## Questions of Air

So I was in a plane earlier today (a small mathematics meeting in another corner of Finland), and I happened to think about the supposedly medieval idea that the world is a disc, and airs surround it. That’s a sketch I’ve drawn many times, making up fantasy worlds because I was bored, but an idea hit me then, looking out of the plane window.

Namely, “I am six kilometers up, and the air up here is very, very thin”.

Consider Earth. It is a sphere, with gravity towards the center. Air tries to fall down, and forms an ocean of air whose bottom is good for human-like creatures, and the upper reaches less so.

Consider Larry Niven’s Ringworld. It is shaped like a bicycle outer tire, spinning as a wheel does; the gravity is pointed outwards, away from the axis, so a ring of air stays in place, not bleeding over the rim.

What about a world disc, a stationary thick pancake? First, its gravity will be mightily strange. That gravity is towards the center of the pancake, halfway through it — so when you are standing at the centerpoint of the pancake (say on the upper side), gravity is where it is supposed to be. Walk towards the rim, and gravity doesn’t point at the ground, but towards that point under the pancake’s center, halfway through it. You’re essentially walking uphill, just walking on the level surface of the pancake world.

That is not a lasting arrangement; every pebble will tend to roll downhill, creating a mountain in the middle of the pancake; and the disc will crumble into the stable shape of a sphere, both on the upside and on the downside. There will be no falling over the edge; instead, the edges will crumble towards the center, until a sphere is born.

Thus, to save the world-disc, we need magic.

Suppose the source of gravity is not mass, but some external force that creates a down as a direction (as it seems to us; say as “the direction of the negative y-axis”), and not as a ring of arrows towards a point in space (or in the most solid… er, most molten core centerpont of mass. Uh.) Then the pancake has a genuine up-side and a down-side; and nothing stays on the down-side unless it is bolted on to it; all else will fall off and disappear downwards. “Gravity” is in the intuitive direction everywhere on the top of the pancake; and you can walk to the edge, lay down, and peer down into the depths, over which this world pancake magically hovers. (Maybe it’s made of an anti-gravity mineral?)

(Also, say goodbye to volcanism. Lava will exit downwards pretty quickly, if there even is enough pressure etc. to make and preserve it.)

This model gets worse, too, though. If the world disc has no rim, and thus no barrier to waterfalls over the rim (hints of Discworld here), the waters will drain away; but it will not be the big problem. Air will be.

Over the rimfall of water, there will be an “airfall”; and shortly afterwards breathing will become very difficult and no-one will have any fun, except in deep valleys in the disc’s interior. Even if there is a barrier range round the rim, well, one should hope for a fairly impervious platter for the pancake (in Ringworld speech, scrith), or all that’s not held up by magic anti-gravity will filter down through the world pancake, bit by tiny bit, and be gone, never to return.

That thought raises the question of what lies around the world disc; if there is a practically endless vacuum, then the air and water will be gone in the down direction, and not seen again. Suppose there is some kind of an envelope somewhere far around the disc, like a black plastic bag for the pancake to float in; and this envelope is filled with air. Then no-one will suffocate and all will be happiness and light, right?

Well, kinda sorta. The air pressure could “happen” to be just right for human-like creatures at the level of the surface of the pancake; but what would lie below it would not be pretty.

There is such a thing as compressed air, you see; I’m fairly certain that our normal air pressure is not because that’s as far as air will be packed, but because we just don’t have any more air to pile atop us. In this model, what lies over the edge of the world, in the “down” direction? Why, an ocean of air, with a step more of air above for every downward step you take. All that falls off the edge of the world will fall into this thickening soup, and gather at the bottom of it, at the end of the world envelope, and form a new world there.

Venus, to be exact; a place with a crushing weight of air above it. Just imagine a pillar of a few more kilometers of air atop you — a few hundred kilometers of air — it will not be a nice, hospitable place. If you fall over the edge, an impact will not be your problem; you will be crushed to pulp by air pressure long before you hit the bottom cup.

One could, having postulated magic coordinate gravity and magic anti-gravity rocks already, add a teleport at the bottom of a funnel-like envelope, a teleport pointed at the very top of this world system. Then, surely, the airs would not form a Venusian hell at the bottom, but zap to the top, and then filter back down, maybe even creating a pleasant breeze —

Well, or then you kick something over the edge of the world, it zips down, falling ever faster, accelerated by the addition of energy from the magic potential of the external gravity; and soon it will zoom through the teleport, appear far above you, and meteor-like make a big fat kinetic impact on your head. Now think what will happen to those air molecules… and you end up with the world pancake smashed flat because magic gravity keeps pumping kinetic energy into the system. (I suppose; I’m a mathematician, not a physicist.)

So remove the teleport; accept the thick Venus of fallen debris at the bottom, and a sparser stratosphere above our floating disc. (What beasts will fly out of the thicker airs to assail the world’s rim? What thin-air angels will live in the voids above?) We can assume, for convenience, that the amount of lost water is offset by some weather action, maybe evaporation caused by the rays of…

Oh, crap. The sun?

A big central sun does not make immediate sense in this model of a disc and an envelope; a small sun would be just a source of light, not of much gravity. But what kind of wild weather do you get if you have a platter of water and mud, and a source of heat somehow going in circles through the airs around it? (You get days and nights if the sun arcs over the disc and then under it; you get seasons if it rises and sets each time a little bit further along the edge. It’s not a exact copy of Earth — if I recall some earlier calculations of mine correctly, the central “pole” will have just one season, the cold one (remember Discworld’s frozen Cori Celesti), assuming the sun is at its highest when above the centerpoint of the disc. The disc’s edges will have a sunrise-summer and a sunset-summer, and winters in between; these seasons will blur when going away from the rim towards the centerpoint.)

Finally, consider the disc itself. It either does not generate gravity through mass, or its mass is insufficient to generate enough gravity to much alter the situation. (How thin is it? Horrors, consider a world where miners risk breaking through the bottom of the world, and falling into a yawning depth below!) The disc stays up because… well, the easy magical explanation is that the rock, or some common mineral, has anti-gravity in it. Which then would imply that it could be mined, refined, shaped, made into flying ships — but this line of thought has surely been examined many times before. (Me, I’m partial to the thought of castles atop flying mountains, floating over the landscape; I blame Dragonlance.)

But wait; what is “anti-gravity”? If our magical gravity means “a force, either a constant or a function of ‘height’, affecting everything, pulling along the same vector”, then our anti-gravity needs to be a counter-gravity to not eventually drop the disc to the bottom. (Doesn’t matter if a major fraction of the disc is unaffected by gravity; the part that is affected will exert a downwards force on the whole.)

So should one assume (for example) that there are two kinds of matter in this system, indistinguishable except for the fact that one is affected by this magic downwards gravity, and the other by an “upwards gravity”? That’s a horrible system; the disc would dwindle, shed matter upwards and downwards, wobble out of balance, and crash either upwards or downwards depending on which force dominates.

What then? Assume there are materials that long to be at some fixed height, that gravitate towards some level of air pressure? (A rock that “floats” at 1 bar?)

Assume some lifting engine, regulated by some wish to remain at a certain altitude? (That’s an end-of-the-world scenario if I’ve ever seen one; tap the right place and half the disc breaks away and falls, while the other spins out of balance, reducing all aboard to fine jelly.)

So, turns out it’s difficult to think up a system that works half as well as a simple sphere; but still, I think thinking these is more rewarding than just taking a cosmology and ignoring the associated problems of physics.

Then again, I once did integration to find out how much sunlight each spot on the disc gets in the system above; I may be biased towards the worldbuilding geek end of the spectrum.