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Message: <blockquote data-quote="Fieari" data-source="post: 1383823" data-attributes="member: 16221">In one of my campaigns, I've had some success with granting my PCs some time traveling capabilities in addition to planar travelling capabilities, and as such, I've had to deal with making a multiverse up.  I never read planescape, so obviously I'm not using that.My multiverse is considerably more vast, more unimaginably vast than what I've heard about the great wheel.  It works by the iterativly expansive nature of dimensional mathematics.Consider a world.  Perhaps our world.  And then all of the possibilities that could have occured had other events happened.  If you consider all these possibilities to be points on a numberline, every world that can happen naturally without interferance is a Rational Number.  Every world that requires outside interferance... such as someone leaving one world and entering another, altering it from that point on... those are irrational numbers like pi, or e.  Between any two rational numbers, there are an infinite number of irrational numbers, and between any two irrational numbers, there are an infinite number of rational numbers.Now, for any world described as such, the coordinate origin represents the most likely world... however, interestingly enough, the coordinate origin can be set on any given world... your homeworld, to be specific.  Travel away from the coordinate origin is difficult, and the further you progress in either the positive or negative direction, the more difficult travel becomes.  Eventually, the strain will become too much, and there is a point beyond which you may not travel.  However, there are shadow realms you can travel too instead, which have slightly different rules.These shadow realms, or etherial realms, or whatever... are represented by the COMPLEX number plain... that is to say, i and -i.  For those that need a quick brush up on complex mathematics, 1i is described as the number such that when you square it, it equals -1.  These numbers are perpendicular to the standard number line, forming a cartesian coordinate grid.The point is that these worlds are combinations of worlds, and are mostly intangible, although they can be traveled too.  ...er, that was an vastly inadequate explanation.  Let me start using some math now.Our homeworld is at the coordinate origin (0,0).  For the sake of argument, let's say that the limit of physical is (-10,10).  However, we wish to travel to 15. The point we need to travel to is the one such that a 90° angle is formed when you draw a line from your homeworld to the destination world, with a limited distance of 10 away from the homeworld.Since 15 is the hypotenuse of our little right triangle, and 10 is the max of the "opposite" leg, the length of the "adjacent" leg is findable by the pythagorean theorem.  c^2 = a^2 + b^2.  b^2 = c^2 - a^2.  b^2 = 15^2 - 10^2.  b = (225 - 100)^.5   b = 125^.5   b = 11.18...The longer b is, the more ghostly you appear in that world, and the more energy (magical or spiritual or physical, although the amount of physical energy required would be PHENOMINAL) must be expended in order to manifest in any capability.  Positive i worlds are positive energy planes, and negative i worlds are negative energy planes.  This provides an explanation for ghosts.Side note: The length of a describes the similarity of the etherial world to your homeworld, in terms of what you see and move around with.  The proportion of your homeworld to the destination world is a/(1/b), such that the shorter be is, the closer it is to the destination world.  Alternatively, the proportion of the destination world to your homeworld is b/(1/a).Also, if you feel like it, you could work out the exact coordinate position of the etherial world you're located on using sine or cosine, but I think that'd be an exercise in silliness as no real useful information would be derived from it.  You could argue that there's no real use in calculating the above either, but it demonstrates the theory, and you can use common sense from there.Now then, this all merely describes ONE WORLD.  One plane, if you will (a 2d coordinate system is a plane, after all).  One set of laws of physics, including flow direction of time and everything.  If our one number line for physical worlds was the X coordinate system (and remember that the etherial worlds were i), then for other planes, we need the Y coordinate system.---I need to break here, to get something to eat.  I may or may not resume after I return depending on whether or not anyone is interested or cares.</blockquote>

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