Recently,
the Mathematicians of Mechanus have discovered a type of
magic quite different from the traditional method -- a
type that involved great quantities of mathematics. The
Digitologists of Zakhara (a region on the prime world of
Toril, better known as the Land of Fate) uses extensive
mathematical equations to very precisely draw the spell
into effect, rather than bluntly drive a formula into
one's head until memorised and then regurgitate it later.
They develop an understanding of the magic which allows
them to augment it further than was previously thought
possible.
Of
course, the Mathematicians celebrated this
accomplishment. For years, they have been trying to find
the reverse of Wild Magic, and Digitology seems to be it
-- a rigorous and highly organised form of magic which is
not only predictable, but can be exploited to augment the
powers of magic even further. News of this discovery
spread to Sigil, where it was received with virtually no
interest: "Don't the Mathematicians use math for their
magic anyway?" Only a few people really understood the
potential of this type of magic. Before long, the Guvners
(always looking for a good loophole) had gone through the
right authorities to form a collaborative institute of
research with the Mathematicians, to try to discover the
limits of Digitology. This facility, creatively titled
the Institute of Digitology, has become a bit of a
hotspot.
Located
near the Fortress of Disciplined Enlightenment (in planar
terms), the Institute is made up of the most brilliant
Guvner mages and various interested Mathematicians. To
better understand the topic of their research, the
Institute has recruited a fair number of wide-eyed
Zakharan Primes, all Digitologists, to teach and learn at
the Institute. Overall, the facility seems fairly
unobtrusive, on the surface.
Investigators
have found, however, that there are elements to the
Institute which have made several other groups
uncomfortable. Reliable information has reached the ears
of the Athar that the Zakharan Digitologists believe it
is a crime to attempt to spread the belief that no gods
exist -- and have insisted that this rule be enforced in
the Institute. A lawful member of the Athar was captured
and put to death for casually speaking on the subject. Of
course, the Athar are grievously offended by what they
view as 'thought policing' and 'a breach of diplomatic
decency.' The resulting friction between the Guvners and
the Athar in Sigil is evident as Guvner-funded temples
have received significantly more attention from the Athar
(led by the antisocial Hobard).
Wild
mages are also disturbed at what they see as a threat to
their own style of magic. Though they are incapable of
doing any direct harm to the Institute (since it is
located in a Plane which negates wild magic), some have
tried to intimidate the Guvners in Sigil with threats and
a very small number have actually enlisted the aid of
normal mages to commit acts of terrorism against the
Institute.
One
final concern is that the modrons will learn the secrets
of the magic and become all the more powerful. After all,
many high-ups are already spellcasters, and this will
make them all the more powerful. Fortunately, since the
modrons are rarely a threat to anyone outside of
Mechanus, this is a minor concern at best.
In
my forays across the planes, I have discovered a number
of interesting things:
The
Spire on the Outlands: This spire is definitely
defined by a mathematical equation. Trouble is, no-one
can agree on what equation. (Of course, the Bleak Cabal
claim that no such good sense exists, but I know what
I've seen) Because space curves near the base of the
spire, all attempts to measure its curvature have so far
failed. Visual estimates from far off don't square with
what's seen close to.
Infinity:
Not even true-born planars know everything about
infinity, even though it touches their lives so
fundamentally. A prime called Georg Cantor seems to have
had the dark of it quite well. He said that there was not
just one kind of infinity, but at least two. He talked
about 'countable' and 'uncountable'
infinities.
Hold
on, I hear you cry, how can you count infinity? Well,
berk, it assumes you've got infinite time. But if you
stumble on something uncountable, you couldn't count it
even with infinite time. The classical example is of the
whole numbers, or integers as they are called by the
Mathematicians and Guvners. The integers are the
definitive countable set. You can go 'One, two, three...'
forever, and you'll never miss one if you've got long
enough. But if you try to include all real numbers,
including the so-called irrationals, like pi (bane of
modrons!), you'll find that there's no way to account for
all of them. You'll always miss infinitely many for every
and any one you count.
To
see it, just consider how many numbers differ from an
infinitely long number like pi by just a single digit.
Get the idea? Now, the question for the infinitude of
planes is, which things in the planes are countable, and
which uncountable? It is reasonably transparent that
people are countable, and arbitrary points uncountable.
But when it comes to layers of the Abyss, no-one's sure.
If they are uncountable, then some must be empty. What's
in an empty layer?
Space
dimensions: Here's a topic that invariably confuses
those not used to operating in strange environments. Many
primes maintain that space is three-dimensional, and that
time is a fourth dimension. It emerges that this is a
pitifully inadequate explanation when you travel the
planes. For example, all planes with a discernible form
and more than one layer (except Bytopia, but I'll return
to that) have at least four space dimensions: An up-down
dimension, a forward/backward dimension, a left/right
dimension and an up layer/down layer dimension.
There
are exceptions. Mechanus has only one layer and therefore
three space dimensions can describe it adequately.
Bytopia has two layers, but they meet in a plane. This is
like separating numbers into positive and negative. You
still only have one line of numbers, but some are
positive and others negative. Likewise, half of Bytopia
is Shurrock and the other half is Dothion. In this way,
Bytopia has two layers but only three space dimensions.
Gehenna has four layers, but is a three-dimensional space
and all the layers are finite.
The
inner planes are always five-dimensional; for example,
the plane of Fire has the dimensions up/down, left/right,
forward/backward, magma/smoke and radiance/ash. The
Astral Plane, just to be awkward, has no layers and no
time, but is in fact a bizarre non-space. This leads to
many bizarre results.
Limbo
and the Abyss are so badly defined that their
dimensionality is not a comprehensible concept. It has
been suggested that there exist planes we can never visit
that are home to two-dimensional beings who would treat a
visit to the planes we experience much as a clueless
prime experiences the Astral for the first time,
especially if they were bodily adrift in the
Void.
Speaking
of the prime, it might be useful to point out that the
prime may have a layered structure too. The prime most
people think of is one of perhaps three main primes (one
in which magic works but there is no phlogiston, one we
know about already, and one from which I am writing this
which has no inherent magic at all), and in addition to
these, there are a number of 'pocket primes', realms
resembling the primes we have mentioned, but actually
more like demi-planes in size and inhabited by
over-powers. At least, that's the theory.
