Little Psi in the Quantum World

Psíčko v kvantovom svete · Псічко у квантовому світі
A 3D browser game for building intuition about quantum mechanics: its language, symbols, the right pictures and the typical misconceptions — not calculations.

Important

The lectures are your primary learning resource. This game is only a supplement and is likely to contain errors — please verify everything you learn in it against the lecture materials.

Contents

• Play
• Screenshots
• What the game teaches
• Choices on the welcome screen
• Equation glyphs
• Levels
• Controls
• Languages and dialogue files
• Project structure
• License
• Changelog

Play

Double-click index.html (Chrome, Edge or Firefox). No server, build or install is needed — WebGL2 (OpenGL ES 3.0) with no libraries. Progress, settings, the Codex and the Journal are saved in the browser (localStorage), so after a reload the game continues exactly where you left off; for a few seconds a 🗑 Start over button is offered as well.

On the first start (and after a reset) a two-step welcome screen appears:

1. Difficulty → Next ▸
2. History and dialogue (historic scrolls; skip all dialogue / with dialogue) → ◂ Back / Next ▸
3. Equations and Levels → ◂ Back / ▶ Start the game

Defaults: Normal difficulty, historic scrolls on, dialogue on, all levels unlocked. The gameplay style (Selection menu / Classic / Nordic / MMO) is not offered on the welcome screen — it starts as the Selection menu and can be changed in the settings (⚙).

Everything can be changed later in the settings (⚙).

Screenshots

Welcome screen — gameplay style, difficulty, history, equations, levels	🔑 Key — glyph dictionary first, mnemonic rules second
Nordic style — snowy island and the dragon's peak	MMO style — spells, quests, a vendor and dungeons
MMO dungeon — the level boss loses health with every step and correct answer	Hall of Symbols — 17 animated 3D exhibits of the equation symbols

What the game teaches

You play Little Psi, the quantum state ψ — not a little ball with a position, but a rule for predictions. Your guide Spark (✨ a spark of light, deliberately unlike any amplitude symbol) waits in the middle of Hilbert Island. All portals stand in one ring around the centre; behind each one a mentor teaches one topic of lectures 1–3 through small experiments, dialogues and quizzes. Every level ends with language traps — a quiz about correct wording, because many mistakes in quantum physics are made with words, not with calculations.

• Amplitudes are clock hands; probability is the squared length; the phase only matters when amplitudes meet (interference).
• Measurement asks a question in a chosen basis; the global phase is unobservable, the relative phase is not.
• Gates are rotations of the Bloch ball; mixtures live inside it; decoherence erases the off-diagonal of ρ.
• Bra-ket grammar, NMR and Rabi oscillations, entanglement and the CHSH game, and the interpretations of quantum mechanics.

Real machines next to the Bloch sphere. The Bloch sphere is only a picture of the state, not a device, so the levels also show the hardware where the same qubit actually lives, with its axes lined up with the sphere:

• Benchtop NMR processor (levels 3, 6, 9, 10, 11; like the SpinQ from the lectures): magnet with B₀ along z, sample tube in the RF coil (x axis), the sample magnetisation M ∝ ⟨σ⟩ = r that precesses about B₀ in the lab, the coil glowing during gate pulses, and the induced FID signal on the console screen.
• Mach–Zehnder interferometer (level 4): beam splitters = H, arms = |0⟩ and |1⟩, a which-path detector or phase noise in the middle.
• Entangled-photon source (level 7): a laser in a nonlinear crystal, polarisers turned to half the Bloch-sphere measurement angle, single-photon detectors.

They can be switched off in the settings (⚙ → 🔬 real machine).

Correct answers snap into place: once an input is accepted (an arrow on its target, a π pulse, the optimal CHSH angles…), the slider and the 3D picture glide exactly onto the correct value.

How the game makes sure you learn

Finishing a level should mean you have learned it, not just clicked through it (docs/LEARNER_EXPERIENCE.md explains the reasoning; the code is in js/learn.js):

• 🎯 Goals. Every level shows 2–4 goals ("by the end you will be able to…") on its portal and at the start. At the end each goal is marked ✅ (shown on your own: the task without the answer hint and a question right first time), 🟡 (with help or on a second try) or ⬜. 🎓 on a portal = all goals mastered.
• 🔮 Predict → experiment → verdict. Before key experiments (Stern–Gerlach angle, H·H, H·measurement·H, 100 copies of |+⟩, T₂, no-signalling, mid-circuit measurement) you lock in a prediction; whether it was right is shown only after the experiment.
• New numbers. Targets are random on every difficulty, the last puzzle of a series is random, and the final exam adds transfer questions generated by the simulator, so a level can't be passed from memory.
• ✨ Spaced review. Every question you get wrong (or right by guessing) comes back in the warm-up when you enter later levels, until you answer it correctly in three later sessions. Dragon's Peak starts with a mixed review of all levels.
• 🔁 Second chance. At the end of a level you get the questions you missed once more; a wrong generated question is followed straight away by a fresh variant.
• 🎯 Confidence. After picking an answer you say how sure you are; a confident mistake comes back twice, a lucky guess once more (can be turned off in ⚙).
• 💡 Step-by-step hints. Direction → method → answer. The last step marks the task as assisted.
• 🧠 "Why did that work?" Short questions after key solutions (interference, H·Z·H = X, H·H, the π pulse, CHSH, revealing a phase).
• No guessing from the answer length. node tools/build-lang.js checks that the correct option is not the conspicuously longest one in more than 35 % of the questions in any language.
• 📖 Review mode. With ⏭ Skip quizzing a level opens the next one but gives no stars and no mastered goals.
• ⬇ Export. Settings → Progress → Export my progress (JSON) downloads your question results, goals, before/after tests, hints and task times (nothing is sent anywhere) — e.g. to hand in to the teacher.

Choices on the welcome screen

Gameplay style (settings ⚙ only)

Style
Classic (default)	the original blue grid island with 8 portals — nothing distracts from the physics, runs on weaker computers
🐉 Nordic	a snowy island with pines and standing stones, Nordic lettering and detailed procedural textures; every mentor teaches a Word of Power and level 9 is a turn-based battle with the quantum dragon Ketvarr
⚔ MMO	plays like an online RPG: a quantum mage with levels, a spell bar (X and H gates, the Born blade = measurement…), classical misconceptions as neutral enemies whose shields are qubits, quests, a vendor (Max Planck), bags and loot; levels are dungeons with bosses, and the dragon is a raid

1 · Difficulty

Can be changed at any time from the selector in the top-right corner — the open dialogue, quiz and task text update immediately.

• 🫶 Layman — everything in everyday words: an "in plain words" card before every task, technical words translated in brackets, simple tooltips.
• Easy — wider tolerances, fewer trials, step-by-step hints; equations are shown straight away in the colourful glyph language.
• Normal (default) — the original game. ∑ Complete the equation: after every task you fill in the missing parts of the equation you have just seen at work, from drop-downs (e.g. ρ′ = Uρ( )), each blank with exactly one correct option. Equations are typeset plainly (Baskerville-style serif) — no colours, glyphs, live equation stage or Hall of Symbols.
• Hard — as Normal plus theory and equations at every step, more fill-in blanks, extra equation questions, dense texts, random targets, no hints, stricter stars.

Layman and Easy skip the fill-in quizzes entirely.

The fill-in quizzes cover every expression from the lecture PDFs and blackboards (about 300, lectures 1–5). Each quiz shows where its relation comes from (📄 L4, L1 · board) so you can check it in the lecture. After a task at most 2 (Normal) or 3 (Hard) are asked, picked in this order:

• ▣ boxed in the lecture first;
• the task's own equations;
• unboxed side relations — Hard only;
• ⤷ derivation steps ("how did we get to the boxed result?") — Hard only, and only sometimes.

Relations that the game does not show at work (differential equations, series, Hermite polynomials, continuous bases, relativistic equations, algorithms…) are not asked after tasks. All of them, grouped by lecture, are in Codex → 📄 Lecture drill — ungraded practice.

2 · History and dialogue

📜 Historic scrolls (on by default): before level steps a scroll unrolls with the history of the discoveries — years, authors, their conversations and famous words — and every level ends with one history question. Collected scrolls stay in the Codex.

💬 Dialogue (on by default) or ⏭ Skip all dialogue — skipping leaves only the tasks, quizzes, equation cards and scrolls; conversations are still written to the Journal (L).

3 · Equations

• 🖼 Mainly Human Language — the picture and intuition come first (hands, the Bloch ball, experiments); equations live in the 📐 theory panel and the Journal.
• ∑ Equation Language (Experimental) (default) — the real equation that holds right now is shown at the top of the screen and changes as you play; every task starts with its "∑ Equation first" card; all symbols are drawn as glyphs (below); adds portal 0 — the Hall of Symbols (17 pedestals, each symbol as a small 3D experiment, with a question after each one, a review after each chapter and a final exam).

4 · Levels

Unlock everything (default — all portals open right away) or Step by step (the next portal opens after the previous level). Unlocking and resetting are also available at the bottom of the help (H) and settings (⚙) panels.

Equation glyphs

In the Equation Language every symbol becomes an SVG glyph that carries its meaning: colour = who it is, a pictogram behind the letter = what it does, and the frame shape = what kind of object it is. Hover a glyph for its name, a memory phrase and the pictogram on its own; the 🔑 key (top right, key K) holds the full glyph dictionary and the mnemonic rules. The files below are exported from the game (docs/glyphs/).

Glyph	Meaning	Memory phrase
α, β	amplitudes of |0⟩ (blue) and |1⟩ (red)	Alpha points Above, Beta goes Below
|ψ⟩, |0⟩, |1⟩	kets — states; the frame ⟩ points forward	the tick shows the pole
⟨a|	bra — a question; the mirrored frame	⟨a|ψ⟩ is one number
θ, φ, γ	tilt (pink), relative phase (green), global phase (gold)	Tilt from the Top, the Fan's turn, the Gold Gear
H, X, …	operators — 3D boxes acting to the right	X marks the flip, H = Halfway swap
P, |α|²	probability — a white pillar; the frame freezes the phase	frame it and freeze it

Levels

#	Level	Mentor	Topic
0	Hall of Symbols (Equation Language only)	Spark	what every symbol in the equations means
1	Complex Harbour	Leonhard Euler	amplitude as a clock hand, phase, i² = −1, interference
2	Stern–Gerlach Furnace	Otto Stern & Walther Gerlach	two spots, ±ħ/2, sequential measurements Z → X → Z, cos²(θ/2)
3	Bloch Observatory	Felix Bloch	gates X, Y, Z, H, S, T as rotations, relative vs. global phase, measurement, geometry lab
4	Temple of Interference	Richard Feynman	H·H vs. H·measurement·H, density matrix ρ, coherences, decoherence
5	Dirac's Library	Paul Dirac	bra-ket grammar: state, question, number, operator, probability
6	Rabi's Resonator (NMR)	I. I. Rabi	precession, rotating frame, π and π/2 pulses, resonance, T₂
7	Bell's Bridge	John Bell	Bell state, reduced states, no-signalling, the CHSH game
8	Hall of Interpretations	Niels Bohr (+ Kant, Wittgenstein, Stodola, Bohm, Heisenberg, Noether)	collapse, complementarity, interpretations
9	Pauli's Rotation Workshop (lecture 4)	Wolfgang Pauli	θ, φ as coordinates, rotations Rn(ϑ) = exp(−iϑ n·σ/2), measurement as the direction of a question (φ = atan2(ry, rx)), unitary vs. decoherence, Bell state limits
10	Von Neumann's Purity Refinery (lecture 5)	John von Neumann	ρ′ = UρU† keeps |r|, purification by measurement or cooling, NMR pseudo-pure state (r = εn), ⟨A⟩ = Tr(ρA), time evolution e−iHt/ħ
11	Born's Readout Hall (lecture 5)	Max Born	phase → interference → probability, mid-circuit measurement, measure → decide → continue, Bell state vs. classical mixture, decoherence ≠ readout
12	NMR Workshop (hands-on, unlocked from the start)	Edward Purcell	tuning the transmitter to ν₀ = γB₀/2π, current pulses in the transverse RF coil (θ = γB₁τ, phase = axis), measurement sequences and the FID, pulse calibration from the signal null, shimming and the spin echo
13	Dragon's Peak (Nordic and MMO styles)	Erwin Schrödinger	turn-based battle: the dragon's ward is a qubit, a strike is a measurement with P = ½(1 + r·n)

Each portal shows a small animated preview of its level, and its tooltip lists the level's tasks. Stars depend on the number of mistakes (fill-in-the-equation mistakes count too); 📖 = done in review mode, 🎓 = all goals mastered. New Codex cards (symbols, people, concepts, scrolls and every task's ∑ equation) unlock as you play.

Controls

Key	Action
WASD / arrows	move around the island (Shift = faster)
mouse drag, wheel	camera
E	enter a portal / talk
Enter, Space · ← / Backspace	next / back in a dialogue
L	Journal — every conversation, task equation (∑) and quiz explanation; read or replay
C	Codex — symbols, people, concepts, scrolls, equations
K	🔑 key — glyph dictionary and mnemonic rules (Equation Language; unavailable during conversations)
V	👁 views — the same state as clock hands, Bloch cuts, bases and the ρ matrix
M · H · O · Esc	map (click a portal to travel) · help · settings · close windows
1 – =	spells (MMO style) · B bags · Tab target · Space jump
F9	unlock all levels

Hover anything (button, symbol, 3D object, underlined term) for a short explanation. Controls that do nothing at the moment (e.g. spells or panel buttons while a dialogue is open) are shown greyed out.

Languages and dialogue files

The game is in Slovak, English and Ukrainian. Without a saved choice, Czech and Slovak browsers get SK, browsers with Ukrainian, Russian or Belarusian among their languages get UA, and everyone else EN. Switch with the selector in the top-right corner or on the welcome screen.

All dialogue text — conversations, quizzes, language traps, "in plain words" cards, theory, scrolls and quests — lives in lang/sk.csv, lang/en.csv and lang/uk.csv (columns key,text; a missing translation falls back to English). The code reads them with DL('key', values…).

• Equations are written in double square brackets — this tells the game where to draw the equation background: [[P = |α|²]] inside a sentence becomes an inline chip, [[…]] on a line of its own becomes an equation block. Matrices are written [0, 1; 1, 0] so they don't clash with the brackets.
• {0}, {1} … are values filled in by the game (counts, percentages, names); a translation may move them.
• After editing a CSV run node tools/build-lang.js. It regenerates lang/*.js (browsers refuse to read CSV files when the game is opened from disk) and checks the [[ ]] brackets and {n} placeholders. When served over http(s) the game reads the CSV files directly.
• Interface strings (buttons, HUD, tooltips, Codex) stay in the code as tr('slovensky', 'English', 'українською').

Project structure

Path	Contents
index.html, style.css	page, help, themes, welcome screen
js/main.js	game loop, island (hub), portals, base Level class, saving
js/levels/*.js	levels 0–13; registry.js sets their order
js/eqblanks.js	∑ fill-in-the-equation items for every level step (correct option first), the lecture-only set for the 📄 Lecture drill
js/learn.js	learning: level goals, transfer-question generators, spaced review (Leitner boxes), second chance, confidence, step-by-step hints, before/after tests, progress export
js/ui.js	dialogues, quizzes, Journal, Codex, settings, tooltips
js/gl.js · js/math.js · js/quantum.js	WebGL2 renderer and procedural meshes · vectors, matrices, complex numbers · 1- and 2-qubit simulator
js/eqglyphs.js · js/eqmnemo.js	SVG equation glyphs and [[…]] rendering · live equation and the 🔑 key
js/i18n.js · lang/ · tools/build-lang.js	language choice, tr() and DL() · dialogue CSV files · CSV → JS generator and checker
js/knowledge.js · js/content.js · js/scrolls.js · js/layman.js	theory and equations · Codex and language traps · historic scrolls · layman cards and glossary
js/machine.js	3D models of the real machines next to the Bloch sphere (NMR processor, Mach–Zehnder interferometer, entangled-photon source)
js/views.js · js/tips.js · js/audio.js · js/wow.js · js/welcome.js · js/settings.js	👁 views · tooltips · generative music and sound effects · MMO style · welcome screen · settings
assets/ · docs/	icons, theme pictures · README screenshots and exported glyph SVGs

License

MIT © 2026 Ondrej Špánik

Changelog

Built from the commit history (newest first).

Unreleased

• Learning guarantees (see docs/LEARNER_EXPERIENCE.md): level goals and mastery 🎓, locked predictions, random targets on every difficulty, generated transfer questions, spaced review and a second chance, confidence ratings, step-by-step hints, "why did that work?" questions, before/after tests, progress export
• Fill-ins come after the task (at most 2 / 3), lecture-only relations moved to the 📄 Lecture drill
• Skipping quizzes is review mode (📖, no stars); Easy no longer drops a random wrong option
• Rewritten wrong options so the correct one is no longer the conspicuously longest; tools/build-lang.js checks it

2026-10-10

• 732fa4f Easy is the default difficulty and Equation Language the default game type; task equations in the Codex; fixed the selection border of the game-type cards; temporary "Start over" button when continuing a game
• ef294fa Unlock all levels and Reset game at the bottom of the settings as well
• 039a4b7 Welcome-screen notice: the lectures are the primary learning resource
• 8abfe1c Task equations in the Journal in both game types; two-slide welcome screen with an "Unlock everything" choice
• 422fc9a Updates
• 93b1c02 History (historic scrolls) separate from difficulty; welcome screen update
• a099a7f Improvements
• c40f099 Correct inputs snap into the exact state
• c81f684 Updated welcome-screen visuals for the game type
• bc51d08 Renamed the game types; dialogue adjustments
• 4868b79 Adjusted the glyph and key approach
• 9795bdb Better key location; disabled buttons are shown as such during dialogues
• 41a41cd Glyph tooltips show the pictogram separately
• cd46e7e Dialogue moved to CSV translation files with generated JS

2026-10-09

• 6da6dc7 Improvements to the mnemonic version
• 835ad3b Improved equation backgrounds and colours
• aca7afd Bigger equation display with mnemonics
• cfa7fa5 More equation mnemonics
• b0bb51b Live equations
• f0ce1d6 Ukrainian translation
• f557568 Welcome setup wizard

2026-10-08

• dc72d04 Fast-changing numbers are easier to read
• 3e9b5e6 Larger panel text
• 7f18729 "Ask Google AI" button in dialogues
• fccb2c0 Removed dialogue keys
• bb20ed8 Custom cursor, hidden while rotating the camera
• 75a8efb MMO-style gameplay
• 8848080 Music volume off is truly silent (reverb routed through the volume); quieter 15 % default
• 2d3f005 Theme selector: Classic (8 levels) and Nordic (Skyrim look + dragon level 9); music and sound effects in both
• c756187 Music, sound effects, better textures depending on computer performance
• b67baed Nordic (Skyrim-style) look
• d3ddc94 Teleport mid-dialogue; Layman as the default difficulty
• cfe7805 Hotfix: labels per difficulty
• 88a22be Layman version added to the difficulty selector
• 4387991 WASD hint and teleport through the map
• d535264 Banner, favicon and metadata
• 425fe1c Update
• 55bc677 Difficulty updates; "ancient" difficulty with scrolls of knowledge
• 2b968b3 Difficulties, localStorage save, reset button
• 830d16e Slovak and English (i18n); unlock the whole game from the help section
• 4c941e1 v1: lectures 1–3 as a game world