Seasons and days on Māinṃ

When I set out to create Māinṃ, one of the main goals was to create a flatworld with a seasonal system as close as ours as possible (an old hobby of mine). I think I have finally come up with a system I am reasonably happy with.

I went through several ideas and iterations, but this final version finally came to me as a result of taking a few of the ideas from before, and simplifying them. Sometimes, coming up with a good solution can be difficult, because you usually only start with a few basic things to build on: then, you come up with things that you add to it, to fix a thing, which then breaks another thing, until finally you have a complicated monstrosity on your hands that just doesn’t work, but you know to be oh so close to what you want. It’s time to bring your ideas to the chopping block, and see if you can come up with a new system from all the new bits you came up with. This is basically how I came to the current system I will describe later in this post.

Let me start with a small introduction to the problems of flat worlds. The main problem with flat worlds is that they’re not round: if they were round, it would be much simpler to come up with a day/night cycle and seasonal system, but alas. Usually we expect a fantasy world to work reasonably close to our own: the sun rises, day dawns, winter comes and days shorten, etc. On a roundworld, this is all taken care for you: you just need a solar system (Copernican or Tychonian or even Ptolemaic, doesn’t matter), where a sun orbits an earth or an earth orbits a sun, and that earth has an axial tilt that sometimes points towards the sun, sometimes away. This gives us three main things:

  • some places on the globe have the sunlight that comes in angled so that it comes straight down, and others have the sunlight come in at an angle: for the latter, there is less aggregate sunlight for the same reason that a shadow is longer during winter.
  • as the axial tilt of the globe shifts around during the year, days lengthen or shorten

These two things create the seasons as we know it and the various climates we have all around the world, all due to the roundedness of our world and its axial tilt. On a flat world, you have to come up with some ways to emulate these things, because if we start from the simplest expectations, the day on a flat world should start and end at the same time everywhere, and thus you can’t have diverse climates that are based on seasonal changes being more or less severe depending on area.

The simplest flat world system is thus this: the sun rises at one end, and sets at another. Everywhere has 12 hours of day and 12 hours of light. If we expect that the sun is stationary, there are no seasons, but there are probably climates: the further away an area is from the sun (in aggregat), the colder it is. In this case, the world would have a cold “north” and “south”, and very hot “easts” and “wests” that heat up during the morning and evening respectivelly. The center is either warm or hot, depending on how high the sun goes in its orbit.

To create seasons, the simplest method is to keep the 12/12 day-night cycle, but somehow change the orbit of the sun. There are two obvious ways: the first is used in Terry Pratchett’s Discworld series, and in it, “east” rotates around the world. On the actual Discworld, this rotation happens once per two cycles of seasons, because the seasons are determined by whether an area is closer to parallell or orthogonal to the sun’s orbit. Despite this, on the Discworld, the center of the world is encased in ice (something we’ve been told is due to magic in a retcon), and the rim areas are hot. Ankh Morpork is known to have winters and summers, and it is closer to the center, while the rim houses the Discworld’s ersatz-Africas, Australias and Far Easts. A more logical structure would that the rim of the world has extreme variations in seasons, while the center has milder or no variation.

The second one is to wibble the orbit of the sun so that, instead of East and West moving, the highest point of the orbit moves north and south during their respective summers. The northern and southern halves of the world would have seasonal variation, while the center would have some, and the east and west remain hot. This would give seasonal variation and climates, but no shifts in the balance of day and night-time. Having this system is reasonable: if we expect that the sun is small, then the further away you are from it, the less bright it is due to square-distance laws, so winters would indeed be “murkier” than summers.

But for Māinṃ, fool me, I wanted changes in day-night cycles, mainly because Māinṃ is a world based on Finnic mythology (with a bunch of extrapolation), and in Finland, we have extreme variations in the day-night cycle: the midnight sun and the sunless days above the arctic circles during the winter. The darkness of winter is a depressive force, with its own name (kaamos) that drives people to drink and suicide, and we live with it waiting for glorious summer, during which we have days when the sky is blue through the night.

To get variable length days, an idea pops up into mind immediately: make the orbiting sun some kind of spot-light or light-faucet that illuminates only areas directly below it, and the higher it is, the larger the area. Combined with a seasonal orbital wobble, some parts of the world would have shorther day-light hours during the winter, as the spotlight’s center target moves away from them, and they get only a little light per day (otherwise, the sun is “dim” in the sky). The most obvious problem with this that it doesn’t contribute any *more* daylight hours anywhere: “summer” is always twelve-hours maximum, and probably always less unless you fudge the orbit by raising its center a bit, because a spotlight sun will illuminate a very small area at the start of the day. I never did solve the problems that a spotlight sun have, but decided to ignore it, and add a new thing to the mix: somehow getting more sunlight at areas that are in their summer season.

The gap between the sky and the ocean, through which primordial light comes through. The world’s sky dome would be slightly askew on top of the world pillar, and thus, one edge would be submerged in primordial waters, while the other edge would be slightly raised, and through the gap would the outerworld of sky-spirits and gods illuminate the summer. As the sky dome rotates on the Axis Mundi (once a year, now), the area illuminated by the gap moves around. During the Autumn-Springs, the East or West are illuminated, during the Winter-Summers, the North or South are bathed in perpetual day. The center is the furthest away, so it gets the least effect from this, and you have to introduce some sort of fading-out-mechanism or wobble to the light that streams in if you don’t want places to transfer from 12-hour days straight to perpetual day. The end result should look like something like this:

Of course, you have to fudge things a bit.. A lot. A huge amount. For example, you probably want to have an elongated shape for the sun’s spotlight (or parabola faucet light shower), so that the East and West get their daylight hours roughly the same times… And the afore-mentioned wobble of the gap. And then you realise that almost nowhere will ever have equinoxes, and that the day-night balance of each place is, in aggregate over the year, different from every other place. In the end, I finally had something like this on my hands:

This shows how much each area gets sunlight per day, animated to show a whole year. The red areas are in perpetual day, the cyan in perpetual night, and it’s all a big mess. The orbit of the sun is higher than the center of the world, and thus it is up in the sky longer than 12 hours… But hardly nowhere gets that 12 hours. The falling pattern of the light streaming down from the sun is elongated to an elliptic paraboloid on the east-west axis, and I had to generate the above image using a ridiculously complex GIMP Scheme script. Somewhere along this, I came up with a solution to some things (like the fact that light that works like a Newtonian fluid is problematic) by introducing a fluid ether that acted as a medium: this is what pumps out of the sun and the gap (with varying intensities during the day), and if I could just come up with a way to get it to pool so that days and nights would get better in synch with the sun.. A big mess.

Finally, I decided to try to simplify things, and see if I could come up with a system from the bits I’d come up with on the way: the idea of using an ether to distribute day-hours, the gap, and all the basics, like a wobbling sun orbit and so forth. I came up with this:

The world is flat, with a dome above it rotating slowly on its Axis Mundi, askew and with a gap on one side that leaks in light. The sun rises from the sea in the East, and sets down in the West: twice a year, it flies right over the center of the world, otherwise its orbit is skewed towards the north or south. But the light from the gap and the sun are such that they cannot interact with material things in such a way that moonlight or starlight does: they need a fluid medium that acts as a catalysator, and which they consume. This is provided by the sky, as defined by an arc in the sky that swings like an upside-down pendulum during the day. At midnight, when most of the world is in darkness, it has reached one end of its swing, closer to the edge of the Sky Dome that has the Gap, and at midday, its center lies on the opposite side of the world. This arc has two sides: night-side, and day-side, and on the day-side the sky provides the earth with fluid ether (which is coloured sky blue).

The above gif shows a looping image of a single day on Māinṃ: specifically, this is the Eastern Solstice, the day when the Gap is centered on the Eastern radius. The image does not show the movement of the sun: when the yellow area (the area lit by the gap during night) is at its smallest is midnight. When the border between night and day passes right over the center of the world is when the sun rises in the East, and when the daylit area is at its largest, the sun is at the highest point of its orbit (during the Western and Eastern solstices, directly above the center). Then, when the arc swings back and passes the center again, the sun sets in the West. Of course, it’s been night-time in the West for a long time now, because there is no ether there to let the sun’s light interact with matter: instead, the sun just looks like a moon. The areas that are shown in the image to not pass into day or night at all have at that moment perpetual night and day: the further away they are from the center, the longer those times are. In the farthest East, the islands north and south from the Eastern pole are half in perpetual day and half in areas with very short (one, two, three hours) nights. In the West, it’s the opposite. The North and South pole, in contrast, have their equinoxes: the days and nights are equally long. Fortunately for the West, the ocean is still warm, though it is not as warm in the East because of the ocean currents coming in from the North and South on their way to the Maelstrom at the center of the world.

In 180 days (because of course Māinṃ has 360 days, it’s so much more myffic) the situation is the opposite: then, the East is dark, and the West is lit, though the North and South poles are again in their second equinoxes. 90 days, and either the North or the South are in winter or summer, and the East and West are not. Equinoxes are divided into 360 sectors of the world, which shift over one per day, as the center-line of the Gap and the Day Arc move with the rotation of the Sky Dome.

This system fulfils some criteria that my others don’t: one is that each place on the world has about as much sun hours per year as another, because the night and day cycles during summer and winter months cancel out, much like our own world. Yet, the East-West corridor is warmer than the north and the south because the sun is closer to the surface there, creating a very interesting pattern for climates.

Mechanically, the Arc has to move by some rule. The simplest one would be that it moves according to a sine-motion, but if you do that, the center areas have much more variation in day-hours than I would want (i.e. they’d get much larger differences in days and nights during the winter and summer because the arc moves slowly above them). To alleviate that and have the arc move somewhat faster when it goes above the center, I let its motion be decided by the motion of a moon orbiting below it, so that the arc of the angle and the angle of the moon’s placement in regards to the Dome’s Center Line are the same. This way the movement is exaggerated: in the center, it’s faster, and on the edges it is slower.

All in all, after much thought over these past months, I think I’ve come up with a system that I am reasonably happy with. You can never come up with a system for a flat world that perfectly emulates a round world, but if you drop some of the requirements (like the fact that “dawn” and “rise of the sun” should be equivalent, or that if the sun is in the sky, it should be day) you can get pretty close, and this one does it relatively well. The difference that it has with a round world are either very fantastical in quality (the sun’s dimness without ether, that you can actually measure the distance of the sun as it comes closer or goes further away) or local in scope (the strange climates in the East and West, a really nice addition that doesn’t replace anything: you still have a roughly “equatorial” climate you move closer to the center). It has day-night cycle balancing, changing seasons, areas of perpetualness and it does it in a relatively simple way. I am happy with it (until the moment I come up with a shortcoming again), and hope you have enjoyed this extended history and explanation of the day-night system of Māinṃ.

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