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Comment by mcdonje | Hacker News Reader

Classic Carl Sagan clip relaying this story: https://m.youtube.com/watch?v=8hZl3arO7SY

This article had one detail that was not included in the video that had always bugged me. Carl says "how could it be .. that at the same instant there was no shadow at Syene and a very substantial shadow at Alexandria". That seemingly requires coordination between 2 people across a vast distance and accurate time measurement. I rationalized that it could be accomplished with people at each location, each with a sundial, making records of shadow length, and later comparing their measurements, but it still seemed like a messy explanation.

The detail of no shadow at the zenith on a specific day solves that problem. That removes the complication of the coordination of 2 observers and the lighting of the well better explains why the phenomenon was noticed to begin with.

The other unresolved problem for me is that it still requires the assumption that light is parallel i.e. the sun is (relatively) incomprehensibly far away, and that was not established fact at the time afaik.

> The other unresolved problem for me is that it still requires the assumption that light is parallel i.e. the sun is (relatively) incomprehensibly far away, and that was not established fact at the time afaik.

It seems like it very recently had been:

https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Ar...

There are some Stack Exchange questions that give more background:

https://astronomy.stackexchange.com/questions/38892/how-did-...

https://hsm.stackexchange.com/questions/14722/how-did-eratos...

Pretty clever to use the illumination of the moon to figure it out!

That is clever! Thanks for sharing these. It's endlessly fascinating to read about how such accurate conclusions were made via simple observation and deduction.

>I rationalized that it could be accomplished with people at each location, each with a sundial, making records of shadow length, and later comparing their measurements, but it still seemed like a messy explanation.

I'd like to know how ancient people figured out how to make a sundial. They need to point the stick called a gnomon north if they're in the northern hemisphere or south if in the south. Not just pointed an old way it needs to be tilted at the angle according to their latitude it's not just a vertical stick in the ground.

Another way to word it would be "the shortest shadow of the entire day"

I think that approach might only work if both locations are directly north/south from each other, unless I'm thinking about this wrong. If the locations are east/west relative to each other, the shortest shadow won't occur at exactly the same moment.

edit: I guess that would still be a problem if you're using the zenith to determine the time of measurement. The best map I can find of the 2 locations used is [here](https://mathigon.org/step/circles/eratosthenes) and seems to indicate that Alexandria and Swenet/the other location are relatively north/south to each other.

edit 2: some more thoughts. If 2 points at the same latitude but on the opposite sides of the world were chosen, Eratosthenes method wouldn't have worked. The sun would have the same position in the sky at the zenith, but they'd be separated by thousands of miles, implying a flat world. Whether by design or luck, it seems that Eratosthenes experiment only works if the same longitude is used for each location, and otherwise he would have arrived at a very different answer for the circumference of the earth.

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