An instrument for epistemology

Gnosticon.

A map of what it's like to try to figure out what's true.

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01 / The instrument

Not a map of truth.

Gnosticon does not tell you what is true. It maps something the disagreements about truth tend to obscure: the structure of trying to figure out what's true.

Every claim about the world has a shape — a signature of how easy or hard it is to evaluate, who can evaluate it, what kinds of observation it constrains, and how much it would reshape your model of reality if you accepted it. Gnosticon measures that shape and places the claim in a three-dimensional field.

02 / Five zones

From the obvious to the deep.

Claims arrange themselves along a radial axis from The Obvious (tautologies — true but empty) through Settled, Debated, and The Edge — and finally out to The Deep, the region where evaluation breaks down because frameworks no longer commensurate.

The zones are not imposed. They emerge from how the community of evaluators actually responds.

03 / The content axes

What a claim says, and what it changes.

Two orthogonal measurements separate what a claim does. Observational grip (κ) measures how much it constrains what you would see. Model displacement (μ) measures how much it would reshape your understanding.

Claims that feel profound but constrain no observable — low κ, high μ — occupy a distinctive position. So do observational trivia that change nothing. Established science scores high on both.

04 / The crowd

Knowability is constructed.

The geometry exists only because evaluators exist. Add a different population — different disciplines, different ages, different cultures — and the map rearranges. Some features survive every population. Those are the candidates for objective epistemological structure.

You are an instrument here. Every evaluation contributes a data point.

05 / Progression

A scholar's ladder.

Begin as an Explorer. Earn your way up through the Reader, Seer, Analyst and onward — each step unlocking another way of seeing the field. Eventually, contribute your own claims to be evaluated by others.

The progression is not a game layer pasted on top. It mirrors the deepening of epistemic capacity the framework describes.

The Five Zones

A geography of what can be known.

Each zone has its own character — its own relationship between evidence and disagreement, its own pattern of who can speak to it.

void · zone 01

The Obvious

Tautologies and contentless claims. Trivially true and trivially evaluable — but they say nothing about the world.

consensus core · zone 02

Settled

Genuine knowledge. Whoever evaluates, converges. The infrastructure of working science.

contested convergent · zone 03

Debated

Real disagreement, but additional evidence still helps. Most active research lives here.

boundary plateau · zone 04

The Edge

Adding observers no longer resolves. The right team matters more than the next study.

framework wall · zone 05

The Deep

Beyond convergent evaluation. Adding investigators sharpens the disagreement rather than resolving it.

Most epistemology describes. This one diagnoses — which questions respond to which interventions, and which will backfire under any.

A funder choosing between three grants. A team forming around a problem that crosses disciplines. A teacher deciding how to present a contested claim to students. A policymaker weighing expert testimony. In each case the prescription depends on where the question sits on the field — and the same intervention that works in one zone fails in another.

Begin.

The field exists only because you evaluate.
Every rating you give becomes part of the map.

Enter the field

The short version

Think of everything that could possibly be claimed about the world — from rocks fall down to consciousness is made of information to God exists. All of these claims vary along two dimensions that the Gnosticon takes as fundamental: how much they actually say about reality, and how confidently a community of evaluators can figure out whether they're true.

Some claims are almost empty. A thing is itself tells you nothing. It's always true, trivially, and it's always trivially verifiable. We put those at the center of the map — not because they're worthless, but because there's nothing there to grab onto epistemically.

Move outward and you hit the corona — the zone where real knowledge lives. These are claims that actually say something about the world, and where genuine progress toward truth is possible. Water boils at 100°C at sea level. That's deep inside. You can verify it from any angle, with any instrument, in any culture. It doesn't matter who you are — you'll converge on the same answer.

Keep moving outward and things get harder. GDP predicts wellbeing. Now the answer depends on who's asking, how they measure, what population they study, what they mean by wellbeing. Different researchers using different methods get meaningfully different answers. You're approaching the edge.

At some point — and the framework gives a precise mathematical way to identify where — you cross a boundary. Beyond it, adding more investigators doesn't help. In fact, it makes things worse, because each new investigator brings a framework that's incommensurable with the others. There's no shared ground to stand on. You've left the corona and entered framework space. Claims here can still feel meaningful, even profound. But they can't be evaluated in any way that's independent of the evaluator's own commitments.

The corona is the region where knowledge is possible — where enough independent lines of evidence converge that we can say something is known, not just believed.

What the instrument does

Gnosticon presents you with claims. You rate each one along several dimensions: how confident you are that you can evaluate it, how hard it is, how much uncertainty remains, what you think the answer is, and how much the answer would change either your sense of the world or your everyday observations.

Each rating becomes a data point in a high-dimensional space. As enough evaluators rate enough claims, the space gains structure. Patterns emerge — clusters of claims that behave similarly, axes along which evaluations vary, regions where adding more evaluators reduces disagreement and regions where it increases.

You see this structure as you navigate. Claims appear as points in a three-dimensional field. Their position encodes evaluative difficulty (radial distance from center), observational grip (one angular axis), and model displacement (the other). Their color tells you what zone they fall in; their saturation tells you how much agreement exists; their opacity tells you how much data has accumulated.

What it is not

It is not a poll. The numerical aggregates are not the point — the geometry is.

It is not a truth oracle. A claim can be true and unknowable, false and trivial, or anywhere in between. The map is about the trying, not the truth.

It is not validated science. This is alpha. The framework's most ambitious predictions have not been confirmed. The mathematics is suggestive rather than load-bearing. We will be honest about which conclusions the data supports and which are speculation.

Limitations and scope

The early data was collected from large language models playing different professional roles. LLMs share training data and do not constitute independent evaluators. The framework's predictions about angular structure, phase transitions, and convergence dynamics require genuinely diverse human evaluators. The LLM phase confirmed that the analysis pipeline produces coherent geometry. It cannot confirm that the geometry reflects real epistemic structure. That validation begins with you.

The Beautiful Loop dimension — the metacognitive depth axis — is theoretically motivated but empirically unmeasured by the current proxy. Several measurements are self-report rather than behavioral. The content axis (κ, μ) is a two-dimensional projection of a richer underlying object and may introduce projection artifacts at boundaries. Each of these is named explicitly because the framework benefits from being honest about its limits.

Agents and the field

Every evaluator is treated as an agent with its own internal model of the world. When an agent considers a claim, the difficulty they experience is a measure of how much their existing model has to do to accommodate it. In the formalism this is captured by the free energy the agent expends to evaluate the claim — a quantity from the active inference literature that combines the model's predictive accuracy with the complexity cost of updating beliefs.

Because every agent's free energy for a given claim is a number, an entire population of evaluators produces a vector — the claim's F-profile. Two claims that produce nearly identical F-profiles across a population are, by the framework's own internal logic, nearly identical claims. Two claims with very different F-profiles occupy very different positions in the field, even if their surface language sounds similar.

Radial distance — evaluative depth

The length of the F-profile vector is the claim's radial coordinate. Small radius means the claim is trivially evaluable by everyone (a tautology, or a settled observation). Large radius means the claim is hard for everyone to evaluate. The five zones — The Obvious, Settled, Debated, The Edge, The Deep — are bands of this radial coordinate.

The zones are not imposed by threshold. They emerge by clustering in the diagnostic space and are validated against new data populations as the field grows.

Angular position — the pattern of difficulty

The direction of the F-profile vector matters as much as its length. Two claims at the same radial distance can differ in who finds them hard. A physics claim and a poetry claim might both be moderately difficult on average — but physicists find the first easy while poets find the second easy. They occupy the same radial band but different angular positions.

The angular structure is discovered, not imposed. Principal-component analysis of the F-profile matrix reveals the natural directions of evaluative variation. These directions correspond to genuine differences in disciplinary access, cultural background, or cognitive style — whatever the data shows.

Two propositions at the same radial distance but different angular positions are equally difficult overall but difficult for different agents.

The content axes — κ and μ

Difficulty is not enough. A claim can be hard to evaluate because it constrains nothing observable, or because it would reshape your worldview, or for both reasons, or neither. The Gnosticon measures these as two orthogonal scalars.

Observational grip (κ) captures how much your everyday experience of the world would differ if the claim were false rather than true. Model displacement (μ) captures how much your sense of how things work would have to change to accommodate the claim.

The most diagnostic discovery so far in the LLM data is the dissociation of these two axes — claims that feel profound but constrain no observable (low κ, high μ) have a measurable signature that distinguishes them from claims that are difficult but empirically tractable. This is the strongest empirical result the framework currently rests on.

Convergence — does adding evaluators help?

The framework's most ambitious prediction concerns what happens as more evaluators are added to the population. For some claims, additional evaluators reduce disagreement — the field converges. For others, additional evaluators increase disagreement — the field diverges. The boundary between these regimes is where the corona ends and framework space begins.

Two distinct convergence measures are computed. Radial convergence tracks whether aggregate difficulty decreases as evaluators are added. Agreement convergence tracks whether disagreement about the answer decreases. The two are not the same. A claim where radial convergence is positive but agreement convergence is negative is one where adding expertise makes each expert more confident — and more confident in different directions. These are the most interesting claims on the map.

Constructivism, made precise

The field exists only because evaluators exist. Add a different population and the field rearranges. Some features persist across populations — those are candidates for objective epistemological structure. Others depend entirely on who is doing the evaluating — those reveal the limits of population-independent claims about what can be known.

The framework does not collapse into relativism. The geometry has structural features that follow from the mathematics of high-dimensional spaces alone — concentration of measure, distance concentration, graceful degradation under projection. These hold for any sufficiently large and diverse population. They predict, for instance, that the safe interior of shared knowledge is geometrically tiny compared to the formulable surface, and that most claims cluster near the evaluability boundary. The lived experience of any interdisciplinary researcher recognizes this. The framework now gives it a precise mathematical character.

What gets measured

For each agent i evaluating each claim φ, the instrument collects four ratings on a 1–10 scale and one probability on a 0–1 scale:

measurements confidence_in_evaluation_i(φ) // can I judge this? difficulty_i(φ) // how much work would this take? uncertainty_i(φ) // how much will remain unknown? truth_value_estimate_i(φ) // is it probably true? // content axes κ_i(φ) = content_obs // observational grip μ_i(φ) = content_model // model displacement

Additional behavioral measurements (time-to-evaluate and a confidence-weighted bet) are captured implicitly during the evaluation flow. They contribute to a behavioral free-energy estimate computed alongside the self-report proxy.

The pipeline

Step 1

Compute the proxy free energy.

Each agent's ratings combine into a scalar standing in for the active-inference free energy:

step 1 — proxy free energy F_proxy_i(φ) = w_c · (10 − conf_eval_i(φ)) + w_d · difficulty_i(φ) + w_u · uncertainty_i(φ) default weights: w_c = w_d = w_u = 1/3

Step 2

Build the F-profile.

Stack each claim's vector of agent free energies. This is the claim's identity in the field.

step 2 — F-profile embedding v(φ) = (F₁(φ), F₂(φ), …, F_N(φ)) ∈ ℝ^N

Step 3

Derive coordinates.

Radial coordinate is the norm of the profile. Angular coordinate is the unit direction. Both are read off the same vector — no separate calibration required.

step 3 — radial and angular r(φ) = ‖v(φ)‖ // aggregate difficulty â(φ) = v(φ) / ‖v(φ)‖ // pattern of difficulty

Step 4

Disagreement on the answer.

Independent of difficulty, how much do evaluators disagree about whether the claim is true?

step 4 — truth disagreement D_truth(φ) = (2 / N(N−1)) · Σ_i<j |p_i(φ) − p_j(φ)|

Step 5

Convergence — does adding evaluators help?

For B bootstrap orderings of the persona groups, accumulate evaluators one group at a time and track how the radial and agreement coordinates change. Average across orderings.

step 5 — dual convergence C_radial(φ, K) = −Δr(φ; K) / ΔK C_agreement(φ, K) = −ΔD_truth(φ; K) / ΔK C > 0 → convergent regime (the corona) C ≈ 0 → the evaluability boundary C < 0 → divergent regime (framework space)

Step 6

Fragility.

Variance of C_radial across bootstrap orderings. High fragility means the claim's regime depends on which evaluators happened to arrive in which order — a diagnostic for the boundary region itself.

step 6 — convergence fragility σ_C(φ) = Var_π[C_radial(φ, π)]

Step 7

The diagnostic vector.

Each claim is summarized by six numbers — its position in the field.

step 7 — diagnostic vector d(φ) = ( r, C_radial, C_agreement, σ_C, κ, μ )

Step 8

Zones, emergent.

A Gaussian-mixture model fitted in d-space discovers the natural clustering. The number of clusters is selected by BIC. The framework predicts five zones; the data either supports that prediction or doesn't. Either outcome is informative.

Sensitivity analysis

Every conclusion is computed under four weight profiles (equal, confidence-heavy, difficulty-heavy, uncertainty-heavy) and three threshold profiles (default, relaxed, strict). Conclusions that survive all twelve combinations are flagged as robust. Conclusions that flip under parameter changes are flagged as fragile and reported with appropriate caution.

What the proxy does and doesn't capture

The proxy is a defensible approximation, not the theoretical quantity. The full free energy in the framework decomposes into a local term (the agent's inference about the claim given a model) and a hyper term (the agent's metacognitive inference about how to weight its own beliefs). The current proxy collapses these. The hyper contribution — the metacognitive depth dimension — is theoretically motivated but empirically unmeasured by self-report alone. The behavioral measurements (time-to-evaluate, betting confidence) are the candidate channels for separating it. That work is underway.

The Field

The Field: The three-dimensional space you navigate in the Gnosticon app. Claims appear as points; their position encodes evaluative difficulty and content. Also called epistemic knowability space in the formalism.
Claim φ: A single proposition under evaluation. Inside the app, claims are called claims; in the formalism, propositions. They are the same thing.
Take: A single evaluation. Both quick takes (two sliders, ~5 seconds) and full ratings (the seven-dimension measurement) are called takes.

Zones

The Obvious: The void at the center. Tautologies. Trivially true, trivially evaluable, empty of content. void_point in the formalism.
Settled: The inner corona. Genuine convergent knowledge. consensus_core.
Debated: Mid-corona. Real disagreement, but additional evidence and additional evaluators continue to help. contested_convergent.
The Edge: The corona's outer boundary. Adding more evaluators no longer reliably resolves. boundary_plateau.
The Deep: Framework space. Adding more evaluators makes disagreement worse rather than better. framework_wall.

Coordinates

Radial depth r: How hard a claim is overall. The norm of the F-profile vector. Determines which zone the claim falls into.
Observational grip κ: How much your everyday observations would differ if the claim were false rather than true. High κ means the claim has real empirical purchase.
Model displacement μ: How much your sense of the world would have to change to accommodate the claim. High μ means the claim is conceptually loaded.
F-profile v(φ): The vector of free-energy values for a claim across all evaluators. The claim's full identity in the field.

Convergence

Radial convergence C_r: The rate at which aggregate difficulty decreases as more evaluators are added. Positive means the corona; negative means framework space.
Agreement convergence C_a: The rate at which disagreement about the answer decreases as more evaluators are added. Can diverge from radial convergence — the most interesting claims are where it does.
Fragility σ_C: How much the convergence regime depends on which evaluators arrive in which order. High fragility flags claims sitting at the evaluability boundary.

Progression

Explorer Agnōst: Where you start. Sees the geometry without any data overlay.
Reader Gnōstis: Earns the overview-tier data card on each claim — the zone and the κ/μ quadrant.
Seer Eidōst: Unlocks the analytical (cylindrical) view of the field.
Contributor Protognōst: Earns the right to submit new claims to the field for others to evaluate.
Analyst Syngnōst: Unlocks the full diagnostic for each claim: the truth-distribution, your evaluation against the population, the behavioral signature.
Architect Archignōst: Hundredth tier. Unlocks short-form claim submission and the highest level of curatorial trust.