IN> 355/113

[William Keith]

The heavens girdle the Earth around
and, standing athwart the poles, extend
as much farther than straight plumbs sound
as circles about their centers bend

A distance named, but never known
corraled above, corraled below,
but forever forever more unshown
an Abyss across which none can go

But falls the Spark, from God to Man
Quickens, inspires, illuminates,
And ascending, prayers, from Man to God
Knowing, for a moment, what Omniscience can
Closing, a little, the length to where it waits,
Measuring a truer, straighter rod.

-----

      The celestial realms are a place separated from Earth by a shadow 
and an infinity.  They overlap and wrap around the corporeal world in 
subtle dimensions, touching here and there at Tethers where 
understanding reaches across the gap that separates the material world 
from human conception.  What humans are really capable of understanding 
not only ties the world to Heaven and Hell, it in large part defines 
them, and thus the boundaries of that knowledge are a crucial front in 
the War.

      One of those boundaries is pi.  The ratio of a circle's 
circumference to its diameter is symbolic of the extent of the heavens 
above Earth, and its irrationality is symbolic of the inability of the 
material world to encompass all of reality.

      While these facts were known to angels in theory before the Fall, 
the true ramifications of their collected import were not made clear 
until humans began to codify and bound an understanding of pi.  Often 
bound up with astronomical and calendrical concerns, echoing with 
metaphorical connotations of the structure of reality itself, advances 
in human understanding in this area had the possibility to change the 
very rules of such things as Tethers, ascents and descents from the 
celestial realm, and Essence flow.  This is not something so mundane as 
the mere accumulation of digits: the necessary advances involve 
fundamental changes in human awareness of the nature of pi.

      Discoveries that tend to "push the heavens away" make pi less 
accessible.  They include the realization that pi is not a whole 
number, that it is irrational, that it is transcendental.  When such 
discoveries are made, codified, and published, pi collects a greater 
air of ineffability, and the separation between celestial and corporeal 
grows.  The most famous example of such a thing is the closing of the 
Higher Heavens, but over time, Roles have begun to need noticeably more 
maintenance.  Statistics suggest disturbance for a given amount of 
damage to the physical world has also increased, and Superior fuzz has 
gotten stronger.  A GM who has gotten this far and is still intrigued 
by the notion may wish to make more radical changes, such as 
historically having ascent to celestial form cost a mere 1 Essence, or 
having use of a Tether be possible without having to take celestial 
form.

      (One theory floated among Ethereals is that YHVH stole pi from the 
Babylonians, who had codified the idea of its non-wholeness, and used 
this characteristic to create the first abyss of separation between the 
celestial and ethereal realm.  Later, he employed its transcendental 
nature to further wall off the Higher Heavens.  Uriel's desire for 
purity rebelled against drawing power from a fundamentally unknowable 
irrationality, and he had to be absorbed into concept to put Heaven 
back under control before he Fell.)

      All is not entirely separating, however.  Mankind increases its 
understanding of what pi is as well as what it is not: the number is 
bounded above and below, we learn that it takes on values of certain 
geometric limits, or that it appears as the extension of this or that 
series or continued fraction.  When such things are learned, the 
celestial realm comes closer to the corporeal world.  For simplest 
starters, breakthrough discoveries often spark a Tether.  Lightning has 
gotten the lion's share of these, but Destiny has seen a few.  In the 
20th century, the Hindu goddess Namagiri obtained such a pi-Tether from 
the belief and work of Srinivasa Ramanujan. (Ramanujan consistently 
claimed that Namagiri appeared to him in his dreams and wrote his 
discoveries on his tongue; he was, indeed, known to arise from sleep 
and write down, instantly, wonderful formulas which were later to be 
formally proved sound.)  More than this, however, are the beneficial 
effects of closer ties between the celestial and corporeal realms.  
These include the appearance of Tethers with the Quiet feature, that 
subdue Disturbance within them, and the discovery of an ability of 
celestials to switch Vessels without taking celestial form.  These 
"advances" would have defrayed the difficulties imposed by an increase 
in the Essence cost of taking celestial form, or Tethers suddenly 
requiring taking celestial form to ascend.

-----

      So what does this all have to do with China?  Around the year 470 
CE, the Chinese astronomer and mathematician Zu Chongzhi wrote the Zhui 
Shu, in which he demonstrated that a circle of some 10,000,000 chang in 
diameter would have a circumference of more than 31415926 but less than 
31415927 chang.  A change being a bit less than 12 feet, this 
interesting distance meant that Zu was calculating on a circle of 
diameter roughly the same as the circumference of the Earth; so some 
strange realm that somehow encircled the Earth about in another circle, 
in some odd direction, would have its size thus bounded.  Upon this 
datum he propounded the Tam-ing, the Calendar of Great Brightness, 
which would have been exceedingly accurate for its time.

      Alas, court intrigue got in the way, and the calendar was never 
promulgated.  Still the Zhui Shu was widely praised, and Zu Chongzhi's 
easier approximations for pi, 355/113 and 22/7, came in to widespread 
use.  Generally agreed to be due to this advance was an increase in the 
appearances of what are now called Friendly Tethers, which interfere 
less with each other.  Lightning also got a minor Tether out of the 
affair at Zu's workplace, although it rated only an Attuned Seneschal 
and faded after a few centuries.  Kronos, however, was the Superior who 
gave a Distinction to the Factions demon who had engineered the delay 
and dismissal of the Tam-ing.  Few beings are quite sure why: it is 
rare that a demon ever has reason to dig through intel reports from the 
era to find demons reporting a peculiar, migraine-like sensation of 
brightness when they were in Divine Tethers, despite being in corporeal 
form...

-----

      Among open questions about pi, by the way, there remain several 
doozies.  Is pi normal?  That is to say, do all its digits appear 
equally often if one looks at a very long string of them?  If it is, 
such a discovery would, using the concepts above, probably "bring the 
heavens closer."  On the other hand, is pi random, that is to say, do 
its digits pass various strong randomness tests?  If true, this 
discovery would likely "push the heavens away."  Either could be used 
as the MacGuffin for a Lightning/Technology, Destiny/Fate game, with 
the result having a substantial effect on the game world *as the 
celestials experience it*, without disrupting the background "real 
world" too much.

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Oh, and happy Pi Day, everybody.  :^)

William