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.


Entry for the Thousand Year Game Challenge

Some years ago I worked on a steampunk/space opera setting called the Steamopera, and developed a simple board game for Venusian (human) cultures. It was called Sáto, and it went something like this:

(fig. to the left: arrows show possible movement, a crossed out piece is captured, a circled piece is not captured)

The game-board is a set of hexes arranged symmetrically around a centre hex, usually four hexes deep in concentric “circles” that are coloured in alternating hues. Each player has a number of pieces (five seems good, ignore the old illustration; for an attractive initial pattern, remove two pieces from the “corners”) that are arranged opposite of the other player’s. The players take turns moving one piece at a time, with the purpose of capturing the opponent’s pieces by actively bracketing them with two of the player’s own pieces. Further complications arise from the (approximately) circular layout of the board: one of the movements of the pieces is explicitly that of moving around the board in a rough circle, moving on one of the concentric layers of hexes.

Here is a codification of the above summary:
1. The board is made by setting down hexes, starting with a central hex that is surrounded by 6 other hexes, which are surrounded by 12 hexes, etc. The central hex forms a group with itself, while the 6 hexes surrounding it form a “circular” group, and the 12 hexes surrounding those form a third group, etc. (A good size for a board seems to be four hexes deep, with five pieces: if the board gets bigger, increase the number of pieces.)
2. Each player has the same number of identical pieces that are initially set on the board in a symmetric pattern. Using five pieces seems to be a good number, because using more than six pieces may bog down the game at the beginning because forming defensive walls become possible.
3. Each player takes a turn moving one of their pieces on the board.
3.1. There is no passing, and each player must make a move on their turn with one of their pieces (with an exception if there are no legal moves).
4. The pieces may move in straight lines, as defined by the hexes, as far as possible without colliding with another piece, like a rook in chess, except hexagonally.
4.1 Pieces may also move in a circular movement around the board on the Concentric Circle group they stand on at their turn. They may move clockwise and counter-clockwise as far as they can without colliding with another piece.
5. A piece is captured when the player moves one of his pieces into such a position that that piece becomes the neighbour of an opposing piece, which is the neighbour of a third piece that is not the neighbour of the first piece, capturing the opposing piece between the player’s two bracketing pieces.
5.1 It is not sufficient to have two pieces touching an opponent’s piece: the bracketing counts only if it takes place on the capturing player’s turn, and two bracketing pieces are on opposite sides of the captured piece. For example, two of the player’s pieces may be touching one of the opponent’s pieces, but they are also each other’s neighbours (i.e. all of the three pieces are touching each other). The player can capture the opponents piece by either moving one of the two neighbouring pieces in another position touching the opponent’s piece, or introducing a third piece that can be seen as bracketing the opponent’s piece with one or the other (or both) of the pieces already there.
5.2 If a player moves his piece between two of the opponent’s, that piece is not captured. If the opponent wishes to capture the piece, it must be done with a move on his own turn.
6. The game ends when one of the player loses all but one of his pieces (though it’s possible to lose all with a double-capture, but I’ve never seen one happen), and the player doing the last capture wins.

Originally I used seven pieces, but that made it possible, even easy, to create an impenetrable wall and just move around your pieces behind it.

This is a relatively simple game, except for the circular movement around the board, the original Thing I wanted to build a game around, inspired by game-boards with sectorial movement, or the one in Star Wars. Otherwise the rules are a simple bracketing/capturing game like latrunculi or tafl games (well, much simpler than those), except complicated slightly because its played on hexes.

The name “Sáto” was a tolkienism in the Venusian conlang stub I never bothered to work on, from Finnish saarto, ‘surrounding, siege’.

Written on May 23rd,
Kristian Järventaus

Small preview of upcoming map.

Here’s a preview of a possible color-scheme for the mountains on the Māinm map. Red and yellow denote dry mountains in rain-shadows, the others are wet mountains that get rain-fall, or don’t impede rain-fall, or which cause rain-shadows.

The wind patterns on Māinm are relatively simple: no coriolis force, for one, which means no wind bands. Usually the wind travels towards the Sun, which warms up most the bits it sails over, and the east-west corridor more than north-south: lots of centerward winds.

Why the giant desert in the east (left)? The sun rises in the ocean right there, so the water is really hot. So hot, that it creates a low pressure area that is stronger than that of the desert itself: that, plus the land-mass to the west, and the mountain ranges north and south means there are no wet winds towards the desert.

The eastern sea is hotter than the western sea due to sea currents. Which are all caused by the giant maelstrom at the center of the world, that sucks in water, sends it into the underworld, where it falls “down” a mountain into rivers, then back into the sea. So, all currents are towards the center: and the eastern seas are dominated by currents from the center towards the north and south, warming up the eastern coast of the continent. Similarly, the western coast and ocean are cooled down by the currents then passing through the icy seas in the north and south.

Fudge dice and modifiers.

I’m a big fan of roleplaying in general. Too bad I’ve never actually played, which is a story for a day when I feel more sorry for myself. In any case, one of my favourite dice rolling systems is Fudge.
Fudge rolls are relatively simple: you roll a set of dice, add or remove modifiers, and then compare the result to a difficulty threshold or another roll. The twist is that Fudge uses dice that have minuses, zeroes and plus: mathematically, a Fudge die is a d3 with -1, 0, and +1, though physical Fudge dice are six-siders with two of each. One die results in a result from -1 to +1: four dice -4 to +4, with 0 centered on the bellcurve (AnyDice calculator; click on “Graph”). In practice this results in a more intuitive system than using simple numbered dice; an “average” is no more an arbitrary number somewhere in the middle of a 3d6 distribution, and you can easily expand into further reaches as you wish, creating something that is theoretically quite scaleable even regarding small numbers.
For the Game Project, I’ve been thinking of using the Fudge system for internal rolls. The only downside with Fudge rolls comes to the fore here: the granularity of modifiers is very high. A +1 or -1 can make a huge difference. There are several systems on the net that remove some of this granularity, and it’s been on my mind, too. Here is my solution:
The simple version of my Fudge modifier system is to use a numbered N-sided die, together with an ordinary 4dF roll. Modifiers are summed together into a single number: “1 modifier +2 modifier -1 = 2”. Roll the modifier die: if you roll equal to or below the target number, add a bonus +1 (or minus -1) to your roll. If your bonuses equal or exceed the number of sides on your bonus die, “carry” that into a set bonus or minus modifier. So: if you use a d6 as a modifier die, and you get a “+6” modifier to your roll, transform your “small” bonuses into a set +1 on your result. If you have “+12”, that’s a +2. ( Check out more AnyDice graphs )
You can adjust the granularity of the bonus system by changing the size of the modifier die: everything from d2 to d100, and beyond if you want. On a computer, the possibilities are endless. For the game, I’ve decided to use the inbuilt random functions: specifically, the basic floating point random function, that gives you a random result between 0.0 and 1.0. It becomes a simple thing to change the system so that all modifiers can be expressed as a single floating point number: +2.444444444 would be completely valid, and represents a +2 plus a 44.44444% chance of getting a bonus. The mathematics become simple: you can simply subtract arbitrary floating point numbers, and you can have arbitrary precision when giving or taking away modifiers. -0.0001 is just as valid as +3.0.
The Fudge systems simplicity also means that I can change everything that has a stat into this kind of (signed) floating point number: -2.5555 would be a very poor stat, while anything about +5.0 is legendary in status. You can have a steady flow of change (through experience, and other such events), without introducing further complications other than simple addition and subtraction.

The world in that game

[I am reposting this from a thread on the ZBB: it is chronologically older than the previous repost]

I’ve left the gods unnamed for now until I can bother with making up a conlangette for this, here goes.

[quote]In the beginning, there was the Sea before the World, and the Sky before the world, and the Demiurge was riding a blue elk upon the water (if you know Finnic mythology, you’ll probably see where this is going). But an enemy of His shot Him down from the elk, and He fell into the water, wounded.
He lay in the water for nine hundred and twenty seven years, until He saw a bird of the sky flying and seeking a nest. He raised His knee from the water, and the bird lay its nest on it. But the eggs were too hot, and the Demiurge moved his leg, and they fell into the water, and the pieces of the eggs became various bits of creation. (Maybe I’ll have a bird of the water, who dredges up stuff from the bottom of the Sea, too…)
The Demiurge formed the Earth from the stuff that was in the eggs, and rose onto land to continue working, and there he met the Sky Smith. The Demiurge tasked the Sky Smith with making a Dome of the Sky for the new world, and the Sky Smith started on it immediately. He forged the World Pillar that lies at the center of the world, and put up the dark night sky on top of it.
The Trickster was fascinated by his work, and came to the Sky Smith to ask if he could help him with it, and the Sky Smith tasked the Trickster to put up stars in the sky. The Trickster started putting stars in the sky with great enthusiasm, though little skill, but then his interest started to vane, and he didn’t put many stars on one side of the Dome of the Sky.
Because of this, the Dome was off balance, and started to wobble on the World Pillar, and the sky started to tip over; when the Trickster saw this, he became panicked and fearful, and he quickly asked help from the spirits of the Above, but no one could help him; then he asked help from the spirits of Below, but they could not help him either, for they did not know how. Then he heard a voice at the bottom of the barrel where the stars had been. It was the voice of a star that told him to take it and hang it in the sky in the place where the Trickster had lost its interest. The Trickster threw the star in that place, and the star grew in size until it became the greatest of all stars in the sky, and the Dome stopped tipping over, and disaster was averted.
When the Sky Smith came and saw what had happened, he was angered, because now he would have to create a haphazard imprompty mechanism to keep the Dome from topping over in the future. He took the Moon, that he had planned to put in the sky to light the nights when the Sun would not be there, and set it rotating around the sky so that the Dome would not wobble, and he took the rest of the stars in the barrel (six all in all), and put them likewise in motion upon the Dome, but in more complex patterns to compensate for the smallest wobble that the Moon could not fix. The Sky Smith also had to adjust the Sun’s orbit in the sky so that it reached North in one part of the year and South in the second. Finally, he attached the Dome fast to the World Pillar with the Pinion Star that was second in brightness only to the moving stars and the Counterweight Star.
Then the Sky Smith kicked the Trickster in the arse.
And to this day, the Dome of the Sky is tipped to one side, even as it rotates around the Pinion Star, as the World Mill at the bottom of the Pillar turns; one side of the Dome is under the water level of the Cosmic Ocean, and one side is above it, and from this gap there comes light from the outside chaos that lits up the rim of the world, and creates the the months of day and night at the farthest Northern and Southern reaches.[/quote]


The Ship of the Sun moves over the world from the East to the West each day, rising from the sea and descending into it (which creates clouds). From the ship, the Sun God casts out light that falls down to the Earth like rainfall, but it is easier to throw further in alignment with the keel, so the light doesn’t reach as far at the sides. In the Northern Summer, the Ship travels above the North, and in the Northern Winter it is South. Coupled with the gap in the horizon, this means that the farthest north and south (the “poles”) have a day(summer) and night(winter) months long. The sun rises and sets in 12 hours, but the light of the gap remains. Conversely, in the winter, the sun is so far away that the falling light doesn’t reach, and it resembles a bright, moving star.

In the East, the Sun rises, so the mornings are always warmer than the evenings. In the Eastern summer, in the farthest east (the “East pole”), there is no night, and the mornings are hot and the evenings are warm. In the West (at the West Pole), the sun sets, so the converse is true: it is the evening that is hot, and the morning that is cool. Likewise, in the summer, there is no night; and, as with the East Pole, the “Winter” is cooler, but the day/night cycle is 12 hours/12 hours. At the East and West Pole, in the Autumn the time of no-sun (12 hours) will get darker and darker, until there is true deep night for a few months in the winter. In the spring, the dark of the night will start to become lighter, until you can’t tell the difference between day and night.

In the center of the world the day is always twelve and twelve hours, and there isn’t much of a change in seasons; it gets a bit hotter twice a year, when the East and West are in their Summer/Winter period, and the Sun moves to its absolute zenith on top of the center.

If you move north or south from the center, you get seasons a bit more familiar to our own experiences: between the center and the North and South poles, there is a seasonal difference due to the distance of the Sun combined with a lesser effect from the gap in the horizon, which lengthens the day a bit due to some magic I still haven’t fudged into here. Let’s say the combined effect of sun and chaos light is tremendously effective, and that as the Sun moves closer to the horizon when it rises from the depths of the Cosmic Ocean, the light from the gap also becomes stronger, which lengthens the day marginally in areas that aren’t that close to the Rim… Something like that.

EDIT: Or maybe it takes longer for the sunlight to evaporate, because there’s more of it than usual… Yes, this makes the best sense. :EDIT

Note that Sunlight and the light that comes from the outerworld is different from our light. It’s much heavier, for one, and will have a kindasorta ballistic trajectory. Can’t help it, really, and it’s all in good fun so no harm done.

Yes, I have mixed up the compass points. I noticed that I have them in the wrong order in my charts (I mean, obviously the sun rises on the LEFT, right, and north is UP, right? So obviously East is left and north is up…), and, eh, I can’t be arsed to change it. Take it as another sign of otherworldliness.

Naturally, the Moon rotates around the dome of the sky; which means only the dome of the sky, and not beneath the Earth, etc. so unlike our very own Newtonian companion. I’ll have to come up with a good myth for its phases, etc. The planets are likewise attached to the dome; maybe their “orbits” will be completely unpredictable?

This is just fantasy. It only has to make Common Sense, which is completely different from Actually Making Real Sense. Verissimilitude is the key here, not whether it makes sense in our physical framework, etc. Gravity, for example, will be completely unexplained: I do not know a single ancient myth that attempts to explain its origin. It’s one of those “so obvious in hindsight why haven’t I even thought about why it exists” things that only philosophers at level 12 and above can even think about.


further disclaimer the thing represented here is the physical truth: this is not really a globular Earth with a mythical explanation for seasons, no, this is a project for making a flatworld that makes at least some sense while resembling Earth as much as possible with only superficial differences (like, who cares about the orbits of sky objects? and some sort of seasons and stuff to create interesting geography should be enough, etc..)