Alternate world
An alternate world is a world that contains notable similarities to some other world, but also possesses significant differences. Usually, an alternate world resembles the base world geographically—having the same large-scale distribution of land masses and major natural features. It also usually is home to mostly the same types of life, or close analogues. The exact degree of resemblance varies widely, however; some alternate worlds may have exactly the same inhabitants, but with some notable difference, while others may share little beyond their layouts. Alternate worlds can even exist in different cosmoi, and possess entirely different physical laws than the base worlds. Beings or objects appearing in multiple alternate worlds (or with different versions that are still similar enough to be recognizably altered copies of the same thing), they are said to be polyyparic, and the word "aliter" refers to the various counterparts. Most often, the copy of a person in an alternate world is said to be an aliter of the person in the base world, but technically the copies on any two worlds can be said to be aliters of each other. (The words "polyypar" and "aliter" have applications beyond alternate worlds—the latter in particular, which applies to panypares as well as polyypares—but it is across alternate worlds that polyypares are most common.)
While any types of worlds can have alternates, usually an alternate world refers to a planetary world of some sort. However, non-terrestrial planes may have alternates as well, as can pocket planes and any other sort of pediological construction. While there is some evidence suggesting that inhabited worlds are more likely to be alternates, some pediologists think this may be merely because uninhabited and uninhabitable alternates are less likely to be discovered.
Alternate worlds are sometimes referred to as "parallel worlds", but strictly speaking this is a misnomer. Some alternate worlds may indeed be parallel in the geometrical sense, but by no means all are, and some planes may also be geometrically parallel that are not alternates.
Base worlds
The "original" world the alternate world is compared to is called the base world. Strictly speaking, however, which world is the alternate and which is the base world is only a matter of perspective—generally the residents of any world, if aware of similar worlds, will consider their own world the base world, and the others the alternates.
There are criteria some pediologists use to determine which world is the base and which the alternates, based on which world seems to share more of the characteristics of one world than others; if there is a world that most of the other alternates seem to be more similar to than they are similar to each other, then that world is the base world. It is on this basis, for instance, that True Earth is generally considered the base world of all (or most of) the alternate Earths. However, such similarity is difficult or impossible to measure objectively, and the possibility remains that the discovery of other alternates, yet unknown, would lead to a different world seeming to be the most similar to the others, and the most appropriate base world. Therefore, even these criteria for defining the base world are somewhat dubious, to the extent that many pediologists prefer to simply call similar worlds alternates of each other, and discard the notion of a "base world" altogether.
Types of alternate world
Alternate worlds can vary from each other in almost any way, as long as there are enough similarities to still leave them classified as alternates. Again, most commonly the basic geography of the worlds are the same (or mostly the same, with perhaps an added, deleted, or altered continent or two), but everything else can vary. Still, there are some categories that alternate worlds can be divided into, based on their relationship to the base worlds. Not all alternate worlds fall into these categories, but they remain useful for discussion because of the large number of worlds that do.
Divergent world
A divergent world is an alternate world that was identical to the base world up until a certain point in its history, and then diverged due to one event that occurred differently. Sometimes this event is easy to identify, corresponding to a major historical occasion; other times it was a seemingly insignificant incident with large repercussions. In any case, even after the point of divergence, divergent worlds, like other alternate worlds, sometimes (though not always) stick closer to their base worlds than strict chance would suggest, with the same people (or rather their aliters) showing up in similar positions in both worlds despite their different histories, and events in the alternate world mirroring events in the other despite their different circumstances.
Ferine alternate
A ferine alternate is an alternate world populated by sonders, that is, anthropomorphic animals (or, rarely, other life forms) of various sorts. These may or may not be aliters of people in the base world. If they are, some people seem to fairly consistently have aliters based on the same animals (though perhaps with occasional exceptions); others have aliters of widely varying forms across different ferine worlds.
Fictive alternate
A fictive alternate is an alternate world that seems based on a fictional work in the base world. Fictive worlds are not necessarily alternates, but may be if the fictional world in question is based on the real world. For example, if one actually traveled to a version of Earth where Sherlock Holmes (and the other characters of his stories) had been real, or where the exotic sites of Gulliver's Travels actually existed, one would be traveling to a fictive alternate, since on the base world (Earth) these people and places exist only in fiction. It's not uncommon for a fictive alternate to combine fictional elements from multiple works, though some pediologists have pointed out the possibility that such alternates are in fact based on other (perhaps unknown) fictional works that borrow from all the works in question.
Magical alternate
A magical alternate is simply an alternate world where some form of magic is possible. The term is usually used only when magic does not exist in the base world. If the base world itself is a magical world, then alternate worlds are likely to be as well, though it's possible to have non-magical alternates of magical worlds. It's also quite possible for a base world and an alternate world to both have magic, but of entirely different arcana.
Mythical alternate
Frequently considered a subclass of fictive worlds, mythical alternates are alternate worlds where elements of myths and folklore of the base world are true. Some mythical alternates realize only the myths of one particular culture, and not even necessarily all of them; others incorporate the myths of many different cultures, with some changes to reconcile any contradictions. Mythical alternates are often found as part of a chorodesis with one or more eschatological planes, spiritual planes, or other planes that play a part in the myths they are apparently derived from.
Temporal alternate
A temporal alternate is an alternate world that resembles the base world at some past (or, rarely, future) point in time. The resemblance need not be exact, and in fact an exact resemblance wouldn't survive first contact with other worlds anyway, since anything introduced in such contact that didn't happen in the base world would cause it to diverge. In practice, however, many temporal alternates somehow tend to smoothe over potentially diversory events and still roughly mirror the history of the base world.
Allodeses
Some alternate worlds seem to be more closely connected than others, in the sense that it is significantly easier to travel among them than outside them, or that there are notable polyypares common to all of them. Such alternate clusters are called allodeses. Allodeses may all be the same kinds of alternates (all divergent alternates, or all temporal), but this is not necessarily the case. As with other chorodeses, it is common for inhabitants of an allodetic world to be aware of the other alternate worlds within the same allodesis but to believe that those are the only alternate worlds in existence, to not be aware that there are other (more difficult to reach) alternate worlds outside their cluster.
Origins
The full reasons for the presence of alternate worlds have never been elucidated. Certainly there are isolated cases of alternate worlds or groups of alternate worlds that do owe their existence to known events, generally involving powerful magics or highly advanced technologies, but only a very small minority of alternate worlds can be thus accounted for. Nevertheless, some pediologists believe that all alternate worlds do ultimately come from such events, even if the causes for most of them have not been discovered, and that there is no general explanation needed. Not everyone agrees with this, however, and the search for the origins of alternate worlds continues. Some hypotheses have been advanced, but none has met with universal accord.
Quantum mechanics
It is sometimes assumed, in Xi, that alternate worlds exist as a consequence of the quantum mechanical "many worlds interpretation", the idea that each time an event could occur in more than one way, the universe divides to form a distinct universe for each possible outcome, and that therefore there exists an infinity of worlds where things went differently. This is a misconception, however; all respected pediologists agree that the many worlds interpretation has absolutely nothing to do with alternate worlds in the sense under discussion. For one thing, it wouldn't account for the fact that alternate worlds also exist outside of Xi. One could argue that perhaps equivalents to the quantum mechanical many-world interpretation also exist in the physics of those cosmoi but have not yet been discovered, but that seems rather like special pleading, and still wouldn't readily explain the existence of sets of alternate worlds spanning multiple cosmoi. Also, even within Xi, the many worlds interpretation is not, as many people mistakenly infer, a necessary consequence of quantum mechanics. It is called an "interpretation" rather than a hypothesis or a theory because it is exactly that: one possible way to interpret the results of quantum mechanics, but by no means the only one. There are several other at least equally tenable interpretations of quantum mechanics that do not involve the existence of an infinite number of worlds corresponding to every possibility.
Perhaps the strongest objection to the idea that alternate worlds are merely the universes predicted by the many worlds interpretation, however, is that the observed distribution of alternate worlds does not in any way match the expected distribution the many worlds interpretation would imply. Because the universe has been around far longer than humanity has, there were many more opportunities for divergence before the rise of humanity, and the vast majority of worlds shouldn't have humans at all. If one assumes that for some reason it should be easier to get to worlds the diverged more recently from one's starting world, then the opposite problem exists; in that case, it seems that most accessible alternate worlds should have diverged so recently they were almost indistinguishable from one's world of origin. Nor, given the diversity of known alternate worlds at various levels of likeness to any given base world, is it workable to suppose that any given age of divergence makes worlds most accessible, or to come up with any other simple formula to account for observations. One might, of course, postulate that there exists some complicated rubric explaining why the particular observed motley set of alternate worlds is accessible, but this, again, seems like shameless special pleading, and just kicks the mystery up a level without doing anything to really resolve it.
None of this implies that the many worlds interpretation is necessarily wrong; it may still be that there are in fact an infinity of universes corresponding to every possibility (although there are philosophical reasons for disliking the idea). However, even if there are, it seems that these universes have no connection to the alternate worlds known to pediologists.
Anthology theory
A somewhat more viable, albeit still dubious, theory about the origin of alternate worlds involves the so-called anthology theory. According to this theory, all alternate worlds are in fact fictive worlds, but they may reflect works of fiction that inhabitants of any given world are unaware of. This includes whatever world one considers the supposed base world, which itself is actually a fictive world based on fiction from another world—either there is an infinite chain of fictive worlds, or a cycle. Since the same work of fiction may exist in multiple alternate worlds (and possibly give rise to only a single alternate world), the number of fictive worlds does not necessarily explode with each "generation".
While the anthology theory isn't actually inconsistent with any observed data, it remains completely unproven, and possibly unprovable.
Alternate universes
Although the term "alternate world" generally refers to a planetary world, if an alternate world is a part of a universe, then that implies the alternate world is a part of an entire alternate universe. The inhabitant of one particular world may not give much thought to the other worlds in the universe, but they may have variations of their own. Oddly, however, different worlds in an alternate universe may be entirely different kinds of alternates—one may be a fictive alternate, one a divergent world, and so forth.
While it seems certain that the presence of an alternate world within a plane implies the existence of an alternate version of the whole plane, whether the same is true of a cosmos remains uncertain. It could be that each alternate world is embedded in an entire alternate cosmos; it could be that alternate planes still lie within a cosmos, and that some planes within a cosmos may have more alternate versions than others. There is evidence for both possibilities, and some pediologists think the truth lies in a third possibility that has yet to be ascertained.