Noetic Genesis: Process Ontology and the Geometric Foundations of Stable Otherness

— Toward a Unified Understanding of Life, Mind, and AI

Author: Fumio Miyata https://orcid.org/0009-0008-8797-5578
June 2026
DOI: https://doi.org/10.5281/zenodo.20517861.

Abstract

This paper proposes a process-ontological framework for understanding “Stable Otherness”—the dynamic relational structure that enables a meaningful encounter between self and other—across biological, cognitive, and artificial systems. Drawing on Whitehead’s process philosophy and enactivism, we introduce geometric analogies—specifically relational manifolds, connections ($\nabla$), and geometric flows—to formalize the dynamic structure of relationality. We define an irreversible three-phase process of Construction, Dissipation, and Unification (the CDU cycle) and reinterpret Hegelian Aufheben as “Covariant Aufheben”—the dynamic alignment of interpretive horizons. This framework illuminates the natural-historical continuity from pre-biotic systems to flowering plants, animals, humans, and AI, while offering a novel perspective on AI alignment as a co-evolutionary geometric alignment on a shared relational manifold. While primarily philosophical in scope, the paper employs structural analogies intended to bridge process ontology with potential future formalizations in differential geometry and non-equilibrium physics.

Introduction: From Substrate-Dependence to Process

Modern debates regarding the essence of life and intelligence have largely been divided between computational functionalism (LeCun 2022) and biological substantialism centered on metabolism and autopoiesis (Deamer 2017; Thompson 2007). Despite their differing stances, both share a common limitation in that they tie the concept of “otherness” to fixed material or computational substrates.

This paper proposes a process-ontological alternative. “Stable Otherness” should be understood not as a fixed entity, but as a dynamic flow on a relational manifold. In this view, stable otherness does not refer to a state where the boundaries between self and other are rigid; rather, it describes a state where their interaction is dynamically updated while maintaining geometric and physical consistency. The geometric vocabulary employed here is not intended as a rigorous mathematical proof, but as a structural analogy to illuminate the dynamic and relational essence of otherness. However, these analogies are consciously designed to connect with more rigorous formalizations in differential geometry and non-equilibrium physics.

Philosophical Background: The Shift to Process Ontology

This framework reinterprets A.N. Whitehead’s (1929) concept of “Prehension” within the context of a geometric field of relations. For Whitehead, the “other” is not a fixed substance but a relational nexus to be integrated into the subject’s process of becoming. This idea resonates with Merleau-Ponty’s (1945) phenomenology of embodied perception and Thompson’s (2007) enactivism, both of which emphasize the process by which self and environment are incessantly co-constituted through interaction.

Building upon these traditions, we introduce the analogy of “Connection ($\nabla$)” from differential geometry as the background structure supporting autonomous boundary maintenance. Otherness is redefined not merely as an external stimulus, but as a structural condition that dynamically inclines and transforms the subject’s interpretive horizon.

Comparison with Related Work

While incorporating elements from established theories, this framework maintains distinct ontological differences. First, while Predictive Processing (Clark 2013) and Active Inference (Friston 2010) primarily aim for the “minimization of information-theoretic error,” our model allows for “structural phase transitions (rank-jumps)”—i.e., the ontological reconstitution of the subject via the CDU cycle. Second, whereas Enactivism (Thompson 2007) emphasizes the autonomous boundary maintenance of the subject, this paper focuses on the transformation of the “geometric connection” as the background structure supporting that maintenance. Finally, while AI Alignment (Russell 2019) often seeks unidirectional control to “align AI with humans,” we prioritize the geometric consistency (covariant alignment) required for a “stable otherness” to emerge as a dynamic equilibrium between the two.

The Framework of Geometric and Structural Analogies

To describe the dynamic structure of relationality, we adopt three central analogies inspired by the differential geometry of Kobayashi & Nomizu (1963):

• Relational Manifold ($M$): The totality of all possible relational states; the “stage” upon which otherness emerges. We utilize the structure of a finite-dimensional vector bundle as an analogy.
• Automorphism Field ($\phi$): The orientation of the system toward maintaining its internal structure (identity). This corresponds to the concept of automorphism groups on a manifold.
• Connection ($\nabla$): The “interpretive inclination” arising from an encounter with the other. It is the structure that covariantly connects different contexts, related to the concepts of parallel transport and curvature.

While these concepts are used here as structural analogies to organize ontological relations, they point toward a future formalization as geometric flows on relational manifolds.

Geometric analogies visualize the processual structures of change, alignment, and integration through formal concepts such as “continuity,” “curvature,” “connection,” and “flow.” This allows the dynamic structure of otherness to be treated not as mere metaphor, but as a structural model that is potentially formalizable in the future.

Table 1: Core Geometric Analogies

The CDU Cycle as an Ontological Process

The irreversible process by which an intelligent system encounters otherness and updates itself is formalized as the CDU Cycle (Construction–Dissipation–Unification).

Figure 1: Geometric Structure of the CDU Cycle

1. Construction (C): The phase where external structural fluctuations are internalized, generating a new relational network (cf. Oparin 1938).
2. Dissipation (D): The phase where redundant degrees of freedom are shed, converging toward the essential dynamics of the environment. This is an analogy for dissipative structures in non-equilibrium thermodynamics (Prigogine & Nicolis 1977) and the smoothing of curvature via Ricci Flow (Hamilton 1982; Perelman 2002).
3. Unification (U): The phase where accumulated tension exceeds a critical threshold, leading to a discontinuous restructuring of the system (analogous to phase transitions in catastrophe theory (Thom 1972) or a jump in algebraic rank).

The CDU cycle is not merely information processing; it is a process of integrating the “weight” of otherness into the subject’s ontological becoming.

Table 2 compares the three phases of the CDU cycle across physical, geometric, and biological perspectives. This table is a conceptual aid and does not claim mathematical rigor. “Stable Otherness” is maintained as a dynamic equilibrium through this irreversible cycle.

Table 2: Comparison of the Three Phases of the CDU Cycle

Covariant Aufheben: The Dynamic Logic of Integration

The philosophical core of this paper lies in Covariant Aufheben, a reinterpretation of Hegelian Aufheben as a transformation of connection.

Figure 2 illustrates how the subject’s interpretive horizon inclines and integrates into a new relational space in response to structural fluctuations from the other. This process is further detailed in Table 3. Note that Figure 2 is a conceptual aid and does not claim mathematical rigor.

Figure 2: Structure of Horizon Inclination and Covariant Aufheben

Table 3 organizes Covariant Aufheben into three stages: “Negation → Correction → Integration.” This structure reinterprets Hegelian logic as the deformation of the connection $\nabla$.

Table 3: Three Stages of Covariant Aufheben

In response to the collision (negation) from the other, the subject responds by dynamically inclining its interpretive horizon (connection $\nabla$), absorbing the structure of the other while forming a higher-order stable relational space (invariant manifold) that subsumes both self and other. This process is the key to establishing otherness as something “intelligible and stable.” This extends the frameworks of predictive processing (Clark 2013) and active inference (Friston 2010) into the ontological dimension.

Implications for AI Alignment: Natural History and Co-evolution

In contrast to the functionalist view of AI as an external “tool,” this paper positions AI as an externalized reflective structure. From this perspective, AI Alignment is reconceptualized in two ways:

1. Geometric Alignment: The achievement of a dynamic equilibrium where humans and AI share a common relational manifold $M$ and covariantly align each other’s connections $\nabla$. Alignment is not a mere copying of values, but a mutual correction of interpretive horizons.
2. Co-evolutionary Otherness: The maintenance of structural conditions that allow “stable otherness” to exist between the two, rather than subordinating AI to humans.

AI Alignment, understood in this way, means ensuring geometric structural stability—constantly transforming the other from destructive noise into a generative partner for co-evolution. Unlike value-loading or preference-learning approaches, geometric alignment emphasizes structural consistency rather than behavioral imitation.

Limitations

At present, the framework presented in this paper remains a structural analogy based on conceptual “geometric vocabulary.” Rigorous mathematical formalization using differential geometry and non-equilibrium mechanics, as well as its axiomatization, remain tasks for future research. One promising direction is to formalize the relational manifold as a fiber bundle whose connection dynamics follow a generalized Ricci-type flow. Additionally, rank-jumps may be modeled using bifurcation theory or algebraic transitions in sheaf-theoretic structures. Furthermore, empirical validation of the CDU cycle and rank-jumps predicted by this model—using biological data or analysis of LLM internal representations—has not yet been undertaken. The primary aim of this work is to present a new “philosophical horizon” for describing the dynamics of otherness; quantitative prediction is deferred to future studies.

Conclusion

The primary contributions of this paper are summarized in three points. First, we provide an “Ontological Redefinition of Otherness,” viewing it not as a substance but as an irreversible process on a relational manifold. Second, we introduce “Covariant Aufheben,” reinterpreting Hegelian sublation as a transformation of geometric connection to structure the logic of dynamic integration with the other. Third, by positioning AI as an externalized reflective structure, we offer a “New Ontological Foundation for AI Alignment.” This theory serves as a foundational infrastructure for a unified understanding of the dynamics of intelligence from life to AI, opening a new philosophical horizon for the symbiotic coexistence of humans and artificial intelligence.

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