[LoveScience]

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.

[Tom Bishop]

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?

[edby]

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?

[Tom Bishop]

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.

[LoveScience]

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.   

[RonJ]

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.

[LoveScience]

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.

[edby]

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.

[LoveScience]

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.

[edby]

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?

[Tom Bishop]

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."

[edby]

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?

[Tom Bishop]

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?

[edby]

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.

[Tom Bishop]

Why do you need to compare what you observe at local noon with other observers?

Because that's the experiment.

[edby]

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.

[stack]

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.

[RonJ]

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.

[Tom Bishop]

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. 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 "

[RonJ]

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.