When I was participating in an exchange on Twitter recently, one flat-Earth proponent presented me with this graphic:

Now, a few people who saw this mentioned that the problem with the graphic was the assumption of a flat Earth. But I didn't have a problem with that; it's what I expect a flat-Earth proponent to do. But I saw two other, quite different, problems with this graphic.

The first problem is that it's a lie. Portland, Oregon, is not 3,000 miles from New York, it's closer to 2,500 miles. And the sun is never, ever directly overhead in Portland. I know, I've been there. It's too far north for the sun to ever be 90 degrees above the horizon. So, this entire graphic is made of whole cloth.

The second, and much bigger problem, is the assumption that, since you can take these two points on the Earth, triangulate the position of the sun, and arrive at a distance that is much closer than the accepted figure, that you've proved your case and your work is done. Let's see how this works out.

Okay, we're going to assume a flat Earth in the following calculations. And we're going to simplify the scenario, while using actual data instead of made-up data. The simplification consists of two parts, neither of which is fudging: first is to choose locations along the Tropic of Cancer on June 21st, so that the sun can actually be overhead, and the second is to pick locations where the solar noon and noon on the clock line up, so that we're comparing apples to apples from different time zones.

All of the coordinates I'm giving are at 23.43 degrees north, so I'll only give longitudes. My anchor point is near Indore, India, at longitude 75.5 E, which is at UTC+5. It will be noon there, and the sun is, indeed, directly overhead, 90 degrees above the horizon. That's my version of Portland, with the benefit of having real data instead of assumptions.

My version of New York will be in Taiwan, at 120.5 E, UTC+8, where it's 3:00 p.m., same as in the graphic. But at 3:00, the sun isn't quite at 45 degrees; that was another assumption, a convenient halfway point. The real angle is 48.86 degrees. The distance from Taiwan to Indore is 2,841 miles, making the height of the sun, if the Earth is flat, 3,252 miles.

Sounds good. That's really close to the figure given by flat-Earthers. So, without the assumption that the Earth is a globe, we have an alternate figure that's just as valid. Right?

Not so fast. Two data points don't constitute proof. Let's up the ante a little. We'll start small, and move over just one time zone, a little north of Vietnam, 105.5 E, UTC+7 at 2:00 p.m. at a distance of 1897 miles from Indore. Now the angle of the sun above the horizon is 62,5 degrees. With these new figures, the calculated height of the sun is now 3,644 miles. That's quite a discrepancy.

What if we move further away? When it's noon in Indore, it's 7:00 a.m. at the Prime Meridian, which at this latitude is in Algeria. So, we're at 0 degrees longitude, UTC+0, and Indore is now 4,724 miles away. The sun is to the east now, at an elevation of 21.71 degrees above the horizon. If we triangulate on that, the altitude of the sun now calculates out at 1881 miles.

What happened? I think you know the answer. These elevations all make sense on a globe.

Measuring the actual distance to the sun is not easy. It took literally a couple of thousand years for astronomers to get close, thanks mostly to insights by Edmund Halley, who didn't live to see his work put to use. To think that these oversimplifications and cute and completely misleading graphics can usurp the work of brilliant minds over millennia is the pinnacle of hubris, and unfortunately a common thread in the arguments of proponents of the flat-Earth.

ADDENDUM: A Twitter user took me for task for calling the data I used real, stating that I was just assuming that the data were correct. His argument was that, as I didn't collect or verify the data myself, I was wrong to trust them or use the word "real." This is a common misunderstanding used (and abused) by pseudoscientists who, out of ignorance or malice, misuse the words verifiable and falsifiable.

The data I used are both verifiable and falsifiable. They are straightforward numbers which could, at any time, be challenged by independent observers all over the globe, who would either confirm them or discover them to be wrong. It is not necessary for every single user who employs the data to verify all of it; what would be the point of collecting, publishing, and calculating data if everybody had to do it all over again? No progress would ever be made with that kind of burden.

And so I stand behind my use of online data, in this case from NOAA, to demonstrate the fallacy of measuring the distance to the sun assuming a flat Earth. I suggest that any flat-Earther who wants to challenge my conclusions stick to facts and avoid attacking tried-and-true methods and data sources.