practical now than they ever have been.

If the same geometric trade-off between optimization and diversity recurs across minds, machines, and societies, identifying its parameters may reveal universal constraints on learning itself—and, by extension, design principles for systems that can learn without forgetting how to learn.

8. Summary

Experience, in Ashby’s original sense, is less about knowledge gained than variety lost. The Hypernetic Law of Experience reframes this insight for recursive probabilistic systems. As systems learn from themselves, they approach determinacy in the limit. Entropy declines, adaptive responses decay, and collapse becomes inevitable unless new information is continually introduced. By articulating this geometry explicitly, the law offers a powerful cross-domain principle. Persistence requires careful management of entropy. Systems that fail to balance the compression of experience with the injection of variety will converge upon collapse—in data, in genes, or in thought.