Wednesday, February 24, 2016

The Distance To the Sun

Flat-Earthers say that the sun is not 93 million miles away, but a mere few thousand. There are variations, of course, but most give the figure 3000 miles for the altitude of the sun above the Earth "plane." There have been several ways of calculating this, though most who give the figure just don't know where it comes from.

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.

Tuesday, February 23, 2016

Flat Earth Credibility

Dear Purveyors Of the Flat Earth:

You know how I feel about your beliefs. I would be perfectly willing to let your beliefs alone, though, if you would stop trying to dress them up as science, or even worse, "real science." But, I would like to point out a couple of subjects you should just avoid mentioning altogether if you want to retain even the appearance of credibility.

Andrea Barnes
Honestly, everyone who's paid any attention should know by now about Andrea Barnes, the woman who, in the film In Search Of the Edge, goes on a quest to find the edge of the Earth and is lost in Antartica, leaving nothing but a note, which is found three decades later, saying, "I have been there, the debate finally comes to an end," and a camera which is inadvertently opened, spoiling the film.

What you should certainly know by now is that Andrea Barnes and her story are fiction, not a hoax but a mock documentary created under the auspices of the Canadian Film Board for the purpose of teaching Canadian students critical thinking skills. There are clues scattered throughout the film that it is completely bogus, and the disclaimer at the end notes that all the characters are fictional, save for some of the on-screen talent and famous scientists from the past.

So, if you're tempted to use the story of Andrea Barnes to show that Antarctica is not a continent, but an impenetrable ice ring, resist the temptation.

Jarle Andhøy
Yet another Antarctic explorer, who was supposedly stopped at the ice wall, arrested, kidnapped, and heavily fined. Here's a more accurate account from The Old Salt Blog:
Last February, Jarle Andhøy and Samuel Massie set off from the yacht Berserk II in McMurdo Sound on the Antarctic coast in an attempt to drive ATVs towards the South Pole. Shortly thereafter, in an Antarctic storm, the EPIRB [emergency position indicating radiobeacon] from the Berserk II was activated. Following an extensive search by the New Zealand Coast Guard and private ships, the only sign of the yacht or the three crew aboard was debris and an empty life raft. Andhøy's ill-fated expedition was mounted without authorization or insurance. He later paid a fine of 25,000 NOK to the Norwegian Polar Institute.
It is important to note that 25,000 Norwegian kroner is about $3,000US. Jarle is still out on the high seas and getting in trouble with the law, but nothing that's killed him or even put him behind bars.

Cold Moonlight
I don't know where this one started, but it's long past its prime. There are two problems with the argument that moonlight is cold, and therefore the moon shines by its own light and not the light of the sun.

The first problem is that it's simply not true. Experiments designed to test this end up only demonstrating that something used to shade a thermometer from moonlight ends up trapping the heat rising from the ground from the day's sunshine. Even a flat-Earther, who did the obvious control of repeating the experiment during the new moon, concluded that cold moonlight is a non-starter.

The other problem, of course, is that it does nothing to prove that the Earth is flat. I supposed it's just supposed to be something else that "they" are lying about, but that's not evidence of any kind. And while we're on the subject of moonlight:

The Moon In Front Of the Clouds
There are lots of videos on YouTube purporting to show that the moon is closer to Earth than the clouds. They are shots of a big, featureless, fuzzy white moon, with clouds passing by and not showing up in front of it.

Of course, this can only be seen when the cloud cover is very thin, and the reason is simple: the moon is shining light through the clouds. If the shot were exposed for the moon instead of the clouds, you might be able to see them in front of the moon, but not easily because they are so thin, This never works with thick cloud cover.

And it has, again, nothing to do with the flat Earth, for the flat-Earth model has the moon 3000 miles above the ground just like the sun, which is far higher than any clouds, as anyone who's done any flying knows. And we're not done with the moon yet:

The Moon and the Sun Together In the Sky
I've lost count of how many videos I've seen showing the sun in the sky at the same time as the moon, with some comment about how the moon should be full, or how the moon isn't pointed toward the sun.

Okay, here's a basic rule about trying to overturn a standard model of anything: you can't debunk something by misrepresenting it. In the standard model of the solar system, the moon is a quarter million miles away, and the sun in around 93 million miles away. It's not going to look as if they are at the same distance. It just doesn't work that way.

And moon phases are not caused by the Earth's shadow on the moon. That's an eclipse. If you can't figure out what you're seeing in the sky, get a book on astronomy. If you still think it doesn't match up, then you make your own model that makes it work. But don't think you're onto something just because you don't understand what you're looking at.

Bali To Los Angeles By Way Of Alaska
You must know this story by now. A woman went into labor on a flight from Bali to Los Angeles. The pilot diverted to Alaska, but the baby was born on the plane before the plane landed. Flat-Earthers made a big deal, doing videos that showed how the plane was going way out of the way on the globe map, but right on the way on the flat-Earth map.

Except that they weren't using the globe at all; they were using the Mercator projection. Plotting the path on an actual globe, it makes perfect sense. In fact, it would be something like this (the plane took off from Taiwan):

So if you're tempted to trot out the story of the baby born on the plane, just don't.

In fact, any time you're thinking about using the Mercator projection to make a point about the globe, just stop. You're comparing one distorted projection to another, and it's making you look ignorant or dishonest.

This has been a public service message. Carry on.

Friday, February 19, 2016


Gravity is a problem for flat-Earthers. Because of the way gravity works, anything as large as the Earth would certainly have to pull itself into something resembling a sphere.

Not only that, but if the Earth could somehow retain a disc shape, gravity on such an Earth would behave quite differently than what we experience. As we moved south (which, on the flat-Earth model is toward to outside of the disc), we would encounter more and more force drawing us back toward the center. IN the Southern Hemisphere, or outer circle, we would increasingly experience the feeling of going uphill when, in fact, we were not.

So how do the flat-Earthers deal with the problems posed by gravity? Simple: they deny that gravity exists at all.

In the flat-Earth world, the effects that we see from gravity are easily explained by buoyancy and density. Things that are more dense move downward past things that are less dense, and things that are less dense move upward through things that are more dense.

Thus, hammers fall, oceans stay put, and helium balloons float. Really simple. And completely wrong.

Now, I'm not a physicist. I can't give you all the details of how gravity works. For that, I suggest you read a good book on elementary physics, or if you're really ambitious, Newton's Principia. But there are some things so obviously flawed in the flat-Earth denial of this most basic of physical laws that pretty much any thoughtful layman can easily see right through it.

Let's start with this: the existence of gravity is an established scientific fact. It isn't "just a theory." There are theories of gravity, which attempt to describe what gravity is and why gravity is, but that gravity is is not in doubt. That's why there is the Law Of Universal Gravitation.

And we need to get another thing straight in our minds: gravity is not a one-way street. It isn't just the Earth pulling things toward its center; those things that are being pulled are doing a little pulling themselves.

So, let's kill the density argument very quickly. Take two steel balls, one an inch in diameter, the other three inches in diameter. They are of equal density, but the three-inch ball has 28 times the mass of the one-inch ball. drop the two balls into a body of water (I don't recommend a tub unless you want to damage it). Which one makes a bigger splash?

Same density, different mass, different amount of force applied by (you guessed it) gravity.

So now let's work on buoyancy. Buoyancy is what makes a rubber raft float on a lake, and a helium balloon float in the air. But the helium balloon is not defying gravity any more than the rubber raft is. The Earth is still pulling on the balloon, and the balloon is still pulling itself toward the center of the Earth. But it's being pushed as well, the exact same way the rubber raft is being pushed to the surface by the density of the water.

But at some point, both the raft and the balloon will stop rising. The raft meets the point where it is not longer being pushed up by the water. The balloon either reaches the point where the air is no longer more dense than the gas inside it, or it bursts.

Both are the result of gravity. It's gravity that makes air pressure higher close to the ground than several thousand feet up. Buoyancy means nothing without gravity.

So let's eliminate buoyancy altogether, and see how gravity works in a vacuum. Here's a video from the BBC:

Not only do the feather and the bowling ball fall at the same rate, but notice how much damage the bowling ball causes, while the feather causes none at all. Density, buoyancy have nothing to do with it. It's all about that mass.

Flat-Earthers claim that no experiment has ever shown that two objects attract each other except by magnetism. They discount the Cavendish Experiment as a failure, or a fraud, and claim that it has never been duplicated. But even physics students can prove the effects of gravity.

And so can you, using your phone. Your phone has a gravity sensing system that uses accelerometers. If you try to attribute the phone's ability to detect rotation to acceleration from the turning of the phone, however, you're left to explain how the phone knows its initial position when you first turn it on (even from the state of having removed all its power). It detects this state from the acceleration of Earth's gravity.

We haven't just proved gravity, we measure it and use it every day. And because gravity exists, the flat Earth doesn't.

Monday, February 15, 2016

Where Are the Stars?

In order to counter the many pictures of Earth from space, ranging from low-orbit satellite photos and International Space Station video, to distant photos taken from the moon, to the "Pale Blue Dot" image taken from 3.7 billion miles away, flat-Earthers have to claim that all such pictures are faked.

Most of their "proof" comes down to, "it looks fake to me," or more commonly, "come on, you don't think that's real, do you?" But the one argument they make that might, at first blush, sound plausible is: "Where are the stars?"

In the famous "Blue Marble" photo taken from Apollo 17 in 1972, there are no stars visible in the space surrounding the Earth. Most pictures taken from the International Space Station also fail to show stars. Doesn't that show that they weren't actually taken from space?

Only if you've watched too many movies.

Stars are very bright. But they are also very far away. If you're out in an isolated area on a very dark night, you can see perhaps as many of 5000 stars in the sky. Any light pollution, from the moon, from lights in a nearby city, and the number drops off very sharply. And your eyes can discern a much wider range of light and dark than any photographic system.

I don't know if you've done enough star-gazing to recognize the difference between the planets and the stars in the sky (assuming you believe in planets), but if you have, you know that the closer and larger planets appear brighter in the night sky, and they don't twinkle nearly so much.

That's because, although the planets are smaller by far than stars (well, Jupiter is almost big enough to be a star), and shine by reflected light instead of producing their own light, they are simply much, much closer to Earth than the stars are.

So back to the photography. If you are taking a picture of something big and bright against a background of black plus some lights that are relatively dim (in this case because they are so far away), the dim lights in the background just won't show up. If you want to get them to show up, you have to expose for them.

Which means you are vastly overexposing for the big bright object, which means it will register as a big white circle, and maybe a big white circle that's very fuzzy around the edges.

So why, in the movies, do we see lots of stars in the background? Because it looks cool, that's why. And also because we expect to see them there, something that art directors figured out many decades ago. The producers of Star Trek did a lot of tests with shots of the Enterprise using information from astronomers to make it look as realistic as possible, including having no "whoosh" sound when the ship sped by in the opening credits, as would be true in space.

It didn't work. Nobody thought it looked real. With no experience in space, we have preconceived notions of what it would be like to be in space, to watch a spaceship zip by, and they just don't match the reality.

Which brings me, briefly, to another topic: the moon in front of the clouds. I've seen a lot of footage that purports to show the moon (or the sun) in front of the clouds, and so thus much lower than we've been told.

Two problems with that. First, the moon is not is front of the clouds; it's an illusion caused by overexposing the moon. If you expose the moon so that you can see all its features, then the clouds will also be visible drifting in front of it (it only works with relatively thin cloud cover).

The second problem is that having the moon closer than the clouds also violates the flat-Earth model, at least as far as most understand it. It's something that's not often brought up, but if any flat-Earther tried to claim that the moon is closer than the clouds, especially because plenty of people have flown above the clouds in an ordinary jetliner, they would suddenly have a lot of explaining to do, even more so than they do now,

We like to think that our everyday experience can tell us the real from the fake, but that's only true if our everyday experience takes place in the realm of what we're trying to judge. We can't judge what outer space looks like, because flew of us have been there. We can't judge what the microscopic world looks like, because we don't live at that scale.

Sometimes, and I know this is an uncomfortable idea for some, you have to trust the people whose job it is to actually explore those realms, and who, because of the time they've spent at it, know much more about it than you do.

You can't trust everything that everyone says. But the fact is that most people are telling you the truth.

Thursday, February 11, 2016

Gleason's Map

When flat-Earthers talk about the shape of the Earth, most of them propose that it is a disc, with the North Pole as the center, and what we think is the South Pole around the rim, forming a great ice wall. As I showed on my previous post, the idea is that the sun and moon circle around the disc and create day and night, and somehow moon phases and eclipses.

But that's not the subject of this post. There was quite a stir awhile back on YouTube when someone found a map in the collection of the Boston Public Library. This is the map:

Look! there it is! North Pole in the middle, big ice ring around the perimeter. The flat Earth!

Well, maybe. Closer examination reveals a few clues. The first is in the upper left corner, where is says: Longitude and Time Calculator. There is also that weird something sticking out from the center, that seems to be riveted in the middle and torn off at around 30 degrees north. What is that for?

And there are numbers around the rim that must serve some function.

More telling, especially to anyone who's had a little bit of cartography education, is one very important word near the top. It says that this map is "On the Projection of J. S. Christopher, Modern College, Blackheath, England." Projection means that it is derived from some other shape, like maybe a globe.

Flat-Earthers make much of the words "As It Is" and "Scientifically and Practically Correct," and even more of the descriptions of the motion of the sun in the lower corners. But what did Gleason have to say about it? Do we know?

Well, we certainly know what he said on his US Patent application from 1895.  Here is Gleason's concept drawing as submitted:

You can read the entire patent, which describes the map's use as a time calculator for students. But the most important passage from the flat-Earth standpoint is this:
The map is not so extorted as to lose the relative latitude and longitude of any places on the land or sea, but retains all latitudes and longitudes of places agreeing with other recognized authors; and as the proper relations of continents and countries all stand in their relative position to each other, they are thus impressed upon the mind of the student. The extorsion of the map from that of a globe consists, mainly in the straightening out of the meridian lines allowing each to retain their original value from Greenwich, the equator to the two poles.
 The use of "extorted" in the sense of "distorted" is interesting here, but the intent is clear; the map is not "as it is" (which I think may have been a slogan of the map's publisher), but a projection that preserves the positions with regard to longitude lines, but not the distances between them (distances between lines of latitude, however, are preserved). And note his phrasing "the equator to the two poles." A flat Earth does not have poles.

This type of projection is know as an azimuthal equidistant projection, and when properly used it has many applications in navigation, telecommunications, and even military planning. The projection method has been known for about 1000 years. Azimuthal projections are not always centered on the North Pole; they can be generated mathematically from any point on the globe. You can generate one for yourself online.

The fact that so many flat-Earthers automatically dub this a "flat-Earth map" everywhere they see it shows a profound lack of willingness to do deep research, and a penchant for jumping onto bandwagons.

I think Gleason would be appalled.

ADDENDUM: Well, apparently I was wrong about Gleason. He really was a flat-Earther after all. I will do a full post on this when I get the chance.

So why did the patent examiners of several nations grant a patent to a flat-Earth map? Because the patent application conveniently left that little detail out. More to follow, along with revisions to this post.

Tuesday, February 9, 2016

Sunrise, Sunset

One of the biggest problems with the whole flat-Earth idea is the lack of any model which comes close to explaining how we see the sun and moon appear to rise and set at the horizon.

Not the the flat-Earthers haven't tried. They present computer models that look like this:

It's almost plausible. The disc world is part in darkness and part in light. Some versions even show the disc exactly half lit, though how the sun manages that is never made clear.

But it's never rendered from the ground. Well, I've seen it done once, and it completely blew the disc world model to bits, which was more-or-less the point.

So how do flat-Earthers explain sunsets? Perspective. They say the sun just gets smaller and lower in the sky as it moves away from you, creating the illusion that it is being blocked by a horizon.

And that, too, sounds plausible. As long as you don't actually know anything about perspective.

Perspective is a set of techniques employed by artists to simulate a three-dimensional world using a two-dimensional medium, like a drawing. It's all based on one real-world observation: things appear smaller when they are farther away from you. That's the whole thing.

This means that everything appears smaller, not only objects, but the spaces between objects. And they all shrink at the same rate.

So, for example, if you hold a one-foot-diameter ball one foot above a table, and then walk away from it until the ball looks about half its actual size, then the space between the table and the ball will appear to be half the diameter of the ball. Simple.

So, why, then, are we asked to believe that the sun on a flat Earth, which is supposed to be 36 miles in diameter and 3000 miles above the ground, could ever appear to even touch the ground, much less sink beneath it?

When I bring this up, flat-Earthers tell me that I don't understand perspective. But they can never explain perspective in any way that coincides with any of the principles of perspective that artists have developed over the past 600 years.

And their attempts to demonstrate perspective and sunsets are laughable. Like this video showing a hand sliding a coin on a table, as if the sun is actually touching the ground.

Like pictures of railroad tracks and telephone poles from an art book, as if the size relationship between the sun and it's altitude above a plane could compare with the distance between two railroad tracks.

If they want to sell this idea (and make no mistake, they are pushing it hard), they have to come up with, at minimum, a model that explains this one simple thing.

Or, and this is just a thought, they could just give up on this crazy idea altogether. 

Saturday, February 6, 2016

Playing Fast and Loose With Polaris

One of the most frustrating things about dealing with flat-Earthers is the way they will suddenly change the subject from whatever you were talking about to a completely new line of thought. I saw an example of this on Twitter recently when the question of seeing the North Star, Polaris, from Reunion Island, which is more than 21 degrees south of the equator, came up out of nowhere.

This is, of course, impossible. There was an illustration, showing that this is impossible. But no proof that it had ever actually happened. The poster just took it as read. So I decided to find out where the story came from.

A little searching brought me to the only place I can find where anyone claims that Polaris has ever been seen from Reunion Island: a massive book called The Greatest Lie On Earth: Proof That Our World Is Not a Moving Globe by Edward Hendrie. There is no other source for this claim, even on flat-Earth websites.

Fortunately, Google books has a preview inside where I found page 105, where Hendrie says:
Below is a time lapse photograph of the North Star (Polaris). The photograph was taken in October, 2008, from the Le Make Reunion Astronomical Observatory on Reunion Island.100 That observatory is at an altitude of 4,921 feet and is located at 55.39° east longitude and 21.5° south latitude. The photograph was taken by Laurent Foumet and lean-Philippe Olive, who are members of the Club Astro Astrium in Toulouse, France. Olive and Foumet used an Olympus camera, 28mm f/8 lens, 2 hours and 40 minutes exposure time; Ektachrome 210 ASA film.
Note how detailed this is, how it looks so accurate and well thought-out. It even has a source reference. Very convincing. Except for two things: the photograph, which I will give you the link to presently, which shows, in the center of the star trails, not a bright star, but a dim cluster; and second, that I know what is described is impossible.

So, let's check out that reference. Hmm. Seems that this picture is not of Polaris at all. It says right in the text that these are southern circumpolar stars.

So, is Hendrie just missing something? Or was he just counting on everyone who read the text not bothering to check the reference? In either case, it seems that anyone who writes a 400-page book claiming that the Earth is not a globe should have a better standard of evidence.