General Numogrammatics, Part 1: CX Tabulation

The Lemurian numogram is a powerful system of accretive mathematics for the way it derives philosophical, mythical, magickal and polytical insight from immanent mathematical structures. Landian neolemurianism is adamant on the exceptionality of base-10 due to its global hegemony, yet there is nothing either in nature or culture which privileges the decimal  over all other systems. That there exist other numogram-like structures is a fact: Yves Cross reports on a base-16 “hexadecigram” in an article over at Vast Abrupt. Recent discoveries, however, suggests the panorama of still-unexplored numolabyrinths to be overwhelmingly big.

The surfacing of documents previously believed lost reveals that from 1958 to 1968, Mexican anthropologist Teodora C. Lombardo and her colleagues over at the Mexican Institute for Experimental Education (IMEX in spanish) worked on a system which described a large quantity of numograms, which  were the occult basis for a “Xenodidactic” educational program intended to prepare revolutionary subjects. The system, called General Numogrammatics, consisted in its fullest form of 256 numograms with thorough mythical and scientific attributions and used a special numbering system with 256 characters which also served as ideograms. Sadly, the full version of the system, contained in the unique copy of an IMEX-printed book called The Numogrammaticon, was lost after a police raid shut down the clandestine college in 1968, but the surfaced documents (police reports, confiscated notebooks, and folders upon folders of IMEX research materials) allow us to reconstruct the system, albeit partially.

We at Tzitzimiyotl Central (Surface Web beacon here) have so far calculated the information necessary for constructing all numograms from base 2 to 36. These have been organized to form a partial version of a structure first discovered by Lombardo’s team in 1964: the Digital Pyramids. The Greater Pyramid, or Pandemonic Pyramid, arranges all syzygies of all number bases in a single table; the two Lesser Pyramids, on the other hand, show only even or odd bases. According to Lombardo, these three structures reveal the mechanics of expanding, conquering civilizations in a process known as Pyramidal Expansion. Sadly, technical limitations have stalled the work at this point, and so Tzitzimiyotl Central has reached out to the CEO to tackle the problem together.

 

We Tzitzimimeh believe the Numogrammatics of Lombardo were only the beginning of a much more powerful system. A letter apparently written only hours before the raid suggests that Lombardo’s team was looking to expand numogrammatics beyond the realm of integer numerations, but their suppression by the Mexican government (then led by known CIA asset Gustavo Diaz Ordaz) cut short this possibility. We intend to finish their job.

To this end, we present the current status of research into General Numogrammatics.

Any numogrammatical (a.k.a. pandemonic) system base-n can be described as n zones named by the integers 0 through n-1, paired into syzygies which add to n-1. Each zone x has a cumulative gate equal to the tellurian plexing of the xth triangular number number. Each syzygy is in turn linked to a “tractor” zone determined by the difference of its members; i.e., the tractor for syzygy 8::1 is 7 because 8-1=7. By calculating gate and tractor functions, a graphical representation of the desired numogram can be constructed.

N-16
Base-16 numogram.

 

The graphic approach to numogrammatics, however, becomes unwieldy as radix increases; the sheer number of zones and syzygies results in complex structures with many possible geometrical arrangements. This problem was side-stepped in the 60s by two members of Lombardo’s team: mathematician Marina Constantino and computer scientist Adela Xirón, who devised a tabulated form to describe base-n numograms. A Constantino-Xirón tabulation, as it is known today, consists of three tables: the Zones table lists all zones and gates; the Tractor table lists the tractor currents for each syzygy; and a Circuit Map providing a color code for the tractor regions. All entries in the first two tables are colored according to the Circuit Map code.

 

CX-10
CX tabulation for N-10

Using an algorithm written for a clandestine Soviet implementation of ALGOL-60, the two scientists generated the CX tabulations for bases 2 to 256. During this process, a fundamental structural distinction between even and odd bases quickly became apparent. Even numograms have only complete syzygies, closed traction cycles, 3 current lines and one periodic structure appearing every 6 bases from 16 onwards known as the Cave System. Odd numograms, on the other hand, have one unpaired zone along with its syzygies, open traction regions, 2 current lines and one periodic structure, still unnamed, every 2x bases beginning in base-3. We will deal with current lines and periodic structures in the next post dealing with the Digital Pyramids; for now we will explain the particularities of odd numograms.

In all numograms base-n where n is an odd number, there is one self-cumulative non-paired zone equal to (n-1)/2; because there is no other zone to calculate tractor difference with, Zone (n-1)/2 can be considered to have Zone 0 as its tractor zone, and no syzygy ever has Zone (n-1)/2 as its tractor. Further, odd numograms have “open” traction regions, meaning a terminal, or central, loop (be it a 1-step plexing or an n-step cycle) is fed into by a linear sequence of syzygies with a beginning and an end; Aracne Fulgencio, who illustrated the Numogrammaticon, likened these open regions to comets, and biologist Eva Lombardo speculated about their connection to the times of the Late Heavy Bombardment. CX representations of odd numograms use colors differently from those of even bases: darker hues represent the “core” closed loop of the traction region, while ligther ones represent the “tails” which feed into one or more of the core’s syzygies. Although we know Constantino-Xirón used a special method for noting which tails coupled onto which part of the core loop, it hasn’t been found. Our provisional CX representations of odd bases look like this:

CX-11
CX tabulation for N-11

We Tzitzimimeh have so far generated the CX tabulations for bases 2 to 36, divided into two workbooks, one for even and one for odd bases. Work is currently underway for expanding this into higher bases, with base-62 as the current landmark.

Despite their differences, even and odd numograms seem to be connected by an undercurrent which is not yet understood. An anachronic multi-base expansion of Barker’s Spiral devised by Fulgencio, called The Gyre points to a possibility. The Gyre maps all bases n and under in a single spiral that continually opens forwards. Whilw Fulgencio’s original rendering is said to have consisted of a three-dimensional wire sculpture, it was destroyed along with the IMEX building. A two dimensional rendering up to base 10 is presented here:

Multibase Barker Spiral (2-A)
The Gyre

Base 2 and 10, the lower and upper limits, have their connections in black. Bases 3 and up are color-coded by descending color frequency, indicating progressive opening up of The Gyre (increasing wavelength). As in Barker’s spiral, left hand connections indicate (n-1)-sum pairing, while those on the right hand indicate n-sum pairings. Interestingly, these connections correspond to the syzygies of even and odd numograms, respectively. Color circles around a number indicate it having the (n-1)/2 position in the corresponding base. The fact that the spiral pattern is born of the alternation of even- and odd-base numograms suggests a connection between these apparently different bases. A note in Xirón’s diaries records a hypothesis by another unnamed IMEX professor, who suggested numograms as “pneuminous atoms”, with different properties determined by the number of zones much like chemical properties are determined by the number of protons. According to this hypothesis, odd numograms act like “excited states” or “unstable isotopes” of the more stable even numograms. Sadly, not much more information on this has been found yet.

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