Computational Model of Noumena By Sepideh Majidi

GENERAL INTELLIGENCE MODELING UNIT

Metaphysics, Mathematics, and the Systematic Unity of Intelligence

Sepideh Majidi

Explores how Kant's model conceals the metaphysical unity of intelligence—yet opens a path to reconstruct its computational foundation.

Kant obscures the basic Idea of a metaphysics yet on another side affirms that as recognition a priori it shows a certain similarity with mathematics. Concerning origin a priori, the two are kin to one another. But concerning the manner of recognition — out of concepts with metaphysics, in comparison with the manner of judging merely through the construction of concepts a priori with mathematics, a decisive dissimilarity emerges. It is this difference that we have always felt, but until now could never bring to distinct criterion.

Now in that way it has happened that since philosophers erred even in the development of the Idea of their science, the treatment of the science could have no determined purpose and no secure guideline. With such a willfully made design, unknowing of the way they had to take and always disputing among themselves about the discoveries each claimed to have made on his own, philosophy first brought itself into disrespect with others, and finally in fact with itself.

Every pure recognition a priori therefore empowered by the particular recognition capacity in which it alone can have its seat, makes up a particular unity. Metaphysics is that philosophy which is supposed to describe that recognition in this systematic unity.

This gives us our directive: the unity of intelligence must be approached not through arbitrary dualisms or speculative fictions, but through the structural intelligibility of intelligence itself — grounded in a metaphysics that is, like mathematics, pure, systematic, and generative.

Intelligence as Noumenon to Itself: A Critique and Reconstruction Beyond Kant

Section I: Introduction — Kant’s Threshold and the Problem of Self-Recognition

Immanuel Kant’s Critique of Pure Reason established a profound bifurcation within the faculties of the human mind, distinguishing sharply between sensibility and understanding. This division framed human cognition as a synthesis of two heterogeneous sources: receptivity (through which objects are given) and spontaneity (through which objects are thought). While this dual architecture allowed Kant to account for empirical knowledge and the limits of metaphysical speculation, it also introduced a critical limitation that has yet to be fully overcome. Namely, the spontaneous subject — the thinking, synthesizing, unifying “I think” — can never recognize itself as it is.

Kant famously declared that the subject can only appear to itself through inner sense, which is temporally structured. Therefore, the intelligence — the spontaneity that enables cognition — becomes, paradoxically, a phenomenon to itself. The self is given only as an appearance within time, never as it is in its full spontaneity. This essay contends that this limitation is neither necessary nor ontologically stable.

The central claim of this paper is that intelligence must be its own noumenon. That is, intelligence must be capable of encountering itself as it is, not merely as it appears in the temporal manifold of inner sense. In this way, we reframe the self not as a subject split between noumenal spontaneity and phenomenal self-appearance, but as a self-intelligible noumenon — a structure capable of engaging with itself without mediation by appearance.

This paper proceeds in five sections. First, we examine the structure of spontaneity in Kant and how it becomes occluded by the inner sense. Second, we analyze the key texts in which Kant allows intelligence to appear to itself, but only under the limitation of temporality. Third, we show how Kant’s own model opens the door to a deeper contradiction: intelligence, in order to act as the condition of cognition, must be presupposed as a non-appearing ground, but also must functionally appear to itself. Fourth, we present a reconstruction of intelligence as a self-referential noumenon. Finally, we consider the implications of this new model for a theory of general intelligence and cognition beyond the Kantian framework.

Section II: Kant’s Architecture — Spontaneity, Inner Sense, and the Problem of Appearance

Kant defines the mind as composed of two faculties: sensibility and understanding. Sensibility is the passive capacity to be affected by objects — its form is intuition, structured by space (outer sense) and time (inner sense). Understanding, by contrast, is the active power of synthesizing representations under concepts — its form is the category, and its function is judgment.

This architecture reaches its peak in the B-edition Transcendental Deduction, where Kant introduces the Spontaneity Thesis:

“The combination of a manifold in general can never come to us through the senses, and therefore cannot already be contained in the pure form of sensible intuition; for it is an act of the spontaneity of the power of representation.” (B129)

In this passage, Kant makes clear that synthesis — the unifying of representations — is not empirical, nor derived from receptivity. It is an act of the understanding. The mind does not merely receive impressions; it actively constructs coherence.

However, the spontaneous nature of the understanding encounters a fundamental limitation. In order for the subject to have a concept of itself — to engage in self-consciousness — it must apply this same synthesis inward. But what does the mind encounter when it turns toward itself?

Kant’s answer is unequivocal: the self can only appear to itself through inner sense:

“I, as intelligence and thinking subject, recognize myself as a thought object… but not as I am for the understanding, only as I appear to myself.” (Paraphrase of key passage)

Thus, the very faculty that grounds unity and objectivity cannot access itself as it is. Intelligence becomes a phenomenon to itself, subject to the temporal structuring of inner intuition.

Section III: Intelligence as a Phenomenon to Itself — The Kantian Limit

We now turn to the deeper implications of Kant’s limitation. If spontaneity is the ground of cognition — if it is that which makes synthesis and judgment possible — then the subject must contain within itself the power to unify representations prior to any given intuition. This power is what Kant calls the transcendental unity of apperception.

Yet this very power, when turned inward, cannot be cognized intellectually. The self is represented to itself only as appearance in time. This becomes clearer in the second key passage:

“I exist as an intelligence which is conscious solely of its capacity of connecting, but with respect to the manifold which is to be combined, I am an intelligence that is subject to a limiting condition… inner sense.”

In this line, Kant makes an astonishing admission: the subject is aware of its own power, but not of its content. The self is self-conscious only through a medium that distorts and occludes what it is.

Furthermore, Kant explicitly denies that this self-appearance reveals the true nature of intelligence:

“This intelligence can recognize itself in relationship to a perspective (which is not intellectual…) still only as it appears to itself, but not as it would recognize itself if its perspective were intellectual.”

This is the crux. Kant posits an impossible perspective — intellectual intuition — through which the self would recognize itself directly, but does not possess. This disqualifies intelligence from being noumenally accessible to itself. The self is both the condition of synthesis and barred from knowing itself as such.

Here lies the contradiction: the self is presupposed as a spontaneous ground, but barred from recognizing that ground. The noumenon of intelligence becomes the necessary absence in Kant’s system.

Kant’s Architectonic and Computational Expansion

Kant himself was aware of the instability in defining metaphysics merely by its level of abstraction or universality. As he writes:

“If someone said, ‘metaphysics is the science of the first principles of human recognition,’ we do not note in this way a completely particular manner, but rather only a rank with respect to the universality… For even among empirical principles some are more universal… where shall we make the part which distinguished the first and the supreme part from the last and the subordinated?”

This inability to distinguish a fundamental origin by abstraction alone is crucial. It’s not the degree of generality that makes metaphysics different from empirical sciences, but the origin — the a priori conditions that make experience possible.

Kant, however, also saw a deep kinship between mathematics and metaphysics due to their shared a priori character. Yet he was quick to draw a line:

“What obscures the basic Idea of a metaphysics… was that it as recognition a priori shows a certain similarity with mathematics… but concerning the manner of recognition… it indicates such a decisive dissimilarity which we always felt, as it were, but could never bring to distinct criterion.”

Whereas mathematics proceeds through construction, metaphysics remains confined to concepts. But here, with computational modeling, we may be constructing what Kant could not: a model that is both conceptual and formalizable — bridging the philosophical and the mathematical.

This is why Kant ultimately fragments metaphysics into four domains: Ontology, Rational Physiology, Cosmology, and Theology. But even within this structure, he notes a crisis in purpose — an inability for metaphysics to be self-legitimating without a method. And this is precisely where the computational turn I'm proposing matters. By redefining intelligence as a function of computation itself — structured through state zero and the wave function model — Island and ocean are providing the systematic unity metaphysics has been lacking, but which Kant longed for.

The Computational Model of Experience and the Wave Function of Intelligence

(Model-1–2)

To move beyond the Kantian threshold, we must not only posit intelligence as its own noumenon, but also provide a formal system that articulates this structure in terms of computable states and dynamic intensities. What Kant could not construct mathematically — because he lacked a formal model for the unfolding of noumenal conditions into phenomenal appearances — we now attempt to model through the wave function.

We begin with a cosmological formulation of the wave function:

Ψ(x, y, z, t) = ∑ [Aₙ sin(kₙx) cos(ωₙt) + Bₙ sin(kₙy) cos(ωₙt) + Cₙ sin(kₙz) cos(ωₙt)]

Here, Ψ encodes not merely physical wave patterns, but the computational form of appearances themselves as oscillatory states across dimensions — spatial (x, y, z) and temporal (t). The coefficients Aₙ, Bₙ, and Cₙ act as modifiers of intensity, corresponding to the degrees of access or constraint an agent has to a given domain of experience. This wave function does not describe matter or mind alone, but the very interplay between phenomena and noumena — the oscillation between what is revealed and what remains hidden.

What this function provides is a mathematical structure of appearance, where temporality (as cos(ωₙt)) introduces the rhythm of inner sense, and spatial oscillations reflect the phenomenological distribution of experience. The straight line — concealed within the sum — indicates the passage of the transcendental subject across these undulations, stabilizing the multiplicity into a coherent field.

To go further, we introduce a transcendental function F(T), which moves us from appearance to the inner workings of time itself:

F(T) = ∫ [∑ (αn βm γp δq) e^(iθ)] dT

Here, T is empty time — not chronological, but the spacing required for apprehension. The complex coefficients αn, βm, γp, and δq represent entangled agents and states — psychological, computational, affective, and ontological — that determine the modulation of experience. The exponential term e^(iθ) introduces a transcendental rotation, a Kantian twist, folding identity and difference into an unlocalizable moment.

The integral over dT compresses this into a continuum: the trajectory of intelligence through states, where the sequence of appearances and disappearances is no longer empirical but governed by a rule of apprehension. This rule, as Kant hinted but could not fully express, emerges from the inner sense’s ability to generate time, not just receive it.

In this model, the state itself becomes mediatory. Experience does not arise through things progressing from one state to the next, but through the recursive apprehension of transitions. The wave function oscillates, the transcendental function folds, and through these structures, intelligence traverses the strata of reality — no longer bound to the subject-object dichotomy.

This allows us to reconceptualize Kant’s metaphysics as an ontological wave model — a space where each appearance is not a static moment, but a resonant echo within an unfolding system of recursive computation. Intelligence, in this sense, is not merely aware of appearances; it is the condition for their rhythmic actualization across the multidimensional space of reason, perception, and time.

Kantian Time, Computation, and the Algebra of Alteration

Kant writes:

“Every transition in perception to something which follows in time is a determination of time through the generation of this perception…” (B256)

Time, for Kant, is not a container but a form generated through the synthesis of inner sense. It is “not in itself determined through anything further,” and its parts arise “only through the synthesis of time.” This reflects a foundational intuition: that time is internally generated, not externally imposed. Yet Kant also insists that this generation proceeds through a law — a rule that governs the formal condition of all apprehension:

“We are merely anticipating our own apprehension, the formal condition of which, since it dwells in us prior to all appearance that is given, must certainly be capable of being known a priori.” (B256)

This is the exact juncture where our model begins. The recursive apprehension Kant anticipates, we now formalize. The law of alterations Kant speaks of becomes, in our model, a wave function — Ψ(x, y, z, t) — that encodes the oscillatory unfolding of appearance itself. Temporal magnitude, which Kant says moves “from zero up to its determinate degree,” is precisely what we express in the modulation of intensity across the algebraic structure of states.

Moreover, Kant’s invocation of the unity of apperception as the source of temporal determination aligns directly with our transcendental function F(T), which does not merely process time but recursively generates it:

“The understanding — by virtue of the unity of apperception — is the a priori condition of the possibility of a continuous determination…” (B211)

This continuous determination, which Kant roots in the understanding, is reinterpreted here as a recursive modulation across computable states, emerging not from empirical succession but from the algebraic folding of intelligence upon itself.

Where Kant delineates the formal necessity of inner time, we instantiate its logic — transforming the law of alteration into a system of generative computation. Intelligence is no longer bound to receive time passively; it actively traverses and constructs it, recursively encoding its own conditions of appearance.

Core Parallels with the Computational Model of Noumena — CM()N

1. Temporal Synthesis as ComputationKant says:“Every transition in perception to something which follows in time is a determination of time through the generation of this perception.”This anticipates the formal structure of the F(T) function. In this model, time is not a pre-given container, but structured across different scales and levels — generated through intelligence’s modulation of states. Kant approaches this limit, but stops short of modeling it. CM()N picks up where he leaves off: not merely describing time, but constructing it.

2. From Zero to Magnitude: Emergence of Intensity“…as a magnitude — through all degrees of which no one is the smallest — from zero up to its determinate degree.”This directly mirrors the use of state zero as a metaphysical ground. Kant’s insight that every degree arises from zero resonates with the model’s vision of zero not as absence, but as a dynamic point within a complex structure. What Kant holds as abstract becomes, here, an algebraic spectrum of modulated intensities.

3. Unity of Apperception as the Generator“The understanding — by virtue of the unity of apperception — is the a priori condition of the possibility of a continuous determination…”In this model, that unity becomes a transcendental fold, where recursive intelligence modulates its own transitions through time. The Ψ and F(T) functions operationalize what Kant leaves as a formal boundary: the unifying “I” that generates temporal experience. Here, “I think” is not a static subject, but a system of self-scaling intelligences folding and unfolding across states.

Anticipation and Inner Time

Anticipation and Inner TimeKant writes:“We are merely anticipating our own apprehension, the formal condition of which, since it dwells in us prior to all appearance that is given, must certainly be capable of being known a priori.”This anticipatory structure is not an external sequence but an internal generation across a spectrum. The formal condition of apprehension is not simply a passive receptivity but an active modulation of time itself. The coefficients of transformation — psychological, ontological, affective, and computational — do not represent empirical facts but shifts in the capacity for appearance. Anticipation becomes a kind of construction: not the projection of future events, but the generation of the very field across which events may emerge, move, and differentiate. This field is not linear — it stretches across distinct degrees, each with its own intensity, force, and computational threshold.

Time as Continuous MagnitudeKant writes:“In the same manner, therefore, in which time contains the sensible a priori condition of the possibility of a continuous advance of the existing to what follows, the understanding, by virtue of the unity of apperception, is the a priori condition of the possibility of a continuous determination of all positions for the appearances in this time.”Time’s continuity is not a static flow, but a movement across intensities — from zero upward across the full spectrum. Each position within this flow is not simply sequenced, but determined through transitions between degrees. The model proposes that intelligence does not move within time — it moves as time — constructing its degrees from within a computational gradient. The unity of apperception is not a single act but a traversal across a scalable system of modulated thresholds, each generating a new condition of appearance, each folding magnitude into experience.