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Flat earthers claim their view is the “default,” similar to ancient cosmologies; and that belief in a globe is the anomaly. This is a lie, because of one simple question of cosmology: Where does the sun go at night?

Ancient cosmologies generally believed the sun went either below the earth at night, or out of the firmament to somewhere unknown. This means they assumed the whole world experienced one universal time of day or night.

In the age of time zones, modern flat earthers try to resurrect flat earth by saying that at night the sun goes “too far away to see.” This not only separates their model from ancient ones, but also violates basic observational science. It traces back to a 19^th-century misfit named Samuel Rowbotham, and for that reason I call it “Rowbothamism.”

I did my best to survey ancient cultures all over the world. Here is what I found:

Highlights opposing Rowbothamism

• Sumerian cosmology

  This culture believed there is a tunnel under the earth called the “Road of the Sun.” There's a whole scene in the Epic of Gilgamesh, tablet 9, when Gilgamesh travels along this tunnel to the underworld.

  More information →

• Egyptian cosmology

  The Egyptian sun god Ra travels in a boat through the underworld every night, and is reborn in the east every morning. This nightly journey was central to Egyptian religious practices, and was described in great detail in the Book of Gates.

  More information →

• Aztec cosmology

  In Aztec belief, the earth goddess Tlaltecuhtli swallows the sun every evening and vomits it again in the morning.

  More information →

• Hebrew cosmology

  The Bible does not give any clues about where the sun goes at night, except the use of “rise” and “set” in Matthew 5:45 and Ephesians 4:26. For more detail most sources, including Michael Heiser, look instead to the Book of Enoch.

  This 1909 Mormon source summarized the evidence well:

  “It was represented that in the eastern side or the face of the firmament there were six doors or portals through which the sun entered from chambers outside the vault, and that in the western side of the firmament there were also six portals. For thirty days the sun passed through the first portal and at evening, after traversing the sky, passed out through the corresponding opening in the west. At the end of the month the sun entered by the second portal; and so on until the sixth had been reached …”

Best scraps supporting Rowbothamism

• Greek

  “[Anaximenes] says that the stars do not move under the earth, as others assume, but round the earth as a cap is turned on one's head, and that the sun is hidden, not because it is under the earth, but because it is hidden by the earth's higher parts, and by reason of its greater distance from us.”

  — Hippolytus Refutation of all Heresies; Book I, sec. 6 “Anaximenes”

  This idea was highly peculiar: from only one Greek school (Miletus) among many, and apparently idiosyncratic even within that school. Anaximenes' own fellow (and possible teacher) Anaximander imagined the sun moon and stars as holes in giant “chariot wheels” with earth at their center, contradicting Anaximenes' idea. Hyppolytus seems to have found it noteworthy precisely because it was so contrary; and the idea was clearly defeated in general Greek thought by the likes of Pythagoras and others.

• Chinese

  “It is like a person carrying a torch. When he walks away, the light becomes fainter and fainter until it is extinguished. When the sun sets, it is the same.”

  — Huainanzi 3.12 (“Patterns of Heaven”)

  Chinese cosmology evolved many times over the centuries, and the quote above seems to be a blip on the radar. One of the most classic Chinese myths, “Houyi and the Ten Suns,” strongly suggests that times of sunrise and sunset were considered universal. Other sources say the earth was “bulging up slightly” to account for time differences. More info →

• Hindu

  “The sun, stationed, as it were, in the middle of the day and of the night, enlightens all the regions, whilst its rising, or its setting, is always relative to some portion of space. By this twofold cause, the vicissitudes of day and night ever recur.”

  — Vishnu Purana, Book 2, Chapter 8

  “When the sun travels from Devadhani, the residence of Indra, to Samyamani, the residence of Yamaraja, it travels thirty-four thousand three hundred yojanas (275,440 miles) in fifteen ghatikas (six hours). Similarly, when it travels from Samyamani to Nimlocani, the residence of Varuna, it travels the same distance in the same amount of time. Then, when it travels from Nimlocani to Vibhavari, the residence of the moon-god, it travels the same distance in the same amount of time. In this way, the sun continues circumambulating Mount Meru.”

  — Bhagavata Purana, Canto 5, Chapter 21, verses 7-9

• Persian

  “Of Mount Albûrz it is declared, that around the world and Mount Têrak, which is the middle of the world, the revolution of the sun is like a moat around the world; it turns back in a circuit owing to the enclosure of Mount Albûrz around Têrak. As it is said that it is the Têrak of Albûrz from behind which my sun and moon and stars return again.”

  — Pahlavi Texts, Part I, Chapter V, verses 3-4 (SBE05), E.W. West, tr. [1880], at sacred-texts.com

  This text, though at first seeming to parallel the Bhagavata Purana above and thus favoring Rowbothamism, goes on to discuss the “apertures” in this uncertain “enclosure of Mount Albûrz” through which the sun enters and exits, now seeming to parallel the Book of Enoch in opposition to Rowbothamism. What this author actually imagined may be more complex than it first appears.

The all-time favorite argument of Rowbothamists, for some reason, uses the worst scientific methodology imaginable. I wonder why?

It's like trying to see outside, but instead of choosing the large clear window nearby, you choose the small dirty one:

Flat earthers present a photograph or video showing some distant object (a mountain, city skyline, etc.), seen in blurry haze across miles of lake or ocean. They also give the “globe prediction,” according to pure geometry, of linear drop from a tangent at the horizon to some part of the visible object (but in far less coherent terms), and boldly declare that it “shouldn't be visible” with curvature. One of their sources tried to tabulate these observations here.

The issues with this argument are almost too many to name, but I will try:

• Their evidence is often obtained through a long chain of memes and other careless (or even dishonest) means, which leads to a plague of misinformation and poverty of data. Errors and missing variables abound; confidence and rigor is an absolutely foreign concept.
• They often neglect observer height, especially if they cite the “8 inches per mile, squared” curvature approximation (which fundamentally excludes observer height).
• They almost never denote the actual height of the target that's visible (unless they think it helps their argument).
• They never coherently address why some part of the target might not be visible. (They give word salad about perspective, opacity, and ocean waves.)
• They give the “missing curvature [drop]” in linear units, which is not coherent for an optical measurement that should be in angular units.
• They try to gatekeep the use of atmospheric refraction as an explanation, despite a source that they cherry-pick clearly describing it as a “nasty complication.”

All of these issues boil down to one simple fact: flat earthers are bad at science. They have almost no power of deductive reasoning beyond a brutish intuition. Taking their tabulated data (linked above), even disregarding the virtual certainty of some falsehood in the left hand columns, the data we can cross-check is riddled with errors.

Additionally, when we consider these alleged anomalies as angular displacement in the observer's eye, we find that 94% of them are smaller than a U.S. dime held at arm's length (conservatively speaking).

This, along with the 4-degree outlier in the top-right, all makes sense considering the stochastic nature of the weather conditions that drive refraction. There is no true “maximum distance” beyond which it is “impossible” to ever see on the globe; it's simply a matter of the requisite conditions being more and more rare for larger distances. It would require more and more air masses of certain types to perfectly align in a longer and longer refractive corridor around the earth's surface along our line of sight, which is a matter of sheer dynamics.

Notice that flat earthers never perform any measurement or analysis of this refraction whatsoever. Considering its complexity, I hardly blame them for that; but it does completely invalidate their attempt at science.

More info on the graphics above:

• Google spreadsheet
• code on Github

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Now, if that were not enough, I wrote a simulation to model atmospheric refraction on a globe. It uses all the most exact, most standard globe and atmosphere metrics, combined with a simple straightforward implementation of Snell's Law:

Before any turbulence whatsoever is added, with 100% standard atmospheric gradient, here's how it looks. It renders a vertical cross-section showing density; a straight line in red for reference; and a white line showing continuous deflection due to Snell's Law. The curvature of earth is exaggerated by a factor of 4, just so the diagram will fit on the screen.

We can also plot this on our previous angular anomaly chart:

But the atmosphere is far from static. Let's see if we can add some turbulence, lightly chosen to imitate the obvious selection bias in the flat-earthers’ data:

How does that compare with the observation data? Uh-oh …

But that's just random turbulence. The reality is, conditions on clear sunny days, especially over water, create something called a temperature inversion. Others like Michael Toon and Danny Faulkner have provided info on this in more depth, but allow me to connect the dots a little bit.

Here is the Ideal Gas Law:

where:

• p = pressure
• V = volume
• T = temperature
• n = number of molecules (basically)
• R = the ideal gas constant

This form of the gas law is useful when you have a fixed number of gas molecules like in a balloon or a piston chamber, where n is constant and V might be variable; but it's but not so useful for analyzing open portions of the earth's atmosphere. This lack of intuitive applicability is something that flat earthers try to endlessly exploit, while cherry-picking science literature and spewing abject nonsense.

To make the analysis, we have to use the molar form of the gas law, solved for density d:

where M is the air's molar mass. What happened to V? With the introduction of molar mass, we unlocked total mass as a variable which then got combined with volume and became density. We can now treat M/R as a constant, which leaves a fairly simple three-way correlation between density, pressure, and temperature.

But the weird thing is, under standard atmospheric conditions all three of these variables decrease with altitude. How? Because the numerator (pressure p) falls off much faster than the denominator (temperature T), which causes the quotient (density d) to fall too.

Notice what a temperature inversion does to this situation: if the numerator already decreases quickly with altitude, but now the denominator starts actually increasing … then the quotient is going to drop off very, very fast. None of the gradients invert except temperature; and the density gradient becomes extreme.

Let's try to imitate this in the simulation:

But with a superior mirage involving internal reflection, the gradient doesn't even have to be very extreme:

In conclusion: have flat earthers “falsified the radius value?” No, not even close. The observed data is not only possible, but fully expected given the basic facts about earth, its atmosphere, and simple 11^th-grade optics.

Any claim otherwise is sheer ignorance of those topics.