Zeno's paradox of motion: how infinite steps add up to finite distance

A 5-beat faceless video outline for “Zeno's paradox of motion: how infinite steps add up to finite distance” in the Math paradoxes explained niche, derived from caption timing of 2 reference videos.

Angles

• Cold-open on Zeno walking to a park: first half the distance, then half of what remains, forever — so how does he arrive?
• Pair it with Achilles and the tortoise so viewers see the same structure twice
• Resolve visually: chop a unit square in half again and again — the pieces fill the square, so 1/2 + 1/4 + 1/8 + … = 1
• Close on the honest philosophy beat: convergent vs divergent series, and the lingering "infinite process with no last step" question

Beat-by-beat structure

1. Hook (0:00–0:30): a walker and a halving path.
2. Two versions (0:30–1:45): dichotomy and Achilles vs the tortoise.
3. Common sense (1:45–2:30): one hour at constant speed — so where is the catch?
4. Square proof (2:30–4:00): geometric series filling a unit area; the multiply-by-½ algebra trick.
5. Limits card (4:00–5:30): convergence vs divergence, what mathematicians and philosophers still debate. Original narration only.

Reference videos

• What is Zeno's Dichotomy Paradox? - Colm Kelleher EfqVnj-sgcc
• Zeno's Paradox - Numberphile u7Z9UnWOJNY

Method

yt-dlp VTT captions (manual/uploader only) → timed beat heuristics → editorial topic synthesis (no ASR). Structure only; write original narration.