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You are a flat-earther (Or How I Learned to stop worrying and model less)

by Joe Bloggs

Original post via scribe.rip

So. You’re building a world, and it’s glorious. You’ve got it all sorted. From climate maps to the ever shifting webs of political intrigue in the palace. From the tiniest vole to the highest star in the heavens. You’ve got it all.

But what about explaining the tidal bores that rush up the river of the Shining City every evening? Is there a way to explain those that’s consistent with the two-moon system that you’ve concocted?

Oh no. Panic. There is no way to reconcile these tidal bores and having two moons! But the tidal bores are critical to the fishing industry, and the Priesthood of the Two Sisters is an integral part of the government of Lesser Numoria!! Aaargh! The entire world is in danger of becoming inconsistent!!!!

Stop.

I’ve been where you are. I’ve modeled a world to the nth degree. I’ve pored for hours over hydrostatic equilibrium equations and tried to solve boundary problems that probably can’t be solved analytically. I’ve built elegant narratives that fall apart as soon as a modicum of real world sense is injected and twisted my mind into knots trying to justify the most ludicrous of contrived setups, all in the name of ‘consistency’.

But I’m a flat earther. And so are you.

Before I continue I’m going to introduce a world. This world is the appropriately named ‘Abyss’. It’s a series of city-states that hang from the roof of a vast cavern, suspended above a seemingly endless drop into the darkness. Abyss started, as many worlds do, as a cool idea. Who doesn’t love upside-down buildings and people riding around on spider-palanquins?

It developed over time from a simple “city in a cave system” to “entire hollow world shaped by some baffling god’s hand”.

And that’s where the troubles began, because I wasn’t thinking like a flat earther.

I tried to work out if there was any way to make the hollow world more ‘realistic’. Of course, some things had to be handwaved. The overall sphere of the world clearly needed to be made of unobtanium of some kind, or it would collapse in on itself, but could I make the inhabitants of the sphere fight against 1g of gravity?

Now I know a lot of you are instantly going to think “No! Shell Theorem! There is no gravity inside a hollow sphere!!”, and you’d be wrong. This isn’t a theoretical construct in a vacuum. Abyss must have an atmosphere, or all it’s denizens would die. Therefore the mass of the atmosphere will exert a gravitational pull on the people on the shell. Aha!

Gauss’ law of gravitation gives us the wonderful result that from radius r away from the centre of mass of a blob of matter we can treat that blob of matter as though it’s a point of the same mass at distance r. The reason for this includes the word ‘integrate’, so I’ll avoid it, but basically all it meant for the world of Abyss was that with enough mass inside a small enough radius I could create a force at the surface of the bubble of 1g. It’s also the basis for the aforementioned Shell Theorem, which lets us ignore any mass above us (as we can consider that to be a true shell that doesn’t contribute to the forces felt at all)

If we assume the gas is homogeneously distributed then it’s easy to see (using the fact that gravitational force is proportional to 1/r^2 and the volume of a sphere increases proportional to r^3) that the gravity felt increases linearly as you move away from the center of the sphere. Whoopee! Airship pirates fighting in low gravity far below the roof!! Awesome!

Except no. The above ignores the fact that air likes to compress. So much in fact that if this ball of gas did exist (and it would actually have to be a very, very large ball of gas indeed to create the gravity I’d like it to have) it would compress an awful lot, passing swiftly through “big ball of gas inside an unobtanium shell” into “furiously hot gas giant hovering somewhere near the middle of unobtanium shell” before finally becoming “furiously hot gas giant crashing ponderously but implacably into an unobtanium shell”.

Things are simpler on a flat earth.

To solve this problem we need to turn to hydrostatics, the mathematics of working out when fluids reach stable states. The hydrostatic equations for getting a ball of gas (with a solid boundary) to be stable and have 1g at the boundary are, frankly, impossible. Simulating the gases (as a series of layers) is possible, if awkward to code. But then we run into a new problem: Gases like to mix in different layers!! Oh no!

By this point it should be obvious the rabbit-hole that I fell down. Rather than simply coming up with a model that gave me a cool result and running with it I got bogged down with ‘realism’. I’ll admit, I was trying to be realistic while simultaneously trying to justify an atmosphere on the inside of a giant ball of unobtanium, but I wasted weeks on this problem, and many others beside it (How exactly do solids that fall make it back up to the outer shell??). In those weeks I could have been focusing on intra-city intrigue, air-piracy or elegant methods of moving from one city to the next along the roof of an endless cavern, but instead I spent my time learning about gaseous flow. What a waste.

So I moved back to being a flat earther. And you should too.

Now I think I should explain a little about models, specifically about how I have (despite all evidence to the contrary) the soul of a scientist. I like to observe, hypothesize, experiment and then rejoice when what I thought was true is conclusively disproven. I know for a fact that the Earth is a ball (well, oblate spheroid, but it would probably match most people’s definition of ‘balls’).

I am still, when appropriate, a flat-earther. I am also a volumeless-point-earther and a the-mass-of-the-planets-is-negligible-earther and an oh-my-god-this-mountain-is-steep-earther. The reason for this is simple, and I promise it will tie back to world building (and Abyss) in a second.

Knowing the Earth is round doesn’t help me hang a shelf.

When I am hanging shelves or throwing balls or putting down a cup of tea the model of the world that I use is ‘Flat’, because if I tried to consider the curvature of the Earth every time that I tried to take a step I would quickly go round the bend. Pun thoroughly intended.

Our brains are actually very, very good at switching between different models of how the world works. This is true in our every-day lives, where we happily accept that water comes from the sky because of “the water cycle” and also because “It always rains on my day off”. Humans are practically built to switch from one idea to the next. So I’m a flat earther. So are you. So is everyone you meet.

So how does this apply to world building?

Quite simply: actually. When world building you need to ask yourself ‘what is the purpose of the thing I’m trying to describe’. If I’m trying to describe how to hang a shelf then modelling the world as round is unhelpful. If I’m trying to launch a satellite then modelling the world as round is mandatory.

Similarly: If I’m trying to build a world of swash-buckling on airships above an endless drop then modelling that world as a ball of gas wrapped in an unobtanium sphere is unhelpful. It’s much better to picture and describe a flat-Abyss hanging across an endless void, a sea made of air in which the airships can move in three dimensions. Setting out what you would like to achieve from any given worldbuilding exercise ahead of starting it will give you more clarity about what kind of models you should be building or thinking about, and will help you avoid the pitfall of modelling something that’s practically not that important in excessive detail.

In other words: If you’re setting out to build a shelf, don’t start with the maths to work out how much curvature you need to account for. Assume the earth is flat and you’ll have a much nicer time.