# Sagan on Eratosthenes

After getting himself all grumpy about the ways in which statistics are abused, Joshua Hall decided to relax with a little Carl Sagan.

Fun fact: the philosopher Poseidonios of Apameia (c. 135–51 BCE) repeated Eratosthenes’s experiment about a century and a half later. He observed that on the island of Rhodes, the bright star Canopus was just touching the horizon, while at the same time in Alexandria, the star was a few degrees above the horizon. Because the Earth curves between the two places, the star was seen from different vantage points, and thus the angle between Rhodes and Alexandria could be found. Poseidonios was luckier than he knew: both his figure for the distance between Rhodes and Alexandria and his measurement of Canopus’s position were wrong, but the two wrongnesses canceled each other out, giving a reasonable final answer.

(And yes, I employ BCE/CE dating just to irritate people.)

## 8 thoughts on “Sagan on Eratosthenes”

1. Sili says:

Thank you.

This is the first time I realise that it’s a North-South distance. Suddenly it all makes sense! I’d at some point wondered how one determines that it’s the same time in two different places. I’ve been pondering an East-West difference, but never really looked into it. Just goes to show that I’ve never possessed the true scientific mindset.

I seem to recall hearing that the main reason we’re not sure how accurate Eratosthenes’ measurement was, is that we don’t actually know the length of the measure he used – the stadion. Is that right?

2. AFAIK, yes: you can make the figure in kilometers change by a few percent one way or the other, which doesn’t diminish the awesome factor of Eratosthenes’s accomplishment.

3. Sili says:

Of course! What I (failingly) was trying to get at that Eratosthenes may well have been even awesomer than we can be sure of.

If only he’d invented SI while he was at it (and done something about that rather masochistic way they handled fractions).

4. windy says:

Iâ€™d at some point wondered how one determines that itâ€™s the same time in two different places.

You might enjoy Dava Sobel’s Longitude (about the related problems of keeping time and determining your location in the east-west direction)

5. Pseudonym says:

And yet, some people still think that everyone in Columbus’ day thought the Earth was flat.

6. The algorithm says:

The longitude story is fascinating on a few levels. For one thing, one practical solution was ultimately in the down-and-dirty engineering of building a clock that would work in spite of changes in temperature that made metal expand and contract and would handle the jostling the chronometer gets in a ship. For another, it’s the most famous example of government offering a prize for an invention, an approach philanthropists and governments wouldn’t be foolish to consider now for problems where the solution isn’t profitable or needs to be public domain (think malaria control). Finally, it’s surprising how resistant some folks were to a solution that wasn’t what they expected. The Longitude Board fought to avoid giving the watchmaker his prize; they thought only another, more complicated method could possibly work, even after testing showed otherwise.

See Wikipedia on the history of longitude, the watchmaker John Harrison, and the Longitude Prize.

7. Sili says:

I’m aware of the longitude problem (but I still appreciate all the links and recommendations!).

That’s exactly why I’d wondered how it was done in ancient Egypt. But somehow my brain seems to have considered the Earth a cylinder rather than a sphaere somewhere along the way.

8. windy says:

By the way, isn’t Sagan wrong in saying that a round Earth is the only explanation for the different angles of sunlight observed at the same time? What if the Sun had been relatively small and hovering above Syene, not too far away… ;)