Revision 7T · Full Tutorial Edition · Updated 1 September 2026
PWR-091 · SELF GUIDED full tutorial
Estimate a homeward vector from remembered displacements without walking blindfolded
Path integration updates an internal estimate of the starting point as successive translations and turns occur. Drift normally accumulates. This safe fixture uses coordinate traces on paper or screen, never eyes-closed locomotion. The learner follows a sequence once, conceals it, marks a straight homeward bearing and magnitude, then quantifies angular and length error and tests the effect of one fixed external reference cue.
What you will produceThe learner calculates homeward-bearing and magnitude error on six novel coordinate traces and reports how an external reference changes those two errors.
Full step-by-step individual tutorial · TLU-PWR-091
The learner calculates homeward-bearing and magnitude error on six novel coordinate traces and reports how an external reference changes those two errors.
Follow fictional displacement sequences on paper or an accessible screen while seated.
Keep normal orientation and mobility aids during all real travel.
Qualified help is required for
Physical homing where falls, traffic, disorientation, cognitive impairment or disability makes consequences meaningful.
Orientation-and-mobility assessment or vestibular testing.
Never do this from the page alone
Walk blindfolded, close the eyes while moving, spin, remove travel aids or practise near traffic, stairs, water or obstacles.
Use a paper score to certify outdoor or community travel safety.
2 · Get ready
Gather what you need and check the starting conditions
What you need
Six printed coordinate traces, each with a start, two to five straight segments and quarter turns.
Blank coordinate sheets, pencil, ruler, protractor or accessible angle tool and correction overlays.
Optional raised-line traces or screen-reader-compatible turn-and-length lists.
Before you start
Work seated with no physical motion challenge.
Learn how up, right, down and left on the sheet represent four fixed headings.
Set the scoring rule: bearing error in degrees and magnitude error in grid units.
3 · The method
Follow these steps in order
Read the start frame
Mark the origin, the initial facing arrow and the fixed upward axis.
Why: A homeward vector is meaningless without an origin and heading frame.
Check: Origin, facing arrow and upward axis are visible before tracing.
Trace each segment
Follow the sequence once, counting units and naming every clockwise or counter-clockwise quarter turn. Do not calculate the final vector yet.
Why: Segment-by-segment updating supplies the self-motion analogue in a consequence-free fixture.
Check: The learner reaches the endpoint with the prescribed segment count.
Maintain a heading ledger
At each turn, draw a small arrow showing the new facing direction and state the estimated east–west and north–south change so far. Cover the ledger before the final return estimate.
Why: A heading ledger teaches how successive rotations and translations update position while still preserving an unaided final test.
Check: Every turn has one correct facing arrow, and the final answer is committed without reopening the ledger.
Hide and estimate the bearing
Cover the sequence and draw one arrow from the endpoint straight toward the remembered origin.
Why: The arrow captures the accumulated heading-and-position estimate.
Check: One homeward arrow is committed before feedback.
Estimate vector magnitude
Write how many grid units the direct homeward line should span without reversing the outbound sequence.
Why: Displacement magnitude differs from total travel length.
Check: One magnitude estimate is written beside the arrow.
Reveal and quantify error
Place the correction overlay on top. Measure the smaller angular gap between arrows and the absolute difference between estimated and exact magnitudes.
Why: Bearing and magnitude reveal two different forms of drift.
Check: Both numerical errors are retained for every trace.
Resolve the displacement components
Only after scoring the memory estimate, give eastward units a positive horizontal value x, westward units negative x, northward units positive y and southward units negative y. Add each axis. The exact homeward vector is (−x, −y), and its length is √(x² + y²). Draw that vector from the endpoint and use a protractor to measure the smaller angle between it and the estimated arrow.
Why: Component arithmetic provides a transparent correction key while keeping the earlier perceptual estimate uncoached.
Check: The horizontal and vertical sums reproduce the answer-key arrow, and any arithmetic slip is separated from the original estimation error.
Relate drift to sequence complexity
After several traces, order them by turn count and total travelled length, then compare their bearing and magnitude errors without deleting exceptions.
Why: Accumulated drift may respond differently to rotations and translations.
Check: The summary identifies the largest miss, its complexity features and any trace that contradicts a simple accumulation pattern.
Compare an external-reference condition
Repeat matched traces with the origin marker left visible, then try a fresh sequence after 48 hours. Keep unaided and reference-cue scores separate.
Why: A stable external reference can correct accumulated drift; a delayed unfamiliar sequence checks method use.
Check: The report compares both cue conditions and includes a delayed trace.
4 · Worked example
See the whole method used once
Scenario
A coordinate trace moves 4 squares up, 3 right and 2 down from origin A.
Walkthrough
Kai marks the upward axis and follows all three segments once.
After concealing the sequence, he draws a down-left homeward arrow from the endpoint.
He estimates a magnitude of 3 grid units.
The overlay shows an exact displacement of 3 left and 2 down, magnitude about 3.6; bearing error is 11 degrees and magnitude error 0.6.
On a matched trace with origin A still visible, his angular miss falls, which he reports as reference-assisted performance.
Result
Kai distinguishes direct displacement from reversing the outbound sequence and quantifies two error components. The paper result does not show safe physical homing.
5 · Right and wrong
Compare correct or safer execution with the common wrong version
Right and wrong comparison
Moment
Right / safer
Wrong / riskier
Why it matters
Fixture
Use a paper, tactile or screen trace while seated.
Walk with eyes closed to make self-motion realistic.
Blindfolded movement adds fall and collision risk.
Return
Draw the direct displacement to the start.
Reverse every outbound segment as the answer.
Route reversal and path integration are different tasks.
Scoring
Measure bearing and magnitude error separately.
Mark the whole attempt simply right or wrong.
Separate errors show whether heading or scale failed.
External reference
Report fixed-cue and unaided results apart.
Combine them into one orientation score.
Visible origin information can correct an accumulated internal estimate.
6 · Common mistakes
Spot the error and apply the correction
Common mistakes and corrections
Mistake
Fix
The reference axis changes when the page rotates.
Keep the page fixed and reproduce the upward arrow on every blank sheet.
The learner retraces instead of drawing displacement.
Require one straight return arrow.
Signed magnitude differences cancel.
Use absolute magnitude error per trace before averaging.
A practised sequence is called transfer.
Use a delayed trace with new segment lengths and turn order.
7 · Practice
Turn the steps into a usable skill
First session
Learn one demonstrated coordinate trace.
Complete three unaided traces.
Measure angular and magnitude errors.
Complete three matched origin-visible traces.
Write which reference corrected the largest drift.
Repeat plan
Complete six new sequences twice a week for two weeks, divided equally between unaided and origin-visible trials. After 48 hours, use a fresh set. Increase turn count only after scoring remains stable.
Progress when
All estimates are committed before feedback.
Median angular and magnitude errors improve on unfamiliar traces.
The learner explains when an external origin cue corrected drift.
Do not progress when
The learner memorises correction overlays.
The next step involves actual eyes-closed motion or removal of aids.
Visual, vestibular or cognitive symptoms make the task distressing.
8 · Check the result
Measure what changed
Angular and magnitude error of a direct homeward estimate.
How: For each concealed sequence, sum horizontal x and vertical y displacement, use (−x, −y) as the homeward vector and calculate exact length √(x² + y²). Record the smaller protractor angle between estimated and exact arrows plus the absolute difference between estimated and exact lengths, separated by cue condition.
Good result: Every exact vector and error calculation reproduces, an unfamiliar matched set is reported without hiding larger errors, and reference-assisted results stay separate from unaided results. A lower median is evidence to retest, not a validated pass threshold.
This does not prove: It does not establish community travel, vestibular function, fall safety or physical homing transfer.
Self-check
Did you mark the origin and initial heading?
Is the homeward estimate one straight vector?
Are angle and magnitude errors separate?
Was physical blindfolding excluded?
9 · Stop, adapt or get help
Keep the safety boundary practical
Stop and get help
Stop for dizziness, nausea, headache, visual strain or distress.
Do not convert the task into movement with closed eyes or reduced aids.
Seek qualified orientation or clinical support if getting lost, balance change or travel difficulty affects real safety.
Accessibility and adaptations
Use raised-line coordinate sheets and tactile heading arrows.
Provide turn-and-length text with an accessible vector-response format.
Allow extra processing time and a scribe while preserving concealed-sequence commitment.
10 · Evidence and limits
Why these instructions are here
primary research
Vision and proprioception made comparable contributions in one novel homing task, so cue configuration must be reported.
Progress is saved only in this browser on this device.
Step-by-step learner mode
Each activity includes its success check, a nearby accessible alternative and an “I’m stuck” correction path. Alternatives preserve the target where possible; when they change the task, Titan labels them as related rather than equivalent.
01
Read the start frame
Mark the origin, the initial facing arrow and the fixed upward axis.
Why this step exists
A homeward vector is meaningless without an origin and heading frame.
Success check
Origin, facing arrow and upward axis are visible before tracing.
I’m stuck on this step
Reset: Re-read this authored instruction — “Mark the origin, the initial facing arrow and the fixed upward axis.” — and its success check, then attempt only this step.
Possible snag: The reference axis changes when the page rotates.
Correction: Keep the page fixed and reproduce the upward arrow on every blank sheet.
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
02
Trace each segment
Follow the sequence once, counting units and naming every clockwise or counter-clockwise quarter turn. Do not calculate the final vector yet.
Why this step exists
Segment-by-segment updating supplies the self-motion analogue in a consequence-free fixture.
Success check
The learner reaches the endpoint with the prescribed segment count.
I’m stuck on this step
Reset: Re-read this authored instruction — “Follow the sequence once, counting units and naming every clockwise or counter-clockwise quarter turn. Do not calculate the final vector yet.” — and its success check, then attempt only this step.
Possible snag: A practised sequence is called transfer.
Correction: Use a delayed trace with new segment lengths and turn order.
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
03
Maintain a heading ledger
At each turn, draw a small arrow showing the new facing direction and state the estimated east–west and north–south change so far. Cover the ledger before the final return estimate.
Why this step exists
A heading ledger teaches how successive rotations and translations update position while still preserving an unaided final test.
Success check
Every turn has one correct facing arrow, and the final answer is committed without reopening the ledger.
I’m stuck on this step
Reset: Re-read this authored instruction — “At each turn, draw a small arrow showing the new facing direction and state the estimated east–west and north–south change so far. Cover the ledger before the final return estimate.” — and its success check, then attempt only this step.
Possible snag: The learner retraces instead of drawing displacement.
Correction: Require one straight return arrow.
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
04
Hide and estimate the bearing
Cover the sequence and draw one arrow from the endpoint straight toward the remembered origin.
Why this step exists
The arrow captures the accumulated heading-and-position estimate.
Success check
One homeward arrow is committed before feedback.
I’m stuck on this step
Reset: Re-read this authored instruction — “Cover the sequence and draw one arrow from the endpoint straight toward the remembered origin.” — and its success check, then attempt only this step.
Possible snag: The result from “Cover the sequence and draw one arrow from the endpoint straight toward the remembered origin.” does not yet meet this declared check: One homeward arrow is committed before feedback.
Correction: Return to the start of “Hide and estimate the bearing”, reduce complexity or pace, and repeat only the part needed to satisfy: “One homeward arrow is committed before feedback.”
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
05
Estimate vector magnitude
Write how many grid units the direct homeward line should span without reversing the outbound sequence.
Why this step exists
Displacement magnitude differs from total travel length.
Success check
One magnitude estimate is written beside the arrow.
I’m stuck on this step
Reset: Re-read this authored instruction — “Write how many grid units the direct homeward line should span without reversing the outbound sequence.” — and its success check, then attempt only this step.
Possible snag: The result from “Write how many grid units the direct homeward line should span without reversing the outbound sequence.” does not yet meet this declared check: One magnitude estimate is written beside the arrow.
Correction: Return to the start of “Estimate vector magnitude”, reduce complexity or pace, and repeat only the part needed to satisfy: “One magnitude estimate is written beside the arrow.”
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
06
Reveal and quantify error
Place the correction overlay on top. Measure the smaller angular gap between arrows and the absolute difference between estimated and exact magnitudes.
Why this step exists
Bearing and magnitude reveal two different forms of drift.
Success check
Both numerical errors are retained for every trace.
I’m stuck on this step
Reset: Re-read this authored instruction — “Place the correction overlay on top. Measure the smaller angular gap between arrows and the absolute difference between estimated and exact magnitudes.” — and its success check, then attempt only this step.
Possible snag: Signed magnitude differences cancel.
Correction: Use absolute magnitude error per trace before averaging.
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
07
Resolve the displacement components
Only after scoring the memory estimate, give eastward units a positive horizontal value x, westward units negative x, northward units positive y and southward units negative y. Add each axis. The exact homeward vector is (−x, −y), and its length is √(x² + y²). Draw that vector from the endpoint and use a protractor to measure the smaller angle between it and the estimated arrow.
Why this step exists
Component arithmetic provides a transparent correction key while keeping the earlier perceptual estimate uncoached.
Success check
The horizontal and vertical sums reproduce the answer-key arrow, and any arithmetic slip is separated from the original estimation error.
I’m stuck on this step
Reset: Re-read this authored instruction — “Only after scoring the memory estimate, give eastward units a positive horizontal value x, westward units negative x, northward units positive y and southward units negative y. Add each axis. The exact homeward vector is (−x, −y), and its length is √(x² + y²). Draw that vector from the endpoint and use a protractor to measure the smaller angle between it and the estimated arrow.” — and its success check, then attempt only this step.
Possible snag: The result from “Only after scoring the memory estimate, give eastward units a positive horizontal value x, westward units negative x, northward units positive y and southward units negative y. Add each axis. The exact homeward vector is (−x, −y), and its length is √(x² + y²). Draw that vector from the endpoint and use a protractor to measure the smaller angle between it and the estimated arrow.” does not yet meet this declared check: The horizontal and vertical sums reproduce the answer-key arrow, and any arithmetic slip is separated from the original estimation error.
Correction: Return to the start of “Resolve the displacement components”, reduce complexity or pace, and repeat only the part needed to satisfy: “The horizontal and vertical sums reproduce the answer-key arrow, and any arithmetic slip is separated from the original estimation error.”
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
08
Relate drift to sequence complexity
After several traces, order them by turn count and total travelled length, then compare their bearing and magnitude errors without deleting exceptions.
Why this step exists
Accumulated drift may respond differently to rotations and translations.
Success check
The summary identifies the largest miss, its complexity features and any trace that contradicts a simple accumulation pattern.
I’m stuck on this step
Reset: Re-read this authored instruction — “After several traces, order them by turn count and total travelled length, then compare their bearing and magnitude errors without deleting exceptions.” — and its success check, then attempt only this step.
Possible snag: The result from “After several traces, order them by turn count and total travelled length, then compare their bearing and magnitude errors without deleting exceptions.” does not yet meet this declared check: The summary identifies the largest miss, its complexity features and any trace that contradicts a simple accumulation pattern.
Correction: Return to the start of “Relate drift to sequence complexity”, reduce complexity or pace, and repeat only the part needed to satisfy: “The summary identifies the largest miss, its complexity features and any trace that contradicts a simple accumulation pattern.”
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
09
Compare an external-reference condition
Repeat matched traces with the origin marker left visible, then try a fresh sequence after 48 hours. Keep unaided and reference-cue scores separate.
Why this step exists
A stable external reference can correct accumulated drift; a delayed unfamiliar sequence checks method use.
Success check
The report compares both cue conditions and includes a delayed trace.
I’m stuck on this step
Reset: Re-read this authored instruction — “Repeat matched traces with the origin marker left visible, then try a fresh sequence after 48 hours. Keep unaided and reference-cue scores separate.” — and its success check, then attempt only this step.
Possible snag: The result from “Repeat matched traces with the origin marker left visible, then try a fresh sequence after 48 hours. Keep unaided and reference-cue scores separate.” does not yet meet this declared check: The report compares both cue conditions and includes a delayed trace.
Correction: Return to the start of “Compare an external-reference condition”, reduce complexity or pace, and repeat only the part needed to satisfy: “The report compares both cue conditions and includes a delayed trace.”
Stop / get help: Stop for dizziness, nausea, headache, visual strain or distress.
Correct versus incorrect execution
These accessible process diagrams are built from the tutorial’s own right/wrong teaching. They are not anatomical illustrations and do not add technique beyond the canonical tutorial.
Fixture — Blindfolded movement adds fall and collision risk.
Correct / safer
Use a paper, tactile or screen trace while seated.
Wrong / riskier
Walk with eyes closed to make self-motion realistic.
Return — Route reversal and path integration are different tasks.
Correct / safer
Draw the direct displacement to the start.
Wrong / riskier
Reverse every outbound segment as the answer.
Scoring — Separate errors show whether heading or scale failed.
Correct / safer
Measure bearing and magnitude error separately.
Wrong / riskier
Mark the whole attempt simply right or wrong.
External reference — Visible origin information can correct an accumulated internal estimate.
Correct / safer
Report fixed-cue and unaided results apart.
Wrong / riskier
Combine them into one orientation score.
Method-structure checklist
10 of 10 structural checks present
✓ Ordered, Power-specific instructions — present
✓ Every activity has a success check — present
✓ Materials or supplied records are declared — present
✓ Measurement or assessment rule is present — present
✓ Tutorial-specific troubleshooting is present — present
✓ Stopping or escalation boundary is present — present
✓ Every activity has an adjacent alternative — present
✓ Correct-versus-incorrect comparison is present — present
✓ Evidence context is bound to the Power record — present
✓ Planning metadata is present — present
The method-readiness band and presence checklist assess tutorial presentation and are separate from evidence quality for the underlying Power. They are automated editorial aids, not human approval.
Manual editorial sign-off: Pending. This tutorial must not display a human-approved state until an identified editor signs the exact content hash.