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I'm currently having a (possibly useless) argument with somebody over the internet who is adamantly claiming that the Earth is flat. I know that this person could just be pulling my leg or trying to get a rise out of me but I'm still taking the challenge.

They are using this image in response to almost any argument.enter image description here

What is this document even 'proving' and why is it wrong (or misleading)?

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    $\begingroup$ See en.wikipedia.org/wiki/Bedford_Level_experiment - yes you would expect about a (slightly less than) 6 feet drop in 3 miles as described. Clearly the water does bulge (and a lot more than that over longer distances). As @casey points out you can fool yourself into thinking the water is flat if you don't take refraction into account. $\endgroup$ – Francis Davey Jun 17 '15 at 6:23
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    $\begingroup$ It's kind of missing the part that includes any evidence. Where is the image from? Perhaps there is a second page? $\endgroup$ – naught101 Jun 17 '15 at 15:38
  • $\begingroup$ @naught101 The source appears to be Zetetic Astronomy by S. B. Rowbotham, the original architect of the Bedford Level experiment. You're right, of course, that on its own this page provides no evidence of anything. $\endgroup$ – Pont Jun 17 '15 at 17:33
  • $\begingroup$ @FrancisDavey The Wikipedia page provides a satisfyingly brief answer to the question as phrased in the title ("Why is this “independently reproducible proof of non-curvature” wrong?"): the proof is not independently reproducible, as Wallace demonstrated. $\endgroup$ – Pont Jun 17 '15 at 17:36
  • $\begingroup$ @Pont - yes, I think the WP article should answer the question. Alas I haven't the time to put something together based on it right now. $\endgroup$ – Francis Davey Jun 17 '15 at 18:08
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The biggest flaw I see in a cursory look at this work is failure to compensate for atmospheric refraction. Density varies in the atmosphere enough that the refractive index varies. At low angles above the horizon the temperature structure of the atmosphere becomes very important in determining optical refraction and at low angles very close to the ground it becomes extremely important.

When cool air is at the surface and warms with height (e.g. a temperature inversion), which is likely above a cool body of water like a canal (or in winter, or at night and early morning), the resulting density gradient causes light to bend toward the ground. This means whatever you are observing is actually lower than you perceive it.

enter image description here
http://images.tutorvista.com/content/light-refraction/looming.jpeg

In the situation where it is warm near the surface and cools aloft you get the opposite and light bends up toward the sky. This gives rise to the water mirages you can see on hot days on roads or sand (where there is a very strong temperature gradient with height).

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    $\begingroup$ P.S. Don't argue with the flat-earthers. You can't win because they don't use logic and will freely disregard evidence that doesn't align with their theory. $\endgroup$ – casey Jun 17 '15 at 2:14
  • $\begingroup$ There is speculation that cold air refraction may have contributed to the sinking of the Titanic because of the possibility of false horizon being seen by the ship's crew. (Smithsonian Inst) [smithsonianmag.com/science-nature/… $\endgroup$ – Fred Jun 17 '15 at 2:30
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    $\begingroup$ @casey - Re Don't argue with the flat-earthers. You can't win. Some who argue that position are immune to logic and evidence because they aren't that smart, others are immune because they are very smart. I can't imagine a better assignment to a lawyer-in-training than "you are to create a user account at somecrackpotsite.org and vehemently defend the crackpot position. Remember that in the future you will be defending clients whose defense looks flimsier than those who claim that the Earth is flat. If you can't defend that claim, you have no business being a lawyer." $\endgroup$ – David Hammen Jun 17 '15 at 18:19
  • $\begingroup$ @casey Sure. Of course people on either side of almost any controversial issue say the same about their opponents. $\endgroup$ – Jay Nov 23 '15 at 15:29
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Zounds, good point! I guess the world is flat after all!

But okay, seriously, the writer has given a good and accurate argument why it should be possible to tell whether the world is round or flat by making observations on the ocean or a sufficiently large sea. But as far as the quoted page goes, he doesn't cite any experimental results to prove anything, one way or the other. To say, "I can imagine an experiment which would prove my theory correct" is a long way from "I have conducted this experiment and the results actually did prove my theory correct."

In fact, making observations across an ocean or large sea is one of the easiest proofs that the world is round. It was observed in the days of sailing ships that as a "tall ship" sailed away, the last thing you would see was the top of its sails. Look across a sufficiently large sea today and, no matter how clear the skies, etc, you cannot see the opposite shore. Get the most powerful telescope available and you still can't see the opposite shore.

One could argue that you can't see the far shore because of haze rather than curvature. You could resolve that by observing what you CAN see: at long distances, where you can barely see the far shore, do you just see the top of mountains or tall buildings? Or do you see the whole mountain or building but very hazy? (Okay, I haven't done that experiment, so maybe I'm just a dupe of the round-Earth conspiracy.)

Yes, as others have noted, refraction and optical illusions add extra complexity. That's why in general, one experiment is not sufficient to prove or disprove a theory.

Of course there are other ways to demonstrate that the Earth is round. Like, in ancient Egypt, Ptolemy measured the circumference of the Earth by measuring the lengths of shadows at different latitudes.

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Alternative earth models and their origins are awesome to review. The ignorant adherence to the flat earth model in the 21st century is sad. Looking at the material cited for the 'Bedford Level experiment' it's clear to me that those still using Rowbotham's formula have another fundamental problem aside from refraction distortion.

You cannot site 8 inches per mile squared if the observer and target(ways off in water) have a positive y-axis value relative to sea level. Somebody using this formula without getting their eye wet is wasting their time! Learn to solve for the height of a curve, anything inside the peak height of an arc equal to the height of the observer will be visible provided conditions are clear and one looks down about .025 degrees from their 0• level visual field.

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