The solstice, the librarian, and the size of the Earth

June 20, 2017 6:11 AM

The Guardian: "Eratosthenes of Cyrene was the chief librarian at the great library of Alexandria in the third century BC. So the story goes, he read in one of the library’s many manuscripts an account of the sun being directly overhead on the summer solstice as seen from Syene (now Aswan, Egypt). This was known because the shadows disappeared at noon, when the sun was directly overhead. This sparked his curiosity and he set out to make the same observation in Alexandria. On the next solstice, he watched as the shadows grew small – but did not disappear, even at noon..."
posted by Wordshore (45 comments total)

I love this, because it's so easy to replicate and do with students. I did it a few years back with my sixth graders, and we came to a circumference of the Earth of 40995 km, only about 920 km off. And the kids felt like they'd done something absolutely amazing - which, when you think about it, they had. Thanks, Eratosthenes!
posted by Chanther at 6:26 AM on June 20, 2017 [27 favorites]

Relevant segment from Cosmos.
The wonder of discovery, and the power of science and a stick, it makes me tear up.
posted by The Legit Republic of Blanketsburg at 6:46 AM on June 20, 2017 [5 favorites]

 /
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(Alexandria)

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(Aswan)

posted by leotrotsky at 6:55 AM on June 20, 2017 [1 favorite]

Seventeen hundred years after Eratosthenes' death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe, based on a map by Toscanelli, that the Earth's circumference was one-third smaller. Had Columbus set sail knowing that Eratosthenes' larger circumference value was more accurate, he would have known that the place that he made landfall was not Asia, but rather the New World.

Following a long tradition of disregarding inconvenient knowledge when significant dollars are involved.
posted by leotrotsky at 6:58 AM on June 20, 2017 [32 favorites]

"(pre-modern) People all believed the Earth was flat" has to be in the top 10 falsehoods taught in school (#1: "There is no gravity in space"). Eratosthanes' work was not forgotten. I mean, the Divine Comedy, written about 1300, has a spherical Earth. It has no land in the Southern hemisphere except for the mountain of Purgatory, but the sumbitch is round.
posted by thelonius at 7:05 AM on June 20, 2017 [14 favorites]

This trick only works if the sun is very far away. The same observations could be explained by a flat Earth and a sun that is about 4000 miles away.
posted by Hatashran at 7:10 AM on June 20, 2017 [15 favorites]

I've heard he could sieve like a mofo, too
posted by scruss at 7:14 AM on June 20, 2017 [6 favorites]

I've heard he could sieve like a mofo, too

Are there Prime Number truthers? Perhaps there exist "dark integers", which evenly divide what the sheeple think of as "primes". It hasn't been disproven!
posted by thelonius at 7:21 AM on June 20, 2017 [16 favorites]

This trick only works if the sun is very far away. The same observations could be explained by a flat Earth and a sun that is about 4000 miles away.

And yet when I write NASA about this they either ignore me or call me a nut. What are they afraid of?
posted by Sangermaine at 7:30 AM on June 20, 2017 [12 favorites]

Eratosthenes realised that the only way for the shadow to disappear at Syene but not at Alexandria was if the Earth’s surface was curved. Since a full circle contains 360 degrees, it meant that Syene and Alexandria were roughly one fiftieth of the Earth’s circumference away from each other.

He obviously detected curvature, and made some clever deductions from that observation. Sadly, he was thrown off track by his completely unfounded assumption that the Earth's curvature wrapped all the way around so the ends meet and form a sphere. Of course as we now know, the disc of the earth isn't truly flat but is slightly convex. This is due to the greater pressure exerted by the ether against the thinner edges of the disc than against its thicker center as the earth moves forward, thus creating inertial force that presses objects "down" to the surface.
posted by Naberius at 7:40 AM on June 20, 2017 [8 favorites]

He obviously detected curvature, and made some clever deductions from that observation.

Pretty easy to see if you live on a large body of water. Ever watch a ship sail away? It disappears from the bottom up. This is even more obvious with sailboats.
posted by leotrotsky at 7:51 AM on June 20, 2017 [6 favorites]

I remember reading about this in the book version of Cosmos and goddamn it was like lightning for my 4th grade mind.
posted by kmz at 7:53 AM on June 20, 2017 [5 favorites]

Yes, sadly many ships do sail away and disappear, almost always from the bottom up. Let us observe a moment of silence for all the sailors lost to this phenomenon.
posted by Naberius at 7:55 AM on June 20, 2017 [27 favorites]

This is due to the greater pressure exerted by the ether against the thinner edges of the disc than against its thicker center as the earth moves forward, thus creating inertial force that presses objects "down" to the surface.

Huh. That might also explain the curvature of the Parthenon's stylobate. That would easily have been a data point available to Eratosthenes if he had only, you know, looked up.
posted by Capt. Renault at 7:57 AM on June 20, 2017 [3 favorites]

I remember reading about this in the book version of Cosmos and goddamn it was like lightning for my 4th grade mind.

My daughter is in the summer before her 4th grade year. She's a great reader. Do you think it'd be better to read it to her, or let her read it herself?
posted by leotrotsky at 8:00 AM on June 20, 2017

We did this experiment in high school Physics class and got pretty close as well. The best part was when the teacher would forget to go out at the same time of day and would be spotted running through the halls with a yardstick yelling "The sun! The sun! We forgot the sun!" and we'd all have to bolt after him.

It was the second closest to Marty McFly I ever felt.
posted by robocop is bleeding at 8:02 AM on June 20, 2017 [15 favorites]

And yet when I write NASA about this they either ignore me or call me a nut. What are they afraid of?

Maybe don't start every call by assuring them that you're wearing pants.
posted by Etrigan at 8:02 AM on June 20, 2017 [6 favorites]

Do you think it'd be better to read it to her, or let her read it herself?

I'm sure either would be great, but I read it by myself back then, and then went on to devour a whole bunch of other Sagan books. I think there might be adult-ish themes in Cosmos somewhere, but honestly I can't remember now.
posted by kmz at 8:53 AM on June 20, 2017

Are there Prime Number truthers? Perhaps there exist "dark integers", which evenly divide what the sheeple think of as "primes". It hasn't been disproven!

There are! 13 isn't prime; it's equal to (3+2i)(3-2i).
posted by madcaptenor at 9:17 AM on June 20, 2017 [14 favorites]

"(pre-modern) People all believed the Earth was flat"

Yeah, if you want to waste an afternoon of your life, mentioning on Facebook that this is a myth is a pretty good way to go about it. It's the closest I've ever come to triggering Stewart Lee's "well you can prove anything with facts" response, and the closest I ever wish to.
posted by howfar at 9:51 AM on June 20, 2017 [1 favorite]

Man, the posts here are giving me flashbacks to way back when in the NASA and Space Google+ communities, where the flat earthers and the climate change deniers would trade off in clogging the community with their spewage. Every other post was one of those guys recycling old arguments.

Oh wait, that was last week. Never mind.
posted by happyroach at 9:51 AM on June 20, 2017 [5 favorites]

There is quite a bit in Cosmos about the threat of nuclear war. I went into fourth grade in 1984, and that was something that scared me a lot at that time. Your fourth grader may vary.
posted by Anne Neville at 9:58 AM on June 20, 2017

Are there Prime Number truthers?

It's not exactly a prime number thing, but Terrence Howard (star of Empire, among other things) is absolutely convinced that 1 x 1 = 2:

"How can it equal one? If one times one equals one that means that two is of no value because one times itself has no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told its two, and that cannot be."

posted by Mr. Bad Example at 11:40 AM on June 20, 2017 [2 favorites]

Uh, no one says the square root of 2 is 2...
posted by RustyBrooks at 11:49 AM on June 20, 2017 [2 favorites]

The edge of the Earth's shadow upon the Moon during a lunar eclipse is always circular, even as the moon rises up the sky. A disc-shaped Earth would give ellipses of varying eccentricity depending on the angle of the Moon to the vertical. Only a sphere always projects as a circle.
posted by heatherlogan at 11:56 AM on June 20, 2017 [1 favorite]

The edge of the Earth's shadow upon the Moon during a lunar eclipse is always circular, even as the moon rises up the sky. A disc-shaped Earth would give ellipses of varying eccentricity depending on the angle of the Moon to the vertical. Only a sphere always projects as a circle.

You are dealing with people who, when confronted with the truth that gravity on a disc planet would be much stronger at the edges than in the center, say that this proves there is no gravity, and that the disc is being accelerated (by what?) at 9.8 m/s^2. I'm sure they have some rationalization for the eclipse thing.
posted by thelonius at 12:01 PM on June 20, 2017 [1 favorite]

This is due to the greater pressure exerted by the ether against the thinner edges of the disc than against its thicker center as the earth moves forward, thus creating inertial force that presses objects "down" to the surface.

Wait--where does the fifth elephant come into play?
posted by Halloween Jack at 1:07 PM on June 20, 2017 [3 favorites]

I have an acquaintance from childhood who happens to be a facebook friend and through that medium I have realized is a rabid flat-earth truther. I still think it might be a wild ruse, a long-running troll. But alas I fear it is not.

Whenever I see these I think, "Aha! This will be the evidence I can post that will finally convince him."

But I never post because I know better. There's nothing I could use to prove it. There's nothing that will convince him.
posted by joecacti at 1:19 PM on June 20, 2017 [1 favorite]

I've heard he could sieve like a mofo, too

One of the seminal early contributions to computer science in the Western tradition.

What I mean: the Sieve is an algorithm for generating prime numbers which is valuable because of its efficiency. Generating prime numbers was already a solved problem, but the naive method is extremely slow. The contribution of the sieve is not that it allows you to compute any new values, but that it allows you to compute old values more efficiently. This is typical of (perhaps definitive of) the study of algorithms in computer science.

I wish I knew more about the ancient history of the study of efficient algorithms. I'm not sure there is a book on this. As a result of my ignorance, I don't really know the Sieve's place in this history. Greek mathematics was full of calculation algorithms, including famous and still-relevant examples like Euclid's algorithm (one of many algorithms published in the Elements). But I don't know to what extent time-efficiency was something the Greeks sought after. There were no computers, and apparently there were very few mathematical applications. I am not an expert in this history, but from what I have heard results were sought because of their beauty and surprisingness, not because of any practical usefulness. So efficiency might not have taken on the importance it holds in the computer age.

(Wikipedia seems to say that the first worst-case time performance result was published in 1844, putting a linear bound on the execution of Euclid's algorithm. This suggests that the ancients didn't formally study computational complexity, which doesn't surprise me. But it doesn't speak to whether they informally considered it in evaluating published algorithms.)
posted by grobstein at 1:23 PM on June 20, 2017 [3 favorites]

This trick only works if the sun is very far away. The same observations could be explained by a flat Earth and a sun that is about 4000 miles away.

Oh, and I suppose you're going to claim it's just a coincidence that the Earth is also 4000 years old?
posted by straight at 1:25 PM on June 20, 2017 [1 favorite]

Wait--where does the fifth elephant come into play?

The fifth elephant is named Boron.
posted by straight at 1:33 PM on June 20, 2017 [6 favorites]

I used to maintain the Earth was flat for many years as a long-running joke. I had lots of ridiculous arguments prepared for anyone who wanted to debate the matter. Those were the days before the internet. I can't do it anymore since crazy on-line truthers took all the fun out of it. Sigh.
posted by fimbulvetr at 1:53 PM on June 20, 2017

You are dealing with people who, when confronted with the truth that gravity on a disc planet would be much stronger at the edges than in the center, say that this proves there is no gravity, and that the disc is being accelerated (by what?) at 9.8 m/s^2. I'm sure they have some rationalization for the eclipse thing.

I assumed that all the flat-Earth comments here were just snark.

I report the eclipse thing for its beauty and (non-)surprisingness (when you think it through). When you're actually watching a lunar eclipse, you feel the roundness of the Earth as a visceral thing. Same thing when you go to Sweden and see how shockingly low the sun is in the sky, compared to how it is at ~45 degrees latitude. I guess my point here is that there are certain observations for which the obvious, visceral interpretation is the correct one, and that let you see something with your mind that is not immediately obvious to your eyes.
posted by heatherlogan at 2:07 PM on June 20, 2017 [1 favorite]

The fifth elephant is named Boron
What? I'm sure she was called Leeloo.
posted by Miss Otis' Egrets at 2:09 PM on June 20, 2017 [2 favorites]

Also, a disc planet is effing ridiculous. How would such a planet form? What keeps the atmosphere from running off the edges? Who built, and what fuels, the rocket engines on the bottom of the disc that are providing the acceleration? And show me just one other example of a disc planet among all the planets we've observed within our solar system and elsewhere.

The whole flat Earth thing is just an elaborate troll.
posted by heatherlogan at 2:10 PM on June 20, 2017

The whole flat Earth thing is just an elaborate troll.

Oh, really? Then explain if gravity is not strong enough to stop a small stream from flowing to its lowest point then what is stopping the oceans north of the equator from emptying into oceans south of the equator? This is what the earth would look like if we lived on a globe.
posted by straight at 2:56 PM on June 20, 2017 [3 favorites]

That's just surrealism! The incomprehensible statement about gravity and small streams is what's supposed to tip you off.
posted by heatherlogan at 4:15 PM on June 20, 2017

Where's Cyrus R. Teed when you need him?
posted by hearthpig at 5:42 PM on June 20, 2017 [1 favorite]

Who built, and what fuels, the rocket engines on the bottom of the disc that are providing the acceleration?

And what stops me from continuing to move upwards when I jump with an acceleration of greater than 9.8m/s , thus, without gravity to slow me down, continuing moving faster than the flat earth "upwards" until I encounter some other force? Inertia is a bitch, especially when you don't understand, you know, basic observable phenomenon.
posted by AzraelBrown at 7:33 AM on June 21, 2017 [1 favorite]

I choose to believe that the people running flat earth twitter (also on facebook) and creating hollow earth theories, and so on, are really intentionally promoting critical thinking. They hope that readers will work out the logical problems themselves and then turn that process into a habit of thought! Ok, maybe a little bit of trolling for fun in the process. Also, if they start actual cults and then demand celibacy this confirms my theory (as in Mr. Teed, mentioned by hearthpig.)

On inertia and gravity: note that there is (locally) no way to experimentally differentiate between being on an accelerated floor and being on a floor suspended over a large planet. This inspired Einstein.

On spheres, discs and their shadows: how about explaining the curve by casting the shadow of one disc onto another disc--the moon--which is tilted at the same angle? (open question)
posted by TreeRooster at 10:57 AM on June 21, 2017

Hint to my question above: shadows are inherently projections, of the profile of the object casting them...but so is my view of the universe, as it is projected onto my optic receptors.
posted by TreeRooster at 11:08 AM on June 21, 2017

[H]ow about explaining the curve by casting the shadow of one disc onto another disc--the moon--which is tilted at the same angle?

I'm not sure what you're getting at with the two-discs idea. It's pretty obvious that the Moon is a sphere because it exhibits phases as the relative angle between our eyes and the sun's illumination changes.

The same observations [of solar zenith angle varying by latitude] could be explained by a flat Earth and a sun that is about 4000 miles away.

Sure, maybe between Syene and Alexandria. But this cannot explain the different day length at different latitudes, nor the 24 hours of sunlight (as the sun circles around the sky) near the poles during high summer. And yes, I have an eyewitness report from a friend who spent time at the South Pole.

And you can even forget the sun and moon: watch all the visible stars as they rotate about you, make a map, and then move to a different latitude. The only way to model the effect is a sphere (Earth) within a sphere (celestial projection).

All of this stuff is so beautiful and compelling that we who know about it become easy prey for trolls who want to "debate". I'm coming to think that the appropriate response is not to try to convince the wilfully ignorant of the error in their ways. They can think what they like. Instead, let's put it on them to convince us that they're not idiots. For example: "You think the Earth is flat? That's interesting. What led you to think that?" And then, "What observation or evidence can you think of that would distinguish between these two hypotheses [flat vs. spherical]? Do you have any such evidence?" Make them do the intellectual work. They'll pretty quickly stop having fun.
posted by heatherlogan at 5:49 PM on June 21, 2017 [1 favorite]

"Following a long tradition of disregarding inconvenient knowledge when significant dollars maravedís are involved."

FTFY

Hey everyone, guess what my kids get to calculate this week!
posted by Eyebrows McGee at 6:39 PM on June 21, 2017 [1 favorite]

kmz: "I think there might be adult-ish themes in Cosmos somewhere, but honestly I can't remember now."

I think it's fine for a 4th grader who is interested. It's beautifully illustrated, as well. I would point out to them that science has marched on and a fair bit of it is outdated.
posted by Chrysostom at 8:05 PM on June 21, 2017

And what stops me from continuing to move upwards when I jump with an acceleration of greater than 9.8m/s ,
Just issuing a mea culpa after reading TreeRooster's comment; when I jump I stop accelerating when I stop pushing off the floor, so no matter how fast I get myself going, the accelerating floor will eventually catch up with me. I am concerned I have unintentionally proven that the earth is flat.
posted by AzraelBrown at 2:09 PM on June 26, 2017 [1 favorite]