A Theory Gone Flat

Flat Earth and spotlight sun, by Towarzysz Przewodniczący (Wikimedia Commons)

Am I really going to do this? Am I going to spend time on a topic so far from legitimacy as Flat Earth? Doing so risks affording a tiny bit of credibility to an idea that hasn’t earned it, as if I doth protest too much.

Reasons to bother: 1) illustrate direct observation in action; 2) emphasize the power of listening to what the universe tells us rather than insisting on insufficient mental models as “truth”; 3) provide examples of how mental models go wrong; and 4) I made some graphics worth sharing. While a bit of a tangent from my usual “serious” topics, I figure I can have a little fun once in a while.

The focus will be on conspicuous observations anyone can confirm, personally, without too much effort—even from memory, in fact. I’ll skip the literally dozens of ways I have personally measured and confirmed the spherical Earth, which would make for boring reading. Lots of things break in Flat-Earth scenarios, including GPS navigation (no satellites; broken math), gravity (would crumple a disk-Earth into a sphere in no time; plumb bobs would point more north the farther south one went), and what we’ll focus on here: sunsets. No more sunsets, folks—and any sunsets (or sunrises) you might believe yourself to have seen aren’t what you made them out to be, according to Flat-Earthers.

Rather than denigrating the people who subscribe to Flat-Earth beliefs, I’ll focus on observation. I’m not aiming to convince Flat-Earthers; nothing I say (as an obvious shill for the mega-conspiracy) can replace the sense of community and unconditional support they receive from their FE-family. Any of us might go to extremes of twisted and easily-refuted logic to preserve what’s most important to us. Modernity fails humans in countless ways—loss of intimate tribe being among them. We can forgive those seeking to recapture what’s been lost.

The Premise

It’s not possible to lay out the theory of Flat Earth, since there really can’t be one coherent theory consistent with the body of observations, and various factions bicker about various thorny points. But most seem to agree that Earth is a flat disk, wrinkled by terrain, of course. The north pole is at its center, and Antarctica spans the outer periphery like an ice wall circumscribing the disk’s edge. I’m not aware of any Australian versions imposing the polar reverse, which might be construed as yet another slight to the Global South. Actually, the ocean-dominated southern hemisphere is what allows this bias to persist: much harder to “pace off” distances in a car, for instance.

Let’s pause to celebrate the elements of reality here: they agree there are continents and oceans, and that a sort of map can be made, however distorted it may become as one approaches the outer edge. They also acknowledge some special status of the north pole. We can work with this.

As far as I can tell, they also cop to the fact that it’s not noon everywhere at once (time zones are real/necessary), and that some areas on Earth experience nighttime while others are in full daylight. This (reluctant?) admission will turn out to be a serious challenge to their platform, in this post.

Implications: Solar Distance

In order to satisfy the previous paragraph, the sun can’t be very far off the disk, and must engage in a sort of spotlighting to concentrate light on one side of the disk while leaving the other in the dark (see banner image).

If the sun were very far (like 25,000 times Earth’s characteristic scale in the round model), its motion would look similar to all Flat-Earth residents: rising and setting at essentially the same time everywhere, simultaneously plunging the whole surface into darkness. No: in a Flat-Earth model the sun must be relatively close to the disk to be seen at different elevations at the same time in different regions of the world, and to account for simultaneous day/night conditions.

Some Flat-Earth enthusiasts build attractive display models that generally include a rotating light extending off a post through the north pole, illuminating one side of the disk at a time. To build a physical model is to have put some thought into where to position the light. Keep going…

Implications: Solar Racetrack

In order to have noon in Los Angeles happen three hours later than noon in New York, the sun has to move over the disk. Because midnight and noon are experienced at the same time on opposite sides of the world (e.g., Venezuela and Borneo), the sun must make some sort of circuit over the disk taking 24 hours to complete a loop, alternating which side it’s on every 12 hours.

Where is this track? Well, it would need to vary seasonally, of course. At the equinoxes, it is easy to experience/confirm the fact that the sun travels directly overhead at all points around what Round-Earthers call the “equator.” In the Flat Earth model, this would be a circle centered around the north pole roughly 10,000 km in radius.

On the solstices, the sun passes overhead all along the Tropics of Cancer and Capricorn: what Round-Earthers call latitudes ±23.5°. No problem, the racetrack circle shrinks to about 7,400 km in June and expands to 12,600 km in December. The math here is that 90 degrees of “latitude” translates to about 10,000 km, and just represents distance from the center of the disk: still an important/real construct.

Solar Height: Satisfying Eratosthenes

Having defined the ground-track path of the sun, the last step is to establish a height for the sun above the disk. Over 2,000 years ago, a dude named Eratosthenes measured Earth’s circumference by using shadow lengths on the same day for positions separated in “latitude.” The simplified idea is that if the sun is directly overhead in some place (only happens in the tropics), the shadow of a vertical pole has zero length, but a pole one degree to the north on a round Earth would be tilted relative to the first by one degree, and would thus sport a shadow whose length is the height of the pole times the tangent of one degree (0.0175). From this observation and measurement of the distance between poles, it is possible to calculate a circumference for Earth—assuming a very distant sun. The technique also works for arbitrary locations, just requiring more trigonometry.

Pole and shadow geometry for a round Earth / distant sun (left) and flat Earth / near sun (right); angles exaggerated for better visibility.

For our Flat Earth: no problem (sort-of): just set the height of the sun off the disk so that a pole one-ninetieth of the 10,000 km pole-to-equator distance north of the first pole casts a one-degree shadow at the same moment. If we denote the equatorial radius as R (~10,000 km), the height becomes 2R/π, or about 6,370 km (awkwardly the round-earth radius, by no coincidence).

Excellent: now we have a fully-defined geometry for solar motion. We’re sciencing!

Implications: No Sunset

We get our first big oops, here. Maybe you saw it coming well in advance, just by glancing at the banner image. In this geometry, the circular track of the sun in the sky satisfies the observations of the overhead-noon-sun in the correct places, and can even account properly for seasonal variations and noon shadow lengths in a band not too far from the sub-sun path. That’s a feat, but there’s more to a day than noon.

Following such a racetrack, the sun never dips below the horizon, or even deigns to get very close. If the sun went below the disk, the entire planet (top-side) would be cast into darkness at once—counter to what we observe so that Flat-Earthers don’t allow this to happen in their mental model.

As seen from the north pole, the equinox sun would ride 32.5° up in the sky all day, rather than the full-circle horizon-skimming motion actually witnessed. At winter solstice, when the north pole endures a months-long dark period, the Flat-Earth sun would still be 27° high in the sky 24/7. Just pretend you don’t see it, or that its light is not beaming toward you, allowing the stars to burst out (the sun’s brightness being suppressed to less than a trillionth its normal radiance, somehow).

At a mid-northern latitude of 35° (like my hometown of Chattanooga), the noon sun would work out reasonably well at summer solstice based on our Eratosthenes-satisfying height, but would be 4° too high at the equinox and 13° too high in December. Far worse, though, is that the midnight sun would be 22° above the northern horizon (29° in summer; 19° in winter). Never a sunset. Oh dear: I’ve seen those!

If the “spotlighting” effect is sufficiently narrow to have the sun go dark at these midnight elevations, then presumably we’d never see the sun when it’s below about 20°. Yet, we do—daily…and brightly.

Fixing Sunset?

Based on the fact that we’ve all seen the sun descend to touch the horizon, what would it take to require the setting sun to get within a quarter-degree of the horizon (half it’s apparent diameter so its bottom edge can touch the horizon, as we know it can)?

Preserving the racetrack path that satisfies 24-hour cycles and high-noon over the appropriate places on Earth, we must lower the sun’s height over the disk to get it low in the sky around the time of sunset. How low? On the equinox track, we would require it to be approximately 50 km up in order for the “setting” sun to get so close to the horizon.

The math, for what it’s worth, is based on where the sun is on the racetrack 6 hours past local noon (at equinox) appearing 1/4° above the horizon from a “latitude” of 35°.

Vrooooom!

We got our sunsets back (sort-of: see silly path graphic below). But at what cost? A sun on a 24-hour schedule around a 10,000-km-radius racetrack moves at 0.73 km/s. If passing overhead 50 km off-the-deck, the zenith angular rate would be about 0.82 degrees per second, which is about 200 times faster than observed—making shadows swing around as if in time-lapse. If overhead at 12:00:00, it would be above 45° elevation angle for only a few minutes: from 11:58:50 to 12:01:10. Don’t bother with the sunscreen. Sun’s got a date in Borneo!

A sun at this height would be above 5 degrees for only 0.2% of Earth’s surface at a time (less than 0.1% for the Flat-Earth disk area, which is larger than the round surface by a factor of pi-over-two-squared: good news for southern real estate!). Anyone farther than 2.5 degrees (280 km) from the sub-sun racetrack latitude would never see the sun more than 10° over the horizon, even in summer. That’s basically the entire U.S. (anything north of 26° latitude). We broke daytime, all so that we could get the sun to flirt with the horizon!

Angular Size

It’s not terribly challenging to confirm that the sun extends approximately half-a-degree on the sky (no matter where in the sky). At our Eratosthenes height of 6,370 km, this would make it about 56 km in diameter. Hey: don’t judge. For our horizon-visiting height, we’re talking 445 meters across to present half-a-degree when straight overhead. Either way, the geometry works out so that if the sun is at constant height over the disk (required for overhead noon observations to all report similar angular size), then when the sun is at 45° above the horizon, it would only appear 70% its customary size, or 0.35° across. At 30° elevation, it’s half the normal size. By the time we let it get down to a quarter-of-a-degree off the horizon, it would be a mere 0.0022° across, or 8 arcseconds (Jupiter and Venus and Saturn are bigger than this in the sky).

Does this sound like the sunsets you’ve enjoyed—a tiny star-like dot just above the horizon, never visibly setting? Didn’t think so.

Graphics

Below is a comparison for two different models of the sun’s apparent trajectory in the sky approaching “sunset” on the equinox, for “latitude” 35 degrees north. The sequence starts three hours after local noon, in 30-minute increments up until 6 hours after noon, when we observe the sun to set, due west. One shows the appearance of a very distant (but correspondingly large) sun in a rotating (round) Earth model, while the other shows the Flat-Earth racetrack at a height satisfying Eratosthenes for the same times. Sizes are exaggerated for all cases by about 3× for better visibility, but notice the small and diminishing size of the Flat-Earth track, and most importantly its refusal to set just before darkness mysteriously kicks in.

These paths are not at all hard to differentiate, even without measurement tools. Now compare to a photo sequence of a sunrise (reflected horizontally to be oriented like my sunset graphic) at a latitude of 43° (Also, it’s worth looking at a gallery of such images).

What sunset looks like for 43° north, bee-lining to the horizon (LynceanEducation; Wikimedia Commons).

Note that the path is a pretty straight line toward the horizon, and that the size is not changing. [I attribute the darker low-elevation instances to a constant exposure time through a dense filter and more atmosphere. The horizon shot removed the filter to get the bright apparition and expose the horizon bathed in sunset colors.]

Most of us have noticed the sun setting due west (or rising due east) around the time of the equinox—especially if driving on streets aligned to the cardinal directions. Many are observant enough to notice the sun rising and setting well to the north of the east–west line in northern-hemisphere summer and well-south of the line in winter. The Flat-Earth sun refuses to comply. In fact, the next plot shows the all-sky view of trajectories and relative sizes at the equinox (again in 30-minute steps; the previous plot is a subset of these exact same positions). One refuses to set, traveling to the north and getting very small (sizes now exaggerated about 10× for better visibility).

All-sky view showing the solar path for three models (round, plus flat at two solar heights).

The FE folks would say the “spotlight” effect makes the sun invisible to us when it’s on the far side of the disk, but one would still never see a sunset, or even the sun close to the horizon! And somehow whatever the sun is doing when far away, its light must be suppressed by at least a factor of a trillion for it to be outshone by the stars. That’s some impressive spotlighting! It’s not sufficient to make an artistic rendering like the banner image. Making the sun effectively invisible while still high in the sky is no joke.

The oddball blob to the south in the polar plot is a “dummy” case of a 50 km-high sun that I contrived to coast “high” in the sky for our test latitude (and made even larger, 15×, to better see the next bit). Looking closely toward the eastern and western horizons, you’ll also see very small—and diminishing—dots trailing toward the north, still at a 30 minute cadence. One would experience a brief flash of daylight lasting less than an hour, then a tiny sun hugging the horizon the rest of the time. Most regions of the planet would not be lucky enough to receive an overhead pass, and would experience a perpetual dim state during which a tiny sun clings to the horizon. That’s no way to live.

Stars

Another easy test: Polaris happens to be very close to the celestial north pole, which means it is basically straight overhead when standing on the north pole (in winter when the sun is—ahem—below the horizon and the sky is dark). It is easy to confirm for those living north of the equator that the angle up to Polaris from the horizon matches your latitude: something I have personally verified across a broad swath of latitudes. At the equator, it’s on the horizon. At “southern” latitudes, it isn’t visible at all, but the undistorted constellation of Ursa Minor and other surrounding asterisms on the northern horizon will point to where it would be, below the horizon, if not straying too far south.

In the Flat-Earth “model,” if stars are “far” then Polaris is straight up no matter where on the disk one goes (easily falsified). If situated lower, it will appear to descend as one travels farther from the pole—as should be the case. But it won’t somehow be on the horizon at the “equator,” and will never creep below the horizon (unless it becomes invisible to all on the flat surface, simultaneously). That would be some news!

Also, if not very, very far away, constellations would become highly distorted as they moved across the sky and toward the horizon, yet we do not witness such behavior and photo-evidence of squeezed constellations is utterly lacking.

Refraction to the Rescue?

Can we somehow fix this mess with refraction? The phenomenon actually goes the other way, making the situation even worse for the Flat-Earth case. Refraction responds to the refractive index of a medium, whose deviation from 1.0000000 (as in vacuum) is proportional to density for a medium like air. Density is proportional to pressure divided by temperature (in absolute scale like Kelvin). Both tend to change with height (climb a mountain and measure for yourself!). We know that the vertical pressure gradient at the surface is always decreasing at approximately −14% per kilometer, while temperature tends to change more modestly (and variably), decreasing by up to −4% (in Kelvin) per kilometer. Because one is in the numerator and the other in the denominator in computing density, these usually cancel somewhat, but pressure always wins. Sometimes a temperature inversion sets up, which serves to amplify the refractive effect on top of what pressure alone does.

The effect is to curve rays down: the opposite of a mirage over hot pavement. Distant objects therefore appear to be higher than they really are. What follows applies to the limiting case of the dry adiabatic lapse rate (steepest temperature profile, in practice), which serves to minimize the effect. Generally, it will be even more pronounced than what I show here. Below is a plot showing raytrace trajectories for light in a density profile decreasing exponentially with height (as observed). The vertical axis is exaggerated by about 300× in order to make out anything at all. Launch angles correspond to 0.25, 0.50, 0.75, 1.0, 1.25, 1.30, 1.33, 1.34, 1.35, and 1.36 degrees above horizontal (the first one is all-but invisible, making it “only” 200 km downrange).

Raytrace trajectories of light refracted by the density gradient in our atmosphere, for a flat geometry (vertically-exaggerated by 300×).

Once above 1.35 degrees, rays “escape” toward infinity. But short of this, sight-lines curve back down toward the Flat Earth. The effect would be the appearance that the ground curves up at its edge, like the lip of a plate! It’s not subtle, either, crawling up to almost three (normal) sun-heights over the horizon! The first degree over the horizon (two sun-heights) catches all terrain within 2,000 km, the rest of the great expanse being progressively squeezed toward a “vanishing line” 1.35 degrees up. Sure: limits to atmospheric transmission would suppress visibility, and intervening air would take on a blue-sky appearance in daytime. But at night! The sparkle of distant cities would become apparent as stationary ground-hugging constellations—the likes of which we’ve never seen, importantly. At midnight, the sunlit side of the planet would shimmer above the northern horizon. Are the Flat-Earther’s even looking for such phenomena? Attenuation is not as serious as it might seem from the distances in the plot, since most of the distant trajectories lie well above the troposphere where attenuation is most pronounced.

Incidentally, the curvature of the low-angle trajectories is about one-sixth that of the round earth (six times the radius), so that the ground falls away far more rapidly than the light curves, resulting in a crisp, local horizon (which is a smidge farther than it would be without refraction).

Hoh boy!

I really could go on and on, as every investigative line opens up a gaping gulf of disconnect between observation and (terribly flawed) “theory.” I suppose a determined Flat-Earther could contrive all sorts of funky effects and twists to bat down one thing at a time (but not in a self-consistent all-hang-together sort of way: just a pile of distracting incoherent “fixes”). Any theory would simultaneously have to nail (to high precision, not just casual glance) the following observations, among many more:

  1. The (solar) experience of a day needs to be the same on a given date for all people at the same “latitude” (distance from north pole) throughout the world.
  2. The non-tiny sun must be able to at least touch the horizon, as we’ve all seen it do.
  3. The angular width of the sun can’t change appreciably (even by 0.02%) across the sky on a given day, aside from a refractive vertical “scrunching” near the horizon.
  4. Likewise, constellations wheel overhead, rising and setting without noticeable distortion, in the same manner for same-latitudes, with north and south poles sharing no stars in common (other than some refracted “bonus” overlap within ~0.5° of the horizon).
  5. A distant flat horizon is crisp rather than curving up and fading: lights from all the cities within thousands of kilometers are not made visible by refraction. The daylight side of the world is not shimmering on the northern horizon.

But can you guess what makes all these myriad observations and more come together without weirdness? Allow Earth to assume a spherical shape—as gravity forces any hunk of rock bigger than a few hundred kilometers to do anyway. We get sunsets back; ships disappear over the horizon rather than curving up while remaining in sight; stars make sense; and constellations don’t scrunch as they get lower in the sky. It’s really a tidy explanation for so much of what we actually witness!

A lesson for me is that these people pay too much attention to their brain chatter and not enough to the actual universe full of sunsets and stars. We could all learn from this: consult the actual universe, not what you would wish to be true. That latter tendency is almost universal: not at all confined to a fringe group. Whether it’s belief that renewable energy will save us, that modernity can in principle continue for thousands of years, or that we’ll colonize space, false beliefs are quite common in our culture. The Flat-Earthers might actually teach us something of immense value, after all.

Note: If you haven’t seen the documentary Behind the Curve, I recommend it—offering a fascinating window into psychology, belonging, and our ability to preserve beliefs in the face of countervailing evidence.

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19 thoughts on “A Theory Gone Flat

  1. To borrow from Winston Churchill, language is the worst form of communication, except for all the others. (What others?) It is not possible to determine what is going on in the head/brain/mind/mindbody of another person. So when someone, Bob, says 'I believe the earth is flat,' there is no way for me to be certain that what I mean when I say 'I believe…' is the same as what Bob means. (Certainly I can make some assumptions…for instance, I assume that Bob is a person.) It is also impossible to determine what might constitute 'proof' to Bob, or what Bob's motivation might be for 'believing' that the earth is flat.

    At the end of the day, all I can reliably do (and not quite so reliably as I used to think, considering recent events in the news) is avoid getting shot by Bob, given our disagreement on the shape of the earth.

    • For language to 'work' at all, words have to have commonly accepted meanings. Words such as "believe", "Earth" and "flat". So when someone says they believe the Earth is flat, it is quite clear what they mean.
      No reasonable person believes the Earth is flat.
      Fear of getting shot does not alter the truth (that the Earth is not flat).

      • James, that is exactly what I mean. "For language to 'work' at all…" Which is why, I contend, language 'works' so rarely. When you have two (or more) people who DO have commonly accepted meanings for words, then language CAN work…at least within the confines of those commonly accepted meanings.

        You say "No reasonable person believes the Earth is flat." In which case, with your 'commonly accepted meaning' of the word 'reasonable,' anyone who believes the earth is flat is, by definition, 'unreasonable.' Of course, the Flat Earthers will say you are unreasonable. Who has the biggest gun?

        • I suppose your point is that whoever is in the majority 'wins' the argument. Still, the idea of the Earth being flat clearly does not stand to reason, whatever any human says or believes, or whoever has the biggest or the most guns.

          Although, probably due to propaganda, Criminal Columbus is often credited with 'discovering' the Earth's shape, it was known since at least ancient Greece (and probably long before then, just no one wrote it down). I sometimes wonder if the original flat-Earth story came from the 'authorities' of the time and people just accepted it.

  2. You missed the most obvious observation: Basic curved Riemannian geometry! Pick any point not on the equator and any bearing not due north or south. Now walk on a geodesic and you will quickly observe your path is deflected from every map grid. This is a practical example of the "vector carrying" definition of curvature.

    You can demonstrate this with laser surveyor equipment on a relatively modest scale. You can easily setup an experiment that shows the angle of a triangle on Earths surface add up to more than pi! Or equivalently that the circumference of a circle inscribed on Earth is less than 2 pi times the radius, because the radius is deflected.

  3. I actually briefly worked with a flat-earther who had also fallen down the Q-Anon rabbit hole. He would go on for hours about how the Queen of England was pulling all the strings and was basically the Anti-Christ. He was upset about how his (now adult) daughter refused to have any contact with him after he beat her in a godly way, like the Bible told him to. At some point, a few years prior, he had been a biology teacher who taught kids about the scientific method, I'm not sure exactly how he got from point A to B. Then there was the millionaire company owner who told me that there was no need to worry about fossil fuel depletion because they are being replenished by tectonic plates and climate change is a hoax. Then the tech guy of that same company was convinced that he had solved nuclear fusion with a hydrogen fuel cell that he melted, and would tell me about the ancient nuclear wars that occured in Jodhpur, as well as the magic healing properties of triangles, among other things. – I am not making any of this up.

    When I was growing up, my step-father had dementia and was extremely irrational. I resonate with learning how to think by observing how not to think. He also believed in the Illuminati, that he was a prophet from God, and had some uncontrollable anger problems, it wasn't a great time for me. I later learned that in the DSM, dementia is defined as 'a disease of the organic brain', so there was something physically wrong with my step-father's brain. That helped me let go of some things. However, today, I feel like I am encountering demented people continually.

    I am reminded of how animals are sometimes driven insane by captivity, such as can happen at zoos, taken out of their natural context. We've done this to ourselves, creating a society that is structurally crazy-making, even at the Marvin Harris infrastructure level. Modernity provides a million and one ways to be confused about reality, the majority of people seem to fall into that vortex of confusion somewhere.

  4. I hope and pray (well, just hope really) that you weren't inspired to write this because you have a close friend or relative who subscribes to the Flat Earth model. If you do, you'll quickly learn that arguments like this will not work. This is because they involve math(s) which they will probably not understand and will definitely not trust. I challenge you to provide a proof that the flat earth model is incorrect which can be understood by someone who is not willing to work through any mathematics, or to trust in any authority, or to travel beyond their back yard.

    • You are probably correct, but if their back yard has a view to the east or west, and they can make a tabletop model (even in their head) of the track of the sun, they'll see that it can't go the horizon unless skimming the surface (in which case most places are dark) or it's not noon anywhere on earth. The math is a bonus, but the basic layout creates severe problems that aren't very hard to picture.

      • I made a video for my flat earther brother in law where I used a globe, with a small plasticine sundial, and a torch to represent the sun, to trace out the round earth prediction for the path of the shadow. Then I used the exact same globe and sundial the next day to confirm the prediction. I thought this could work, as it required zero maths and could be reproduced by anyone anywhere. The response I got back was pages and pages of gobbledygook. There's no winning this argument. Btw, here's my video https://dorkscratchings.blogspot.com/2019/07/earth-not-flat.html

  5. @AlexZ:

    "How easy it is to make people believe a lie, and how hard it is to undo that work again!" was the actual Mark Twain quote, often phrased: "It's easier to fool someone than convince them that they've been fooled."

    Part of the trouble is, to convince someone that they've been fooled, you must convince them that they were foolish to believe such nonsense in the first place, the human ego resists this. It gets worse when the lie that they believe has become part of their identity or is connected to their social fitness within their in-group, even extending to their success within modern society. Another factor, perhaps boosted by the culture of human supremacy, is that one often finds the perspective that the world is the way that people wish it to be. And I also wonder about the gluttonous ease with which fossil fuels have enabled survival, whether humans have commonly developed psychologies unfit for survival. And no doubt there are myriad other psychological factors. – After all, a sixth mass extinction and being in the red-zone in seven out of nine planetary boundaries are serious situations, and widespread awareness should be the norm, yet how many people are talking about these issues or even know about them?

    I've tried arguing with people against irrational perspectives many times and have had a very low success rate. It's often when I get a little traction in demonstrating the fallacy of an idea, when the cognitive dissonance starts to seep in, that people avoid talking to me further. – On the flip side, my success rate at being thought of as an obtuse argumentative jerk must be pretty high.

    Since part of the phenomenon of collapse ties to irrational thinking and beliefs, akin to mass-psychosis, the voice of reason becomes muted and rare. I suspect that this situation will only get worse as things progress.

  6. Another easy observation: If one accepts (as I believe FE folks do) that the moon is a sphere illuminated by the sun, then the outer, illuminated edge (limb) points toward the sun—across a great circle path. You can confirm this any time you see both the moon and sun in the sky at the same time (it happens). Or try it with a plain ball in the sun to get the illumination geometry down. Often, we see that outer-edge curve pointing down, placing the sun below the horizon (in which case the entire FE disk would be in darkness all at once, counter to daily evidence). Think about a crescent cupping upward: the outer/full curve points down.

    If the moon followed a racetrack above a disk earth similar to that of the sun (as in banner image), the outer/smooth curve would never somehow point to a position below the horizon if the sun is also on the racetrack (however spotlighted it might be). Also, full moon geometry would never obtain if both are on the elevated racetrack, as the observer needs to be between moon and sun for that to happen, not below on a different plane.

  7. "Rather than denigrating the people who subscribe to Flat-Earth beliefs, I’ll focus on observation."

    Nope. We need to denigrate stupid people. After all, the stupid people have been denigrating smart people in general and intellectuals specifically since the US was invented. Check out Richard Hofstadter's Anti-Intellectualism in American Life (1963) sometime. The Long Read
    in The Guardian today (October 2nd) is about the sheer stupidity of the Trump Administration and approaches it via Hannah Arendt. A little too academic perhaps but stupid people really are a major problem when they inherit money and power.

    • "Only two things are infinite, the universe and human stupidity, and I'm not sure about the former." – Einstein. Even geniuses can be stupid at times, though fossil fuels have enabled the intellectually subpar to breed relentlessly, so perhaps there is something to suggesting that 'Idiocracy' was in fact a documentary.

      I'd argue it comes down to scale. Humans are a branch on the tree of life and not the trunk. Our brains are closer to squirrel-brains than god-brains, we have no business pretending that we can manage planetary systems that are orders of magnitude beyond our comprehension. It would have been 'smart' to stay in our lane. (If such a thing were possible.)

  8. We all inhabit the same reality in the sense that we are all made of matter, including our minds. However, in another sense, we humans certainly do seem to be capable of occupying vastly different "realities" to each other, as evidenced by clear "outliers" such as the flat earthers.
    I guess this is because our minds (streams of consciousness) essentially equate to almost real-time models of reality, themselves created by the "stuff" of true reality, i.e. matter (presuming you take materialism/physicalism seriously). None of us experiences reality directly and our individual models (minds) differ from one another, being "centered" differently, and continually updated in different ways based on unique combinations of real-time sensory input, memory, and beliefs based on past experiences. Our minds do not occupy different
    "realities" as such, rather they correspond to (actually *are*) unique "alternate realities" (though many of these "realities"/models share a lot in common).
    Some human's minds/models certainly seem to be more receptive to being updated with scientific data, whilst others are more resistant… I guess there are all sorts of reasons for why this might be so.
    Many people desperately want to be part of a tribe, as you alluded to Tom. Fair enough. In some sense, belief in a flat earth alone might be shrugged off as a pretty harmless/benign thing, since (under most circumstances) it is not really a matter of life or death. A (non-hostile) tribe believing in a flat earth could/should all be fine and dandy. Sadly, there are huge numbers of dodgy operators that will happily exploit tribal desires in nefarious ways these days. There's also certainly money to be made in generating outrage between groups of people, and social media is now optimized to channel belief in one "nutty"/conspiracy theory into belief in many. Manufactured rage and getting people up in each others' grills is all the go!
    I will say/agree that believing in a flat earth (on its own) certainly seems no less balmy, and a whole lot less dangerous, than believing that infinite accelerating growth is possible on a finite planet (hopefully this does not lead some idiot to assert that the earth is, in fact, flat without end!).
    From the perspective of an individual human wanting themselves and their offspring to persist as long as possible, the best models of reality must surely be the ones that stress respect for the world/cosmos from which we emerged, and the need to maintain our finite environment in a habitable state. This does not necessarily mean that our "realities" must include all the physical facts about the world we live in. However, for us modernites there is obviously a way overdue need for more of us to accept obvious physical realities about the Earth and its limits, and to incorporate these facts into our individual "alternate realities".
    (Hardcore idealists will object that mind/consciousness is not a model of reality, and instead claim that the physical world is entirely a creation of the mind. The fully committed solipsist (there can only be one!) will go even further and claim that everything is a creation of only their mind. I go along with others that believe that these stances correspond to models of reality that have managed to fool themselves into thinking they are themselves the true reality…).

    • 'This does not necessarily mean that our "realities" must include all the physical facts about the world we live in.'

      And they can't possibly. I think it's important to recognize that our mental models will always come up short, but also agree that the degree of compatibility to ecological relationships varies substantially among the models—and that we're better off steering clear of the destructive ones (i.e., human supremacist modernity models that pervade).

      • Thank Tom, agreed. Humility (coupled with a sense of awe of the universe) is key, as you stress often. Whilst it is an amazingly impressive feat that evolution has been able deliver creatures that are able to generate two types of models of reality – “lived” ones (minds) and abstract ones (theoretical models) – we should always remain acutely aware that our modelling capabilities are extremely limited and incapable of accessing/fathoming/processing the full complexity of the universe and the true nature of reality. In the cases where we have been able to receive unambiguous answers to our questions about the universe/reality through the process of careful observation, we should also be “humble” enough to accept the answers (e.g. the earth is round!).
        An article on humility that appeared this morning:
        https://www.theguardian.com/commentisfree/2025/oct/06/positive-thinking-can-make-success-feel-like-the-only-acceptable-option-but-humility-allows-for-grace
        The final few paragraphs interested me most – about living “aligned to the flow of creation”, and how “taking a position of humility, of not-knowing, allows us to remember our species is a part of a larger whole”. Rebecca Gigg’s book “Fathoms:
        the world in the whale” sounds interesting from the link.

  9. Tom,
    Thanks for the various examples of observations that easily disprove the flat earth hypothesis. However, I don’t think its proponents really believe in it. I think they are trying to create an alternative social hierarchy where their status is higher. I recently read, “ Status and Culture: How Our Desire for Social Rank Creates Taste, Identity, Art, Fashion, and Constant Change” by W. David Marx. Folks who feel outside of or threatened by the current social order try to create alternatives where they are more important. Holding extreme views helps to bond those in the alternative order tightly together. I think it’s important to counter these ideas but one on one debate is useless, just put the evidence out there and don’t directly engage.
    Best

    • This sounds right to me. Or, at least I can believe it applies to a number of the proponents. The same phenomenon can be seen in political wings: in some cases it seems the more extreme the belief, the more power it has to define the club.

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