A 10-minute video summarizes this article: https://tinyurl.com/AFlatEarthModel
A one-hour physics colloquium based on this article:
In the US and in Britain there are organized groups of people who strongly believe that the Earth is flat. The US group is named “Flat Earth International” and it holds regular conferences (https://flatearthconference.com). A major website for the US flat-earth movement is http://flatearth101.com and that of the UK movement is https://wiki.tfes.org. It is claimed that there is a massive conspiracy to hide the fact that the Earth is flat, with all governments and all scientists working together to maintain the fiction that the Earth is round. This conspiracy, if real, would include most scientists, philosophers, and religious leaders on several continents, going back more than two thousand years. This belief could be considered harmless, but the movement provides additional fuel for the notion that all scientists are conspiratorial liars and are not to be trusted, which is a dangerous notion with serious consequences for society.
There have been many attempts by scientists to rebut the flat-earth notions, but often the counter-arguments are not well chosen. For example, since flat-earthers believe that the Sun is only a few thousand miles away, it’s not useful to start a counter-argument with “Since we know that the Sun is nearly 100 million miles away…” The flat-earthers put great emphasis on naked-eye observations, so here I will emphasize the fact that their own model makes predictions that are wildly different from naked-eye observations.
A popular model of the US flat-earthers’ version of the truth is that the Earth is a stationary flat circular disk (with local hills and valleys) with the North Pole at the center and an impenetrable wall of ice at the edge where, in some accounts, armed guards prevent one from crossing. The Sun and Moon are said to be spotlights circling the disk at a constant height of about 3500 miles and with diameters of about 30 miles. These numbers make the angular size of the Sun and Moon be one-half degree, as is observed in the real world at all times (but only at noon at the equator in the flat-earth world). These numbers also attempt to account for the different angular heights above the horizon of the Sun and Moon seen at different latitudes. A rotating dome above the disk carries spots of light (not distant “stars”) that move in circles around the North Star.
Many flat-earthers believe that there is no such thing as gravitational forces between objects, the proof being that if you place a ping-pong ball in contact with the bottom of a suspended bowling ball, the ping-pong ball falls, so evidently the bowling ball does not exert a gravitational force on the ping-pong ball to prevent it from falling. If you don’t believe there is such a thing as gravity, then Australians can’t be suspended upside-down, and this is taken as additional evidence that the Earth can’t be round (that is, very nearly spherical; actually an oblate spheroid). All the evidence in favor of a round Earth and a huge Universe around the Earth is thought to have been faked, including all of the videos and photos released by NASA and the space programs of all other countries.
The starting premise of all this is that you should believe your own eyes rather than what some authorities claim. This attitude can be seen as positive, since direct observation is a necessary foundation for science and understanding. However, the way that this plays out among flat-earthers has some very serious limitations. The believers generally do not make many careful observations, usually preferring to quote flat-earth authorities. The believers do not make the necessary deductions from the fact that their own flat-earth model makes predictions of naked-eye phenomena that are utterly different from what one actually sees. At the very least this should have triggered attempts to improve the flat-earth model.
Secondly, they fail to understand that progress in science has included the need to invent and deploy ever more sensitive technologies to go beyond what can be understood solely from naked-eye observations. Examples of the latter point abound. No unaided human eye has seen a virus or an atom; we had to invent microscopes of increasing capability to augment human vision. We can’t see the electromagnetic waves that carry conversations to our cell phones, but those waves are very real and are obviously detectable by a cell phone. In 1798 Cavendish was the first to construct an apparatus sufficiently sensitive to be able to measure the extremely small gravitational forces that two large metal balls exert on each other, and the measurements were in agreement with the vastly larger gravitational force that the entire massive Earth exerts on these balls.
Of course the strongest evidence for a flat Earth is that it looks flat (again, ignoring local variations in the form of hills and valleys). The Earth is so large that an initially horizontal beam of light will be only 8 inches (20 cm) higher above the surface after going a mile (1.6 km), and for a distance of N miles, the difference is N-squared times bigger. This is a somewhat difficult measurement to make, and for large distances an object can seem to be raised or lowered by mirage-like bending of light due to atmospheric conditions near the surface. Though such measurements have been made (over water) that verify that the Earth is round, these results are rejected by flat-earthers. At the end of the recent documentary on the flat-earth community, “Behind the Curve,” some flat-earthers repeat the experiment themselves and are stunned that the results are not consistent with a flat Earth, but this seems to have had no impact on the community. Also near the end of the documentary one hears a flat-earther saying that, using a complex device called a ring laser gyroscope, his measurements showed that the Earth does in fact rotate, “but don’t tell anyone.”
There is an unresolvable tension in this community between claiming to be scientific by providing a model that will agree with naked-eye observations, and the need to reject disproof of this model for the sake of maintaining a congenial community that delights in sharing knowledge of a vast conspiracy and feeling the satisfaction of disproving conventional science.
I wrote a GlowScript VPython program to create a navigable computational version of what seems to be the most popular US flat-earth version (it differs in some important ways from the UK flat-earth version). It is to the credit of the flat-earth community that their model of a flat Earth is sufficiently well described as to make it possible for me to create a computer model.
In the section below on “Using the computer model,” which includes a link to the program, you can explore this model yourself. While roaming around in this 3D visualization of the flat Earth, it was easy to identify several predictions of the flat-earthers’ model that disagree dramatically with what one actually sees with the naked eye:
1) The flat-earth model predicts that the visual diameter of the flat-earth Sun can, depending on your latitude, vary by more than a factor of 2 between noon and sunrise or sunset, which we do not observe. At sunrise or sunset the flat-earth Sun is much farther away from an observer than at noon, so it would look much larger at noon, whereas in reality the Sun is so very far away that its tiny change in angular size from sunrise to noon is undetectable. Also, the angular size of the flat-earth Sun is very different when viewed from different latitudes, which is not what is observed in the real world.
2) The flat-earth model predicts that the flat-earth Sun will never get anywhere near the horizon, despite the fact that we see sunrises and sunsets with the Sun at and even sinking below the horizon. Because the flat-earth Sun is about 3500 miles above the disk, an observer on such a flat Earth should always see lots of sky between the horizon and the Sun; at sunrise and sunset the flat-earth Sun is far above the horizon.
3) A closely related naked-eye observation is that at sunset one sometimes sees the bottoms of low-lying clouds lit by the setting Sun. The flat-earth model predicts that this cannot happen, since the flat-earth Sun is about 3500 miles above the Earth.
4) The flat-earth model predicts that the North Star will be visible even from Argentina, despite the fact that it is not visible from anywhere a few miles south of the equator (the North Star is a small angular distance from the point around which it seems to circle, so that at a short distance south of the equator you can see it some of the time). In fact, from the edge of the flat-earth disk, the North Star will be about 25 degrees above the northern horizon. Similarly the flat-earth model predicts that the angular height of the North Star should be about 60 degrees in Dallas Texas, but it’s actually only 33 degrees above the horizon, which is a huge naked-eye discrepancy. The latitude of Dallas is 33 degrees, and on a round Earth one predicts that the North Star will be 33 degrees above the horizon, as is observed.
5) The flat-earth model predicts that if you watch a constellation that is near the eastern horizon at nightfall, it will grow larger until midnight, as it comes closer to you, then smaller as it moves away from you toward the west. No such effect is in fact observed. Closely related is the prediction that as you move farther from the North Pole, the larger will be constellations in their closest approach to you. Moreover, in all cases the brightness of the flat-earth stars and flat-earth Sun will vary depending on how close or far you are from them, which is not observed in naked-eye observations. This implies that the stars and Sun are very far away, so that moving large distances on the Earth’s surface hardly changes the large distance to stars and the Sun. Also, except at the North Pole, a constellation in reality never moves parallel to the horizon during the night as it does in the flat-earth model.
There is no room for the well-known southern-hemisphere constellation, the Southern Cross! Just as the North Star should be well above the horizon even in Argentina, so should all the constellations of the southern hemisphere be well above the horizon in the US. Not only do we not see these constellations in the US, there isn’t room for all the southern-hemisphere constellations and all the northern-hemisphere constellations to be jammed into the single hemisphere that is the rotating flat-earth dome.
6) If you move away from the North Pole you’ll see that the tracks of the stars around the North Star are no longer circles but are now ellipses, which does not agree with long-exposure photos of the night sky such as, oddly, this photo displayed on a page of the major US flat-earth site (scroll the page to find the image): http://flatearth101.com/fact-vs-theory
Note too that if you are at the equator of our real world, and you see a star rise straight east of you, that star continues up to the zenith and then down to set in the west, whereas in the flat-earth model the stars are on the rotating dome and move parallel to the horizon; they can’t move perpendicular to the horizon.
Incidentally, that flat-earther’s page contains a major error, namely the claim that “the North Pole Star is situated perfectly over the North Pole center of earth and never moves a single inch night after night year after year century after century.” If you use Ctrl-+ to blow up the image, you will see what is well known to amateur astronomers, namely that Polaris is not “situated perfectly over the North Pole” and leaves a trail just like all the other stars. Moreover, with the centuries, which star is closest to being above the North Pole changes, due to the “precession of the equinoxes,” the name given to the visual effects that are due to the fact that the axis of the spinning Earth “precesses” like that of a gyroscope. This effect is due to torques exerted by the Sun and Moon on the Earth.
The commonality of these effects is that you don’t need any special equipment in order to make the relevant observations. It’s true that if you want to make the North Star disappear you will have to travel to a little bit south of the equator. As an alternative, check with trusted friends who live south of the equator and can look for the North Star on your behalf. Or just compare the angular height of the North Star above the horizon at your location, and notice that it dramatically contradicts the angle predicted by the flat earth model. There are many other problematic aspects of the flat-earth model that can be tested with some precision equipment, although these are still accessible to anyone who wants to make an investment of time and money. For example, amateurs as well as scientists have verified the earth’s curvature using long-baseline surveying over water or have measured the gravitational forces that ordinary-sized objects exert on each other, as Cavendish did.
The key point is that if the Sun and stars are only a few thousand miles away from an observer as predicted by the flat-earth model, their individual sizes and their distances from each other on the sky, and their brightness, will necessarily change as they move a few thousand miles toward or away from the observer during the day and night. In contrast, if the Sun and stars are very far away compared to the size of the Earth, then changes in their distances from the observer during the day and night will be such a small fraction of those distances that naked-eye observations will not detect any changes, and that is precisely what we actually observe.
The flat-earthers take pride in having created an alternative model of the Earth and its surroundings. However, they have not taken the critical next step, a crucial step in a scientific approach, which is to take their own model seriously. This would mean checking whether the predictions of the model are consistent with observations, including, at the very least, naked-eye observations.
In her 2007 book “Flat Earth: The History of an Infamous Idea,” Christine Garwood documents that while early Babylonian and Egyptian cosmology included a flat Earth, the Greeks realized that it had to be round. Aristotle traveled south in Egypt, saw that he could see constellations that were new to him and couldn’t see some familiar constellations, and correctly concluded that the Earth is not flat. A century later Eratosthenes measured with remarkable accuracy the radius of the Earth by comparing the lengths of shadows of vertical rods in two Egyptian cities on the same longitude, at the same time of day. Garwood points out that from that time forward until the mid-1800s, everyone in the West accepted that the Earth was round.
Eratosthenes’s measurements could be interpreted to determine either the 4000-mile radius of a round Earth or the 4000-mile height of the Sun above a flat Earth, as can be seen in the following diagram. Presumably it was at least in part Aristotles’s analysis that led Eratosthenes to choose the round-earth interpretation. Another reason for rejecting the flat-earth interpretation could have been the fact that the apparent size of the Sun doesn’t change during the day, despite the changing distance that the flat-earth model requires.
Garwood comments that there is a persistent myth that at the time of Columbus, people thought the Earth was flat, but that is not true. Columbus incorrectly believed that the Earth was much smaller than people of his day knew it to be, and he thought it was small enough that his provisions would support his ship voyage from Spain to China. He was way off and would have starved if he hadn’t run into the islands of the Caribbean. Galileo’s heresy wasn’t a claim that the Earth was round; it was stating that the round Earth, accepted by the Catholic Church, wasn’t at the center of the Universe.
As documented by Garwood, in England in the mid-1800s there arose a challenge to the Earth being round instead of flat, and the contemporary flat-earth societies in the UK and the US are inheritors of that movement. She shows that the main motivation was discomfort with secularism in general and with evolution in particular. One of the arguments used by flat-earthers was to find passages in the Bible that could be interpreted as support for a flat Earth. It is probably not a coincidence that the flat-earth movement started in England, where modern geology can be said to have gotten its start, stimulated by the search for minerals in the context of the industrial revolution. The geologists showed that the Earth must be much older than 6000 years, and they uncovered fossils of animals that were completely unknown.
It is relevant that on the first page of the important US flat-earth website, http://flatEarth101.com, there is this statement: “The majority of people believe they are descendants of monkeys living on a giant spinning ball of water hurtling and spiraling through space. All of which was not created but was formed billions of years ago in some outrageous cosmic explosion that created everything from nothing. If this were true it would mean we are insignificant pieces of cosmic dust! We aren’t special in the least, without a purpose in being here. Our self-worth and outlook on others and the world as a whole is warped. Well, the exact opposite is true, we are special and are not some random result of a billion year old explosion!”
There is a larger context for all of this. In her 2000 book “The Battle for God: Fundamentalism in Judaism, Christianity and Islam” by Karen Armstrong, a distinguished scholar of religion, Armstrong shows that although fundamentalists in all of the three major monotheisms think of themselves as returning to ancient tradition, in fact all three fundamentalisms are quite recent phenomena. She makes a distinction between “logos” (the word; logic and rationalism) and “mythos” (the stories we tell; the only language we have for discussing some kinds of important experiences). Both of these forms of discourse are essential to being human. Fundamentalists saw the growing power of science, logos par excellence, and in reaction wanted their own form of logos. They came to claim for their holy books, works par excellence of mythos, the status of logos. Instead of celebrating the story-telling mythos of the holy books, many fundamentalists are literalists for whom these books have the same logos-based characteristics as scientific works. Of course not all flat-earthers are fundamentalists, but there has been and continues to be a significant connection. It is noteworthy that in a speech at a recent flat-earth conference, there was much applause every time the speaker cited the Bible as proving the Earth is flat.
Members of the flat-earth movement emphasize how much value they place in the friendships and other social aspects of belonging to a community. It is a common human trait to value social connections, and to accept the common beliefs of ones’ chosen peers. Social connections insulate and protect flat-earth belief from the impact of the many discrepancies and observable errors in the flat-earth model. In spite of the rhetoric concerning direct observation and scientific reasoning, the flat-earth movement is ultimately not based on logos, but on mythos.
I owe a large debt to Lee McIntyre, a philosopher of science who became interested in the flat-earth movement as an example of science denial and, in an editorial in the September 2019 issue of the American Journal of Physics, asked for help from physicists on how to rebut the arguments of flat-earthers. I strongly recommend his excellent 2019 book, “The Scientific Attitude: Defending Science from Denial, Fraud, and Pseudoscience.” I also owe much to the thoughtful insights and suggestions of my friend Derek Roff. After completing this work I found a 2019 book by J. W. Braun, “The Flat Earth Fallacy & The Globe Earth Proof,” which puts a similar emphasis on naked-eye observations that strongly disagree with the predictions of the US flat-earth model.
Using the computer model
Click tinyurl.com/FEmodel to start up the computer program in a separate browser tab, and drag that tab out of the browser so that you can see this text and the computer display at the same time. You don’t need to install any software; the GlowScript VPython program runs in your browser.
You should see a transparent rotating dome with embedded stars and their long-exposure trails. The dome sits on a stationary flat disk that represents the flat Earth.
Position the mouse just above the center of the scene and press the mouse button to move forward into the flat-earth model. Release the mouse button to stop moving. As you get closer you will see radial longitude lines and circular latitude lines drawn on the green flat Earth. The yellow line lies between your original position and the North Pole at the center of the disk. A red circle marks the equator. You can’t move farther into the model than the east-west light blue line that is perpendicular to the entry yellow line. You can roam backwards with the mouse below the center of the scene, and you can roam left or right with the mouse to the left or right of the center of the scene.
If you click “Look around,” roaming is disabled and you can use the mouse to look in any direction without moving. This is useful for inspecting the model. Look up and you’ll see the stars with their circular trails centered on the white North Star (Polaris). Look about halfway up to find the moving yellow flat-earth Sun that moves in a circle about 3500 miles above the equator, this being a day near the spring or autumn equinox. When this Sun moves beyond the cyan-colored east-west line its color is dimmed to gray to indicate that you are now in darkness. Sunrise for you occurs when the Sun crosses the eastern end of the east-west line, and sunset occurs when the Sun crosses the western end.
1) The changing size of the Sun: In “Look around” mode you can with some care observe the changing angular diameter of the Sun. You might start by observing from the equator, where the Sun at noon has the observed angular width of half a degree. Watch for “sunrise” in the east (when the Sun becomes bright) and click “Pause”. Observe the size of the distant Sun. Click “Run” and then click “Pause” when the Sun is overhead. Note that it looks significantly bigger now, because it is significantly closer to you. Or simply let the model run and watch the “Sun width” degree display below the scene, which is the angular width of the Sun at this moment as seen from where you stand. Move to a different latitude (note the numerical latitude indicator below the scene), and you’ll see that the angular size of the flat-earth Sun changes, because you are closer or farther from it, and this effect is not what is actually observed. The size of the Sun is exaggerated to make it easier to observe it, but the “Sun width” display is the computed angular width for the flat-earth model.
2) The Sun never gets near the horizon: As you watch the Sun move around the Earth, note that it never gets close to the horizon, because it is high above the flat Earth.
3) Cloud illumination: Imagine low-lying clouds, which are very far below the Sun. Since the flat-earth Sun is very high above these clouds, even at sunset it cannot illuminate the underside of the clouds. Yet it is not uncommon at sunset to see the bottoms of low-lying clouds illuminated by sunlight.
4) Angular height of the North Star: In “Roam” mode, navigate to a latitude of 33 degrees (like Dallas, Texas) and in “Look around” mode observe the viewing angle for the North Star by looking toward it. You’ll find that it’s about 60 degrees above the horizon, but in Dallas the North Star is in fact only 33 degrees above the horizon, as is predicted and observed on a round Earth, for Dallas’s location of 33 degrees north latitude.
5) The changing size of constellations: Near the horizon are 12 identical triangular “constellations.” Roam to the equator, click “Look around”, and click “Pause”. Now look around at the various constellations, and of course those nearest to you are bigger than those farther away. Or click “Run” and watch the constellations grow in size as they move from the east to the west. Or, click “Pause” and roam toward one of the “constellations,” noting that it gets bigger and bigger, but in the real world the apparent size of a constellation doesn’t change with latitude. Also, note that the constellations move parallel to the horizon, which is not observed in the real world except at the North or South Pole.
6) If you move far from the North Pole and then look at the North Star in “Look around” mode, you’ll see that the tracks of the stars around the North Star are no longer circles but are now ellipses, which does not agree with long-exposure photos.
All of these effects shown in the computer model ought to be visible with simple naked-eye observations of the sky if the Earth is flat. However, what we actually observe when we look at the sky is very different from what the flat-earth model predicts, as demonstrated by the computer model.