Brake a virtual chair, open a real inner-ear reconstruction, and solve a motion-clue puzzle. Discover why actual movement, sensory responses and what you feel are different.
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Stopping a movement does not instantly settle every sensory response. Different kinds of clues help the brain interpret motion.
The chair has stopped, but the model response is negative. What does that mean?
The actual speed and model state are different. Interpretation and feeling are additional processes.
Start the virtual rider, let the chair turn, then brake. The chair and rider move together. You can remain comfortably still, or use the still-stage cards. Look at the two readouts: actual chair speed and a simplified mechanical response inside the ear.
In this example, the canal response changes sign during braking and takes time to settle afterward. That does not make the chair secretly turn backward. A sensory response and the motion that caused it are different quantities. The brain’s interpretation is another step.
Inside each inner ear are small membranous ducts, housed in bony channels. Fluid mechanics acts on a flexible structure called the cupula in each widened ampulla. Its motion couples to sensory hair cells. The real 3D scan shows bony space; our enlarged moving cupula is a separate teaching illustration.
The utricle and saccule are the otolith organs. Their sensory tissues couple to a layer containing tiny dense calcium-carbonate particles called otoconia. They respond to the combined effects of gravity and linear acceleration. Our two virtual cabins show why that combined clue alone can fit more than one motion.
The eyes provide information relative to a visual scene. Muscles, joints and contact provide information about the body and its support. Inner-ear signals add information about motion. A scene or support may itself move, so these are complementary reference frames—not identical votes with fixed percentages.
Vestibular means relating to the inner ear’s balance-and-motion system. Post-rotation motion sensations involve dynamic signals and their interpretation. This lesson explains one relevant mechanism; dizziness can have many causes, and this model does not assess an individual person.
The selected single-mode reduction is dy/dt + y/τ = α, with angular acceleration α, example time constant τ = 4 s and scaled state y. The plotted index is y divided by π/3 rad/s. Finite ramps avoid treating a speed discontinuity as an ordinary time step. Natural canal, afferent and central responses are more complex than this mechanical reduction.
During a constant-speed interval, angular acceleration is zero and the model state relaxes exponentially. During braking, the acceleration drives it the opposite way. A response can therefore cross zero before physical rotation stops. With no further input, one time constant reduces its magnitude to 1/e, about 0.368, rather than erasing it.
A 2 s start reaches 60°/s; an 8 s cruise precedes a 2 s stop. The normalized response is approximately +0.787 at the end of the start, +0.107 before braking, −0.722 when motion stops, and −0.266 four seconds later. Keeping the same cruise and braking over 8 s instead gives approximately −0.418 at the stop. These are calculated model states, not measured feelings.
The 2016 geometry-based study reports a human lateral-duct model time constant around 4.0 ± 0.8 s. An earlier indirect eye-response fit reports 4.2 ± 0.6 s in ten humans. Other biomechanical estimates report about 16–20 s under different assumptions. We do not resolve this disagreement or claim four seconds is a universal human constant. The 2016 uncertainty is not a between-person standard deviation.
In our head-fixed right/down convention, f = g − a. A stationary 15° tilted cabin has f = [2.538148, 9.472497] m/s². An upright cabin can match it with acceleration [−2.538148, 0.334153] m/s²: leftward and slightly downward. Horizontal acceleration alone matches only one component. These momentary constructed vectors do not make the entire sensory histories identical.
The Wimmer dataset contains co-registered imaging and bony-labyrinth reconstructions from 23 specimens. Our rotatable F01 is a left-side micro-CT surface with 87,155 vertices and 174,318 triangles. Its original sampling is 0.06 mm; the largest source bounding-box extent is about 16.264 mm. No membrane, cupula mechanics or head-aligned yaw frame is inferred from that bony surface.
David et al.’s stained micro-CT shows smaller membranous structures inside bony space. Direct toadfish measurements in a separate study distinguish cupula motion from diverse afferent responses; those fish times are not human constants. Human and primate motion studies test additional neural and sensory-integration processes. Our anatomy, mechanical model and cue cards keep these evidence roles distinct.
Vestibular information contributes to gaze stabilization during everyday head movement. It operates with neural processing and eye movements beyond this one-state model; a canal response is not a finished command for an eye.
A familiar start, cruise and stop supplies an accessible way to compare physical motion with a dynamic sensor. The virtual rider’s finite profiles are authored examples, not instructions for operating a ride or a person.
Researchers and clinicians may compare anatomy, motion, eye responses and other information because no one measurement establishes every part of balance. This learning activity makes no diagnosis or personalized assessment.
Make columns for actual motion, canal model and other information. Use the supplied end-of-start, end-of-cruise, stop and four-seconds-later records.
Place forward, zero or reverse markers for actual speed and model response. Then check the numbers. At the stop, actual motion is zero while the response remains negative.
Keep the 8-second cruise. Compare stopping over 2 seconds and over 8 seconds: approximately −0.722 versus −0.418 at the respective stops. Write what changed and what stayed fixed.
Place the tilted and accelerating cabin cards beside their matching two-axis vector. Choose an extra clue—recent rotation, fixed outside scene or body/support relation—and explain its possible use.
In the full published figure, human anatomy is row a. Find blue bony space and the smaller red membrane. Finish: “The image shows ___. The simulation adds ___.”
Can you explain a movement from its clues without moving yourself?
Use the supplied records while seated. This is a paper interpretation activity, not a spinning experiment, balance test or personal health assessment.
A mechanical response can persist after rotation stops. The state relaxes after the physical input ends.
These are dynamic sensors, not perfect constant-speed meters. Response depends on the time course of movement.
A flexible cupula. The cupula is a compliant structure spanning the widened duct.
Gravity and linear acceleration. The combined input does not separately label its two causes.
That vector alone cannot choose between these cases. A shared output can have more than one physical cause.
They supply complementary clues with different references. The usefulness of a reference depends on its context.
One left human bony labyrinth from imaging. Its static anatomical provenance is visible and downloadable.
An unforced model response becomes 1/e as large in four seconds. An exponential time scale is not a symptom duration.
Agency-owned descriptions of canals, cupula, hair cells, otolith organs and multiple causes of dizziness. No outdated prevalence statistic or clinical maneuver is imported.
NIDCD · Balance DisordersScientific Reports 6, 32772. Full Figures 1 and 2, captions, methods and Table 2 support the anatomy distinction and declared four-second example. Figures CC BY 4.0; human panels/specimen differences remain labeled.
David et al. (2016) · original micro-CT and mechanics paperFitted mean 4.2 ± 0.6 s in ten humans from slow-phase eye-velocity responses. Verified abstract only; no unverified methods or human symptom predictions.
Dai et al. (1999) · original study abstractOriginal simultaneous optical and afferent study in toadfish. Fish parameters are not human constants. The paper is linked; noncommercial-licensed figures are not redistributed.
Rabbitt et al. (2009) · direct cupula and nerve measurementsFive rhesus monkeys and eye-movement outcomes under controlled motions; intervention in two animals. Supports the interpretation problem, not a direct report of a human feeling.
Angelaki et al. (1999) · original tilt/translation studyHuman eye responses tested against internal-model predictions. Our vector construction illustrates the mechanics ambiguity without reproducing provocative laboratory motions.
Merfeld, Zupan & Peterka (1999) · human motion studyControlled visual-surround and support-surface experiments. No fixed universal percentages, personalized weights or home balance protocol are derived.
Peterka (2002) · human sensory integrationCo-registered clinical CT/micro-CT and segmented surfaces from 23 human specimens. F01’s bony space is separate from David’s soft-tissue specimens and this mechanical model.
Wimmer et al. (2019) · original data descriptorVersion 1.0, CC BY 4.0. F01 descriptor confirms LEFT. Exact topology retained; centered, converted from millimeters to meters and recolored. Source and derivative hashes are in the downloadable provenance record.
Wimmer et al. · original dataset, F01Used specifically to disclose the approximately 16–20 s estimate and its assumptions. It does not override the original studies or settle a universal constant.
Rabbitt (2019) · source-owned biomechanical reviewIndependent subject review is pending.
Read the sources and model assumptions
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