Arendsen’s Complex Idealism

Chemical engineer/computational modeling expert Albert R.J. (Richard) Arendsen’s theory of Complex Idealism posits that reality is fundamentally a continuous, mental, and informational flow of duration. He states that consciousness is an “unsplittable unity” that cannot be modeled computationally, while providing a precise mathematical framework for its systemic communication and physical actuation. Rather than viewing consciousness as an emergent property of material structures or as a passive substance, Arendsen’s framework asserts the ontological primacy of a primary, continuous mental mobility. Within this framework, the descriptor "Complex" signifies the dual-aspect architecture of existence, explicitly accounting for the structural intersection of what we conventionally categorize as "real" and "imaginary" domains (Arendsen, 2026a, 2026b, 2026c).

Arendsen argues that most contemporary models of mind fall into the trap of "spatializing" time—treating both the brain and the universe as discrete computing mechanisms that process static, successive states. Complex Idealism turns this perspective upside down, demonstrating that the measured physical universe is not the generator of experience, but rather a secondary, frozen snapshot precipitated out of an underlying, continuous informational flow.

Unsplittable Unity

A central tenet of Complex Idealism is that consciousness is an indivisible, qualitative whole. Consequently, constructing a functional or algorithmic model of consciousness itself is fundamentally impossible; the universe and the biological brain do not compute consciousness because consciousness is not a computational output. To map the boundary between the experiential and the material, the theory distinguishes strictly between human intuition and intelligence:

• Intuition is recognized as non-numerable and continuous, capturing reality in its immediate, flowing state of duration.

• Intelligence is defined as the specific cognitive faculty of labeling and counting. It operates by slicing the continuous flow of duration into discrete, quantifiable past events for the primary purposes of utility, communication, and social coordination.

By acknowledging these boundaries, Complex Idealism pivots away from traditional computationalism and functionalism. It is explicitly framed not as an elusive model of the conscious generator or regularizer itself, but as a rigorous model of communication and actuation—the exact interface where the unsplittable unity of mental flow manifests as discrete, measurable physical events.

Metaphysical Orthogonality: Alignment and Divergence

To position Complex Idealism within the contemporary philosophical landscape, Arendsen grounds its ontology in process philosophy, drawing deep inspiration from the work of Henri Bergson (Bergson, 1889). Arendsen’s framework adopts the Bergsonian critique of modern science's tendency to eliminate genuine mobility from motion. By representing time as a succession of static, spatialized coordinates on a linear axis, traditional physics mistakes a trajectory—the frozen trail left behind by movement—for the act of moving itself. Complex Idealism re-establishes time as duration, an indivisible, qualitative flow that cannot be reduced to a collection of discrete, static snapshots.

This emphasis on the absolute reality of flow creates a strict, orthogonal contrast with contemporary Analytic Idealism, most notably articulated by Bernardo Kastrup. While both frameworks reject materialist physicalism and agree that reality is fundamentally mental, they diverge entirely on the nature of time. Analytic Idealism posits a fundamentally timeless, spatially unified cosmic consciousness, viewing the flow of time and the passage of events as artifacts of a localized ego's perspective—essentially, an illusion.

Complex Idealism stands in direct opposition to this view: flow is not an illusion; it is the fundamental fabric of reality itself. In this framework, it is the timeless, static space and the discrete, isolated objects within it that constitute the abstraction. Spatialized matter is the secondary byproduct generated when the primary mental flow is measured and counted. Consequently, while Analytic Idealism treats change as an appearance within a static cosmic mind, Complex Idealism treats static physical structures as localized, frozen stability boundaries precipitated by a primary, universal mobility. Crucially, this ontology directly addresses the existential dimension of eternity: because the conscious observer is fundamentally an expression of this primary, continuous duration, physical mortality is revealed to be merely a secondary, frozen abstraction of measurement, meaning the perceiving being is never denied the eternity it experiences (Arendsen, 2026a, 2026b, 2026c).

The Mathematical Architecture of Actuation

To bridge the gap between primary metaphysical flow and the discrete observations of empirical science, Complex Idealism claims to provide a rigorous, formal translation layer. This mathematical framework demonstrates how the continuous, undivided flow of duration is structurally registered and transformed into the stable physical phenomena observed in our universe. This bridge is built upon two core mathematical architectures: the Sensory Complex Features Model (SCFM) and the Generative Universal Transformers (GUT) operator mechanics.

The Sensory Complex Features Model (SCFM) (Arendsen, 2025) describes the process by which qualitative, continuous mental flow is structurally mapped into localized, complex informational feature sets. Rather than treating sensory data as a passive projection of an external material world, the SCFM models it as an active geometric registration of duration. The operational grammar of this registration is governed by the Generative Universal Transformers (GUT) (Arendsen, 2026a). Utilizing the formalisms of linear algebra, the GUT models the boundary layer of actuation through active 2x2 matrix rotations and Kronecker products. While the 2x2 matrix rotations represent dynamic, continuous shifts in phase, the Kronecker products provide the mathematical mechanism for the recursive, high-dimensional scaling of these informational structures.

To anchor this computational grammar within the domain of fundamental physics, Complex Idealism projects these transformations onto a 4D orthogonal phase space. This phase space is constructed not from arbitrary material coordinates, but from four foundational universal invariants: Action (h); Velocity (c); Frequency (ν); Charge (e). To account for the simultaneous split of the four invariant axes, a quaternionic representation of the phase space is introduced (Arendsen, 2026d). This transition allows the observer to map the interaction not as a sequence of isolated projections, but as a unified 4D rotation within a rational field.

According to Arendsen, within this 4D orthogonal phase space, the primary actuation impulse undergoes a precise geometric split driven by active phase rotations. This process precipitates the fluid, continuous duration into localized, stable, and recursive timeless movements. It is these recursive movements that function as the structural placeholders observed by physical science, manifesting as the discrete particles, fields, and deterministic laws of the measurable physical universe. Physics, therefore, does not contradict this idealist ontology; rather, the mathematical laws of quantum mechanics and electromagnetism naturally emerge as the secondary, frozen footprints of a primary informational flow (Arendsen, 2026a, 2026b, 2026c).

Implications for Consciousness

Arendsen asserts that Complex Idealism introduces a radical reclassification of the "explanatory gap" within contemporary consciousness studies. Traditional physicalist and functionalist paradigms fail to solve the hard problem of relating mental states to physical states because they attempt to derive qualitative experience from manipulating quantitative, spatialized matter. By shifting the foundational premise from computation to communication, he has Complex Idealism bypassing this conceptual impasse. It demonstrates that the mathematical laws of physics naturally precipitate from a primary informational flow, meaning the physical universe does not generate consciousness but rather serves as the expressive medium through which an underlying, unsplittable mental unity interacts with itself.

According to Arendsen, within the broader Landscape of Consciousness (Kuhn, 2024), this Complex Idealism framework provides a vital alternative to both reductive physicalism and static varieties of idealism. It satisfies the scientific demand for structural precision by offering a concrete mathematical grammar—governed by universal invariants and active phase rotations—while simultaneously preserving the indivisible, continuous nature of subjective duration. By defining the brain not as a computer generating consciousness, but as a specialized generator or regularizer slicing continuous flow into discrete communicative signals, Complex Idealism offers a sophisticated, mathematically robust bridge between the immediate data of intuition and the structured observations of empirical science.

References

• Arendsen, A. R. J. (2026a). The Generative Universal Transformers of Complex Idealism: Metaphysical Model. https://www.researchgate.net/publication/404455471_The_Generative_Universal_Transformers_of_Complex_Idealism_Metaphysical_Model

• Arendsen, A. R. J. (2026b). The Grand Phase Architecture of the New SI Units: Structural Placeholders and Active Rotations in Complex Idealism.https://www.researchgate.net/publication/405192263_The_Grand_Phase_Architecture_of_the_New_SI_Units_Structural_Placeholders_and_Active_Rotations_in_Complex_Idealism.

• Arendsen, A. R. J. (2026c). The Actuation Impulse of Complex Idealism: How the Measured Universe Splits into Recursive Timeless Movements. https://www.researchgate.net/publication/405473400_The_Actuation_Impulse_of_Complex_Idealism_How_the_Measured_Universe_Splits_into_Recursive_Timeless_Movements.

• Arendsen, A. R. J. (2026d). The Quaternionic Split: How 4D Rational Rotations Apportion the Indivisible Continuum of Complex Idealism. https://www.researchgate.net/publication/406067833_The_Quaternionic_Split_How_4D_Rational_Rotations_Apportion_the_Indivisible_Continuum_of_Complex_Idealism
  

• Arendsen, A. R. J. (2025). The Sensory Complex Features Model of Complex Idealism in a Flash. https://www.researchgate.net/publication/389039519_The_Sensory_Complex_Features_Model_of_Complex_Idealism_in_a_Flash.

• Bergson, H. (1889). Time and Free Will: An Essay on the Immediate Data of Consciousness. London: George Allen & Unwin.

• Kuhn, R. L. (2024). A landscape of consciousness: Toward a taxonomy of explanations and implications. Progress in Biophysics and Molecular Biology, 190, 28-169.