← Theory of RelativityPart 0 — Foundations · 02

Why Distant Objects Look Smaller

▶ DRILL

George walks away from Liza and looks smaller and smaller — but he never actually shrinks. The trick is that your eye doesn't measure size, it measures angle: the wedge between the line to his head and the line to his feet. Far away, that wedge gets thin, so he lands on a thinner slice of your eye. That's also why a thumb held close can cover a whole house — or the Moon. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words, names & pictures
HOW FAR IS GEORGEa little way off
he stays 1.4 m tall the whole time
WALK SPEEDnormal
VIEW
Liza 👧 looks at George 🧒this sliceLizaGeorgeGeorge is the same height — the slice just gets thinner
↕ same George — the top picture shows WHY (the angle at her eye), the bottom shows what her eye actually gets
what Liza 👧 sees from herehow big he was up closeGeorgefarther → smaller on your eye
GEORGE 🧒 — OUT THERE
George is still 1.4 m tall — exactly the same as when he stood next to Liza. He didn't shrink one bit by walking away.
LIZA 👧 — LOOKING
From here he looks about 34% as big as up close — because he fills a thinner slice of her eye, not because he got smaller.

The big idea — faraway things look small because your eye measures the angle something makes, not its real size. George never shrank; he just fills a thinner slice of Liza's view. That's the secret behind the trick: a tiny thing held close can make the same slice as a giant thing far away — which is how your thumb can cover a whole house, or even the Moon. Funny thing: far away he looks smaller but not darker — he doesn't fade out. Why doesn't he? That's another drill. (No relativity here yet — just light travelling in straight lines. But when something moves near the speed of light, even these angles get bent — that's a drill for later.)

# formulaθ = 2·arctan(h / 2d) — the angle a height h subtends at distance d; for small angles θ ≈ h/d
# setupGeorge's real height h = 1.4 m (fixed) · distance d = 2–50 m · apparent size scales with the true θ
# scaleside-view distances are compressed to fit on screen; the angular-size math is exact — there is no relativity here, just light in straight lines
# sourceclassical perspective / angular size — the geometric baseline for later drills (seeing the past, aberration)