Eratosthenes' measurement of the Earth's circumference

Eratosthenes was a Greek astronomer living in Alexandria around 200 BC who first worked out a RE.

He calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that, on the summer solstice, at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). Using a gnomon, he measured the sun's angle of elevation at noon on the solstice in his hometown of Alexandria, and found it to be 1/50th of a circle (7°12') south of the zenith. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5,000 stadia (about 500 geographical miles or 927.7 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m,[9] which would imply a circumference of 46,620 km, which is off the actual circumference by 16.3%; too large an error to be considered as 'accurate'. However, if we assume that Eratosthenes used the "Egyptian stadion" of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.

Room for discussion?

*lifted from Wikipedia

What do you want me to do with that? Its a fairy tale.

By the way, those distances between the cities is total bunk. So I'm not even going to try to explain those numbers.


This site tells me Alexandria and Syrene (now Aswan) are 787km apart. However google earth tells me they are 846 km apart. You'll appreciate that making calcs based on trig and picking a discrepancy of 2 degrees is going to be mighty difficult when in three sources I find a land distance ambiguity of over 200km, at a heading of 160 degrees, not due south.

I'm guessing the 2000 years have muddied the water and fudged the numbers a little.

We have dealt with the so-called findings of the charlatan Eratosthenes at length, it has been the subject of careful study by some of our top minds.  The most decisive analysis of the problem occured in 2010 when myself and my colleague "bullhorn" evaluated the major flaws in the work of Eratosthenes' employees (unless you're foolish enough to believe that he made the 800km journey between Alexandria and Syene himself, in which case there is no hope for you), using a combined historiographical-biochemical heuristic.

These two posts are recommended reading for anyone who thinks they have been seduced by Eratosthenes' galling falsehoods:
http://www.theflatearthsociety.org/forum/index.php/topic,4943.msg954305.html#msg954305
http://www.theflatearthsociety.org/forum/index.php/topic,4943.msg954370.html#msg954370

Eratosthenes *measured* nothing.  He simple assumed.

Eratosthenes *measured* nothing.  He simple assumed.

Much like most of the flat earthers on these boards then?

Quote from: John Davis on January 24, 2013, 07:11:20 AM

Eratosthenes *measured* nothing.  He simple assumed.

Much like most of the flat earthers on these boards then?

Much like most of the people in the world, yes.  You are people, are you not?

Quote from: Manarq on January 24, 2013, 07:43:43 AM

Quote from: John Davis on January 24, 2013, 07:11:20 AM

Eratosthenes *measured* nothing.  He simple assumed.

Much like most of the flat earthers on these boards then?

Much like most of the people in the world, yes.  You are people, are you not?

Yes I am.

I have very little knowledge about Eratosthenes but it's not needed in this case. There is essentially a research paper written by someone called Eratosthenes where he gives an outline of his experiment, the results he recorded (made up or otherwise) and what that meant.

Now if you treat it as such then you don't refute it by arguing about whether he was drunk or not etc you go out and either repeat the experiment or create a trimmed down experiment after all 800km is a long way, then take the readings.

Now if the readings you get are consistent with Eratosthenes readings then you have proven that he did the experiment and took those readings and as flat earthers you're left arguing about the interpretation of the experiment, which is fine. If however you get different readings then you can start discussing his intellectual honesty and maybe his blood alcohol level.

When I followed the links James posted above I was taken to a thread that jumped straight to the conclusion he was wrong and assumed reasons why this might be without taking the relatively easy step of proving/disproving his results. This just summed up flat earth research for me.

Its always needed.  In all cases.  Why would knowledge of what you are talking about not be needed?

Its always needed.  In all cases.  Why would knowledge of what you are talking about not be needed?

I'm not quite sure what you're getting at.

"I have very little knowledge about Eratosthenes but it's not needed in this case. "

Knowledge of what you are discussing is always needed.  Would you pick up a gun if you weren't knowledgable in the safe use of it?

"I have very little knowledge about Eratosthenes but it's not needed in this case. "

Knowledge of what you are discussing is always needed.  Would you pick up a gun if you weren't knowledgable in the safe use of it?

Indeed.

Are we discussing Eratosthenes or are we discussing the experiment he performed? They're 2 different subjects.

If we're discussing Eratosthenes then I'll go do a bit of reading past his wikipedia page and we can discuss his favorite party games (if I can find that information).

However if we're discussing the experiment he performed then to a large extent he is irrelevant as the way you prove/disprove an experiments results is to replicate the experiment. When scientists declared they had found cold fusion other scientists didn't refute their claim by calling them drunks, they repeated the experiment as described, found they couldn't replicate the results and then called them drunks.

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

Agreed, he essentially performed the same experiment that appears somewhere in the wiki for how the height of the sun is calculated in FET. If I can find it I'll put the link in. http://blog.modernmechanix.com/5000-for-proving-the-earth-is-a-globe/3/#mmGal

1: If you perform the experiment and assume the earth is round then you get the size of the earth.

2: If you perform the experiment and assume the earth is flat then you get the height of the sun.

Just because you disagree with his interpretation of the results does not mean that he was drunk at the time, that it's all a fairy tale or that he was lying.

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

This is just a personal attack to hide the fact that comparable experiments have been done for thousands of years and have shown the general shape of the Earth over and over, countless times.

Yes, science was not as rigorous then, and yes, he accepted the already strong indications that Earth is round and the Sun is very far away. And no, he did not try to demonstrate the roundness of the Earth, he was trying to measure the diameter of the Earth. Given the limited resources he had he made a very good approximation. The fact that he was surprisingly close to the real value has no scientific importance. Even if he had made a 50% error, the result would have been really useful in that time.

Now, after some 2000 years, sailors and other navigators have verified that all the stars and planets and Sun and Moon move South on the sky one degree for every 60 nautical miles they go North. Since this repeated observation has been done in every latitude from one pole to the other, the Earth can only be round. If you had to move a lot more than 60 nautical miles to get this result when close to the poles, it would have been demonstrated that Earth is flat.

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

This may be true, but a round earth and distant sun is the only model that provides consistent results when performed at different locations on the earth.  This suggests that those assumptions were correct.

Quote from: Ski on January 24, 2013, 09:16:46 PM

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

This may be true, but a round earth and distant sun is the only model that provides consistent results when performed at different locations on the earth.  This suggests that those assumptions were correct.

Or that light itself is consistently inconsistent.

Or that light itself is consistently inconsistent.

Saying nonsenses like that one you do not make flat Earth model funnier...

Quote from: markjo on January 25, 2013, 05:33:13 AM

Quote from: Ski on January 24, 2013, 09:16:46 PM

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

This may be true, but a round earth and distant sun is the only model that provides consistent results when performed at different locations on the earth.  This suggests that those assumptions were correct.

Or that light itself is consistently inconsistent.

Wouldn't that pretty much invalidate any observation concerning the shape of the earth, flat or round?

Wouldn't that pretty much invalidate any observation concerning the shape of the earth, flat or round?

No. As far as I can tell, under discussion are the observations (which may or may not have been affected by a consistent inconsistency of light) of a Greek fellow who is presumed to have lived around the 3rd century BC.  My observations, however, do not appear to be affected.

Quote

Wouldn't that pretty much invalidate any observation concerning the shape of the earth, flat or round?

No. As far as I can tell, under discussion are the observations (which may or may not have been affected by a consistent inconsistency of light) of a Greek fellow who is presumed to have lived around the 3rd century BC.  My observations, however, do not appear to be affected.

The real subject here is the weight we give to experiments and observations from a long time ago.

It makes no difference at all whether Eratosthenes got his experiment right or not, or whether he could have done a better job, or whether he was an alcoholic or not.

Whether through dumb luck, or an inconsistency or his great intelligence, Eratosthenes did an experiment and got a result. Thousands of times after that, under the most impressive variety of circumstances his result was validated. To history the name of Eratosthenes is important, but to science it is not. Even if he just lucked out from a consistent inconsistency, whatever that is, his result has been validated uncountable times.

The real subject here is the weight we give to experiments and observations from a long time ago.

It makes no difference at all whether Eratosthenes got his experiment right or not, or whether he could have done a better job, or whether he was an alcoholic or not.

Whether through dumb luck, or an inconsistency or his great intelligence, Eratosthenes did an experiment and got a result. Thousands of times after that, under the most impressive variety of circumstances his result was validated. To history the name of Eratosthenes is important, but to science it is not. Even if he just lucked out from a consistent inconsistency, whatever that is, his result has been validated uncountable times.

hmm.. i question what you mean by 'real' subject, and wonder to whom you refer to as 'we'; but i'm not going to argue with you about it, because your logic appears muddled to the point that it begins to seem like water already under the proverbial bridge:

premise (or is this your conclusion?): It makes no difference at all whether Eratosthenes got his experiment right..
premise: his result was validated.  (was it?  by whom?  am i supposed to accept your account as gospel?)
premise (or is this your conclusion?): To history the name of Eratosthenes is important, but to science it is not.

what exactly are you trying to say?

premise: his result was validated.  (was it?  by whom?  am i supposed to accept your account as gospel?)

I personally validated the methodology of the Eratosthenes experiment in a 9th grade Earth Science lab experiment.

premise (or is this your conclusion?): It makes no difference at all whether Eratosthenes got his experiment right..

What makes all the difference in the world is that other people have made comparable experiments and observations and have validated the result literally millions of times. Every navigator in this planet has used the Sun, Moon or stars to calculate his location based on Eratoshenes' result or on others who repeated it. By seeing how many degrees the stars, Moon or Sun has moved North, they know they have moved South 60 nautical miles, no matter where they are.

premise: his result was validated.  (was it?  by whom?  am i supposed to accept your account as gospel?)

Every navigator in the world has validated this result. Look at the procedures to use a sextant and you will see how every navigator has found his latitude based on the same principle that Eratosthenes used. And no, it is not gospel. It is life or death for every navigator who does not have modern technology at his disposal.

premise (or is this your conclusion?): To history the name of Eratosthenes is important, but to science it is not.

Every person who needs to use the real dimensions and shape of the Earth for any use at all uses the information that Eratosthenes started to collect and thousands of wise men and scientists have validated and improved. But if you are in the middle of the Pacific Ocean and have no access to GPS or radio navigation, you get your sextant and your watch and find your position. You don't care whether Eratosthenes was the first to calculate the size of the Earth or not.

I personally validated the methodology of the Eratosthenes experiment in a 9th grade Earth Science lab experiment.

neat!  i knew there was something fishy going on here.. probably that pesky consistent inconsistency of light thing, again!

RealScientist~ oh my, that's quite a lot of claims.  'Every navigator in this planet has used the Sun, Moon or stars to calculate his location based on Eratoshenes' result..' you say.  'Every person who needs to use the real dimensions and shape of the Earth for any use at all uses the information that Eratosthenes started to collect..' you say.  etc, etc.. are you sure?  how can you possibly know that?

Quote

I personally validated the methodology of the Eratosthenes experiment in a 9th grade Earth Science lab experiment.

neat!  i knew there was something fishy going on here.. probably that pesky consistent inconsistency of light thing, again!

RealScientist~ oh my, that's quite a lot of claims.  'Every navigator in this planet has used the Sun, Moon or stars to calculate his location based on Eratoshenes' result..' you say.  'Every person who needs to use the real dimensions and shape of the Earth for any use at all uses the information that Eratosthenes started to collect..' you say.  etc, etc.. are you sure?  how can you possibly know that?

Find out how a sextant works and you will have your answer.

i'm quite aware of how a sextant has been perceived to work.  Eratoshenes was certainly not the first to fool around with one (and neither was Markjo i'd wager, as elder as he may be).  but i'm still curious how you found out what every navigator, or even every person has or has not done.  i don't mean any offense, but just to clear a few things up - do you have a God complex?  has anyone in the past suggested that you might have a God complex?

Quote

I personally validated the methodology of the Eratosthenes experiment in a 9th grade Earth Science lab experiment.

neat!  i knew there was something fishy going on here.. probably that pesky consistent inconsistency of light thing, again!

To the best of my knowledge, the light was consistently consistent during that experiment.

i'm quite aware of how a sextant has been perceived to work.  Eratoshenes was certainly not the first to fool around with one (and neither was Markjo i'd wager, as elder as he may be).  but i'm still curious how you found out what every navigator, or even every person has or has not done.  i don't mean any offense, but just to clear a few things up - do you have a God complex?  has anyone in the past suggested that you might have a God complex?

You should research before you blabber. Eratosthenes lived during the third century BCE. The sextant was invented around 1757 CE. That is a small error of two millenniums.  And just as your knowledge about Eratosthenes and the sextant is close to nil, you are showing how poor is your knowledge of navigation.

Quote from: Ski on January 24, 2013, 09:16:46 PM

...

Just because you disagree with his interpretation of the results does not mean that he was drunk at the time, that it's all a fairy tale or that he was lying.

I did not infer that he was lying. I said his assumptions were wrong and led him to the wrong conclusions. Others in the thread touched on the difficulties regarding his methodology.

Quote from: Ski on January 24, 2013, 09:16:46 PM

Eratosthenes assumed the sun was incredibly far away and that the light rays arrive in parallel. One can perform the same experiment on my kitchen table, but it does not make the table's surface a sphere.

This is just a personal attack to hide the fact that comparable experiments have been done for thousands of years and have shown the general shape of the Earth over and over, countless times.

What part of that statement constitutes a personal attack?     If I don't assume a priori the sun is impossibly far away, the inferences of the "experiment" change greatly.

You should research before you blabber. Eratosthenes lived during the third century BCE. The sextant was invented around 1757 CE. That is a small error of two millenniums.

western arrogance.  you're not really buying into that story about Polynesia being settled by people traveling in canoes and following the migration of birds are you?  perhaps your'e also under the impression that Uranus wasn't discovered until 1781?  the Greeks were well aware of ancient technologies, and borrowed from previous cultures.  as did the 18th century Europeans.