Cosmological Topology Of The Multiverse
Don’t Try Dunking This
Doughnut!
Legal Notes
Given the old TSR’s propensity for flinging lawsuit threats left,
right, and center when their material was used for derivative works this notice
hereby declares that I in no manner challenge the trademarks and copyrights held
by TSR, Wizards of the Coast (who bought TSR) or Hasbro (who bought Wizards Of
The Coast).
For brevity’s sake, let’s understand that any time I mention
“TSR” I also mean WOTC and Hasbro, ok? Which means all trademarks,
copyrights, and all the other legal mumbo jumbo really belongs to Hasbro, but
TSR is more familiar (and easier to type!) so I’ll use TSR when talking about
materials created by any of the three entities.
Every place mentioned in this article was created by TSR, for
example the Prime Material Plane, Astral Plane, etc. Worlds like Greyhawk,
Toril, and Krynn are also TSR’s. The various concepts of the planes
of existence were also created by TSR, and any books mentioned here, unless
otherwise specified were also written by TSR. Oh, yes, the AD&D game was
created by TSR.
There, that should satisfy the legal beagles.
Introduction
Players of the AD&D game have a vast canvas on which to paint their
fantasy adventures. Beginning characters start by adventuring around a small
town or village, but soon expand their operations to other countries, other
continents, even to the bottom of the seas between those continents.
Then there’s the Spelljammer campaign setting, that lets players
expand beyond a single planet to explore other planets within their star system,
indeed to expand to other star systems and explore them.
You’d think with the entire universe to play in players would be happy,
wouldn’t you? But sometimes, they aren’t. So TSR came up with the idea of planes
of existence. Basically a plane of existence is an entire infinite universe.
However (and here’s the attraction) in these different universes (coexistent
with our own) the very laws of nature are different in bizarre and interesting
ways. Travel is possible between these other universes by use of spells like plane
shift, planar gates, and other DM provided toys.
We’re not talking about alternate realities like the television show Sliders
or the multitude of alternate-history novels. (At least not yet, but that too is
available to AD&D players!). Instead think in terms of Heaven and Hell. For
political/religious reasons TSR doesn’t call them that, of course. Or call
them angels, demons, or devils. But it’s the same idea. The realms of the
gods, the places the population goes when they die, for good or ill.
And that’s not all. There are planes of transition (like the Ethereal
and Astral) that are universes unto themselves. There are the inner
planes, infinite universes of elemental matter used to construct all the other
planes.
And finally, there’s the city of Sigil, a unique and special
place that has its own unique position among the planes that make it worthy of
special attention.
Oh, and then there are demiplanes, sort of wannabe planes that
drift within the Ethereal plane. TSR’s Ravenloft, The Demiplane Of
Dread is one example. Really powerful wizards can also create small demiplanes for their
own use.
All these planes of existence are detailed in TSR books like Manual of
the Planes, and the Planescape campaign setting. Like the Spelljammer
campaign that has many books and modules, there are lots of books that
describe the various planes in great detail.
Still feeling crowded? Ok, how about time travel to give you some
more elbowroom? There’s TSR’s Chronomancer supplement to allow
players to roam the Demiplane of Time. Basically it’s your typical time
traveler plot. And let’s not forget alternate history timelines (sort of
sideways time travel).
All this marvelous space to play in, but there’s just one small
problem: bringing it all together in one logical, consistent whole that makes
sense and lets you picture the whole thing in your mind.
Cosmology, Quantum Physics and the Multiverse
You might be thinking that the Planescape campaign and the Manual
of the Planes already offer a cosmological model of the planes—and you’d
be correct. There are however, a number of problems with the model that bug me.
The biggest one is that it can’t be visualized as a single entity; it requires
two separate models to accommodate the inner and outer planes. Further it
doesn’t take advantage of topology to explain the peculiar nature of the Astral
plane in regards to portable holes and bags of holding. Finally, it doesn’t
properly describe the relationship of the outer planes to their elemental
correspondences on the inner planes.
In another vein, it makes no attempt to explain the nature of the city of
Sigil or the peculiar nature of the Outlands, also known as Concordat
Opposition, nor does it try to combine the Demiplane of Time into the model. (A
misnomer, time isn’t a demiplane, but no matter).
The new model I propose is based on some cosmological speculations about
our own universe, and its peculiarities as found at the sub-atomic level, known
as quantum effects. I also stole some hyper-spatial theory from physics
as well.
Then I threw it all into the black caldron of my fevered imagination,
stirred vigorously, left to simmer, and found—doughnuts!
A Whirlwind Tour of the Planes
Broadly speaking you can divide the planes of existence into two
categories: the inner planes and the outer planes. The inner planes are also
called the physical planes and the outer planes are also called the spiritual
planes. However, don’t make the mistake of thinking that the outer planes
are immaterial; a person traveling there would find rocks just as hard and water
just as wet (well, generally, the laws of nature being somewhat creative
in the outer planes). The labels physical and spiritual have more
to do with the planes essential essence than their physical nature, we’ll
cover this a bit more thoroughly later.
AD&D’s Quantum Physics
Our universe has several laws that describe behavior at the
ultra-microscopic level of quantum physics, the most famous of which is probably
the Heisenberg Uncertainty Principle.
The AD&D multiverse has its own fundamental laws upon which
everything else is built, its version of quantum physics. There are two so well
known they’re quoted in the Planescape setting, these are the Rule
of Threes and the Rule of Opposites. A third law (speaking of the Rule
of Threes) was one I discovered in creating this topological model, the Rule
of Centricity.
The Rule of Centricity
The Rule of Centricity says that everything will tend toward a
center point. Gravity is a perfect physical example of this effect. In AD&D
cosmology this concept is repeated over and over again, it is perhaps the
fundamental law of the multiverse. This law provides the multiverse with
inertial resistance, order, and static balance.
In terms of hyper-spatial theory this law corresponds to a 0 dimensional
point.
Because we refer to this rule constantly, in this article we’ll
abbreviate it ROC.
The Rule of Opposites
The Rule Of Opposites says that everything has an opposite. You can’t
have down without up, good without evil, and so on. This law provides the
universe with dynamic balance, symmetry, and potential energy. It corresponds to
a 1 dimensional line in hyper-spatial theory.
Because we refer to this rule constantly, in this article we’ll
abbreviate it ROO.
The Rule of Threes
The Rule of Threes says that the “natural” (rest state) of groups is
in multiples of three. There are, for instance three dimensions in physical
space. This law provides the multiverse with motive force, chaos, and
hyper-spatiality. It corresponds to a 2 dimensional plane in hyper-spatial
theory. It also lays the implication for hyper-spatiality itself.
Because we refer to this rule constantly; in this article we’ll
abbreviate it ROT.
The Prime Material Plane
This is the player’s home universe. When you think of most AD&D
campaigns, this is the plane they’re located in. Doesn’t matter if you’re
talking about a DM’s home grown campaign or a TSR setting like Greyhawk
or the Forgotten Realms, or even a Spelljammer campaign, they all
take place on the Prime Material.
The prime can be thought of as an inner plane, although most would
consider it a separate category in itself. Cosmological theory accepts either
view; the former is in accordance with the Rule Of Opposites, the latter
with the Rule Of Threes. However further examination of the model would
seem to indicate the Prime should be considered a separate category.
The Ethereal Plane
The Ethereal plane is another specialized plane. It serves as a
buffer plane between the Prime Material and true inner planes. In this
respect the Prime, Ethereal, and Inner planes satisfy the Rule
of Threes. As a group of three, these planes satisfy the Rule of
Opposites when the Outer planes are considered.
The Ethereal plane is divided into the Border Ethereal and Deep
Ethereal. The Border Ethereal surrounds each plane the Ethereal touches,
and is a “border effect” where the Deep Ethereal mixes with the
planes it touches. The Border Ethereal that surrounds the Prime
Material plane is where effects such as Oil of Etherealness work.
Ghosts also exist in the Border Ethereal, as well as creatures that can
“phase” like phase spiders. Generally, any creature that exists on both
planes, or can affect creatures on the other, operates in the Border Ethereal.
The Deep Ethereal can be thought of as the
“true” or “pure” Ethereal plane. This is where the demiplanes are
found. Demiplanes are sort of planes that never quite made the big time.
The Inner Planes
The inner planes can be thought of as the ultimate in physical reality.
The four planes mentioned most often are the planes of Earth, Air,
Fire, and Water. As you can see, in accordance with the Rule of
Opposites, they come in opposite pairs: Earth/Air, and Fire/Water. These planes
provide all the material to build the rest of the Multiverse.
In accordance with the Rule Of Threes however there are two more planes,
making a total of six. The extra planes are the Positive Material and the
Negative Material, which are also opposites. These planes provide all the
energy needed by the Multiverse, the Positive Material supplies light,
life, and goodness, the Negative Material supplies death, entropy, and
evil.
Where these six planes “meet” (more on this later) you have Para-Elemental
and Quasi-Elemental planes, which also come in opposing pairs. For
the purposes of this model these additional 16 planes are not really important.
Note that there are a total of 24 inner planes (8 groups of 3).
The Astral Plane
This odd duck of a plane is the outer plane equivalent of the inner
plane’s Ethereal plane. In this plane dimensions don’t work quite the
way they should, portable holes and bags of holding are
non-functional here. This plane (like the Ethereal) is a buffer zone, in
this case between the Prime Material and the Outer Planes.
The Outer Planes
The outer planes are also called the spiritual planes, although
anyone traveling to them would discover rocks in the Outer Planes are just as
hard as on the Prime Material.
While the Outer Planes have a real, physical existence they also have a spiritual
existence—in other words they have moral and ethical alignment, good versus
evil, law versus chaos. This is why they are called the spiritual planes.
The City Of Sigil
The city of Sigil occupies a special place in the Multiverse—it’s
right in the very heart of it all. The city is a nexus point, containing portals
to literally everywhere. We’ll cover Sigil a bit later; all you really
need to know is that Sigil (unlike the inner and outer planes) acts in
accordance to the Rule Of Centricity, not the Rule Of Opposites or the Rule Of
Threes.
The Demiplane Of Time
We haven’t forgotten this plane, but as you’ll see in a moment the
plane of Time isn’t really a plane in the sense that the others are. Be
patient, all will be revealed.
Hyper-Spatial Theory Explained
Ok, now that you have a (rough) idea what planes are, it’s time to
start putting our model together.
What Exactly Is Hyperspace?
Hyperspace is any space that needs more than 3 coordinates to locate a
particular point in it. For example, assume our real universe is a sphere. You
can then locate any point in space by describing that point’s distance from
the center using 3 measurements: how far above/below center it is, how far
left/right of center it is, and how far in front/behind center it is. This is
why our universe is described as three-dimensional.
What’s A Dimension?
A dimension can be thought of as a pair of opposite directions,
for example up/down. In addition, dimensions must always cross at 90 degrees to
each other. Consider: up/down, left/right, and forward/back. Each dimension
crosses the others at right angles. You can’t have a fourth dimension in
physical space because it wouldn’t be able to cross the other three at 90
degrees.
Time As The Fourth Dimension
You may have heard that scientists call time the fourth dimension. They
do, and it is—sort of.
What they mean is that it really takes four coordinates to define any
point in our universe. In addition to the standard up/down, left/right,
forward/back you also have to specify future/past. Just because the ship was
docked in New York yesterday doesn’t mean it will be docked there tomorrow,
right?
Thus our own universe is hyper-spatial, it requires more than 3
dimensions to completely describe the location of any point in space-time.
Hyperspace Applied To The Multiverse
As you may have guessed by now, the Multiverse is also hyper-spatial in
nature. But instead of 4 dimensions, it has nine (three groups of three,
in accordance with the ROT).
Why nine? Let’s consider each group of dimensions and why they’re
needed.
The Lower Three Dimensions
Ok, we already know that you can locate any point in (a) universe by
specifying 3 dimensions. Each plane in the Multiverse is a complete universe in
itself, so you need 3 dimensions to locate a point within the plane.
The Middle Three Dimensions
We have a lot of planes to arrange in some kind of organized
model. As it turns out, the planes have a spatial relationship to each other
that can be described in three dimensions. You can easily picture the inner
planes, for example, forming either a cube or a ball with the Positive
Material on top, and the Negative Material on the bottom, with the
other 4 major elemental planes forming the sides of the cube or ball. Think of a
beach ball and you’ll pretty much have the idea.
The Upper Three Dimensions
The upper three dimensions are actually for time. Picture a single
river with the multiverse floating along in it. This gives a simple future/past
dimension.
Now have an infinite number of rivers to the left and right of our river.
These other rivers are “parallel timelines”, places where history runs a
little differently. The further left or right you go, the more changed history
becomes.
Finally, add rivers above and below. This third dimension of time is
predicted by the Rule Of Threes and so undoubtedly exists. Exactly what it is a
dimension of is something of a mystery. Perhaps choices are more than a
simple yes/no, or perhaps the third time dimension measures some as yet
unsuspected aspect of existence.
The Cosmic Doughnut
Now that you know what planes are, that there are nine dimensions in the
Multiverse, and that the planes actually have a spatial relationship to one
another it’s time to put it all together.
Concentrate On The Middle Dimensions
Our model is supposed to describe what the Multiverse “looks like”.
To do that we’re not going to need the lower three dimensions since we
aren’t locating a point inside any of the planes. Likewise we’re only
dealing with a single copy of the Multiverse, so we needn’t consider alternate
histories nor the past or future, so we can ignore the upper three dimensions.
Which conveniently leaves us with only three dimensions, letting us
visualize the multiverse model like we might a model airplane.
So What Does The Multiverse Look Like?
It looks like a lumpy doughnut. Ok, ok, if you want a more scientific
term it’s a torus, the shape you get when you take a round tube and join the
open ends together.
Remember, we’re talking about the middle three-dimensional view, which
is the only place you can see what the Multiverse looks like.
The Skin Of The Doughnut
The skin of our torus is the entire Astral plane. In the middle
three dimensions the astral plane is actually something of a two-dimensional
space, it has “width” and “breadth” but no “depth”. This gives the
Astral much of its bizarre nature when dealing with extra dimensional magic. The
sixth dimension of the Astral plane is “in use” for another purpose.
The Sixth Dimension And The Astral Plane
The purpose of the sixth dimension in the Astral is to “twist” the
dimensional orientation of the outer planes like a hyperspace Möbius
Strip. Here’s a bit of mental contortionism for you, the outer planes actually
switch the position of the lower and middle set of dimensions!
In other words, in the inner planes (and the Astral itself) the lower
three dimensions are used to move physically within a single plane, and the
middle three dimensions are used to travel between the planes.
In the outer planes the middle three dimensions are used to move
physically within a single plane, while the lower three are used to travel
between the planes.
It is this dimensional displacement that allows the use of spell keys and
many of the other unique properties of the outer planes. While creatures may not
be hampered by this juxtaposition of dimensions, there are subtle effects, such
as the outer planes being “more”. Prime travelers always note that mountains
are bigger, seas vaster, water wetter, and so on.
This has to do with the fact that the middle dimensions are higher energy
states than the lower three dimensions. The fact that the outer planes contain
matter constructed entirely within these higher energy dimensions gives them
“more”—of everything. This is why material from the outer planes is so
valuable in magic items.
The Insides Of The Doughnut
Everything inside the doughnut can be considered the Inner Planes, just
as everything on the outside of the doughnut can be considered the Outer Planes.
But it’s the arrangement of the insides that are so vital.
To understand the relationship of the inner planes to one another
you’re going to have to construct a mental model and change it.
Imagine that the Inner Planes are really a sphere for a moment; say a
beach ball. The Manual Of The Planes pictures this ball with the Positive
Material plane being the “north pole” of the sphere and the Negative
Material plane being the “south pole”. Make your sphere hollow, filling
the inside with the Ethereal plane like gray smoke. In the very center of
the beach ball put a softball to represent the Prime Material plane.
This is the traditional view from the Manual Of The Planes but
it’s not quite right for our model. To fix it, turn the beach ball on its
side, make the plane of Fire the North Pole and the plane of Water
the South Pole. Got it? Good, now imagine you put one hand on each pole and
start to squeeze the ball (imagine you’re super strong!)
Squeeze the ball hard enough and what happens is the sphere will turn
into a torus. The Prime Material plane will form the inner ring of the
torus, with the elemental planes (still
buffered by the Ethereal plane) are surrounding it everywhere else,
making the outer rim of the torus consist of the Positive Material, the Negative
Material, the plane of Earth and the plane of Air. This
arrangement is vital to the moral and ethical alignments of the outer planes, as
we’ll see in a moment.
In this toroidal model the planes of Fire and Water form a
ring around the top and bottom of the torus respectively. Notice that all planes
still “touch” each other just as they did in the spherical model, all
we’ve done is change the topology of the model, not the planar relationships
to one another.
Ok, now wrap the Astral plane like a skin around the inner planes.
The Outer Planes
We’re almost finished. The outer planes, of course, sit on the outer
side of the torus, just as the inner planes are inside the torus. But here’s
where our model and the traditional model part company.
Have you ever wondered exactly why the outer planes have
alignment? Good versus evil, law versus chaos? It’s because of their
“proximity” (in the sixth dimension) to the appropriate inner planes.
I bet you can guess what comes next, right? Elysium is the plane
of neutral good, good without regard to law or chaos. As it turns out, the Elysium
sits smack over the Positive Material plane, separated only by the Astral
plane. This physical proximity in the sixth dimension means that the outer plane
is most affected by energies from the Positive Material, which arrive via
the Multiversal equivalent of quantum tunneling, where energy can
“leak” through an insulating layer that’s thin enough. And the Astral
Plane is certainly thin enough because in the sixth dimension it’s almost
not even there! Of course the operative word is “almost”. If it weren’t
there at all then Elysium would simply be the Positive Material
instead.
Likewise, on the other side of the torus the Gray Waste sits
directly on top of the Negative Material plane, which feeds the Gray
Waste a great deal of negative energy. And, as you’d expect, the Gray
Waste is a pretty nasty place.
Sitting on top of the plane of Earth we find Mechanus, the
ultimate plane of Law, and across the torus from Mechanus, we find Limbo,
directly on top of the plane of Air. These planes derive their alignment
from the basic physical properties of the underlying inner planes, but
because of the half-twist the sixth dimension provides in the Astral,
physical properties become spiritual ones.
Planar Layers
Remember I said the Multiverse looks like a lumpy doughnut? The
cause of the lumpiness is that (unlike the inner planes) the outer planes have
multiple layers, each layer infinite in the lower three dimensions. In effect a
layer can almost be considered a separate plane, with one crucial difference.
Planar layers, unlike planes, can be accessed directly from the lower
three dimensions, in other words, you can walk from one layer to another,
just as you would walk from one country to another.
Planar layers are an interesting phenomenon. Their formation depends on
the mixture of lawfulness and raw energy. Too much (or too little) lawfulness
(provided by the plane of Earth) prevents the layers from forming. On the
other hand it doesn’t matter what form of energy is used (positive or
negative) to form additional layers.
Look at Mechanus and Limbo. Neither have multiple layers,
because Mechanus simply has too much order and Limbo has too
little. There are those who argue that Limbo has 4 layers but since
there’s no difference to the layers sages are in disagreement.
The “corner” planes (The Seven Heavens, Nine Hells, Abyss, and
Gladshiem) tend to have more layers than the middle ones (Elysium,
Gehenna, Mechanus, and Limbo) although there can be exceptions (like Gladshiem).
Note that the Abyss has by far the most layers of all, perhaps the
balance of chaos and negative energy is particularly well suited for layer
formation.
Concordat Opposition
The final mystery of the outer planes lies in the neutral plane of Concordat
Opposition, also known as the Outlands. This plane, like the Prime
Material is neutral with regards to law, chaos, good, and evil.
Unlike every other plane it also has a center, a vast pillar stretching
upward infinitely tall. As one approaches this pillar the laws of nature begin
to fail, within 100 miles of the pillar life itself can’t exist, magic fails
long before this point.
Yet floating above the top of this infinitely long pillar is another
torus—the city of Sigil. Our cosmological model needs to account for this
aberration if it’s to become complete.
The Outlands lie along the inner rim of our lumpy doughnut, just
above the Prime Material plane, separated in the sixth dimension by the
merest wisp of the Astral plane.
And like the Astral plane itself the Outlands have a
dimensional anomaly, this time involving not just the sixth dimension, but all
six lower dimensions. In the exact middle of the inner rim these six
dimensions knot upon themselves to form the “hole” in the torus, the force
that forces the “sphere” into a doughnut shape.
It is this collusion of dimensional forces that not only form the
Multiverse into a torus, but also cause the laws of the Multiverse to start
breaking down in proximity to the very inner edge of the torus. Think of this
dimensional anomaly the same way you would a singularity (black hole) in our
universe. The closer you get to it, the less the laws of the Multiverse apply.
Higher dimensional activity is affected first (magic), and then lower
dimensional activity is also affected (chemistry). Even closer and the laws of
gravity and optics start to break down.
In other words, the “infinitely tall pillar” is an illusion caused by
the unimaginably powerful dimensional warp around the inner edge of the torus.
At the inner edge itself nothing can exist, not even raw matter or
energy. The dimensional warp creates a singularity; a 0 dimensional point, a
hole into which the Multiverse pulls itself and then pulls the hole in after it.
The City Of Sigil
Inside the center hole created by the dimensional warp lies another torus
at right angles to the first, balanced in the dimensional “eye of the
storm”. This torus is the city of Sigil.
Unlike the planes of the multiverse the city of Sigil (while quite large
as cities go) is nowhere near infinite. In fact, the city’s toroid is fixed in
size by the size of the Multiverse’s center hole, the city can neither grow
nor shrink, it is exactly the size it must be to maintain its delicate balancing
act inside the dimensional singularity formed around the middle of the
Multiverse’s torus.
Sigil’s torus maintains a reasonably habitable environment, keeping the
dimensional forces outside the boundaries of its own ring. Unlike the closed
Multiversal torus, Sigil’s torus is open along the inner rim; the city is
built inside the torus, with “gravity” actually being supplied by the
spinning of the torus. In other words, anyone falling from the torus’s center
point would strike the inside surface of the outer rim of the torus.
The walls of Sigil’s torus are actually formed by buildings,
built to form one solid surface. These buildings can be up to 10 stories high,
although this isn’t uniform across the entire torus, nowhere are the buildings
less than 3 stories high.
One curious fact, there are no windows or doorways showing the
“outside” beyond the rims of the torus. If anyone climbs to a roof they see
absolutely nothing—literally. Anyone stupid enough to jump into the nothing is
dumped randomly somewhere into the multiverse, with no way to control the plane,
nor the point of entrance onto the plane. Considering much of the Prime
Material is open airless space and that many of the other planes are
inhospitable to life, this is almost certainly fatal.
There’s also a good chance that anyone leaving the torus at the wrong
point will end up falling into the dimensional singularity’s “wall”. This
has roughly the same effect as falling into a black hole would in our
universe—instant and utter annihilation, to the point it would take a wish or
travel into the past to recover the individual.
Odds And Ends
The multiverse isn’t perfect; there are flaws between the planar
boundaries. In the astral these manifest as conduits, color pools, and rifts.
In addition as we’ve pointed out quantum tunneling effects allow energy and
matter from the inner planes to penetrate the sixth dimension of the Astral
plane to give the outer planes their properties.
The Ethereal plane has ether cyclones, basically a tear between
the Ethereal and Astral planes. Such rifts pass through the Prime
Material in the middle three dimensions, so in theory it might be possible
to dump yourself out of an ether cyclone back to the Prime Material,
although it would probably be safer simply to pass on to either the Astral or
Ethereal.
