Eratosthenes

Eratosthenes erroneously assumed the Earth was round to perform this experiment.

That is probably the way you see it. But actually Eratosthenes concluded  that the Earth must be round, based on the evidence available to him.  Aristarchus had already concluded that the Sun was much further away from the Earth than the Moon based on his observations of the phases of the Moon and the angular separation of the Sun and Moon at different phase points in the cycle.

Eratosthenes also concluded that light rays from a distant Sun must arrive at Earth along parallel paths. So it was natural to conclude that if there are shadows being cast at one latitude but not at another latitude on the same date and time, then the Earths surface must be curved. As one of the greatest thinkers of his time, I don't think Eratosthenes erroneously assumed anything. Rather he used observations to reach conclusions as any scientist should. Unlike flat Earthers who twist those conclusions to suit their beliefs.

It is only flat Earthers who have erroneously concluded that the Earth is flat.  I notice there is a dismissal among flat Earthers of any historical accounts like this yet when it comes to those ancient flat Earth maps they are quite happy to use those as 'evidence' to support their claims.   

There's no experiment that proves a globe.

Yes there is, and it has been performed numerous times. It's is very expensive to do, but simple in concept, and has produced reliable, repeatable results. You use a rocket to get a camera far enough away from the earth to take a whole-earth picture.  You know -- like this one:

Sure that works for me but I'm sure you realise that a simple image like that won't cut it with flat Earth believers. Mind you I have yet to see an actual photo of a flat Earth anywhere. Have you seen one anywhere?

I mean there are literally loads of photos of the Earth taken from space showing it to be a globe but I have yet to see any photos of a flat Earth.

Latitude was made in relation to the position of celestial bodies. When the Sun is over the equator it is directly overhead for an observer at the Equator and at the North Pole it is at 90 degrees to the observer, hence why the Equator is at 0 degrees and why North Pole is at 90 degrees North.

The above definition of Latitude proves Flat Earth Theory wrong. (Oops!)

The only way to have the Sun at 90 degrees to the zenith at the North Pole (within FET) when it is at zenith for an observer at the equator is for disc radius of the flat earth to be infinite. Clearly, the Earth's radius is finite. By using typical FET values for Sun altitude and for Earth disc radius, we can calculate what the Sun's angle would be for an observer at the North Pole according to FET.

Typical Flat Earth values are
Disc radius: 12,000 to 12,500 miles;
Sun altitude: 3,000 to 4,000 miles.

Plug those values into any triangle calculator,

[here's one: https://www.calculator.net/triangle-calculator.html?vc=&vx=3500&vy=&va=90&vz=12500&vb=&angleunits=d&x=76&y=12]

... and one finds that the sun angle at the "poles" will be on the order of 74 degrees from the zenith
(16 degrees above the horizontal), not the 90 degrees from the zenith that you use in your explanation. 90 degrees is consistent with the Globe model, of course — so thanks for that confirmation (!)

Nor do we observe minimum sun angles of 16 degrees. The sun often falls below that (for months at a time as observed from the poles, and twice daily for most populated latitudes). Therefore, FET does not describe the Earth we live on.

Quote from: sceptimatic on October 03, 2021, 09:41:20 PM

There's no experiment that proves a globe.

You use a rocket to get a camera far enough away from the earth to take a whole-earth picture.  You know -- like this one:

That is not a whole Earth picture. Looks about half of it.

Quote

Eratosthenes erroneously assumed the Earth was round to perform this experiment.

That is probably the way you see it. But actually Eratosthenes concluded  that the Earth must be round, based on the evidence available to him.  Aristarchus had already concluded that the Sun was much further away from the Earth than the Moon based on his observations of the phases of the Moon and the angular separation of the Sun and Moon at different phase points in the cycle.

Eratosthenes also concluded that light rays from a distant Sun must arrive at Earth along parallel paths. So it was natural to conclude that if there are shadows being cast at one latitude but not at another latitude on the same date and time, then the Earths surface must be curved. As one of the greatest thinkers of his time, I don't think Eratosthenes erroneously assumed anything. Rather he used observations to reach conclusions as any scientist should. Unlike flat Earthers who twist those conclusions to suit their beliefs.

It is only flat Earthers who have erroneously concluded that the Earth is flat.  I notice there is a dismissal among flat Earthers of any historical accounts like this yet when it comes to those ancient flat Earth maps they are quite happy to use those as 'evidence' to support their claims.   

What a silly thing to point out: It is only those who have concluded the earth is flat that have concluded the earth is flat. Also you seem to assume the earth is round in stating it was "concluded" rather than assumed. Are we to imagine on what basis this determination was made since it isn't present in your argument?

It is a fact that Eratosthenes assumed it in his calculations. Why he took on this axiom and whether it is justified is a completely different question. Several others, such as ancient Taoists, have performed the exact same experiment except they did not make any foregone conclusions - such as the shape of the earth. They came to the same conclusion we did - that the earth is flat.

Helenistic astonomy was advented at the time of Eratosthenes and was no matter of settled fact. Your narrative is in contrast to the actual history, and indeed historically the idea was still fought against after that point for hundreds of years. Pliny the Elder was the first, after Eratosthenes death, to conclude the round earth as a widely held belief, but this would not mean it was the only idea in the space at the time or afterwards - it was not. The roots come from the Pythagorean cult and Eratosthenes did indeed have to hold more to faith than evidence to make the statements he did choosing the most popular view of the time.

More than this, we don't even know the actual method Eratosthenes used.

Quote from: sceptimatic on October 03, 2021, 09:41:20 PM

There's no experiment that proves a globe.

Yes there is, and it has been performed numerous times. It's is very expensive to do, but simple in concept, and has produced reliable, repeatable results. You use a rocket to get a camera far enough away from the earth to take a whole-earth picture.  You know -- like this one:

As Leo Ferrari points out - a flat earth in curved space would appear round. Also they don't take pictures of the whole earth - they stitch them together. ( https://www.nasa.gov/centers/goddard/about/people/RSimmon.html )

What a silly thing to point out

I'm not the one who thinks the Earth is flat John.  Now that is a pretty silly thing!

Quote

What a silly thing to point out

I'm not the one who thinks the Earth is flat John.  Now that is a pretty silly thing!

At one time it was a silly thing to believe many things that are now considered fact. Truth doesn't care about silliness.

Well I don't know if you've ever stopped to realise it but the Earth is one thing which certainly ain't considered to be flat no more.  No matter what you might think about that.

Truth doesn't care what you think either. Nor do I for that matter.

Well I don't know if you've ever stopped to realise it but the Earth is one thing which certainly ain't considered to be flat no more.  No matter what you might think about that.

Truth doesn't care what you think either. Nor do I for that matter.

If Truth doesn't care what you think, how do you validate your ludicrous claim that the "Earth is one thing which certainly ain't considered to be flat no more."

There are two North-South points separated by 500 miles. If you know the displacement of the sun in the sky from one point to the other (ie. 7°12'), and if you know that the sun sets relatively consistently as you move through whatever mechanism causes it to set as the sun or observer moves  then you can estimate what the distance on earth will be from 90 degrees North to 90 degrees South (where the Sun would move 180 degrees in the sky overhead between those points) by dividing 180 by 7°12' = 25 and then multiplying that value by 500. This comes out to 12,500 miles, the FE radius (N-S). Double that figure and you get 25,000 miles, which is the FE diameter (total S-N-S across) instead of the RE circumference (total S-N-S around).

(emphasis added)

This calculation approach works in a Round Earth scenario, where the sun moves equal angles in equal time over equal distances of land AND where one assumes a distant sun whose light rays are essentially parallel when they reach different points on Earth. When switching to a Flat Earth Model, you must meet your own condition:
"... you know that the sun sets relatively consistently as you move through whatever mechanism causes it to set ..."

You cannot use the "consistent motion" assumption in your calculation without showing the sun's motion is consistent within the mechanism you specify. You need to specify the sun's motion (that you are assuming) in order to use this approach! "Rotating spotlight" does not meet the condition. "Parallelism" does not meet the condition. No magic hand-waving allowed. Do better.

Your math assumption (consistent motion) requires that the sun go below the horizon (constant angular motion and the passage of time see to that), yet FE Theory requires that the sun never go below the horizon. Good luck reconciling the two requirements.

The RE circumference in the experiment is equivalent to the FE diameter in the FE Monopole model.

No, it isn't. You did your calculation with RE assumptions, then claimed the result for an FE scenario wherein those assumptions are denied. Ridiculous!

So, what is the distance to the Sun.  As pointed out earlier, the "normal" FE claims do not work with simple trigonometry when tested against reality.  Let's start simple, what is the distance and how is that derived.  Then test it against real observations.  If it fails to meet expectations of the mathematical predictions using that distance, then that distance is wrong.
  Queue magical intelligent personal bendy light.

If Truth doesn't care what you think, how do you validate your ludicrous claim that the "Earth is one thing which certainly ain't considered to be flat no more."

We could go on forever with you firing off your colourful adjectives about my 'claims' etc.  Just post me a diagram of what shape you think the Earth is and we will take it from there. It may well be that your definition of what 'flat' means and mine are different. But until I have a diagram from you I cannot possibly tell for certain.

There are many, many people in this world who would tell you my claim is not so ludicrous as you seem to think.

On a different note it seems, as Thunderwolf and Mikey.T are trying to point out flat Earthers are doing their best to try and force the figures to fit in with their beliefs. 'electromagnetic acceleration' is their classic get around. EA has been 'invented' by them to save having to admit they are wrong but never heard of in mainstream physics cos it don't exist! There certainly is no evidence that light can magically bend in the way or to the extent to which EA seems to make out it does.  If there is an experiment which I can perform and which demonstrates EA to me then please tell me and I will do it.

Also you seem to assume the earth is round in stating it was "concluded" rather than assumed.

Because other things already showed it was round.
The experiment didn't prove Earth was round, it merely measured its circumference.

But like I already said, all it takes is the knowledge that the sun is very far away and that allows you to determine the shape without assuming it.

It is a fact that Eratosthenes assumed it in his calculations. Why he took on this axiom and whether it is justified is a completely different question.

No it isn't, as that relates directly to if it is an assumption or if it is a conclusion from prior work.
This then directly relates to if you can honestly discard Earth being round to try to perform a different experiment.

But more importantly, simply having Earth is round is not enough. You also need to have the sun very far from Earth. Otherwise it is still an unconstrained problem.

Several others, such as ancient Taoists, have performed the exact same experiment except they did not make any foregone conclusions

Yes they did. They falsely concluded Earth was flat, with no basis for this at all.

More than this, we don't even know the actual method Eratosthenes used.

So how can you then so confidently assert that he assumed Earth was round in his calculations?

Again, all that he actually needs is to conclude the sun is very far away.

As Leo Ferrari points out - a flat earth in curved space would appear round.

You mean he states, with no justification at all, and it being unclear if it is parody or not.
And where your attempt at justification relies upon first appealing to gravity to show a circular orbit is a geodesic in spacetime, and then ignoring gravity to get a straight path over the Earth at low speed.
And it relies upon a principle of Euclidean geometry when Euclidean geometry is rejected.

Also they don't take pictures of the whole earth - they stitch them together.

Why falsely assert a false dichotomy?
They do both.
They take pictures from close to Earth which they stitch together to form a composite image, and they take pictures from quite far away, showing Earth from one edge to the other in a single image.
For example, one good one for this is EPIC on DSCOVR, positioned at the Earth-Sun L1.
But there are also plenty of satellites in geostationary orbit, like himiwari 8, and the GEOS series.

Even Taoist scholars recognized using an experiment identical to Eratosthenes' that the Earth was flat and the heavenly bodies close - coming to the same conclusion as Rowbotham era researchers.

Can anyone provide a link -outside of any flat Earth supporting website - which provides an independent description of this 'experiment' carried out by these Taoist scholars? This statement taken from TFES website doesn't in itself prove anything. It just provides a claim.

Can anyone provide a link ... which provides an independent description of this 'experiment' carried out by these Taoist scholars?

This link does it:
http://www.adventistas.com/wp-content/uploads/2019/07/An-Ancient-Chinese-Flat-Earth-Cosmology-Details-and-Calculations.pdf
The ancient Chinese ideas presented there are very similar to the ideas put forward today by current FE'ers.
An excerpt: "...not only the earth but also the heaven is flat; the
heavenly bodies describe circles overhead around the pole; rising and setting of the
heavenly bodies are optical illusions; human sight is not infinite but limited; the sun
throws a limited circle of light on the surface of the earth."

The link above is to a chapter of this book:
https://www.amazon.com/gp/product/3319970518/ref=ox_sc_act_title_1?smid=A3TJVJMBQL014A&psc=1
which looks great, but is way expensive.

--------------
Here is a promising link I could not use because the article is behind a pay wall. Maybe someone else is interested enough to pay, or someone else has an ID from a subscribing University and can read the article for free:

A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan Tzu
https://www.cambridge.org/core/journals/bulletin-of-the-school-of-oriental-and-african-studies/article/abs/chinese-eratosthenes-of-the-flat-earth-a-study-of-a-fragment-of-cosmology-in-huai-nan-tzu/42DB4C927104714A18409D224DC7D704

----------------------
Here is another article that I only skimmed. It is all text, no diagrams (the first link above is more user friendly). It does however, confirm the Taoist Flat Earth view. The texts mentioned are circa 200 B.C.
http://www.eastm.org/index.php/journal/article/viewFile/311/245

an excerpt:

Geodesy by Calculation Based on Gnomon Measurements
... ...
Accounts of techniques for calculating distances based on measurement of a
shadow cast by a gnomon and on the properties of right triangles appear in the
third book of the Huainanzi and in the Zhou bi, which includes discussions on
the properties of right triangles and the use of gnomons. Shorter variations on
these techniques occur in the Mozi , the Rites of Zhou or Zhou li , and
the Nine Chapters on the Mathematical Art or Jiuzhang suanshu .
They all assumed some kind of round heaven over a square (and flat) earth.85

In the gaitian theory, which informs the Zhou bi, heaven covered earth
like the canopy of a chariot; that is, a square within the circle of an umbrella-like
hemisphere, defined by an axis mundi at its center. Earth and heaven were
parallel planes, in some versions flat, in others shallow arcs or hemispheres. The
purpose of gaitian-oriented gnomon measurements of the Zhou bi was to
measure the distance between these two planes (or arcs), the "height of
heaven."

Several flaws in the gaitian theory, including its inability to account for
sunrise and sunset, led to its rejection in favor of the huntian theory, in
which heaven was a sphere surrounding the square flat earth.87 Although the
Huainanzi probably predates the gaitian-oriented Zhou bi, it cannot be classed
clearly under either theory.

... end document ...

Quote from: Platonius21 on October 04, 2021, 07:26:11 AM

Quote from: sceptimatic on October 03, 2021, 09:41:20 PM

There's no experiment that proves a globe.

Yes there is, and it has been performed numerous times. It's is very expensive to do, but simple in concept, and has produced reliable, repeatable results. You use a rocket to get a camera far enough away from the earth to take a whole-earth picture.  You know -- like this one:

As Leo Ferrari points out - a flat earth in curved space would appear round. Also they don't take pictures of the whole earth - they stitch them together. ( https://www.nasa.gov/centers/goddard/about/people/RSimmon.html )

Pay attention John.  I talked about the camera being far enough away that no stitching together of images would be involved, because the camera could see the whole earth (one side of, obviously). And even if one allowed the argument that the flat earth in curved space would appear round, why would some of the continents be missing? All the continents would presumably show up the picture if the earth were flat.  Here's NASA picture number AS17-148-22726 taken during Apollo 17 from a distance of about 24,000 km. No stitching involved.

Quote from: sceptimatic on October 03, 2021, 09:41:20 PM

There's no experiment that proves a globe.

Yes there is, and it has been performed numerous times. It's is very expensive to do, but simple in concept, and has produced reliable, repeatable results. You use a rocket to get a camera far enough away from the earth to take a whole-earth picture.  You know -- like this one:

There's no hope left for you.

Sure that works for me but I'm sure you realise that a simple image like that won't cut it with flat Earth believers. Mind you I have yet to see an actual photo of a flat Earth anywhere. Have you seen one anywhere?

I mean there are literally loads of photos of the Earth taken from space showing it to be a globe but I have yet to see any photos of a flat Earth.

There's plenty of pictures of the real Earth taken from high altitude balloons and planes and suchlike. It isn't a globe.

What is it then?

What is it then?

A flat and concave Earth, I would guess at.

So it is both flat and concave?
Are you sure you never contradict yourself?

Whats wrong with that? A valley is concave, a mountain is convex, a plain is flat. All 3 exist on the Earth at the same time. No contradiction

A flat and concave Earth, I would guess at.

Ok and how do you suppose it formed to be both flat and concave?  Or doesn't your theory go so far as to provide an explanation for how the Earth formed yet since you are only guessing? 

Also what is the difference (I'm sure there must be one) between a non-Euclidean (i.e. non-flat) closed flat surface and the surface of a sphere. After all the surface of a sphere could be construed as being flat or level.  Or smooth. The surface of a golf ball is not flat but it is spherical.

There's no hope left for you.

No hope to accept your BS? That isn't a bad thing.

There's plenty of pictures of the real Earth taken from high altitude balloons and planes and suchlike. It isn't a globe.

Care to provide any that show Earth is flat?
Because there are plenty from satellites that show it is ~ a globe.

A flat and concave Earth, I would guess at.

And straight back to your contradictions.
If it is concave, it isn't flat.

All 3 exist on the Earth at the same time.

Which is fundamentally different to Earth being all three.
That would be Earth having flat and concave regions.
It is also nothing like what Skepti suggests with his donut bowl Earth.

Wait..... Why did Bored delete all his posts here?

Whereabouts in this image does the Earth look either flat or concave?

https://phys.org/news/2017-01-students-breathtaking-curvature-earth-high-altitude.html

Or indeed in this video?

Still waiting for that distance answer.

Quote

Even Taoist scholars recognized using an experiment identical to Eratosthenes' that the Earth was flat and the heavenly bodies close - coming to the same conclusion as Rowbotham era researchers.

Can anyone provide a link -outside of any flat Earth supporting website - which provides an independent description of this 'experiment' carried out by these Taoist scholars? This statement taken from TFES website doesn't in itself prove anything. It just provides a claim.

Third chapter of Huai Nan tzu.

Edit: here's a paper on the subject: https://www.jstor.org/stable/616189

Whereabouts in this image does the Earth look either flat or concave?

https://phys.org/news/2017-01-students-breathtaking-curvature-earth-high-altitude.html

Or indeed in this video?

The camera from that video is a fisheye so it's exaggerating curvature. That makes it pretty easy for it to show what appears to be a concave Earth just by manipulating where it shows up in the frame. Like, for instance, in this screenshot I got at the end of the video.


FE, RE, and Concave Earth keyboard warriors can weaponize fisheye cameras to show exactly what they want.