1. Introduction: The Need for a Minimal Structural Model
Attempts to formalize subjectivity have historically oscillated between two extremes:
Empirical reductionism, which grounds consciousness in neural or physical substrates.
Symbolic inflation, which grounds consciousness in mythic, cultural, or linguistic content.
Both approaches fail to identify the structural invariants that make subjective experience possible in the first place.
The former reduces subjectivity to its implementation; the latter confuses structure with content.
What is missing is a minimal ontology:
a structure that is neither empirical nor symbolic, but formal, discrete, universal, and interpretation‑neutral.
SUBIT is proposed as such a structure.
SUBIT is not a theory of the brain, nor a psychological model, nor a symbolic system.
It is a mathematical object that captures the necessary and sufficient conditions for a subjective configuration to exist.
This chapter develops SUBIT as:
a 6‑bit Boolean structure
a graph of elementary transitions
a functorial codomain for experiential systems
an archetype of second order
a universal interface across symbolic, biological, musical, and cognitive domains
The goal is to establish SUBIT as a structural ontology:
a minimal form that underlies all possible subjective forms.
2. The Concept of an Archetype of Second Order
2.1. First‑order archetypes
In classical depth psychology, archetypes are image‑laden patterns:
Hero, Mother, Shadow, Trickster, Wise Old Man, etc.
These are archetypes of the first order:
they possess content, imagery, narrative, and cultural specificity.
2.2. Second‑order archetypes
Beneath these lie structural archetypes:
These are archetypes of second order:
they do not contain images; they define the space in which images can arise.
2.3. SUBIT as a second‑order archetype
SUBIT belongs to this level.
It is not an image, symbol, or myth.
It is a formal topology of possible subjective states.
SUBIT is to archetypes what:
group theory is to symmetries
category theory is to structures
SUBIT is the form of archetypality itself.
3.1. SUBIT Space
Let
S = {0,1}⁶
be the set of all 6‑bit vectors.
Define projection maps
πᵢ : S → {0,1}
for i = 1…6.
Define the Hamming metric
d(x,y) = number of indices i such that πᵢ(x) ≠ πᵢ(y).
Define the transition graph
G = (S, E)
where
E = { {x,y} ⊂ S | d(x,y) = 1 }.
This graph is the 6‑dimensional Boolean hypercube Q₆.
3.2. Interpretational neutrality
SUBIT assigns no semantic content to:
Interpretation arises only through external mappings.
This neutrality is essential:
SUBIT is a pure form, not a symbolic system.
4. Axioms of SUBIT
We now present the axioms that uniquely characterize SUBIT.
Axiom 1. Discreteness
The space of subjective configurations is a finite set S.
Axiom 2. Dimensional Minimality
There exist exactly 6 independent binary axes of variation.
Thus S = {0,1}⁶.
Axiom 3. Locality of Change
Elementary transitions correspond to flipping exactly one bit.
Thus the transition graph is Q₆.
Axiom 4. Symmetry
All axes are structurally equivalent; the automorphism group of SUBIT is the full hyperoctahedral group acting on Q₆.
Axiom 5. Interpretational Neutrality
No semantic content is assigned to any bit or state.
Axiom 6. Universality
Any discrete experiential system X with a finite number of distinguishable states admits a structure‑preserving embedding into S.
Axiom 7. Functoriality
Mappings between experiential systems preserve their SUBIT representations.
These axioms define SUBIT as a minimal, symmetric, universal structure of subjectivity.
5. SUBIT as a Functor
Let C be a category whose objects are discrete experiential systems (musical scales, symbolic systems, genetic codes, archetypal role systems, etc.) and whose morphisms are structure‑preserving maps.
Define a functor
Subit : C → Set
by:
Subit(f) = idₛ for all morphisms f
Each system X is equipped with an interpretation map
ιₓ : X → S.
Thus SUBIT acts as a universal codomain for all discrete experiential structures.
This is analogous to:
semantic domains in denotational semantics
state spaces in dynamical systems
configuration spaces in physics
SUBIT is the configuration space of subjectivity.
6. Cross‑Domain Isomorphisms
This section expands the earlier overview into a full comparative analysis.
3.6.1. I Ching (易經)
The I Ching is structurally identical to SUBIT:
The I Ching is a semantic overlay on the SUBIT hypercube.
6.2. Genetic Code
The genetic code is a biological instantiation of SUBIT:
codon = 3 positions = 6 bits
point mutation = bit flip
Evolution operates on the SUBIT graph.
6.3. Musical Systems
Musical pitch spaces map naturally onto SUBIT:
12‑tone equal temperament = projection of SUBIT onto a cyclic subgroup
22 śruti = non‑uniform refinement of SUBIT axes
modal systems = subgraphs of Q₆
Music is a quotient topology of SUBIT.
6.4. Archetypal Role Systems
Archetypal roles correspond to projections of SUBIT:
8 roles = 3‑bit projection
role transitions = bit flips
6.5. Linguistic Systems
Language maps onto SUBIT through:
Language is a SUBIT‑structured dynamical system.
This section expands the earlier summary into a full scholarly review.
7.1. Mathematical Phenomenology
Prentner (2025) proposes mathematical primitives for phenomenology.
SUBIT aligns with this but offers a discrete minimal model.
Tononi, Kleiner, and Tull formalize consciousness as informational structure.
SUBIT differs by being:
Forti (2025) introduces extended information structures.
SUBIT provides a concrete instantiation.
7.4. F‑Space Models
Weng (2025) models subjectivity as movement in a high‑dimensional manifold.
SUBIT is the discrete skeleton of such manifolds.
7.5. Archetypal Analysis
Cutler’s archetypal analysis defines archetypes as extreme points.
SUBIT provides a discrete analogue.
7.6. Genetic Code Mathematics
Symmetry studies of codons align with SUBIT’s Boolean structure.
7.7. Musical Geometry
Lewin and Tymoczko’s work on pitch‑class spaces parallels SUBIT projections.
3.8. Discussion: SUBIT as Structural Ontology
SUBIT provides:
a minimal model of subjective structure
a universal codomain for experiential systems
a unifying framework for cross‑domain isomorphisms
a mathematically clean foundation for archetypal theory
SUBIT is not a metaphor.
It is a formal object that captures the structural essence of subjective possibility.
3.9. Conclusion
This chapter has established SUBIT as:
a 6‑bit Boolean hypercube
a graph of elementary transitions
an archetype of second order
a universal interface across domains
SUBIT is a structural ontology of subjectivity.
The next chapter may develop:
natural transformations between interpretations
continuous analogues of SUBIT