Eight irreducible positions. Two intersecting matrices. One framework for understanding how minds think differently.
From Lithuanian numatytas — foreseen, anticipated, structurally inevitable
The Problem
Every attempt to map human cognitive difference has either lacked mathematical grounding, collapsed real distinctions into vague categories, or assumed all minds optimize the same way. We can do better.
16 types but no mathematical structure. No principled reason to have 4 axes or 16 types rather than 3 or 32. The categories are empirically unstable — people retype themselves year to year.
Measures trait magnitudes but explains nothing about why people think differently. High Openness and low Openness are positions on a continuous scale — not structurally different modes of knowing.
Assumes all rational agents are Machiavellians: they calculate expected utility and maximize it. This is one of eight positions masquerading as the universal definition of rationality. It blinds theory to every other mode.
The Framework
Numatas derives its structure from two independent 2×2 matrices — one epistemological, one social. Their combination produces exactly eight positions. Not arbitrarily chosen: structurally derived.
| Objective | Subjective | |
|---|---|---|
| Temporal | Strategic | Relational |
| Spatial | Tactical | Experiential |
| Other-as-Subject | Other-as-Object | |
|---|---|---|
| Self-as-Subject | Arthurian | Platonist |
| Self-as-Object | Confucianist | Machiavellian |
The Eight Positions
The two-letter code combines an epistemic mode (S, T, R, E) with a social archetype (C, M, P, A). Each position has its own rationality, its own blind spots, and its own irreplaceable contribution to collective understanding.
The duty-bound strategist. Thinks in data and sequences; acts as an instrument of a structure larger than oneself. Serves others through evidence and anticipation.
“The evidence shows this serves them best.”
The tradition keeper. Thinks in meaning and narrative sequences; acts as an instrument of lineage and community. Serves through story, memory, and continuity.
“Our story demands we honor this.”
The system optimizer. Thinks in data and temporal trajectories; treats self as an instrument and others as resources to be arranged. Calculates the move that maximizes outcomes across time.
“The optimal play given the constraints is…”
The configuration engineer. Thinks in data and spatial arrangements; treats self as an instrument and others as resources to be arranged. Redesigns the current setup for maximum leverage.
“The current setup allows us to…”
The standard setter. Thinks in data and spatial form; acts from sovereign will with others treated as means to the correct order. Identifies the right structure and defends it.
“The right way to organize this is…”
The category intuiter. Thinks in felt sense and spatial configuration; acts from sovereign will with others treated as means to the correct form. Perceives the right structure before articulating why.
“This belongs in the category of…”
The covenant maker. Thinks in meaning and narrative sequences; acts as a sovereign who sees others as full agents. Builds the bonds that survive difficulty.
“We owe this to each other.”
The present companion. Thinks in felt sense and immediate configuration; acts as a sovereign who sees others as full agents. Stands alongside without an agenda to fix.
“I’m here with you in this.”
From Eight to Sixteen
The eight positions exhaust the cube’s vertices. But every vertex has two orientations — directed inward or directed outward. This is the primal chirality of the framework: interior versus exterior, the most fundamental distinction you can make about any cognitive position.
This is what folk psychology calls introversion and extroversion — but those words have been corrupted. Introversion is not shyness. Extroversion is not gregariousness. They are locus of attention: does this position process through self-referential interior space, or through environment-referential exterior space?
The position’s epistemic mode and social stance are directed inward. A Strategic Confucianist turned interior processes duty through internal deliberation — the evidence is weighed silently, the obligation felt before it is spoken. The locus of attention is self-referential: the world is processed through the self.
The same position directed outward. A Strategic Confucianist turned exterior processes duty through environmental engagement — the evidence is gathered by testing the world, the obligation discharged through visible action. The locus of attention is environment-referential: the self is processed through the world.
Mathematically, the interior/exterior distinction is a reflection of the cube through itself — a chirality operation, not a fourth independent axis. The three epistemic axes (Temporal/Spatial, Objective/Subjective, Abstract/Concrete) define the cube’s structure. The chirality determines which face of each vertex is turned toward the observer.
This is why the operation produces 8 × 2 = 16, not 24 = 16. The distinction is real — an introverted Strategic Confucianist and an extroverted one are genuinely different types — but it is structurally subordinate to the three axes that generate the positions. Chirality does not create new vertices; it creates left-handed and right-handed versions of each existing one.
The result is 16 complete types: the full Numatas typology. Eight positions, each in two chiral orientations. The cube reflected.
Why It Matters
Numatas is not a personality curiosity. It is a functional architecture for systems that need to think from multiple genuinely different positions simultaneously.
Mist uses Numatas to create positioned agents that think differently from each other. When the SC agent and the EA agent both evaluate the same decision, they surface different information. This enables genuine multi-perspective deliberation — not N copies of the same model bias running simultaneously, but structurally distinct stances producing structurally distinct outputs. The deliberation process becomes the epistemic mechanism, not just the output layer.
Classical game theory assumes all players are Strategic or Tactical Machiavellians: they calculate expected utility, maximize it, and treat others as objects in the payoff matrix. Numatas reveals this as one of eight positions — a special case, not the general model. Different positions have structurally different utility functions. A Relational Confucianist and a Tactical Machiavellian facing the same game play it differently not because of irrationality but because of genuinely different rationalities. Equilibrium analysis changes entirely.
Individual positions are biased by design. No single position sees the full picture — that is the point. The SM sees trajectories and levers; the EA sees relational texture; the TP sees structural correctness; the RC sees historical continuity. When all eight positions are present, can translate across each other’s frames, and have genuine standing in the deliberation, collective intelligence emerges. This is what healthy human groups have always done, and what institutions systematically destroy. Numatas makes it legible and reproducible.
Mathematical Foundation
The eight positions exhaust the logical space defined by three binary axes. This is not a design decision; it is a derivation. The framework has mathematical closure.
The 8 positions form the 3-dimensional binary cube. Three independent axes, each with two poles, produces exactly 8 vertices. No more, no fewer. The cube is closed under the group operation.
The 4 epistemic modes (S, T, R, E) are quotient projections: collapse the social dimension and you recover the epistemological matrix. The social archetypes (C, M, P, A) are the complementary projection.
Three axes × two poles per axis = 8 vertices. The Abstract/Concrete axis derives from the Social matrix (it is not independent) — which is why there are exactly three axes, not four.
The Temporal/Spatial axis crosses both the Objective and Subjective dimensions. Strategic and Relational share the temporal mode; Tactical and Experiential share the spatial mode. The axis is orthogonal to the Objective/Subjective split.
Principle of Minimum Necessary Distinction (PMND): A framework should introduce no more distinctions than are required to account for the phenomena it addresses, and no fewer than are required for it to be complete. The Numatas framework satisfies PMND: three binary axes are necessary (removing any one collapses genuinely distinct positions into the same category) and sufficient (adding a fourth produces distinctions with no empirical or functional grounding).
PMND = Principle of Minimum Necessary Distinction
Origin
Numatas was developed by Skinner Layne across two decades of direct observation — ten cohorts of residential students at Exosphere (2013–2017), years of independent philosophical work, and the systematic pressure-testing of every existing personality framework against what he actually saw people do.
The word comes from the Lithuanian numatytas: foreseen, anticipated, structurally inevitable. The framework is not a taxonomy imposed on behavior. It is a derivation of what must exist if cognitive diversity has structure at all.
The eight positions emerged not by choosing axes, but by demonstrating that fewer than three binary axes collapse genuinely distinct stances into the same category, and more than three produce distinctions without empirical or functional grounding. This is the Principle of Minimum Necessary Distinction (PMND) — the generative principle behind the framework.
Numatas Ontology Guide — Technical reference covering the two matrices, all eight positions, coherence constraints, position detection markers, game-theoretic implications, and the telos of the framework.
Mist User Guide — How the Waterlight platform’s Mist engine uses Numatas to create positioned agents for multi-perspective deliberation.
The PMND Research Program — The broader mathematical investigation of minimum necessary distinction in philosophy, physics, and information theory.