Mathematical Imagery by Jos Leys

Flat Earth Nonsense

There are about 5 million films on YouTube on the subject of 'flat Earth'. All the claims of this crazy flat Earth doctrine can be very easily refuted...


1. The flat Earth 'movement'.

Enter "flat Earth" as a search term in YouTube, and you will get about 5 million hits.The majority of these films are lame attempts to convince the gullible that our world is actually flat. There is another category of films that debunk the flat Earth with a variety of arguments. The trouble is that the flat Earth 'community' does not listen to any of these arguments.
The shape of the Earth has intrigued scientists throughout history. The general acceptance of the fact that the Earth is round came about in the first century A.D., although Pythagoras had already postulated a spherical Earth 600 years earlier. The flat Earth concept resurfaced now and again in the Middle Ages, sometimes on religous grounds, but it is safe to say that mankind has known for 2000 years that we live on a sphere.

It has surfaced again quite recently, and now we have YouTube and other social media that reach many more people!

2. The flat Earth 'doctrine'

Here is the doctrine in a nutshell. There are of course slight variations, depending on the 'source', but in general, flat Earthers agree on the following:
(You are probably going to be as shocked as I was when I saw all this nonsense for the first time.)

1. A map of the Earth looks like this.
The Earth is a circular disc, surrounded by an ice wall at Antarctica.
This means of course that distances in what we call the southern hemisphere are wildly exaggerated, causing the speed of commercial aircraft to have to necessarily exceed the speed of sound in order to cover a flight like Sydney-Santiago in about 15 hours!

2. There is a worlwide conspiracy by 'the powers that be' to keep this information from us. We have been lied to all the time.
3. Depending on the source there is a glass-like dome over the entire flat Earth. (the "firmament") The fact that we sometimes get hit by meteorites is usually conveniently ignored.
4. The sun and the moon are very small, in fact about the same size, and move on circular paths, not very high ( 3000 km ?) above the flat Earth. The sun completes one revolution per day on circles that move between the tropics throughout the year.( note: the tropics and the equator are circles on the flat Earth).There is no real explanation on what force is holding the sun and the moon up.
5. Permanent summer sunlight and permanent darkness inside the north Arctic circle is acknowledged, but there is no such thing below the south Arctic circle. ("No permanent daylight on Antarctica")
6. There is no such thing as 'space'. We have never been to the moon. Satellites don't exist, including the ISS. Pictures from Earth taken from orbit are all fake, photoshopped by NASA.
7. There is no curvature of the Earth. Ships disappearing hull-first on the horizon can be brought back into view with the proper telescope.
8. Gravity does not exist ("it's just a theory"). The fact that we can keep our feet firmly on the ground is explained by 'density': just as things that are "denser" (sic!) than water will sink, we stay on the ground because we are denser than air.
9. The Earth is fixed and immobile. If it were a spinning globe, the water in the seas would fly off like water flying off a wet spinning tennis ball.
10. For some of the flat Earth believers, all of the above must be true as they somehow read this in their Bible or Quran. (Although all apps and websites that help Muslims find the Qibla, the direction towards Mecca for their daily prayers, are based on a spherical Earth: they calculate the great circles between any location on Earth and Mecca)
11. Some other : there is no such thing as a Coriolis force. Things like the Aurora Borealis are conveniently ignored. The moon gives off its own light, it is not a reflection of the sun's light!....and I have probably forgotten to mention some more wild claims from flat Earth believers...

3. Some simple demonstrations.

My demonstrations are "ex absurdum" : let's assume for a moment that the Earth is indeed a circular disc, and let's see what this leads to, based on everyday observations that anyone can do.
Let's start with the flat Earth map. It seems to me that somebody once came across an Equidistant Azimuthal Projection of the Earth, and thought that this was the real thing! This map is indeed a legitimate projection of the spherical Earth, but that is all it is: a projection. This is shown in this short film:

Next, let's look at sunlight. We know for each moment during the year where there is sunlight on Earth, and where it is night. We can draw this on the flat Earth map to show the resulting patterns of sunlight and darkness. It turns out that the flat Earth sun has to perform some impossible acrobatics to generate these patterns. A sun with a magical giant lampshade is needed, as shown in this film :

There are two moments in the year when the sun is right above the equator: around March 20 and Sepember 20. These are the equinoxes. At these moments, all over Earth, the sun rises exactly due East, and sets exactly due West. Barring some adjustments for the definitions of dawn and dusk, day and night are equal at 12 hours each. The next film shows that this is an impossibility on a flat Earth as the position of the sun becomes completely ambigious :

The equinoxes are probably the simplest to explain ( it seems that it is still too difficult for flat Earth believers, who seem in general to have no clues about simple geometry.) The ambiguity of the sun's position on a hypothetical flat Earth can be shown at any time of the year, but in the next two films I chose the summer solstice (when the sun is above the Tropic of Cancer) and the winter solstice (when the sun is above the Tropic of Capricorn). In both cases it would turn out that the sun is somewhere different for observers in different locations. The data on the sun's heading used in the films can be verified by anyone. is a good reference.

Even without a film like this, this should be clear. At any time of the year, everywhere on Earth where the sun is just coming up over the horizon, or just going down, the heading towards the sun is a line that on a flat Earth would be in the plane of said flat Earth. So how can the sun be 3000 km up between the tropics? (Moreover, except at the equinoxes, the sun's heading would be different for all locations, and these headings do not even intersect in a single point.)

I made three more movies to make the point that if one plots the headings towards the sun on a flat plane, the position of the sun becomes ambiguous. The first of these uses the so-called Gleason map.

The second is a bit more spectacular, but makes the same point. I called it "Funeral March for Flat Earth".

The third is a HD version, but again makes the same point. I called it "Requiem for Flat Earth".

The headings towards the Moon make no sense either on a flat Earth. Watch "The Moon confirms flat Earth's demise".

The shortest distance between points on the spherical Earth is measured along great circles.These distances cannot be plotted on a flat plane as the following film shows.

One of the easiest ways to debunk flat Earth is probably looking at the positions of the celestial poles. In the northern hemisphere, the angle with the horizontal of the pole star (Polaris) is equal to the latitude of the observer. The same is true in the southern hemisphere, looking at the south celestial pole (Sigma Octantis). This makes no sense on a flat Earth. Watch "No star trails on flat Earth".

Finally, flat Earthers always come up with their question : "Show us the curve!". One has indeed to go very far up to see a curved horizon. However ordinary aerial photography can reveal a curve also. Parallel lines that run towards the horizon appear to converge in a vanishing point that is on the horizon, provided these parallel lines are on a infinite plane. On a large sphere, these vanishing points will be above the horizon, as the terrain drops down in the distance due to Earths curvature. See the picture below, and the film "The curve hidden in plain flat Earth".

4. Conclusion.

I said what I wanted to say. I realise, from the comments on my films on YouTube by flat Earth believers, that what I'm showing here does not make the slightest difference to them. Not one have them has come back with some remotely reasonable argument.
So I give up.
It was fun making the above videos: debunking flat Earth is so easy! The sad thing is that it is not going to change anything. Every day there is a bunch of new videos on YT by these flat Earth zealots.

I'm going to spend my time on things that are more interesting...


Copyright 2024 Jos Leys