Rooms, Waves & Quantum Choices · teacher material
THE FOUR-FINGER ECHO BOX
Resonance Code · sixteen fingerings · one quantum choice experiment
Status: pilot candidate, not empirically validated curriculum. Use observation notes to test the open auditory, game, score, cognition and parameter gates.
Design centre: age 14, approximately ages 12–15. Suggested duration: 45–60 minutes. Supplied sample is first-class; nobody must speak or use a microphone.
Learning target
Students should be able to explain: the Four-Finger Echo Box supplies sixteen acoustic fingerings; a game supplies objective scores; the same sixteen labels then also name four-qubit basis states; COST writes objective information into relative phase; canonical MIX coherently couples one-bit-different labels so phase differences can affect probabilities through interference; measurement returns one four-bit label; that label then controls the ordinary Echo Box. The resonator itself does not perform QAOA.
At Screen 5, do not narrate a detached “quantum section.” Say: “Same sixteen labelled configurations; different physical model from here.” Keep the recognisable four-key Echo Box and its fingering labels as the acoustic referent. COST and MIX act on the simulated quantum state, not on the physical keys. Measurement is the point where one classical four-bit label controls the instrument again.
Instrument-first teaching grammar
Every four-bit label names one fingering of the same coupled instrument. The silver-key diagram is a persistent label scaffold, not a quantum state and not four independent effects.
| Mode | Teacher meaning |
|---|---|
physical-interactive | Student is actually changing the ordinary resonator; key movement is meaningful acoustic interaction. |
physical-reference | Static Echo Box fingering beside quantum information. COST/MIX never actuate it. |
measured-actuation | Allowed only after explicit computational-basis measurement. The measured label is used as ordinary classical control. |
Before class
Equipment/browser
- Modern browser with JavaScript and Web Audio.
- Headphones or speakers at a comfortable level.
- Open the staging root and verify the supplied sample plays.
- Optional microphone only if local policy permits; the supplied sample fully supports the lesson.
- Print or open the 16-page Echo Box workbook and matched concept check.
Privacy + safety
- No account is required.
- Microphone permission is requested only after explicit choice.
- Student microphone audio remains in browser memory in the core pathway and is not uploaded/persisted.
- No live microphone-to-speaker feedback path is used.
- Playback is peak-protected; keep device/headphone volume comfortable.
45–60 minute lesson flow
| Minutes | Screen(s) | Teacher move | Student evidence |
|---|---|---|---|
| 0–5 | Pre-check + 1 | Use the supplied sample by default. Frame it as sound waiting at the Echo Box inlet. | Distinguishes ordinary source audio from later resonator and quantum representations. |
| 5–13 | 2 | Require prediction before generation 8. Reconstruct Lucier procedure; keep the room as lineage, not product identity. | Describes repeated transformation and keeps the historical boundary. |
| 13–20 | 3 | Teach the four physical OPEN/CLOSED keys before bitstrings. Reinforce one shared coupled body. | Explains why four binary keys give 16 fingerings of one Echo Box. |
| 20–28 | 4 | Preserve LISTEN → PREDICT → CHANGE ONE KEY → COMMIT → HEAR → REVEAL SCORE. | Uses listening before score reveal; can disagree with the metric. |
| 28–33 | 5 | Keep the same Echo Box visibly in view, then let the invalid quantum fade fail. Stress quantum-only reset. | States “same sixteen labels, different physical model”; recognises that the instrument/game are not reset or made quantum. |
| 33–39 | 6 | Ask whether COST moves bars before reveal. Point to the silver-key patterns as physical-reference · static. | Recognises COST-only probability null and relative phase change without claiming key motion. |
| 39–46 | 7 | Run MIX-only, COST-only, COST→MIX controls. Use one-bit label↔key-position correspondence only as an indexing reference. | Explains coherent coupling/interference without random-walk, neighbour-search or physical-key-motion language. |
| 46–53 | 8 | Separate highest score, highest probability and measured state. Before measurement, the Echo Box is inactive/reference-only. After measuring, follow measured label→four OPEN/CLOSED keys→ordinary Echo Box→cached sound. | Understands stochastic measurement, simulation/hardware boundary and the classical control handoff. |
| 53–60 | 9 + post-check | Read the same four-key glyphs as a fingering score, play the source-derived process piece, and require same/different explanation. | States resonator→game→QAOA→measurement→resonator roles accurately. |
Scientific language: say / avoid
Say
- “The Four-Finger Echo Box gives us sixteen possible acoustic fingerings.”
- “0 means CLOSED and 1 means OPEN for this instrument label.”
- “The game gives those fingerings objective scores.”
- “At Screen 5 we keep the same labels but change the mathematical model.”
- “The silver-key pictures beside quantum labels are static references; COST and MIX do not move the physical keys.”
- “COST uses those scores to mark relative phase.”
- “MIX does not know which state is good.”
- “COST and MIX together can reshape probabilities through interference.”
- “Measurement returns one label; then we use that label to set the ordinary Echo Box.”
- “This browser is classically simulating a tiny statevector.”
Avoid
- “Now the Echo Box becomes quantum.”
- “The quantum computer listens.”
- “The mixer moves one key at a time.”
- “The mixer searches nearby answers.”
- “The box is quantum-like.”
- “The best state wins.”
- “Quantum interference finds the answer.”
- “This score tells us how similar the sounds really are.”
- Any claim of quantum advantage or guaranteed improvement.
Common misconceptions and responses
| Misconception | Response |
|---|---|
| “The Echo Box disappeared at Screen 5 / we started a different problem.” | Return to the same four silver-key fingering language: the same sixteen acoustic fingerings and game scores remain the label/objective source. Only the mathematical model changes. |
| “The box becomes a quantum computer.” | The Echo Box remains an ordinary acoustic model. COST/MIX operate only on the simulated four-qubit state. |
| “COST makes good bars taller.” | Return to Screen 6: the bars remain 6.25%; COST changes relative phase. |
| “MIX checks neighbouring answers.” | The Hamiltonian coherently couples one-bit-different basis labels. The matching key position is an indexing scaffold, not a classical walk or key actuation. |
| “Interference must improve the score.” | Point to the explicit non-guarantee. Parameter choice matters and improvement is not monotonic or guaranteed. |
| “Measurement returns the best answer.” | Compare highest score, highest probability and measured state on Screen 8. |
| “The sound is the quantum state.” | Separate statevector calculation from later classical control: measurement returns a bitstring, then that bitstring sets four ordinary Echo Box keys and selects cached audio. |
| “Lucier invented this quantum idea.” | Use the frozen boundary: the project is compositionally descended from repeated acoustic process, not historically from QAOA. |
Pre/post concept check
Use the same eight prompts before and after. Do not coach the pre-check. For the post-check, accept age-appropriate wording if the causal roles are correct. Suggested scoring: 1 point each; record misconception patterns rather than treating the score as proof of educational effectiveness.
- How many fingerings do four binary Echo Box keys give?
- The Echo Box supplies the sixteen acoustic choices; what supplies the preference/objective?
- What does COST change immediately?
- Does COST alone change computational-basis probabilities?
- What labels does the canonical MIX Hamiltonian couple?
- Is COST→MIX redistribution guaranteed to improve the objective?
- What does measurement return?
- How does the returned four-bit label cause one ordinary Echo Box fingering to be heard?
Screen 9 fingering-score language
Do not let the composition erase provenance. Acoustic choices ≠ objective ≠ quantum state ≠ composition.
Pilot observation sheet
Gate A — auditory
Can learners hear useful target/start and one-key differences? Note replay behaviour and confusion.
Gate B — game
Do learners listen/predict before score reveal? Does SPECTRAL MATCH feel fair enough to support reasoning?
Gate C — cognition
Can learners retain the same-fingerings/different-model transition, COST-only null, MIX-only null, COST→MIX mechanism, measurement uncertainty and simulation/hardware distinction with 16 states?
Gates D/E — score + parameters
Record score/listening conflicts and whether the guided/local parameter behaviour is clear rather than cherry-picked.
Troubleshooting
- If microphone permission fails, use the supplied sample; do not make microphone use a blocker.
- If sound is too quiet/loud, adjust on-screen playback level and device volume; do not alter acoustic model parameters.
- If a route is opened directly, Cloudflare Pages should serve the SPA fallback for the nine journey routes.
- If the supplied WAV fails to load, the UI labels the generated development fallback distinctly; do not treat it as the supplied fixture.
- If a learner thinks Screen 5 starts a different task, return to the displayed four-key Echo Box and same sixteen labels before continuing.
- If a learner is overwhelmed by sixteen states, record it as Gate C evidence rather than silently changing the mechanism during the pilot.
Accessibility teaching checks
- Do not depend on colour: say OPEN/CLOSED and the four-bit label aloud when pointing to a glyph.
- Keyboard and touch users must receive the same required information as pointer users; no human-game score should be hover-only.
- Reduced-motion users must still see the measured label and textual four-key mapping even if key animation is suppressed.
- The web app announces important measured-label→key mapping textually; this guide does not substitute for device/screen-reader verification.
Release boundaries
No QPU, accounts, cloud audio, custom mixer, Hadamard-core pathway, deep QAOA, or quantum-advantage claim is part of this pilot candidate. The Echo Box model is physically motivated, not calibrated hardware. The spectral score is a declared game rule, not validated perceptual truth.