The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: LoveScience on December 01, 2018, 11:15:27 AM
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Under the Wiki page it states,
We can use Eratosthenes' shadow experiment to determine the diameter of the flat earth.
Syene and Alexandria are two North-South points with a distance of 500 nautical miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12' south of zenith at the other city.
7°12' makes a sweep of 1/25th of the FE's total longitude from 90°N to 90°S (radius).
Therefore we can take the distance of 500 nautical miles, multiply by 25, and find that the radius of the flat earth is about 12,250 nautical miles. Doubling that figure for the diameter we get a figure of 25,000 miles.
These figures do on the face of it work out correct. But so too do these figures if you hypothesize (as Eratosthenes did) that the Earth is a sphere. Or a least round but then he would have had to have been on the edge of the Earth to detect any curvature of a flat Earth. He based his calculation on the fact that 7°12' (=7.2°) is 1/50 of a complete circle (7.2° x 50 = 360°) and using the known distance from Alexandria to Syene he worked out that 50x500miles meant that the Earth must have a 25,000 mile circumference. Based on the modern figure according to RET that is very close to the right answer. A very good result for Eratosthenes time.
The FE Wiki version of Eratosthenes experiment however gives 25,000 miles as the diameter of the Earth. Using Eratosthenes figure for the circumference, based on his assumption of a round Earth and dividing that by pi gives a diameter of 7957 miles. That is the accepted value according to RET.
Searching through the Internet at length and several books I have on historical astronomy, all accounts of Eratosthenes experiment appear to agree that from his observations and measurements he deduced that the Earth was spherical with a 25,000 mile circumference. There is no other mention (that I can find at least) of a 12,250 mile radius or 25,000 mile diameter as the FE Wiki version seems to suggest. I'm sure that Eratosthenes was aware of Aristotles assumptions but he drew his own conclusions from his own observations and measurements and they led him to reach a figure of 25,000 miles for the circumference of the Earth.
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At points we were looking to improve that article, but it seems that a lot of people, even scholars, have doubts that he even did this experiment, and that it's some sort of myth. How would you conduct that sort of thing in a B.C. era before reliable time keeping?
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At points we were looking to improve that article, but it seems that a lot of people, even scholars, have doubts that he even did this experiment, and that it's some sort of myth. How would you conduct that sort of thing in a B.C. era before reliable time keeping?
1. Which scholars, citations please; and
2. Why would you need time keeping?
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I don't have the bandwidth at the moment to spend time searching around for citations, its what I've seen mentioned in various books and documentaries. You are free to leave it.
You would need reliable timekeeping because the experiment involves making two observations at far off points at the same moment in time.
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Eratosthenes certainly had assistance during his shadow experiment. In his account of the experiment as part of his highly acclaimed Cosmos TV series, the late Carl Sagan explains how Eratosthenes hired or employed someone to pace out the entire distance from Alexandria to Syene. However I have neither seen or read any mention of doubt that the conception of the experiment or the results and calculations which led Eratosthenes to his conclusion was the work of anyone but him. Eratosthenes was considered nothing short of a genius in multiple disciplines and he is widely credited as being the founder of what we today called Geography.
Contrary to many modern accounts, it was widely accepted by the ancient Greeks that the Earth was spherical and that the size of the Earth was very small in comparison to the apparently infinite distance of the stars. So Eratosthenes conclusions in his shadow experiment would not have come as any great surprise to them.
As regards your other question Tom, I have often paused for a moment and tried to contemplate how we would approach such a problem if we had lived during the era of ancient Greece. We have the benefit of the huge wealth of knowledge that has been accumulated by great minds through the generations. Knowledge that is so easily taken for granted now. Accurate time keeping is a very recent development in human history and I believe it was Galileo who resorted to the regularity of his own heartbeat to solve this problem as best he could.
Given the significant limitations in the tools and knowledge available to them at the time, the Ancient Greeks and other civilisations made many basically correct predictions about the world and what lay beyond it. If such minds existed today, supported by the knowledge and technology available today, we can only speculate about what they might achieve.
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It looks like Eratosthenes knew something about the earth that the FET aficionados haven’t figured out yet. The important thing in this experiment seems to be local apparent noon (LAN) on a specific date. I can easily measure LAN without any clock at all. Mariners have known how to do it for hundreds of years. All you do is carefully watch the angle of the sun at approximately noon. The sun will get higher, higher in the sky (or watch a shadow) until it starts to go back the other way. If you are continuously watching the angle you will quickly see when that angle reverses. A that point when the angle reverses you have just witnessed local apparent noon at your location. Watching the reflections of the sun in well water was a good indication of what’s known as the zenith point of the sun has been found. If you know the zenith point at one location and the angle that the sun makes at another location both at local apparent noon on the same date, then if you know the distance between the points you can figure out a good estimate of the earth’s radius. It seems that Eratosthenes had someone pace off the distance between the two points and that would be where the most potential for error seems to be.
Even if Eratosthenes didn’t do the experiment, it certainly was feasible for someone to do it at that time in history.
It would also be feasible for someone to do it in 2018 and confirm that the earth is round, but that's another story.
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Whenever I study these experiments I always try to consider how it would be from both a FE and a RE perspective. That is only fair.
Certainly if you have two observers on a flat surface with one standing such that the Sun is directly overhead while the second is standing at the same time but sufficiently far away from the first for the Sun to be displaced from the local zenith then one observer will see shadows while the other will not. As I have already said though it was already widely accepted at the time of the Ancient Greeks that the Earth was spherical. So Eratosthenes would have had this in mind when he reached the logical conclusion that he was measuring part of the circumference and not the diameter of the Earth.
If the Earth was flat the only way Eratosthenes could account for the presence of shadows at one end of his measured distance and none at the other as being down to curvature would be if he was literally walking around the edge of the disk of the Earth. For shadows to appear as they do the Sun would have to be to one side of the flat Earth and not above it as FET prescribes. In short he had no reason to consider that the Earths surface was anything else but curved.
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You would need reliable timekeeping because the experiment involves making two observations at far off points at the same moment in time.
Reliable time keeping unnecessary. I think you are confusing this with longitude.
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My only question about this in relation to timekeeping would be how the Ancient Greeks measured the date of the northern summer solstice. At the time the calendar was based on the Moon.
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My only question about this in relation to timekeeping would be how the Ancient Greeks measured the date of the northern summer solstice. At the time the calendar was based on the Moon.
Why do you think the date matters?
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I can easily measure LAN without any clock at all. Mariners have known how to do it for hundreds of years. All you do is carefully watch the angle of the sun at approximately noon. The sun will get higher, higher in the sky (or watch a shadow) until it starts to go back the other way. If you are continuously watching the angle you will quickly see when that angle reverses. A that point when the angle reverses you have just witnessed local apparent noon at your location.
How are they supposed to record that observation to compare with other observations without a reliable time system?
"The sun reached zenith at approximately... wait, it's 205 B.C. and we don't have a reliable time system."
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I can easily measure LAN without any clock at all. Mariners have known how to do it for hundreds of years. All you do is carefully watch the angle of the sun at approximately noon. The sun will get higher, higher in the sky (or watch a shadow) until it starts to go back the other way. If you are continuously watching the angle you will quickly see when that angle reverses. A that point when the angle reverses you have just witnessed local apparent noon at your location.
How are they supposed to record that observation to compare with other observations without a reliable time system?
"The sun reached zenith at approximately... wait, it's 200 B.C. and we don't have a reliable time system."
Again, why do you need a time system so long as you can record local noon? I.e. so long as you can observe when the sun is at its highest position in the sky, indeed is right overhead at 90 degrees?
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I can easily measure LAN without any clock at all. Mariners have known how to do it for hundreds of years. All you do is carefully watch the angle of the sun at approximately noon. The sun will get higher, higher in the sky (or watch a shadow) until it starts to go back the other way. If you are continuously watching the angle you will quickly see when that angle reverses. A that point when the angle reverses you have just witnessed local apparent noon at your location.
How are they supposed to record that observation to compare with other observations without a reliable time system?
"The sun reached zenith at approximately... wait, it's 200 B.C. and we don't have a reliable time system."
Again, why do you need a time system so long as you can record local noon? I.e. so long as you can observe when the sun is at its highest position in the sky, indeed is right overhead at 90 degrees?
That is right. You can see when local noon or zenith occurs for your location. Now how do you record that down to compare with other observers at other locations without a reliable time system?
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I can easily measure LAN without any clock at all. Mariners have known how to do it for hundreds of years. All you do is carefully watch the angle of the sun at approximately noon. The sun will get higher, higher in the sky (or watch a shadow) until it starts to go back the other way. If you are continuously watching the angle you will quickly see when that angle reverses. A that point when the angle reverses you have just witnessed local apparent noon at your location.
How are they supposed to record that observation to compare with other observations without a reliable time system?
"The sun reached zenith at approximately... wait, it's 200 B.C. and we don't have a reliable time system."
Again, why do you need a time system so long as you can record local noon? I.e. so long as you can observe when the sun is at its highest position in the sky, indeed is right overhead at 90 degrees?
That is right. You can see when local noon or zenith occurs for your location. Now how do you record that down to compare with other observers at other locations without a reliable time system?
Why do you need to compare what you observe at local noon with other observers? It may help if you study the exact method that Eratosthenes used. Try Cleomedes' account.
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Why do you need to compare what you observe at local noon with other observers?
Because that's the experiment.
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Why do you need to compare what you observe at local noon with other observers?
Because that's the experiment.
No it isn't. Look up the actual proof. No appeal to time is necessary.
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You can do the same experiment today without knowing what time it is. Just wait for the sun to be in the center of the sky.
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You don't need a reliable time system if everyone does their observations at local apparent noon on the summer solstice. Let the sun be your clock. The experiment probably took Eratosthenes years to complete.
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There was no reliable time system. It is believed that there was not yet a reliable systems of clocks or calendars. No telephones. Here is an article from the esteemed cracked.com (http://www.cracked.com/article_20849_5-cultures-whose-calendars-would-break-your-concept-time.html). The calendars in the ancient greek empire was local, "freestyling," different in different locations. It is not clear at all how this was coordinated.
There are also other questions. It's possible that this was a very coordinated effort that took a long time to complete; but that is why some think it's a myth.
https://www.jstor.org/stable/41134135?seq=1#page_scan_tab_contents
" His accomplishment was generally admired in antiquity, but also aroused considerable controversy in the centuries which followed. Little is known concerning his methods of measurement and his actual results "
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Now you are mixing up the Greeks up with the Egyptians. It has been said that the Egyptians were 'light years' ahead of the Greeks at that time. Alexandria had a nice library where Eratosthenes could check out books. There's a great sea port there on the Med (I've even been there a couple of times) and some other Egyptians figured out how to build the pyramids. No one knows if they had any help from aliens, however. In any event, if I had to bet on an answer, I would bet on the side of Eratosthenes.
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There was no reliable time system. It is believed that there was not yet a reliable systems of clocks or calendars. No telephones. Here is an article from the esteemed cracked.com (http://www.cracked.com/article_20849_5-cultures-whose-calendars-would-break-your-concept-time.html). The calendars in the ancient greek empire was local, "freestyling," different in different locations. It is not clear at all how this was coordinated.
It's possible that this was a very coordinated effort that took a long time to complete; but that is why some think it's a myth.
Myth or not, time-keeping is not needed.
Solar noon is when the sun is at its zenith.
In Syene, solar noon was when the sun was directly over the well and completely illuminating the water.
In Alexandria, solar noon was when the shadow was shortest but the time when it was shortest is quite immaterial. All that mattered was the shortest length of the shadow.
If we use the modern distance between Alexandria and Syene (Aswan) of 800 km and the reported angle of 1/50 part of a circle
the height of the sun comes out as 800/tan(7.2°) = 6333km or 3935 miles above the earth.
But when a comparable experiment is done, as in Voliva's method, with a 45° angle and a distance of 3113 miles (for a FE diameter of 24,900 miles) the sun's height comes out to 3113 miles (very close to 5000 km).
Alexandria had a nice library where Eratosthenes could check out books.
Eratosthenes didn't need to "check out books". he was chief librarian. APS News: This Month in Physics History June, ca. 240 B.C. Eratosthenes Measures the Earth (https://www.aps.org/publications/apsnews/200606/history.cfm)
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Now you are mixing up the Greeks up with the Egyptians. It has been said that the Egyptians were 'light years' ahead of the Greeks at that time. Alexandria had a nice library where Eratosthenes could check out books. There's a great sea port there on the Med (I've even been there a couple of times) and some other Egyptians figured out how to build the pyramids. No one knows if they had any help from aliens, however. In any event, if I had to bet on an answer, I would bet on the side of Eratosthenes.
Eratosthenes was an Ancient Greek, and the Greeks had settlements in Egypt. It's possible that the two places mentioned weren't under Greek control at the time, however.
We can see some of the settlements in Egypt in this map: https://slideplayer.com/slide/8584537/26/images
/2/The+Birth+of+Greek+Civilization.jpg (https://slideplayer.com/slide/8584537/26/images
/2/The+Birth+of+Greek+Civilization.jpg)
Solar noon is when the sun is at its zenith.
In Syene, solar noon was when the sun was directly over the well and completely illuminating the water.
In Alexandria, solar noon was when the shadow was shortest but the time when it was shortest is quite immaterial. All that mattered was the shortest length of the shadow.
We need multiple observations from the two locations, under common time keeping systems, for correlation. It's not as easy as that. I don't believe that remote observers or assistants to Eratosthenes are even mentioned. He just 'did it'.
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My references show that Eratosthenes was recruited by Pharaoh Ptolemy III Euergetes to be the chief librarian at the Alexandria Library and that's why he moved there.
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Now you are mixing up the Greeks up with the Egyptians. It has been said that the Egyptians were 'light years' ahead of the Greeks at that time. Alexandria had a nice library where Eratosthenes could check out books. There's a great sea port there on the Med (I've even been there a couple of times) and some other Egyptians figured out how to build the pyramids. No one knows if they had any help from aliens, however. In any event, if I had to bet on an answer, I would bet on the side of Eratosthenes.
Eratosthenes was an Ancient Greek, and the Greeks had settlements in Egypt. He didn't just wander into foreign nations to conduct science, as far as I am aware. It's possible that the two places mentioned weren't under Greek control at the time, however.
The Ptolemaic Kingdom in 305 BC–30 BC (in blue)
(https://upload.wikimedia.org/wikipedia/commons/1/12/PtolemaicEmpire.png)
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Even so, the Romans were closely related and weren't any better at time keeping:
https://history.stackexchange.com/questions/38658/what-calendars-were-used-in-eastern-rome
"Many different local calendars were used in the eastern and western parts of the Roman empire. The Julian calendar introduced about 44 BC was the official calendar of the Roman republic and empire and was used by Roman citizens, the army, and the imperial administration."
https://www.quora.com/If-you-asked-a-Roman-in-30-AD-what-year-was-it-what-would-he-she-answer
"It depends on who and where you asked. It would also depend on when, since the Roman empire was a confusing mishmash of conflicting calendars which didn’t agree on much, particularly not on the actual start of the year."
Lack of a common calendar system was just one of the challenges.
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Even so, the Romans were closely related and weren't any better at time keeping:
https://history.stackexchange.com/questions/38658/what-calendars-were-used-in-eastern-rome
"Many different local calendars were used in the eastern and western parts of the Roman empire. The Julian calendar introduced about 44 BC was the official calendar of the Roman republic and empire and was used by Roman citizens, the army, and the imperial administration."
https://www.quora.com/If-you-asked-a-Roman-in-30-AD-what-year-was-it-what-would-he-she-answer
"It depends on who and where you asked. It would also depend on when, since the Roman empire was a confusing mishmash of conflicting calendars which didn’t agree on much, particularly not on the actual start of the year."
Lack of a common calendar system was just one of the challenges.
I'm not sure why you are all hung up on calendars and clocks when you go on and on about how all of astronomy is simply predictive and done so by ancient civilizations.
In any case, here's how you do it without knowing the exact day of the solstice and without synchronized rolexs:
- I know the solstice is going to occur some time this week
- I'm in Alexandria and I've got my guy in Syene
- I told my guy to keep an eye on that well and write down on his papyrus what day in the week he got the noon solsticey view of the water in the well
- Meanwhile I'm checking the stick in Alexandria every day around noonish and record the shortest shadow of the stick that day.
- My guy walks up to Alexandria which is good b/c I need him to pace off the distance anyway
- He tells me which day the solstice occurred for him and I look at my papyrus record for the shortest shadow on that same day
- Done
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Wow... this all reminds me of the final boardroom scene at the end of each episode of The Apprentice. All the contestants talking over each other and over complicating things. I cannot put it any simpler so I revert you back to Carl Sagans account of Eratothenes in Cosmos. Give it a watch. Concise, clear to the point and simple.
In science the simplest solutions are generally the best.
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If you look at the account given by Cleomedes (around first century BC), he says we must accept as a premiss that "the rays sent down from different parts of the sun on different parts of the earth are parallel; for this is the hypothesis on which geometers proceed"
It immediately follows that if (1) the earth is completely flat, (2) light rays from the sun are parallel and (3) there is a time in Syene when the sun shines right to the bottom of a well but there are no times further North when this happens, then (4) the earth is not flat.
So if FE wants to challenge his conclusion, they must challenge the parallel assumption. Time keeping irrelevant.
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Wow... this all reminds me of the final boardroom scene at the end of each episode of The Apprentice. All the contestants talking over each other and over complicating things. I cannot put it any simpler so I revert you back to Carl Sagans account of Eratothenes in Cosmos. Give it a watch. Concise, clear to the point and simple.
In science the simplest solutions are generally the best.
Sagan is a secondary source. If you want a primary source, look at the translation of Cleomedes' account on Roger Pearse's website.
https://www.roger-pearse.com/weblog/2017/04/15/cleomedes-how-big-is-the-earth/
Of course Cleomedes is a secondary source too, since no manuscripts of Eratosthenes' work survives, but Cleomedes was a near contemporary.
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The wiki says (https://wiki.tfes.org/Erathostenes_on_Diameter)
It's a common misconception that Eratosthenes was measuring the circumference of the round earth in his shadow experiment. Eratosthenes had simply assumed that the earth was a sphere in his experiment, based on the work of Aristotle.
This is completely false, as is shown by going back to the original Greek, as explained by Cleomedes. See below for the text. Cleomedes says that Eratosthenes made five assumptions
1. Syene and Alexandria lie under the same meridian circle (μεσημβρινῷ - literally belonging to noon, noontide)
2. the distance between the two cities is 5,000 stades
3. rays from different parts of the sun on different parts of the earth are parallel
4. straight lines falling on parallel straight lines make the alternate angles equal (this is Euclid’s fifth postulate)
5. arcs subtended by equal angles are similar
Nowhere is Eratosthenes (on this account) assuming the earth is a sphere, or basing his work on that of Aristotle. He is appealing to the work of geometers such as Euclid, the maps of his day, and the assumption of parallel light rays.
(http://www.logicmuseum.com/w/images/b/b7/Cleomedes_greek-lat.jpg)
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To avoid confusion, the image above is from the 19C Latin-Greek parallel edition. The original would have been much harder to read, and would have looked something like this
(https://content.wdl.org/14757/service/thumbnail/1430184731/1024x1024/1/15.jpg)
And even that manuscript dates from the 14th century. We have very few manuscripts of any sort surviving from before the 9th century. Everything we know about the ancient world is based on copies of the originals (or copies of copies of copies).
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The wiki says (https://wiki.tfes.org/Erathostenes_on_Diameter)
It's a common misconception that Eratosthenes was measuring the circumference of the round earth in his shadow experiment. Eratosthenes had simply assumed that the earth was a sphere in his experiment, based on the work of Aristotle.
This is completely false, as is shown by going back to the original Greek, as explained by Cleomedes. See below for the text. Cleomedes says that Eratosthenes made five assumptions
1. Syene and Alexandria lie under the same meridian circle (μεσημβρινῷ - literally belonging to noon, noontide)
2. the distance between the two cities is 5,000 stades
3. rays from different parts of the sun on different parts of the earth are parallel
4. straight lines falling on parallel straight lines make the alternate angles equal (this is Euclid’s fifth postulate)
5. arcs subtended by equal angles are similar
Nowhere is Eratosthenes (on this account) assuming the earth is a sphere, or basing his work on that of Aristotle. He is appealing to the work of geometers such as Euclid, the maps of his day, and the assumption of parallel light rays.
http://www.logicmuseum.com/w/images/b/b7/Cleomedes_greek-lat.jpg (http://www.logicmuseum.com/w/images/b/b7/Cleomedes_greek-lat.jpg)
[edit]
To avoid confusion, the image above is from the 19C Latin-Greek parallel edition. The original would have been much harder to read, and would have looked something like this
https://content.wdl.org/14757/service/thumbnail/1430184731/1024x1024/1/15.jpg (https://content.wdl.org/14757/service/thumbnail/1430184731/1024x1024/1/15.jpg)
And even that manuscript dates from the 14th century. We have very few manuscripts of any sort surviving from before the 9th century. Everything we know about the ancient world is based on copies of the originals (or copies of copies of copies).
The Library, or part of its collection, was accidentally burned by Julius Caesar during his civil war in 48 BC, but it is unclear how much was actually destroyed and it seems to have either survived or been rebuilt shortly thereafter; the geographer Strabo mentions having visited the Mouseion in around 20 BC and the prodigious scholarly output of Didymus Chalcenterus in Alexandria from this period indicates that he had access to at least some of the Library's resources.
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The Library, or part of its collection, was accidentally burned by Julius Caesar during his civil war in 48 BC, but it is unclear how much was actually destroyed and it seems to have either survived or been rebuilt shortly thereafter; the geographer Strabo mentions having visited the Mouseion in around 20 BC and the prodigious scholarly output of Didymus Chalcenterus in Alexandria from this period indicates that he had access to at least some of the Library's resources.
Indeed, although current scholarship suggests it was budget cuts, rather than fire and the sword https://io9.gizmodo.com/the-great-library-at-alexandria-was-destroyed-by-budget-1442659066.
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In any case, here's how you do it without knowing the exact day of the solstice and without synchronized rolexs:
- I know the solstice is going to occur some time this week
- I'm in Alexandria and I've got my guy in Syene
- I told my guy to keep an eye on that well and write down on his papyrus what day in the week he got the noon solsticey view of the water in the well
- Meanwhile I'm checking the stick in Alexandria every day around noonish and record the shortest shadow of the stick that day.
- My guy walks up to Alexandria which is good b/c I need him to pace off the distance anyway
- He tells me which day the solstice occurred for him and I look at my papyrus record for the shortest shadow on that same day
- Done
All sounds like a good plan to me. And from these observations and measurements do you conclude that the Earth is round or flat?
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In any case, here's how you do it without knowing the exact day of the solstice and without synchronized rolexs:
- I know the solstice is going to occur some time this week
- I'm in Alexandria and I've got my guy in Syene
- I told my guy to keep an eye on that well and write down on his papyrus what day in the week he got the noon solsticey view of the water in the well
- Meanwhile I'm checking the stick in Alexandria every day around noonish and record the shortest shadow of the stick that day.
- My guy walks up to Alexandria which is good b/c I need him to pace off the distance anyway
- He tells me which day the solstice occurred for him and I look at my papyrus record for the shortest shadow on that same day
- Done
All sounds like a good plan to me. And from these observations and measurements do you conclude that the Earth is round or flat?
You can't conclude either from this single measurement. If you presume a round Earth, you get an idea for circumference. If you presume flat, you have height of the sun. If you add a second or more measurements, preferably from different latitudes, you can start to get an idea on round vs flat. But one measurement won't answer that question.
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You can't conclude either from this single measurement. If you presume a round Earth, you get an idea for circumference. If you presume flat, you have height of the sun. If you add a second or more measurements, preferably from different latitudes, you can start to get an idea on round vs flat. But one measurement won't answer that question.
Even Eratosthenes angle of 7.2° and the 45° angle of Voliva's method give height differences to raise questions.
If we use the modern distance between Alexandria and Syene (Aswan) of 800 km and the reported angle of 1/50 part of a circle
the height of the sun comes out as 800/tan(7.2°) = 6333km or 3935 miles above the earth.
But when a comparable experiment is done, as in Voliva's method, with a 45° angle and a distance of 3113 miles (for a FE diameter of 24,900 miles) the sun's height comes out to 3113 miles (very close to 5000 km).
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Eratosthenes certainly had assistance during his shadow experiment. In his account of the experiment as part of his highly acclaimed Cosmos TV series, the late Carl Sagan explains how Eratosthenes hired or employed someone to pace out the entire distance from Alexandria to Syene. However I have neither seen or read any mention of doubt that the conception of the experiment or the results and calculations which led Eratosthenes to his conclusion was the work of anyone but him. Eratosthenes was considered nothing short of a genius in multiple disciplines and he is widely credited as being the founder of what we today called Geography.
Contrary to many modern accounts, it was widely accepted by the ancient Greeks that the Earth was spherical and that the size of the Earth was very small in comparison to the apparently infinite distance of the stars. So Eratosthenes conclusions in his shadow experiment would not have come as any great surprise to them.
As regards your other question Tom, I have often paused for a moment and tried to contemplate how we would approach such a problem if we had lived during the era of ancient Greece. We have the benefit of the huge wealth of knowledge that has been accumulated by great minds through the generations. Knowledge that is so easily taken for granted now. Accurate time keeping is a very recent development in human history and I believe it was Galileo who resorted to the regularity of his own heartbeat to solve this problem as best he could.
Given the significant limitations in the tools and knowledge available to them at the time, the Ancient Greeks and other civilisations made many basically correct predictions about the world and what lay beyond it. If such minds existed today, supported by the knowledge and technology available today, we can only speculate about what they might achieve.
Remember also that Eratosthenes actually calculated the POLAR circumference of the earth, given that Alexandria and Syene are (almost) at the same longitude.
Not that it makes much difference as the actual polar circumference and equatorial circumference only differ by 41 miles.
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Did we have a reliable time system in the 1600s and 1700s?
Summarised by Bryson; feel free to look up more detailed accounts.
"For half a century people had been trying to work out the size of the Earth, mostly by making very exacting measurements. One of the first such attempts was by an English mathematician named Richard Norwood. As a young man ... early seventeenth century Bermuda was well known among ships’ captains for being hard to locate. The problem was that the ocean was big, Bermuda small and the navigational tools for dealing with this disparity hopelessly inadequate. There wasn’t even yet an agreed length for a nautical mile. Over the breadth of an ocean the smallest miscalculations would become magnified so that ships often missed Bermuda-sized targets by dismayingly large margins. Norwood, whose first love was trigonometry and thus angles, decided to bring a little mathematical rigour to navigation, and to that end he determined to calculate the length of a degree.
Starting with his back against the Tower of London, Norwood spent two devoted years marching 208 miles north to York, repeatedly stretching and measuring a length of chain as he went, all the while making the most meticulous adjustments for the rise and fall of the land and the meanderings of the road. The final step was to measure the angle of the sun at York at the same time of day and on the same day of the year as he had made his first measurement in London. From this, he reasoned he could determine the length of one degree of the Earth’s meridian and thus calculate the distance around the whole. It was an almost ludicrously ambitious undertaking—a mistake of the slightest fraction of a degree would throw the whole thing out by miles—but in fact, as Norwood proudly declaimed, he was accurate to “within a scantling”—or, more precisely, to within about six hundred yards. In metric terms, his figure worked out at 110.72 kilometres per degree of arc."
The exercise was repeated in two other locations by the French in the 1700s.
The whole method is based around calculating the angle related to the arc that Norwood paced out on the surface, and this only has relevance on a globe. The method has no meaning on a flat earth.