Spatial interfaces / v1.2 / 13 September 2026
Fog of Probability.
See uncertainty from inside the world.
Interactive study · synthetic canyon
SYNTHETIC TERRAIN
Drag to look · arrows / HomeAmber lines: ±20 m route limit
Crossbar: reference held at 125 m
A boundary you can read.
Sparse 50% and 95% joint cross-sections. The two longitudinal rails show the pointwise 95% lateral interval.
Research → Intelligence → Systems → field feedback → Research
Keep the world visible.
Make the uncertainty spatial.
v1.2 replaces the original flattened “first-person” diagram with a perspective camera, spatial terrain and a shared uncertainty model. Turn the view. Extend the look-ahead. Watch heading uncertainty widen the possible registration of the route.
| Treatment | Promising for | Failure to watch |
|---|---|---|
| 01 / Envelope | Boundary judgment | A crisp edge can imply a hard guarantee. |
| 02 / Volume | Shape and spread | Dense particles can hide scene detail. |
| 03 / Sampled paths | Heading ambiguity | A few samples cannot establish tail risk. |
| 00 / Baseline | Uncluttered scene | The operator must translate meters into space. |
Working recommendation: start with the sparse envelope for boundary judgments. Use volume and sampled paths on demand to inspect distribution and heading ambiguity. This is a design hypothesis; comparative participant results are pending.
v1.2 protocol / what would make one view better?
Question
Can a spatial uncertainty treatment improve boundary judgments compared with the same state shown numerically?
Hypothesis
A sparse envelope may make a boundary crossing easier to perceive. Richer volume and sampled-path views may help inspect ambiguity; each benefit needs comparative evaluation.
Method / matched task
Hold replay time, source, look-ahead and heading scale fixed while switching treatments. Identify whether the 95% lateral interval crosses ±20 m, estimate the margin, and locate the reference obstacle.
Evaluation
Counterbalance all four treatments across nominal, degraded and recovery states. Record boundary accuracy, missed obstacles, response time, confidence calibration and discomfort. Include phone and large-screen sessions, with motion paused first.
Systems implication / promotion gate
Advance only after the spatial treatment improves boundary decisions over the numerical baseline without increasing missed obstacles or over-trust. Pre-register effect thresholds after a pilot estimates baseline variability.
Observation / current evidence
Implemented deterministic prototype and mathematical checks. Participant testing, physical-device evaluation and operational performance remain pending. No comparative winner has been established.
Model / what the geometry means
Renderer: pending. The accelerated view uses depth testing; the software compatibility view uses depth-sorted primitives and approximate occlusion.
Local X is left when facing forward, Y is up, Z is forward, in meters. For independent zero-mean Gaussian position and yaw errors, first-order propagation gives σ² lateral(d) = σ² position + d² σ² heading. Heading is in radians. The numerical interval is ±1.96σ lateral: pointwise 95% marginal coverage.
Envelope rings use radii 1.177σ and 2.448σ in lateral and vertical directions: 50% and 95% joint coverage for the assumed independent two-dimensional cross-section. Vertical σ is fixed at 1.4 m. Longitudinal rails use ±1.96σ lateral; they have a different meaning from the rings.
Position σ grows as √(σ₀² + (age × drift)²). Source coefficients are authored test controls. A manual source choice is a counterfactual with that same scenario age convention. It does not establish source availability. The recovery sequence is authored, not a validated filter.
The volume repeats seeded cross-section samples through depth. Sampled paths instead preserve each position/yaw perturbation across distance. Neither is a collision probability, an integrity protection level, a joint trajectory guarantee, or a posterior over real Ojai terrain. Atmospheric distance haze is fixed across treatments. Terrain, obstacles, and the route are synthetic. The reference obstacle is held 125 m ahead to keep its apparent size comparable during replay.
Shared state / agent and machine view
The human view and this inspectable contract read the same state. Accuracy and integrity stay explicit when unevaluated.
{
"version": "fog-fpv-1.2",
"time": 45,
"source": "contingency",
"age": 5,
"lookAhead": 60,
"sigmaPosition": 4.712748667179271,
"sigmaHeading": 0.014398966328953218,
"sigmaTerrain": 1.4,
"sigmaLateral": 4.791282587453216,
"lateral95": 9.390741311161927,
"margin": 10.609258688838073,
"limit": 20,
"confidence": 0.95,
"integrity": "not_evaluated",
"accuracy": "not_measured",
"phase": "Visual tracking lost",
"provenance": "authored_synthetic",
"frame": "local_x_left_y_up_z_forward_m",
"distribution": "independent_zero_mean_gaussian",
"interpretation": "pointwise_lateral_coverage_not_integrity_or_trajectory_probability"
}Research grounding & version record
Hullman, Resnick & Adar (2015), Hypothetical Outcome Plots motivates exposing multiple possible outcomes. Its findings concern statistical judgments; transfer to first-person navigation is the question under study here.
Kale et al. (2019), Hypothetical Outcome Plots Help Untrained Observers Judge Trends in Ambiguous Data provides a second precedent for distribution-based reasoning. This implementation uses fixed simultaneous hypotheses rather than their animated statistical plots.
v1 / 11 September: shared 2D uncertainty test bench and initial protocol. v1.2 / 13 September: native 3D FPV, four matched treatments, position/yaw propagation, reversible fallback replay, numerical baseline and explicit evaluation plan. The original shared test bench remains available.