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Dark Fire Lily
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The Blood Mire is the simplest, or at least, the most intuitively familiar to RL humans. It's an approximately flat plane adequately described by Cartesian coordinates, infinite in extent along the X and Y axes, with gravity (approximately 10 yards per second squared) oriented along the Z axis. Biospheres get pretty weird if you travel far enough, but massed violence always eventually makes the plants grow, even if leaves and blood alike aren't the color you might expect. Magnetized iron needles point north/south, perpendicular to the track of the sun, while vastly more expensive alchemically-treated silver needles point east/west, parallel to the track of the moon.
The angle between a pair of such needles is usually very close to, but almost never exactly, ninety degrees. Measuring such angles with precision is a keystone of navigation across strategic scales, and relevant to advanced geomancy even in very local applications. For exploration or otherwise drawing new maps that can retain useful accuracy beyond a couple hundred miles, you'll also need a set of gyroscopes, a foucault pendulum, or some other system for tracking absolute orientation (and distance, of course). The optics in ordinary surveying gear can be sufficient, when the horizon includes a mountain range, watchtowers, or some other set of landmarks whose relative positions are known, but doing it that way involves notably more tedious math with corresponding opportunties for error. Across such distances, the apparent direction of the movement of celestial bodies across the sky is not uniform, but rather a swirling vector field, like deep ocean currents or high-altitude prevailing winds, for reasons which will be addressed in more detail below.
The Storm Forge is mainly reached by traveling from the Blood Mire directly against the pull of gravity, or in layman's terms, up. Necessary distance varies considerably by location, time of year, and other factors, averaging 200 feet, and is difficult to identify precisely without magic. At most a hundred miles of straight-line travel in any direction is enough to leave, but "straight-line travel" is harder than it sounds (an uncontrolled fall will almost always work, but might take several hours) because the internal geometry is mostly spherical - that is, large circles have smaller circumference than you'd expect based on their radius. As a result off interface effects (distantly related to the way the surface of water can be transparent or reflective depending on angle), someone looking back down into the Blood Mire after, say, climbing a beanstalk of abnormal size, will see a curved horizon almost exactly as if they were looking at a spherical world of finite size. This also makes extremely high-speed air travel less useful than IRL, since it's a choice between flying low enough to risk crashing into mountains, trees, and waves, or high enough to waste speed going in weird zigzagging loops. Gravity is on average weaker, and much less consistent. You want to have wire-fu duels in an Escheresque cloud palace, this is where to go.
Tiamat (the only Old God referred to by a name that's phonetically consistent across most languages, rather than descriptive titles translated according to their conceptual content) also runs parallel to the Blood Mire, on the opposite side from the Storm Forge, with a similar ambiguous border, and is flat on average but has the highest incidence of topological defects among the Old Gods. Extracting or exploiting the more stable ones is a high-risk, high-reward industry - several different industries, really. Mining, fishing, transcontinental trade through naturally occurring shortcuts, that sort of thing.
The Green Breath has hyperbolic geometry www.roguetemple.com/z/hyper/ which becomes more extreme as you get further from the source plane and closer to the Unbroken Word on the W axis. Conveniently, your position on the W axis is easy to check: the closer you are to the source plane, the more of it is visible as illusions around you. Transetheric communication and scrying effects take advantage of this effect, which is why they're usually limited to observing a 10' radius around the target. Ethereal travel is never a shortcut (unless something seriously weird is going on), in fact under most circumstances it involves crossing at least twice the equivalent distance on the source plane, but has the distinct advantage that what few obstacles are present can almost always be circumvented in some straightforward way. Lots of stuff hides in all that extra space, including the 'back-end machinery' of haunted houses. At least, when it's a real haunting, rather than carbon monoxide poisoning.
The Unbroken Word seems in some respects like it has hyperbolic geometry, but on closer inspection works more like dream logic, or puzzle platforms in Unnatural Selection, or The Wired from Serial Experiments Lain, with locally flat regions connected to each other through vast blackness by links that owe more to conceptual sympathy than spatial proximity. Stars are access points to other planes, and demiplanes sufficiently stable and inhabited to have their own Green Breath. Any given plane forms one star per quarter-million square miles of healthy ecosystem on average. Thin spots or desolate biomes spread regional borders further while dense, complicated areas have them closer together. That, along with the geometry of the Green Breath, is the source of accuracy limitations in cross-planar travel: if you only need to be within a couple hundred miles, aiming for the correct star is sufficient, but anything more specific depends on very fiddly terminal guidance.
Two possible major exceptions to that stars-per-square-mile rule are the sun and moon, though another interpretation would be that they present the expected number of stars, but all clumped together instead of scattered around, corresponding to a stronger conceptual coherence than the other Old Gods, perhaps even a degree of self-awareness. In the cosmos's current configuration, the Horned Queen and the Burning Hate roll along the Unbroken Word's only two consistent horocycles at consistent yet incalculable velocities - literally incalculable, it's one of those infinity-divided-by-zero sorts of problems - which, filtered through the perspective of the Storm Forge, cause the day/night cycle, months, tides, and so on.
Time of day, seasonal weather, and tides vary across the Blood Mire because those are based on the relative position of the sun and/or moon, but the moon phase and apparent position of the City of Brass or other sunspots are everywhere simultaneous, because those depend on the absolute orientation, while the timing of eclipses is also constant (and on a consistent, albeit difficult-to-calculate, schedule) regardless of orientation, because they can only occur at the two points where the solar and lunar horocycles intersect. Some areas see a given eclipse as total, others as partial, again due to relative position - but this is not consistent from one eclipse to the next, though there definitely seems to be a pattern of some sort. Figuring out how to systematically predict the totality distribution of eclipses is an open problem, and there are indications that even the Old Empire muddled along with complex and unreliable epicyclic approximations. Local calendars mostly work the way you'd expect, but occasionally there's an eclipse during, say, the half-moon, which would be absurdly impossible IRL. There are two different types of eclipse, corresponding to the two different intersection points, but the distinction is seldom relevant outside astrology. If you see something that looks like a lunar eclipse, that's either a strictly local phenomenon, such as a giant monster or battlestation occluding part of the night sky, or anomalous activity on the lunar surface. Hiding in the most secure basement available would be a reasonable precaution in either case.
The axioms which define the geometry of the Hollow Pillar contain a contradiction, so everything there is simultaneously possible and impossible.
Serpenthearth has hypergolic geometry, meaning it spontaneously combusts on contact, and accordingly isn't a very popular vacation spot.
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