Geometry of The Soul: The Struggles of Tritopea

[Tritopea]

The inverted tetrahedral frustum balanced precariously above the floor tiled in triangular lattice. Atop it, legs draped over one face, sat Breeding Monitor Tri-015, studying triangular sheets of paper that lay similarly on the triangular table. On it was written, in the angular script of Tritopean English, the population reports for the last month. Near the upper vertex of the first page was the primary number, at which Tri-015 now stared thoughtfully:



Swaying carefully on his well-balanced stool, Tri-015 began his report on a new sheet:

On
The Need
For Increased
Population Growth

For
Twenty
Years, the
Population level
Has been held static
At [14, i.e. 105 people]. But this quantity
is clearly not a desirable point
at which one may freeze growth.
It should be prudent to increase the
efforts of the breeding pools in order to
achieve a net simultaneous birth of [8]
In order to add a new level of population.

Thus,
We propose
An aggressive
Campaign to absorb
Tritopeas into the breeding
Program. According to current
estimates, reducing the accepted age
by [2] years and by coordinating the active
pool to breed within the accepted level addition
threshhold of [one] year. It is imperative that the pool
be maintained at maximum capacity in order to achieve
this new layer and the next, and others past, with expediency.

We
Hope you
will adopt our
recommendation,

Tri-015, Primary Breeding Monitor
Tri-038, Breeding Monitor
Tri-045  Breeding Monitor

His report done, Tri-015 replaced the thin, spike shaped pen into the pyramidal well of ink. Tritopeans knew the secrets of the printing press, and prototype typewriters were in development, yet formal documents by tradition were written on the triangular paper, always. Tri-015 folded each corner of the sheet inward to form a half-sized equilateral triangle, and then retreated to a corner of the room where he sat upon a triangular mat. Closing his eyes and resting each hand on a vertex, he cleared his thoughts, a simple meditation to be done before delivering his report to the council in a mere hour.

Three shrill ringings of a bell awoke him from his trance. Standing and gathering various folded sheets, he walked from his office towards the Council Building to give the Breeding report, unable despite the meditation to dispel the nervousness of what judgment could come of his suggestions.

[Tritopea]

In another office in the Temple of Scientific Endeavours, the Master of Mathematics  Tri-036 paced impatiently around the three sided room. Triangular papers were strewn about the desk, ink stains splotched randomly about the table. Tri-045 twirled the pen in his right hand as he thought furiously about the topic that had been baffling him for the last month.

Much progress had been made in the curious subject of "rate-of-change" mathematics. Mathematicians had, with reluctance and meeting great controversy from social leaders, developed the concept of "rational" numbers. From there came the even more daring development of "decimal" expansions that extended to infinity, forming numbers filling the void between 0 and 1. But then came a curious problem, for when the Tritopeans graphed "functions" like the velocity of a tetrahedral weight falls per second of time, they found beneath the unaesthetic curve an area that represented the distance travelled. It was nearing blasphemy, but they developed a system to handle the rate at which the function changed, but its area was a mystery. Clearly, the ability to find such areas would unlock new, great secrets.

Yet there did not seem any way to find such area. On many of the sheets were drawn curves under which were embedded sets of triangles, equilateral, isoceles, scalene... Yet it did not seem possible to find a formula for such a limit. Tri-036 knew that his position would be in jeopardy if he could not find a breakthrough...

Then, in a sudden epiphany, he realized: If the function's value is a vertical side of a right triangle, then there is another right triangle which would fit to form a rectangle. Such a rectangle... yes... it would work beautifully... Excited, Tri-036 scribbled formulas on a fresh page, knowing that this was the single insight that could revolutionize all Tritopean science, and in only a few minutes, the Council would see its genius...

[Tritopea]

In the tetrahedral Temple of The Elders sat the six at the vertex of the chamber, stolidly watching the massive, three sided wooden doors that lay  closed opposite. In second, they would open, and the council would convene. Along the each face of the chamber stood a triplet of priests, each holding with reverence a corner of an equilateral triangle of quartz. They were clad, like the Elders, in white robes held rigidly in tetrahedral shape, making pyramids of cloth about them. The Elders, though, had robes ornately lined with patterns of silver thread, and wore atop their heads pyramids, capstones to their geometric clothes.

The chamber was lit dimly by glowing lamps on pedestals surrounding the room, but now the huge window, almost a face of the wall cut out of the room near the towering ceiling began to align with the Sun. The first rays of natural light shone furiously into the room, reflecting from the mirror coated face opposite the window, above the door on which there was now a slowly, rhymtic knocking. It brightly illuminated the elevated throne of the elders, the council's pinnacle set apart from the rest of the assembly.

"Tri...top...eaa...." intoned the priests in chorus, each syllable coinciding with a knock of the door.

The Elders rose. Together, they chanted, "The Elders will that we convene upon this Sacred Hour. Let the worthy and the unworthy pass through this threshold, and be judged of their worth. Let the sacred power of the Three," the priests now held their crystals to the air, now glimmering in the afternoon light. One priest, taller than the other two of each group, supported the upper vertex. "Let the people assemble, and bask in the glory of our light."

The knocking stopped and the doors opend slowly. In threes entered the Tritopeans, heads bowed, all clad in triangularly creased robes of grey and white, of blue and green, and of red. They stepped without hesitation into the chamber, forming rows of the triangle before the Elders (skipping the row of four and five, and beginning with six), who continued to recite: "All business is holy business, and so only through the grace of the sacred shall it be conducted. In our place shall each of us stand, and in our place shall each of hear the doings of society. The Elders who see all, who hear all, the Elders whose blood is of the Triangles themselves, they alone will judge the worth of the lower echelons." The first few rows stood at attention, clad all in robes of various colors. Behind them filed in the white. "We do all together, but the Elders alone may sanction it. We think as one, but the Elders must approve. So it is willed. And so it shall be, and shall always be." Twelve rows were in place now. "The time has come, and so shall Tritopea be reforged,  recrystallized into the future ahead." A pause, as the 105th  entered and took her position at the lowest vertex. Then, the Elders bellowed in union, "Thus assembled, the chamber will be sealed!" The doors slammed shut by the force of their will, i.e. a mechanical device. "The assembly, closed in spirit to all but the Truth, is pure and it is sanctified. Thus, the Council begins!" The priests lowered their triangles with more chanting of "Tri...top...eaa" that echoes throughout the chamber as 105 voices chanted in unison. The quartz structures were lain carefully on the ground, and the nine priests took their places in the reserved rows, kneeling in a curious position with hands pressed together as a steeple. The others followed suit, and upon six further recitations of the chant, the Elders sat. The Council of Tritopea had begun in earnest.