A Position Is an Argument

No painted line under the keel

A position is an argument.

Offshore, there is no painted line under the keel. The chart offers latitude and longitude. The sea offers wind, current, leeway, waves, compass error, clock error, and a horizon that keeps no receipts. Where the boat is must be inferred.

A navigator begins with a prior fix. Course and speed advance that position through time. This is dead reckoning: useful, necessary, and doomed to drift. A small heading error becomes a growing cross-track error. An unknown current moves the whole estimate sideways. Uncertainty expands with every mile without a fix.^1,2

Then evidence arrives: GPS, a sextant altitude, a depth contour, a light bearing, measured acceleration, turn rate. Each observation has noise. None deserves blind obedience. The new position is a compromise between prediction and measurement.

The pencil cross on a chart is the center of a probability cloud.

Drift has a covariance

Dead reckoning starts with a state vector. Position, speed, heading, and perhaps current or sensor bias occupy its slots. A motion model predicts the next state. It also predicts covariance: how uncertain each quantity is and how its errors vary with the others.

Time without an external fix is expensive. Gyroscope bias integrates into heading error. Heading error integrates into position error. White sensor noise becomes a wandering track. A crisp line on a plotter may conceal a widening cloud.^2,3

Celestial navigation interrupts the drift. A sextant measures the angle between a body and the visible horizon at a recorded time. Almanac data and spherical geometry turn the observation into a line of position. The boat lies somewhere near that line, within an error band. Two or more lines can form a fix.⁴

The observation does not teleport the boat. Horizon blur, wave motion, sextant index error, eye height, refraction, and time enter the result. A fix is an update, not revelation.

How much should the fix move you?

Modern integrated navigation performs the negotiation rapidly. An inertial system predicts motion. GPS supplies positions when available. A Doppler log or speed sensor adds velocity. The filter computes an innovation: observation minus predicted observation.

If the observation is precise and the prediction uncertain, Kalman gain K leans toward the measurement. If the observation is noisy and the model is trusted, correction is smaller. The filter does not ask which source is true. It asks how uncertain each source is under its assumptions.^1,3

Navigation also separates estimation from control. First estimate course, speed, heading, and disturbance. Then the autopilot compares desired and estimated course and moves the rudder. A poor estimate can make a sound controller steer badly.

The boat itself can become a sensor. Roll, pitch, and heave contain information about wave height and direction. Yet response depends on hull, loading, heading, and speed. An estimator needs a model of the observer.

Navigation inside the skin

The nervous system must estimate heartbeat, breathing effort, temperature, gut state, energy need, threat, and pain from partial signals. Interoception is not a little observer reading flawless dials. It is inference about bodily state.

These dimensions can disagree. Heartbeat counting makes the problem plain. A person silently counts beats while ECG records them, but the score can be influenced by beliefs about normal heart rate, timing skill, attention, and instructions. A high score is not a transparent view of cardiac afferent traffic.

Different instruments, different charts

Borg and colleagues tested 21 women with fibromyalgia and 21 controls. Heartbeat-counting accuracy, confidence calibration, and total self-reported interoception did not differ by group. The fibromyalgia group reported less body trust; within that group, pain-related affect predicted poorer heartbeat performance.⁵

Valenzuela-Moguillansky and colleagues tested 30 women with fibromyalgia and 29 controls. Heartbeat counting again did not differ. The fibromyalgia group reported more noticing, less non-distraction from discomfort, and less body trust. They also judged their body as needing a wider opening to pass, tied more to functional impact than current pain.⁶

A newer study used a phase-adjustment task: participants moved tones until they felt synchronous with their heartbeat. The fibromyalgia group was more accurate than controls, while objective and self-reported measures related to symptom impact in opposite directions.⁷ A different instrument produced a different chart.

A 2025 study of 29 women with fibromyalgia found wide variation across heartbeat accuracy, confidence, discrepancy, and self-report measures. It had no control group. Objective accuracy correlated positively with several memory and inhibition scores, while some confidence and self-report measures correlated negatively.⁸ These are hypotheses, not a settled compass rose.

Prediction is not perception

Longitudinal physiology adds evidence without measuring awareness. In a wearable study of 66 people observed for an average 81 days, night heart rate predicted next-day pain after accounting for prior pain and other factors. Pain did not predict the next night’s heart rate, and the association did not differ between fibromyalgia and back-pain groups.⁹

That concerns temporal prediction in recorded physiology. It does not show that participants consciously sensed heart rate, that heart rate caused pain, or that a Bayesian prior produced the association. A sensor can improve a forecast without explaining the mechanism.

Predictive-coding models describe repeated exchange between top-down predictions and bottom-up prediction errors. Precision sets how strongly errors update the model. Attention may alter precision; prior learning may alter predictions; peripheral input may alter likelihoods.

Applied to pain, this language needs guardrails. A strong prior does not make pain imaginary. A prediction error is not a personal mistake. Precision is a model quantity, not everyday confidence.

Report the error ellipse

Blue-water navigation sharpens one final distinction: position and confidence are separate. A navigator can be wrong and certain, right and doubtful, or accurate within a wide stated uncertainty. Good navigation reports both the fix and its error ellipse.

Interoception research needs the same honesty. Report objective performance. Report confidence. Report self-described awareness. Report the task’s known shortcuts. Do not average them into one mythical sense called body accuracy.

At blue-water dawn, the horizon becomes a hard silver edge. The navigator lifts the sextant. A star descends to meet the sea for one instant. Nothing physical happens at that crossing. Yet the cloud of possible positions tightens, and the boat acquires a more defensible answer to where it is.