Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 | /** * Ramanujan Demo Narration Segments: "The Ghost Note" * * Pure data file — no React. Each segment maps a revealProgress range * to a TTS utterance and a minimum animation duration. * * Progress ranges are derived from ramanujanDemo.ts's PHASE constants. * The demo visualises ζ(s) as a smooth curve that the kid builds up * from shrinking-and-adding experiments, then follows past the pole * to discover ζ(−1) = −1/12. * * PEDAGOGICAL APPROACH: Each segment teaches ONE concept and builds * on the previous. The ending ties all pieces together explicitly. * * Seg 0 0.000–0.040 Question: what happens adding all numbers? * Seg 1 0.040–0.070 Payoff: it zooms to infinity! * Seg 2 0.070–0.100 Hook: a secret number is hiding inside * Seg 3 0.100–0.150 Shrink attempt: 1+½+⅓+¼ still → ∞ * Seg 4 0.150–0.200 Shrink HARDER: square the bottoms → tiny! * Seg 5 0.200–0.260 Convergence payoff: it settles to 1.645! * Seg 6 0.260–0.320 Knob concept: different squishing → different answers * Seg 7 0.320–0.370 Plot the points on a graph * Seg 8 0.370–0.420 Connect the dots: smooth curve! * Seg 9 0.420–0.470 Approaching the wall: knob slides toward 1 * Seg 10 0.470–0.520 The wall: s=1 is infinity again * Seg 11 0.520–0.555 The track is perfectly smooth — how to get past? * Seg 12 0.555–0.600 Failed attempts: sharp corner cracks, wiggly wobbles * Seg 13 0.600–0.650 THE SEESAW: up on right → must plunge down on left * Seg 14 0.650–0.700 Watch the flip: path starts negative, stays below * Seg 15 0.700–0.760 The FLIPPER: negative exponent grows instead of shrinks * Seg 16 0.760–0.810 CONNECTION: knob at −1 = our original question * Seg 17 0.810–0.850 Volcano: sum explodes to infinity at s=−1 * Seg 18 0.850–0.895 WHY TRUST THE BRIDGE: built from real convergent answers * Seg 19 0.895–0.940 THE REVEAL: bridge lands at −1/12! * Seg 20 0.940–0.970 RECAP: putting all the pieces together * Seg 21 0.970–1.000 Ramanujan's letter + the ghost note */ import type { DemoNarrationSegment } from './useConstantDemoNarration' /** Shared voice direction for the Ramanujan demo narrator. */ export const RAMANUJAN_DEMO_TONE = 'You are a warm, patient guide on a treasure hunt with a really smart 5-year-old. ' + 'Explain each step simply and build understanding before moving on. ' + 'Be genuinely amazed when the track reveals the impossible answer. ' + 'At the end, tie all the pieces together so the child feels the whole journey.' export const RAMANUJAN_DEMO_SEGMENTS: DemoNarrationSegment[] = [ // ═══════════════════════════════════════════════════════════════════ // ACT 1: DIVERGENCE + HOOK (0.00–0.10) // ═══════════════════════════════════════════════════════════════════ // Seg 0: The question { ttsText: "Let's find out what happens when you add every number together. " + "One plus two plus three plus four — all of them, forever! Let's watch!", startProgress: 0.0, endProgress: 0.04, animationDurationMs: 4500, scrubberLabel: 'Add all numbers', }, // Seg 1: Divergence payoff { ttsText: 'Look at that! One, three, six, ten, fifteen — the pile gets bigger ' + "faster and faster! It zooms off to infinity. There's no stopping it!", startProgress: 0.04, endProgress: 0.07, animationDurationMs: 4500, scrubberLabel: 'Zooms to infinity!', }, // Seg 2: The hook { ttsText: "But here's the wild part. Mathematicians found a secret number " + "hiding inside that crazy sum. Let's go on a treasure hunt to find it!", startProgress: 0.07, endProgress: 0.1, animationDurationMs: 5000, scrubberLabel: 'A secret hides', }, // ═══════════════════════════════════════════════════════════════════ // ACT 2: SHRINKING & CONVERGENCE (0.10–0.26) // ═══════════════════════════════════════════════════════════════════ // Seg 3: Harmonic attempt (fails) { ttsText: 'First, what if we shrink each number before adding? ' + 'Take one, add a half, add a third, add a quarter. ' + 'The pieces are small, but even those still pile up to infinity! ' + "Shrinking a little isn't enough.", startProgress: 0.1, endProgress: 0.15, animationDurationMs: 7000, scrubberLabel: 'Shrink a little', }, // Seg 4: Square shrinking (works!) { ttsText: 'We need to shrink HARDER! What if we square the bottom numbers? ' + 'One over one is still one. But one over two-squared is just a quarter! ' + "One over three-squared is a ninth — that's tiny! One over four-squared " + 'is a sixteenth. They get SO small, SO fast!', startProgress: 0.15, endProgress: 0.2, animationDurationMs: 7000, scrubberLabel: 'Shrink HARDER', }, // Seg 5: Convergence payoff { ttsText: 'And when you add all those tiny pieces together... watch the pile. ' + 'It slows down... and stops growing! It settles to about one point six four five. ' + 'Not infinity — a real, beautiful number!', startProgress: 0.2, endProgress: 0.26, animationDurationMs: 6500, scrubberLabel: 'It settles!', }, // ═══════════════════════════════════════════════════════════════════ // ACT 3: THE CURVE (0.26–0.42) // ═══════════════════════════════════════════════════════════════════ // Seg 6: The knob concept { ttsText: 'How much we squish is like a tuning knob. Knob at two means ' + "square the bottoms. Let's try other settings! Knob at three: " + 'the pieces get even tinier! Knob at four: they practically vanish! ' + 'Each setting gives a different answer.', startProgress: 0.26, endProgress: 0.32, animationDurationMs: 7000, scrubberLabel: 'The tuning knob', }, // Seg 7: Plotting points { ttsText: "Each knob setting gives us a number. Let's mark them on a graph. " + 'Knob two lands here... knob three over here... knob four right there.', startProgress: 0.32, endProgress: 0.37, animationDurationMs: 5500, scrubberLabel: 'Plot the points', }, // Seg 8: The curve { ttsText: 'Now connect the dots. See that? ' + 'A smooth, beautiful curve — like a roller coaster track!', startProgress: 0.37, endProgress: 0.42, animationDurationMs: 5000, scrubberLabel: 'Connect the dots', }, // ═══════════════════════════════════════════════════════════════════ // ACT 4: THE WALL (0.42–0.52) // ═══════════════════════════════════════════════════════════════════ // Seg 9: Approaching the wall { ttsText: 'Now watch what happens when the knob slides toward one. ' + 'The pieces barely shrink at all. ' + 'The sum gets bigger... and bigger...', startProgress: 0.42, endProgress: 0.47, animationDurationMs: 5500, scrubberLabel: 'Approaching the wall', }, // Seg 10: The wall { ttsText: "At knob one, it's one plus a half plus a third plus a quarter — " + "and THAT goes to infinity too! There's a wall in our track. " + "The roller coaster can't go there!", startProgress: 0.47, endProgress: 0.52, animationDurationMs: 6000, scrubberLabel: 'The wall!', }, // ═══════════════════════════════════════════════════════════════════ // ACT 5: THE BRIDGE (0.52–0.70) // ═══════════════════════════════════════════════════════════════════ // Seg 11: Smooth track + how to get past? { ttsText: "But look at the track we've built on this side of the wall. " + "It's perfectly smooth — no bumps, no kinks. " + 'But how do we get past the wall to the other side?', startProgress: 0.52, endProgress: 0.555, animationDurationMs: 5000, scrubberLabel: 'Smooth track', }, // Seg 12: Failed attempts — SHOWING why only one works { ttsText: 'What if the track makes a sharp turn? ' + "Nope — it cracks! Sharp corners aren't smooth. " + 'What about a wiggly path? Too wobbly — that breaks too! ' + 'Only a perfectly smooth path can survive.', startProgress: 0.555, endProgress: 0.6, animationDurationMs: 6500, scrubberLabel: 'Failed attempts', }, // Seg 13: The seesaw — WHY the smooth path goes negative { ttsText: "Here's the secret. On our side of the wall, the track rockets UP to infinity. " + 'But a smooth path has to reach the wall from both sides. ' + 'And if it goes up on the right... the only smooth way is to plunge ' + 'DOWN on the left! Like a seesaw — one side up, the other must go down.', startProgress: 0.6, endProgress: 0.65, animationDurationMs: 7000, scrubberLabel: 'The seesaw', }, // Seg 14: Watch the flip happen { ttsText: 'Watch! On the left side of the wall, the track starts way down below zero. ' + 'Then it climbs... but stays negative! ' + 'The wall flipped everything to the minus side. ' + 'And the pencil draws the only smooth path, all by itself.', startProgress: 0.65, endProgress: 0.7, animationDurationMs: 6500, scrubberLabel: 'Below zero', }, // ═══════════════════════════════════════════════════════════════════ // ACT 6: THE FLIPPER + ANSWER (0.70–0.87) // ═══════════════════════════════════════════════════════════════════ // Seg 15: The flipper — what does knob=-1 mean? { ttsText: 'Now, what does a knob setting of negative one even mean? ' + 'Remember, knob at two means one over n-squared — it squishes numbers small. ' + 'But the minus sign is like a flipper! ' + 'Instead of squishing numbers smaller, it flips them bigger!', startProgress: 0.7, endProgress: 0.76, animationDurationMs: 7500, scrubberLabel: 'The flipper', }, // Seg 16: Flipper payoff — connecting back { ttsText: 'One over four-squared is tiny — just a sixteenth. ' + 'But four to the power of one is just... four! The minus sign flipped it back! ' + 'So knob at negative one gives us back one plus two plus three plus four forever — ' + 'our original question!', startProgress: 0.76, endProgress: 0.81, animationDurationMs: 7000, scrubberLabel: 'Our original question', }, // Seg 17: Volcano — the sum explodes { ttsText: 'At knob negative one, the actual sum — one plus two plus three plus four — ' + "it explodes to infinity! It's pure chaos at that spot. " + 'Watch the numbers fly!', startProgress: 0.81, endProgress: 0.85, animationDurationMs: 5500, scrubberLabel: 'Volcano!', }, // ═══════════════════════════════════════════════════════════════════ // ACT 7: THE BRIDGE'S SECRET (0.85–1.00) // ═══════════════════════════════════════════════════════════════════ // Seg 18: Why trust the bridge — built from real answers { ttsText: 'But remember what our bridge is made of! ' + 'At knob two, the sum really truly converges to one point six four five — ' + 'and the bridge goes right through it. ' + 'Knob three? Real answer. Bridge matches. ' + 'Knob four? Real answer. Bridge matches. ' + 'Every single point where the sum converges, the bridge nails the real answer. ' + 'Because the bridge was BUILT from those real answers!', startProgress: 0.85, endProgress: 0.895, animationDurationMs: 9000, scrubberLabel: 'Trust the bridge', }, // Seg 19: The reveal — −1/12 { ttsText: 'And this bridge — the one smooth path, built from real math, ' + "the only path that doesn't break — " + 'it flies right over the chaos at knob negative one. ' + 'And it says the height there is... negative one twelfth!', startProgress: 0.895, endProgress: 0.94, animationDurationMs: 7000, scrubberLabel: 'Negative one twelfth!', }, // Seg 20: Recap — tying ALL pieces together { ttsText: 'We squished numbers and found real answers. ' + 'Those answers built the only smooth bridge. ' + 'The bridge told us the pattern hidden inside one plus two plus three forever.', startProgress: 0.94, endProgress: 0.97, animationDurationMs: 6000, scrubberLabel: 'Putting it together', }, // Seg 21: Ramanujan + ghost note { ttsText: 'Over a hundred years ago, a genius named Ramanujan wrote this ' + 'in a letter to a famous professor. ' + 'One plus two plus three forever equals negative one twelfth. ' + 'The smooth bridge proves he was right. ' + "It's the ghost note — hidden inside infinity.", startProgress: 0.97, endProgress: 1.0, animationDurationMs: 8000, scrubberLabel: "Ramanujan's letter", }, ] |