Flat Earthers or the Case of the Casual Scientist

Introduction

The Flat Earth Movement, inconsequential and absurd as it is, is nevertheless very interesting from a scientific analysis perspective.

It seems to be a consequence of several causes:

1. Misunderstanding or lack of knowledge of the scientific method
2. Misuse of critical thinking
3. Confusion between the concepts of hypothesis and theory
4. Logical fallacy
5. Exacerbated individualism

In this article we will cover these items and how they lead to such false concepts.

We will also show how a number of the arguments proposed by flat earhers can be debunked with some analysis of the proposals.

The Misunderstood Scientific Method

The scientific method started in the 17th century with Rene Descartes, Francis Bacon and Isaac Newton and has been evolving since then.

In its modern form it is comprised of 7 steps:

1. Question: the question we want to answer
2. Research: collect information about what is already known about the question
3. Hypothesis: provide an answer to the question and make predictions based on the hypothesis
4. Experiments: execute experiments — if possible — to verify the hypothesis
5. Observation: collect the data from the experiments or passively from the environment if experiments are not possible
6. Conclusion: determine if the hypothesis is correct or not
7. Communicate: publish the results

One can add other steps here: peer review, reproduction of the results by parties not involved in the original experiment, statistical significance of results etc. since the scientific method is not immune to cognitive biases (the current list of cognitive biases has 124 different types of them).

Before the scientific method became the norm for scientific research the Aristotelian method was the way to go; it lasted for almost 2000 years.

In its core the Aristotelian method prescribes that any general principle can be derived by passive observation of events and application of logic, in particular induction. For example, the statement that “people are mortal” is a generalization from the observation that some people die.

These concepts already allow us to see several issues with the ideas proposed by Flat Earthers:

1. Several cognitive biases, in particular ignoring or dismissing evidence that contradicts the flat earth hypothesis and selecting only observations that — at least apparently — confirm the hypothesis.
2. Proposing a hypothesis but not testing or verifying it via experimental data
3. Using a version of the Aristotelian approach — the Zetetic Method — where general principles are derived from passive observation of phenomena

Critical Thinking or Critical Believing?

Critical Thinking is the act of analyzing the information provided and make your own judgement instead of accepting it as true without questioning: don’t believe on everything you hear. It’s a sound advice.

Unfortunately critical thinking can easily be distorted: don’t believe on anything that contradicts your beliefs. Not so good.

Belief is a powerful force and difficult to deal with. Belief bias affects the best of us.

“God does not play dice with the Universe”, a famous quote from Einstein, incapable of accepting the evidence that quantum mechanics is inherently probabilistic and therefore allows for weird phenomena that should not be possible in a deterministic world.

It’s even harder for some to reconcile scientific discovery with religious beliefs. In these instances critical thinking becomes critical believing; one tries to find logical explanations for phenomena that fits their belief system.

I heard this one from a very religious classmate in Engineering college whom believed the Earth was only 6000-ish years old: “God buried fossils on Earth to test mankind’s faith”. Get it? In his view God buried a bunch of fossilized bones from animals that never existed, neatly distributed and stacked in geologic layers, tricking man into thinking the Earth is very old but expecting mankind to reject that evidence in favor of a literal interpretation of the Bible.

It is just a theory

I’m sure we all heard that before in different contexts.

This stems from a confusion on how the term theory is used by different branches of science. For example, Physics is more or less grouped in theoretical (folks that do the math) and applied (folks that test the math).

In mathematics — an inherently abstract science — there are axioms, theorems, corollaries, conjectures and theories.

In Sociology most of the explanations for human and social behaviors are called theories.

So it is understandable that people without higher scientific training can be confused.

In general, a theory is the conclusion of following the scientific method steps described above.

Theories are always incomplete and ephemeral. Newton’s Theory of Gravity was replaced by Einstein’s General Relativity when it could not explain certain observed phenomena. The current version of the Theory of Evolution has changed quite a bit from the original one proposed by Darwin. These are considered — albeit incomplete — theories because they make predictions that have been confirmed by observations/experiments over the years and no experiments were found — yet — that contradict their predictions.

A good example of a hypothesis that is not a theory is the existence of dark matter, used as explanation for the movement of stars at the edge of galaxies. It’s not a theory because dark matter is yet to be detected.

So the Theory of a Flat Earth is not really a theory; it is a hypothesis. For it to become a theory one must:

1. Show how it explains objective phenomena that cannot be explained otherwise
2. Make predictions based on such hypothesis that can be verified experimentally

To close this section, I’d like to emphasize the distinction between an incomplete theory and an incorrect theory. An incomplete theory is such that it cannot explain all phenomena. For example, Newton’s gravity can’t explain black holes or gravitational waves. Newton’s gravity is incomplete.

The Theory of Spontaneous Generation is incorrect. An experiment using a sterilized and closed jar did not develop any life. Same was the theory that malaria was cause by the “bad air” from swamps (mal air).

When it comes to science, one has to always keep Einstein’s words in mind:

No amount of experimentation can ever prove me right; a single experiment can prove me wrong.

The fallacy trap

Simply put, a logical fallacy is “(…)a flaw in the structure of a deductive argument which renders the argument invalid(…)”. It is very common in scientific research, in particular when trying to establish cause and effect relationships.

In logic, a one-way relationship can be stated like this:

if p then q is true then:
1. if p is true then q must be true
2. if q is false then p must be false
3. if q is true then p can be either true or false, a cause and effect relationship cannot be established
4. if q is false but p is true then we have a contradiction and there’s no cause/effect relationship

A two-way relationship can be stated like this:

if and only if p then q is true then:
1. if p is true then q is true
2. if p is false then q is false

So, when a fallacy occurs? For example when one assumes the condition p or q can be true when in reality they can never be or when a one-way statement is assumed to be a two-way statement.

Flat Earthers have several fallacies in their logic. Let’s take a look at one.

if and only if the Earth is flat then I cannot see Earth’s curvature from an airplane

Then I get into an airplane and, sure enough, verify I cannot see Earth’s curvature. Therefore, my conclusion is that the Earth is flat. Well, nope. The two-way statement in itself is incorrect and therefore the logical conclusion is also incorrect.

If we correctly rephrase this as a one-way relationship then condition 3 of one-way relationships informs us that not being able to see the Earth’s curvature does not say anything about the Earth’s being flat or not.

Let’s state the same idea in a different way:

if the Earth is not flat then I can see the Earth’s curvature

I hop again into a plane and since I can’t see Earth’s curvature this cause and effect relationship cannot be true; therefore the Earth is flat.

The fallacy here is assuming that it would be possible to see Earth’s curvature from an airplane; it’s not. Ever. Unless the airplane is flying much higher than the normal cruise altitude, it’s impossible to see Earth’s curvature with the naked eye. The statement is always false, regardless if the Earth is flat or not.

The statement ignores Earth’s size. It implicitly assumes that one can see the curvature of a sphere regardless of how big the sphere is and how far one is from it.

Another problem here is that this statement is not specific, objective, measurable and testable. “Be able to see the curvature” is too subjective and open to interpretation; a better statement would be “be able to measure a non-zero curvature at different points from the airplane using such and such instruments”.

We will revisit this topic later showing a better way of stating this relationship and reaching a logical conclusion.

My feeling is a fact

In more recent years, maybe as a consequence of the visibility and power provided by social media to individuals and, as we discussed above, a misunderstanding of critical thinking, many people started favoring personal opinions and views over data and facts.

Just look at this interview with Newt Gingrich, where he explicitly rejects the data that crime in the US is down and prefers to go with the feeling that it’s not.

This type of approach affects even seasoned researchers, when it’s not uncommon for scientists to be tempted with rejecting data contradictory to their hypothesis; imagine when it comes to laypeople.

This is very well represented in the Zetetic Method, which favors deriving conclusions directly from direct observations, without much regard if the observations and experiments are performed in a suitable way.

Now to the good stuff

We are now going to explicitly address some of the main statements used y Flat-Earthers to justify their ideas and see if they hold water.

1. There’s no such thing as gravity; the Earth is constantly accelerated by dark energy and therefore ewe get pushed down
2. Long-exposure photography is prove that the Earth is not round and spinning around its axis; if it were the stars would not show up as a circle around the North Star but instead would cross the sky in parallel lines; the only way stars would behave the way they do is if they were spinning around flat Earth
3. If the Earth was round, airplane pilots would have to constantly push the airplane nose down to follow the Earth’s curvature; since they don’t the Earth is flat.
4. If the Earth was round we could see the curvature from a plane (we’ll go into more details on this)

There are more but let’s focus on these since they are good examples of all the scientific issues we addressed in the previous sections.

There is no gravity

Yes, gravity is annoying. Einstein himself, when explaining his thought process for General Relativity, described that a person in an accelerated elevator with no windows would not be able to differentiate his experience and measurements from someone under the effects of gravity.

In General Relativity gravity is indeed not quite a force; it uses very complicated math to explain that we are actually in free fall through bent space-time and are just being pushed up by the ground.

With that said, replacing gravity with the idea that the Earth is constantly accelerated by dark energy has several problems:

1. Gravity is not an effect only for planets; every physical body with mass exerts a gravitational pull over another; that can be measured in laboratory, normally using a torsion scale
2. Dark energy is a hypothetical entity not yet verified to exist, used to explain why the Universe is expanding in an accelerated rate. If it exists it expands the entire space-time continuum, not individual planets and therefore it’d not create such acceleration effect
3. Even if the Earth was being accelerated at a rate of approximately 10 m/s², if we consider the planet is 4 billion years old, it would be travelling at a speed of 1.26e+18 m/s; this speed is 4.2 billion times faster than the speed of light which we know experimentally is not possible

This is a good example of several scientific biases:

1. Cherry picking the facts that agree with my proposal (the experience of gravity and acceleration are indistinguishable)
2. Ignoring other known facts that contradict my hypothesis (any object with a mass has gravity)
3. Using generic statements instead of precise ones (mathematical verification if an accelerated Earth is possible)
4. Using personal understanding of a concept as fact (using dark energy as the force behind Earth’s acceleration)

The proof is in the stars

The argument around long-exposure photography is easier to address. It is just a case of looking at an effect in a qualitative way instead of actually making the measurements and looking at the geometry of things, in particular the concept of parallax.

The image from the second star forms closer to point A when the camera is at the right and closer to point B when the camera is on the left

As it can be seen in the image, as Earth revolves around its axis, the camera is continually pointing to the North Star; the light from other stars hit the film at different points as the camera “spins” around with Earth, creating a path around the North Star. This effect is called parallax caused by the relative positions between objects.

it’s important to notice that the path is not quite a circle but is still a closed loop.

It’s also clear from the image that such image can only be obtained from the north hemisphere; the North Star is not visible from the south hemisphere. In a Flat Earth scenario it would be visible from everywhere on Earth.

The pilot dilemma

This one is actually quite complicated to dissect. It derives from a superficial understanding of how airplanes actually work. The math is also very complicated so we’ll try to simplify it as much as possible without compromising the analysis.

Before we start with the mathematical analysis, let’s take a look at the statement itself:

If the Earth was not flat, the pilot would have to continously “nose down” the aircraft; since they do not do that he Earth must be flat

This statement that pilots do not make flight corrections is false. Either manually or via automatic pilot the altitude and attitude of an aircraft is always being corrected; the same way a driver in a car makes small corrections to keep the vehicle inside the lane.

Now, to the fun part.

a) airplane with all forces aligned and balanced; b) airplane moved to an hypothetical higher position (the distances and angles are exaggerated to facilitate visualization)

Let’s assume that the situation in the picture above is possible and the airplane will move away from Earth unless the pilot applies some correction to the airplane attitude.

For position a), we have:

Also the total energy of the aircraft is the sum of its kinetic and potential energies:

From position b), we will balance the forces radially (positive forces are outwards):

From conservation of energy, the total energy must be the same as position A:

The radial acceleration must be outwards, at least for sometime, otherwise the airplane would not be able to reach the new higher altitude. This means that the outward radial forces must be larger than the inwards radial forces. Therefore, using results from position a), we can re-write the equation for position b) as:

or, rearranging:

But:

Therefore:

Since sine of an angle can never be greater than 1 we can conclude that our hypothesis that the outward forces must be greater than inward forces is false.

In other words, if we assume the Earth is round, the airplane would not be able to keep climbing and escape Earth’s atmosphere and the pilot does not have to adjust for the Earth’s curvature.

Consequently this cannot be used as an argument for Flat Earth since the pilot does not have to adjust for neither a round or flat Earth.

Look, I can’t see the Earth’s curvature from my airplane window

We already covered the issues with the way this problem is proposed. Now we will look at a better proposal that is more suitable for a scientific analysis.

One can state this:

if the Earth is flat causes I can see places on Earth over 400 miles away from an airplane

This is easily verifiable using elementary geometry.

Assuming the Flat Earth is a disk and my airplane is flying at the center of the disk at 40,000 ft than at a view angle of 1 degree below a horizontal line one could be able to see as far as 434 miles (just to give some perspective, 1 degree is the angle one sees a 6 ft tall person about 340 feet away, a little less than the length of a football field).

Then all you have to do is go in an airplane and determine how far you can see. You’ll find out you can only see up to 250 miles, regardless of how flat the terrain and how clear sky are.

So your observation indicate that you cannot see places over 400 miles from an airplane; therefore the we have a contradiction and the original one-way statement cannot be true; therefore the Earth is not flat.

Conclusion

I hope this article helps understanding the complexities of scientific investigation and how important it is to follow the scientific method in order to avoid the risks of masking personal beliefs as scientific information.

Using common sense, qualitative arguments or subjective observations to prove a hypothesis must be avoided; objective measurements and calculations must be used instead, whenever possible.

It’s important to avoid “one off” or anecdotal observations as the basis for scientific conclusions. The scientific method works well with repeatable observations and experiments; explanations for single events remain in the realm of speculation.