I’m a few chapters into Our Mathematical Universe by Max Tegmark. By this point he's covered the ingenuities of the ancient Greeks, taking my knowledge of physics to within two and a half thousand years of the cutting edge.

And what ingenuities they were. A whole series of them, strung together, and culminating in a pretty good estimate of the size of the Sun. I think it's a remarkable feat to even just ask the question ‘How big is the Sun?’ and recognize that it has an answer. The fact that the ancient Greeks actually managed to figure it out (more or less) is astonishing.

I don’t know the exact path they took with their reasoning. History is messy. But here's a plausible route they could have taken, basically matching the one you’ll find charted in OMU.

Step 1: Discover that the Earth is round.

One way to discover that the Earth is round is to wait for a lunar eclipse, where the Earth casts its shadow on the Moon. If you look carefully, you’ll notice that the shadow is curved.

Another sign of Earth's roundness is the way that departing ships disappear over the horizon: hull-first and mast-last.

[...]

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Outline:

(00:57) Step 1: Discover that the Earth is round.

(01:37) Step 2: Use the disappearing-ship trick to estimate Earth's size.

(02:24) Step 3: Use Eratosthenes' shadow trick to estimate Earth's size again.

(03:43) Step 4: Use the similarity of your estimates to surmise that the Sun is really far away.

(04:51) Step 5: Use the Sun's distance and apparent size to infer that it's bigger than the Earth.

(06:02) Step 6: Use the Earth's shadow on the moon to estimate the Moon's size.

(08:15) Step 7: Use the Moon's real size and apparent size to estimate its distance.

(08:58) Step 8: Use the Moon's distance to estimate the Sun's distance.

(10:24) Step 9: Use the Sun's distance and apparent size to estimate its real size.

(10:56) Epilogue

The original text contained 3 footnotes which were omitted from this narration.

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First published:
July 9th, 2026

Source:
https://www.lesswrong.com/posts/Bc4Ch63cx8KHdQABw/how-big-is-the-sun-how-could-you-figure-it-out

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Narrated by TYPE III AUDIO.

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Images from the article:

Moon partially obscured by Earth's shadow during lunar eclipse.

Three-masted sailing ship on choppy blue ocean waters.

Diagram showing Earth with parallel sunlight rays, measuring 7.2° angle between Alexandria and Syene.

Diagram illustrating how a small, nearby sun creates shadows on flat Earth.

Moon partially obscured by Earth's shadow during lunar eclipse.

Diagram showing Earth, Moon, Sun positions during lunar eclipse with umbra and penumbra shadows.

Total solar eclipse with visible corona surrounding the moon.

Half-illuminated moon showing craters against black background.

Diagram showing eight phases of the moon around Earth.

Diagram showing Sun, Moon, and Earth positions with distance and angle measurements.

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“How big is the Sun? How could you figure it out?” by Elliott Thornley

LessWrong (30+ Karma)

“How big is the Sun? How could you figure it out?” by Elliott Thornley