## Sunday, September 10, 2023

### Positions I Don't Hold: Flat Earth Theory

Part of a series of posts of ideological turing tests.

I had originally intended this post to be first in the series, as an illustration.  Then suddenly the existence of alien life was in the news, so I went with that one.  But I already had this written, so figured I'd post it.

#### Ideological Turing Test

It is plainly obvious from immediate observation that the world is flat.  This is the position we all start with, and have to be brainwashed out of.  But I need to be clear about exactly what a "flat Earth" means.

Firstly, "flat" doesn't mean smooth like glass -- there are mountains, hills, valleys, etc.  That's quite apparent.  Flat here is more describing the earth's topology, that the Earth does not wrap back around itself.  A flat sheet of paper, and one that has been crinkled or crumpled up, are topologically identical.

Many people think that by a flat Earth we mean that the world is shaped like the Mercator projection map your school teacher used to put up.  Then it's easy to make the argument, flight times from Main to France are much much shorter than flight times from Panama to Senegal.  Whether you measure it in time, in distance, or in fuel expended, it's always more from Panama to Senegal, than Maine to France.

Obviously this wouldn't make sense if the Earth were shaped like the Mercator projection.  But that doesn't mean the Earth isn't flat.  It just means the Earth isn't shaped like the Mercator projection.

The flat Earth is "round."  It is a disk.  The direction that we call North is actually towards the center of the disk.  The lines we usually call latitude are concentric circles, so that moving East or West is actually moving clockwise or counterclockwise around the disk.  The lines we usually call longitude are rays from the center (North pole) outward toward the edge of the disk (South).

There is no South pole.  No one has ever made it to the edge of the Earth, so we don't know what's there.  We don't know if there is an edge, or if it extends infinitely in all directions.  We do know that moving outward (Southward) as far as possible, from every direction, eventually leads to a land of ice.  This suggests that our part of the Earth is completely surrounded by an ice ring.  This ice ring might be the edge of the Earth, or it might merely be some annular region separating us from the rest of the disk.

God only knows what else is beyond to explore.

You have no doubt been told to immediately reject this idea as laughable.  From a very young age, you have been taught to scoff at the stupid people of the past who used to believe this.  But apart from your upbringing, and knowing to laugh and make fun, what are your actual reasons for believing the earth is not flat?

With your own eyes, you can clearly see that it is flat.  What convinced you it wasn't?

Your parents said the Earth was round?  But your parents also told you the tooth fairy collects your lost teeth.  What a poor reason to believe anything.

Your teachers said the Earth was round?  But what were the arguments they used?  Did they use even use arguments at all, or did they simply refer to the textbooks claiming so?

Scientists said the Earth was round?  But on what basis?  Do you understand the arguments they are making?  Did they plainly explain them in terms that enable you, personally, to verify, by performing the observations?  And did you perform those observations?

So then why are you taking the word of people, when they make claims that directly contradict what is apparent to your own eyes?

That was a rhetorical question.  I know why.  It's because you were raised to immediately dismiss the idea as laughable.  Ignore your early brainwashing, and try considering this seriously.

This theory has itself been proven in countless ways.

Consider the disk of the world.  People have circumnavigated the globe --- a word which means they sailed in a circle.  A circle around the world.   Going from East to Eest, they moved on one of the concentric circles of the Earth's disk until they arrived back where they started.  It fits perfectly.

Airlines need more fuel to travel from Panama to Senegal than they do to travel from Maine to England --- this is because it's a longer distance, because the radius of the circle on the disk is larger.  Larger radius, larger circle, larger distance around.

If you begin walking East in a straight line on the disk, you will end up also moving South (toward the ice ring) -- this is an issue known as bearing, which has been well-known to navigators since the age of sail, and it is accounted for perfectly by flat Earth theory.

Why can't we see infinitely far in all directions?  Ask any science teacher, the opacity of air prevents us from seeing arbitrarily far in any given direction.  Air is not empty space, but full of molecules of gas, which scatter light.  At long distances, this scattering renders distant objects effectively invisible.

Where do ships go when they sail over the horizon?  If you observe water in a glass, it forms a meniscus, rising up near the edges.  The oceans do something similar near land.  The ships are simply sailing down the meniscus.

But why would scientists lie?  Why would there be a giant global conspiracy to trick everyone into believing in a round world?  It seems like such a stupid waste of time.

Well, there isn't a conspiracy.  It's a simple matter of the Emperor's New Clothes.  The Middle Ages were full of superstitions, and one of those was that the Earth was round.  Medieval thinkers started publishing this idea and trying to guess the "radius" of the Earth.  Later thinkers have had to build off of what the earlier thinkers had said, and were too afraid to contradict the consensus of other thinkers at this time.  And for good reason --- the thinkers who did publish defenses of a flat Earth have been almost entirely forgotten.  Today, the view is almost a dogma, and it would be impossible to publish any denials of a spherical Earth in a scientific journal.  Despite the manifest proofs, scientists are too concerned with their reputations to try to challenge what has become cemented through centuries of erroneous thinking.  It would take a revolution on the level of Copernicus to seriously change the established norm.

It's clear from living on the Earth that it is flat, it is clear that this idea properly understood is in accord with scientific observation and navigation, and it is clear that this idea is in accord even with those observations that are often used to dismiss it.

Don't follow the superstitions of medieval philosophers, or mockery of deniers when you can instead believe your own observation.  The Earth is flat.

#### Steelman:

This is what I consider the strongest form of Flat Earth Theory.  It might not be the position that most Flat Earthers hold, but it is what I consider the strongest Flat Earth view.

Geometry is both more fundamental and arcane than most realize.  Geometry at the level of fundamental physics is not just  a matter of shapes, but in fact the distortion of distances, angles, even time in response to the presence of energy.  This geometry leads to forces, and those forces themselves create energy that can feedback into the distortion of geometry.

We do not yet completely understand the implications of geometry on fundamental science, though it is suspected change in geometry can somehow be fundamentally linked with forces like electromagnetism.

Because we do not have a complete picture of the actual geometry of the universe, we cannot possibly have a complete picture of the geometry of our planet.  When we describe the Earth as being a sphere or a  disk, we're talking about as though it were a 3D object floating in blank space --- but it is in fact a 4D object floating in a complicated sea of interactions and distortions in geometry.

What is more likely is that the Earth only seems round, due to geometric interactions that we do not yet have the science to understand.  Seeing the true shape would require understanding exactly how geometry and gravity in the universe work, and that understanding is still a long way off.

It is true, the Earth seems round, even spherical.  However, this is conflating the topological and differential geometric understandings of what it means to say a thing is "round."  The Earth can only be proven to be spherical in the sense of differential geometry, in terms of how paths change as we move on it.  In a topological sense, this can be true, and yet the Earth not be topologically "spherical," meaning it does not in fact connect back to itself forming a closed surface.

The part we have explored is spherical, but the remaining parts beyond the South pole might expand outward again forming something more like a hyperboloidal or "saddle" shape.

To try to illustrate what I'm talking about, think of a flat rubber sheet.  Think of stretching the rubber around a metal ball and pinching it off at the top near the sheet so the ball in inside a little pocket.  The part of the sheet around the ball is spherical, except for the vast rubber sheet at the top.  Observations on the sphere part of it would look almost exactly like observations on a spherical earth, but the overall shape would be classified by topologists as "flat."  And there would remain an infinite unexplored world beyond the southern ice wall.

To make it more intriguing, imagine tucking all of the rubber sheet inside of that pocket.  The sheet is still there, still flat, still unexplored, but also unseen from the spherical outer portion.  This could be the situation we are in, due to curvature in spacetime near the Earth causing spacetime to fold in over on itself.  This would be entirely consistent with the picture we have now, but open an exciting possibility of more world to explore, on the far side of the southern continent.

#### Why I Don't Hold This Position:

Firstly, there are no serious Flat Earthers.  Maybe in some remote places with no contact with the outside world, there are.  But the ones you hear about online are doing an elaborate parody which strictly maintains kayfabe.  The parody is not a parody of people in remote places who sincerely believe in a flat Earth, but a parody of how easy it is to make arguments for basically anything.  The real goal of "Flat Earthers" is to argue so convincingly for a false idea that others will become convinced of its truth.

I frequently see New Atheist youtube channels seriously devote time to "debunking" Flat Earthism.  This is akin to arguing that the Undertaker isn't actually hitting Hulk Hogan with a chair.  Which, also, is something I imagine New Atheists would seriously devote time to.

A hinge point of the arguments for a flat Earth deal with our modern insistence on verificationism and Cartesian certainty.  We demand high levels of directly observable proof for our beliefs.  But this comes back to bite us.  Most of the major evidences for a spherical Earth are outside of our direct ability to measure or observe.  For almost all of it, we have to rely on scientists.

I am a scientist, so I do have access to many more arguments than a non-scientist.  By that I don't mean equipment, but mathematical arguments.  For instance, the issue with bearing.  It is true that while sailing in a straight line on either a disk or a sphere, your bearing will change.  You begin moving east in a straight line, but this soon becomes south.  Qualitatively, this is usually similar on both a disk and a sphere -- but numerically, the exact rate of change can be predicted, and measured, and found to be quite different.  Mathematically we can distinguish the two, and see which is the case.

Using the wrong equations for bearing could cause ships to go missing or missiles to strike hundreds of miles away from their targets.  Obviously both merchants and the military have the most interest to use whichever bearing equations simply work.  They have no interest to stick to incorrect equations out of loyalty to an idea.  The equations merchants and militaries actually use, that actually work, are derived from the surface of a sphere, and not a disk.

Since direct experiences of things like transatlantic airplane flights can be taken as evidence, then it would be possible to predict exactly how much longer flights at different "latitudes" would take assuming the flat disk model and the spherical model.  Not merely saying longer/shorter, but predicting an exact ratio as a function of latitude, using two different geometric models.  You yourself could do this, and you yourself would find the spherical model much better in accord with the data.

But where it would really become obvious that the Earth cannot be flat is when you take a trip south of the equator.  While both a disk and the Northern hemisphere of a sphere would have transatlantic flights becoming longer the further south they were, the critical difference comes at the equator.  On the disk model, flight times continue scaling up linearly the further "South" (outward) we go.  Whereas on a sphere they sort of stop increasing, so that flight times in the belt of the tropics are all pretty similar, until suddenly past the equator the flight times actually begin shrinking again.

It takes less time to travel from Argentina to South Africa than it does from Panama to Senegal.  Less time, less fuel, less apparent distance.

The only way to explain this is that after the equator the Earth begins to fold back in on itself.  In fact, the land of ice we all come to is pretty small.  The disk model above would have it an enormous supercontinent larger than Asia and all of Earth's oceans, but it can be completely circumnavigated in a few days.

This suggests that the circumference of southward latitudes at first increases, then decreases, which is only possible if the disk folds back over at the equator.  Folding back over will make it into a sphere.

But then you could imagine a situation like my steelman, which seems to already anticipate this.

I think most simply, then, the Earth has to be a sphere, because gravity is a radiative force.  This means the force of gravity from a small point mass is the same in all directions at the same distance.  Gravity is not simply "down".  That gravity is radiative can be tested with something like a Cavendish experiment.

This radiative force will pull particles together, and they will want to take the most optimal shape possible.  Since the force is the same in all directions, this shape will be the same in all directions.  That is, it will be a sphere.  The particles want to be as close together as possible, and a sphere will minimize the total distances between all particle pairs (not of any given pair of particles, but the total summed distance of all particles).  Think of a cube: the vertices are much further away from the center than other points on the surface.  This is suboptimal, so gravity will want to pull the vertices closer to the center so that everything is as close as it can be.  Even if the Earth started off as some other shape --- a disk, a square, a cylinder, whatever ---  the edges would become gradually pulled toward the center of the mass until it smoothed out into a spherical shape.  Spheres are simply inevitable with a force like gravity.

Because the nature of gravity is to pull everything together, the Earth cannot have some unknown complicated shape.  It cannot take the form of a big sprawling rubber sheet folding inward on itself.  It must be spherical.