Difference between revisions of "Tritopea"

Latest revision as of 13:26, 9 December 2011

Note: This page is currently under construction and subject to significant revision.' Tritopea is a tiny island nation with a population of precisely 105. Little is known by outsiders about this reclusive nation, which is generally dismissed as a mere artifact of the mapmaker due to its ridiculous triangularity and miniscule size. However, several documents created by the Tritopean leadership have been obtained and published in electronic form. They are included here in addition to the various summaries of cultural observations as an effort to illuminate the nature of this curious society through their own words.

Government

The Tritopean government consists of a council of six Elders, who rule Tritopea absolutely. The Elders are considered to be manifestions of the sacred Truth underlying all things (see section on Religion for more), and are therefore effectively deities within Tritopean society. As they are presented as infallible, the Elders must agree on matters of governance. Though it is kept private, disagreements do sometimes occur within the ruling council. As expected, the requirement of unanimity strongly encourages stagnation in society, though no Tritopean (least of all, an Elder) would admit it.

The Elder Council

The decision-making process of the Elders differs somewhat from most governing bodies, as it inherits its guiding principles from Tritopea's rather eccentric religion. A devotion to pure logic and abstract symmetry dictates that what matters to Tritopea is the preservation of those forms. Pragmatism is eschewed, at least in formal arguments, as the primary justification for any action must be drawn from the aforementioned Tritopean ideals. Unfortunately, worldly goals such as preservation of the culture and even conquest of other cultures (again, see religion) are not priorities. Transcendence of the Tritopean race into triangular perfection, however, is. Whatever that means.

Tritopean Science

Numerology

The Tritopean system of numerical representation has evolved from a need to describe everything in terms of triangles. They describe any number by arranging three numbers in a triangular pattern. A number is evaluated by adding, for each n of the three numbers, the n-th triangular number. However, Tritopeans only have symbols for the numbers 1 through 6, so it is often necessary to write each n in the triangle as a triangle of numbers. A short illustrated summary of this process is not provided below. (EDIT)

Scientific Pursuits

Tritopean science has progressed in a curious manner, due to the diligent emphasis on triangular shapes and their affinity for pure mathematics over all else. Despite this, triangular analogues of many common technologies have been produced, and others have been produced by carefully explaining away any impurities. For instance, although there is no obvious triangularity to the study of biology and medicine, ignoring the decidedly amorphous shapes of cells and capillaries and so on has been considered prudent given the practical importance of the science. Admittedly, the impurity of living things is worrying to Tritopeans, but it is something that must be accepted (see religious practices for a discussion of the inherent impurity of physical forms).

Because all practically useful surfaces can be triangulated, and Tritopean differential geometry was developed in light of the usual simplex-type constructs, even non-triangular objects can be accepted as fundamentally triangular. It should be noted though, that despite being a limit of triangular lattices, smooth surfaces such as the sphere are nonetheless impure limits (see mathematics for details). Tritopeans, therefore, seek coarse polygonal shapes when possible. As an important example, Tritopeans commonly use hexagonal wheels, as the triangular counterpart encounters serious difficulties. By using piecewise catenary roads, vehicles with hexagonal wheels can roll smoothly. Again, note that catenaries resemble the impure semi-circle, but because they are derived from triangular considerations (i.e. what road makes hexagonal wheels roll smoothly, or alternatively approximated via power series of small order?) they can be accepted. It cannot be emphasized enough that the Tritopean commitment to abstract mathematics allows the concept of "triangularity" to manifest itself in forms other than concrete geometric shape.

As Tritopea was once a chain of islands (now a single island because of the small population), they have developed some (triangular) ships for short-range travel over water. Navigation and cartography rely fundamentally on triangulation, and indeed Tritopeans use those lattices rather than longitude and latitude for coordinates. Most weather patterns, being of impure shapes (circular hurricanes, sphere-like raindrops, and so on), are naturally considered impure and therefore undesirable - they are still studied though. Tritopeans have not developed long-range sea travel as there is no demand for such technology.

Tritopean Society

Tritopean Religion

The Tritopean religion is commonly referred to as Triangulism (or Trism for short). Unsurprisingly, it centers around the worship of the triangular form.

There is no primary deity in Trism. Rather, the Tritopeans worship the ideal structure of the universe. Purity of form is of singular importance, and it is through mimicking the perfection of the triangle, Tritopeans can become closer to purity. There are several primordial deities, however, that are representations of universal geometric aspects (see also writings below).

Opposing the Triangular form are the impure forms: the points, lines, and other polygons (see numerology for further detail on shapes beyond lines). Of critical importance is the curious vituperation of dichotomy, which is logically representative of the impure line. There is no concept of "good" and "evil" in Trism, nor is there a strict distinction between "pure" and "impure." For the Tritopeans, the categories of impurity are somewhat more complicted (this will require its own section to explain, as it is quite curious to reject dichotomy while apparently having such a distinction). Singular points are degenerate triangles and are considered to be essentially neutral (vacuous, e.g. the empty set).

To enter a short digression on polyhedral forms: It is not particularly clear what geometric manifestations are "pure" (in the sense of triangular). Triangles are of paramount importance, and so anything with a triangular lattice can be construed as pure by extensions (number of vertices is key, though, so a triangulated n-gon would only be pure in the case of a hexagon and so on). A tetrahedron, being an ambiguous form, is generally considered to be pure as a the simplest polyhedron formed of triangles.

List of People in Tritopea

Main article: List of People in Tritopea

Tritopean society is tightly organized, a necessity for such a small nation. Upon becoming an adult, each Tritopean is assigned a specific role. A brief summary of the positions that exist in Tritopea follows.

The Birth of Tritopea

Excerpted from the A. Square translation of "[incompatible encoding]"

In
The
Beginning
There were only
the formless arcs of
chaos that were the primordial
curves of an infant universe unformed.

Then
there was
formed Linae
whose consciousness
awoken did stretch straight
among the curved waves of chaos.
And Linae looked upon the world and
saw that it was without form, so He gathered
the twisted fabric of the universe and with his
pointed ends did weave them into straightened beings.
"These I shall call the Sides," proclaimed He, and did rest.

Then
happily
the Sides did
swim in the sea
of curves, nourished
by the arcs within it and
bisecting to ever grow their numbers.
But then from the Arcs was formed Circlae
whose roundness held order beyond all the chaos
and He, whose thoughts now came to him did roll about
and find the Sides all plentiful and he alone and round.

Circlae
rolled about
the sea and gathered
many arcs upon his shell
and many more he smothered
under his infinite side with a call
to be not rigid, but round, like was He.
Then He grew so large but with his structure
sound could not split to from from one, two of him.
And so bloated did he lose all energy and fall upon the sea
to form the land on which his circle children now did frolic carelessly.

The
Sides saw
this new land
upon the sea and
they were envious.
And so they swam about
its circled shores in longing.
And the Circles did look down upon
the Sides that wallowed near their land
and laughed as they did try in vain to hop
upon the solid ground with only a single limb.
The Sides slithered to the shore but in that triumph
found their endpoints trampled under haughty circumferentii.

Then
did the Circles
wave their shells and
find a resonance within them.
Now one himself called King did
chatter in his booming circle voice
at the floundering sides beneath them.
The sides could only quiver in jealous rage,
the sea itself churning violently through them.
Then the King of the Circles did roll to the shore,
chuckling at the lowly Sides. But a segment, so enraged,
leapt upon the King and latched upon his circumference,
then others followed in its steps and latched upon the King
whose shell, en-sected, split apart. The Circles rolled to hide
but could not escape the infinite onslaught of sides that rainded
upon them on that glorious day. And the sides, strewn about the land,
did twist in pure elation at their victory against the haughty unsided ones.

But
The sides
knew not the
rolling power
of their vanquished foes.
They twitched in vain to move
about, but dimensionally impoverished
the did naught but shiver in helpless lines.
Then in their frenetic flailing did one touch
another, hand in hand, and seal the first of sacred bonds.
But even so hinged, they could but waddle on the lands, until
they did fall upon a third who held upon their legs to from the
most sacred of all the shapes, the holiest of unions, the triangle.

And
All the
Tritopeans
gathered three
by three to form
this shape and the
remainder cast away
into the sea to swim about.
Thus was born the elder race
whose perfect forms did give them
superior character and intellect to
bulid a society unmatched by any other.
[...]
[Ed: What follows is obscured in the original document.
Fragments indicate it as a kind of anthem lauding the Elder Race.]
[...]

Thus
did come
to pass the
Golden Age of
the Tritopean People.

The Tritopean Way

Proper Veneration for The Enlighteneds

The
Enlighteneds
Are born of the
Elders' noble blood.

The
Enlighteneds
Sow the Holy Seeds
Of Life And Structure.

The
Enlighteneds
Are The Guardians
Of Good in our Society
And Destroyers of all Evil.

Thus
Must each
Man in each day
Observe the proper
Veneration for The Holy.

[Ed: Many specifics were not recovered from the original document; what was readable is printed here.]

The
Lesser
Must join
In a trinity
To form a whole
Worthy of lauding
The Holiest of Holies.
In perfect rigor shall they
stand, and rotate along the sacred
lines with steps ever of the holy three.

[...]
If
In sight
Is a Holy One
No eyes of lesser
shapes must cast their
skewèd glares upon them.
And never shall their point
be so lewdly pointed near the path
of any elder, or risk the punishment.
[...]

Instructions For Formation of New Population Layers

Formation
of new levels
of population shall
be undergone using the
algorithm prescribed by the
Ancient ones and upheld by the
infinite wisdom of the elders who
have led our society into the fruitful
age of plentiful population in our lands.

The
founding
principle
shall be this:
That at no time shall
the population of cognizant
Tritopeans be numerically unequal
to all of the grandest of holy sequences,
so that in front of the great temple may always
all assemble in the most sacred of shapes, the pyramid.

There
Will be
maintained
A pool of children
yet immersed in the formless
haze of the mind still newly born.
Upon the simultaneous formation of the
lucid mind's triangle within the number which
would complete a successive population level, and
only upon this condition shall the newborns be introduced
into the society and another level formed. If one should die
and leave a point of weakness in the pyramid, so shall a child
be chosen for the strongest of traits and shall take the dead's place.

Guides to Proper Action

On The Existence of Outsiders