A Visual Proof of Bayes' Theorem
A narrated math explainer proves an identity with color-coded area diagrams, then tests its limits with concrete examples.
Field notes / why it works
The same colored probability region is reconstructed from two directions around 0:25–0:52, making the algebra visible; the strongest replay peak occurs at 0:29.6–0:31.9 during that construction. The lesson renews interest at 1:45 with a tempting misconception, then uses highlighted example grids and a corrected condition at 2:01–2:55. Only 5 cuts occur in 3:47, but 32 internal graphic changes keep the reasoning moving.
Plate 01 / The format in one breath
A calm, fast-spoken narrator promises a short proof, then shows the same quantity two ways by rearranging colored regions under a persistent equation. Once the elegant identity is established, a familiar real-world misconception tests its boundary; small example grids turn the exception into a useful rule.
Why it works
- The promise is explicit by 0:08: a quick mathematical explanation. The first visual update at 0:10.8 brings in the formula and diagrams as soon as the argument needs them.
- The same colored area is shown from two directions at 0:25–0:51; the highest replay peak is 0:29.6–0:31.9, precisely during the second orientation of that construction.
- At 1:45 the lesson turns to a common mistaken shortcut. Coin, dice, and family examples at 2:01–2:46 show when the shortcut does and does not work.
Plate 02 / Format card
| Platform · aspect · length | YouTube · 16:9 · 3:47 · source capture 640×360 at 30 fps |
| Pace | 6 detected shots, 5 cuts, 1.3 cuts/min; 32 internal graphic changes, 9.8 total picture changes/min; mean shot 37.84 s, median 15.47 s |
| Script | 613 spoken words; 179 wpm over full runtime, 212 wpm while speaking; 25 sentences averaging 24.5 words; 2 questions; 20 number mentions |
| Voice | One medium-register, articulate, curious narrator; brisk mathematical reasoning with expressive pitch |
| On screen | Almost entirely designed 2D motion graphics: set symbols, area diagrams, Venn circles, tiny character icons, grids, and a distribution plot; no live presenter |
| Captions | No burned dialogue captions; selective math labels and equations act as reading guides |
| Sound | Low tonal music-like bed about 20.5 dB beneath voice; 104 BPM estimate; −17.0 LUFS integrated, +0.1 dBFS measured true peak |
| Structure | Promise → two-view visual proof → usefulness → misconception → independence boundary → broader takeaway; spoken payoff at 3:19–3:25, music-only end card to 3:47; no spoken CTA |
Pro / 13 plates + recipe
The first plates are open. The full dissection is Pro.
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Open the full blueprint- Plate 03 / The hook, frame by frame (first 3 seconds)Pro
- Plate 04 / Structure (beat sheet)Pro
- Plate 05 / Shot grammarPro
- Plate 06 / Visual style guidePro
- Plate 07 / Voice and deliveryPro
- Plate 08 / Sound designPro
- Plate 09 / PackagingPro
- Plate 10 / Script templatePro
- Plate 11 / Production planPro
- Plate 12 / PromptsPro
- Plate 13 / Edit recipePro
- Plate 14 / QA checklistPro
- Plate 15 / Make it yoursPro
- Recipe / runnable promptPro