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.

In this informal chat Johns continues his thoughts on the threefold of experience (Heidegger) and the constant conflicts of concepts which create productive difference (Hegel’s dialectic). Johns suggests that the contemporary ‘subject’ is determined by societies power to employ it as yet another object of value within its system of arbitrary value. Johns explains that this operation functions on the false notion of reality as tautological (pragmatist) and the subject as tautological (the subject as tool).

Philosophy can a be tedious business. Repetition of the same matter is often the plat de jour. These recent notes do not alter this pattern. The situation we have here is an interesting one insofar as we have two philosophies that seem to have some potential to overlap. Is it an overlapping or a synthesis (or a struggle)? The repetition is the grinding over the same territory in search of the point of clarity.

The two philosophies in question are the pneuminous accretive theory and the assimilative-neurotic theory. Both notions instantiate autonomy to concepts.  The former by means of the way in which a concept accretes information (pneuma) and (under the strong magickal version) persists in existing as outside of the entities that create and are inhabited by them. The autonomy is pointed to by the phenomenology of synchronicity which suggests rogue pneuminous interference. Assimilation is not derived from occult phenomenology but more by the observation of a endless proliferation of concepts that synthesise with ourselves and with others. The pneuminous theory’s plug in of concept to vector is achieved (in assimilation) by the notion of tautology. This is also the case in accretive theory, the vector is the concept (though it can be taken over by others).  Object (vector) and concept achieve a kind of identity (tautology).

Assimilation is less ontologically restricted insofar as accretive theory is more descriptive of an actual ontology. This though is only true if one chooses a specific aspect (strong (magick obtains) or weak (magick does not obtain)) accretive theory. Any decision one way or the other results in a partial manifestation disclosure (and ontological decision). However remaining agnostic we still note reasonably that accretion takes place. This kind of accretion though must bracket off any ontological commitment. It can only note that information sticks together and note the hugely complex historical nature of these accretions that occur in NAA(assimilation-accretion)RP field. Assimilation likewise can only note the conceptual region’s ability to be plugged into (a bar, a board game, flatpack furniture, a piece of art). Every ontological description is just a further assimilation.

What we must note here is that assimilation can slide into ontological decision when we push a certain agenda too far. The agenda suggested here is that of pneuminous determination i.e. of the concept’s ability to control the NAARP (or not). It is easy to comprehend the NAARP as being purely controlled by the accretion-assimilations (since they are rendered autonomous). The version of this theory that commonly appears in here is that the self is one specific type of  AA (the neurotic accretion-assimilation or NAA) amongst various AAs. In the normal situation the NAA has the appearance of control whereas mental health issues can variously be described as the NAA being controlled by the AAs.

But how much control does the NAA have? Johns’ work sometimes suggests very little. It is this suggestion that can tip assimilation out of its meta potential into a conceptual determinism. The underlying manifestation concerns the nature of the NAA. Every which way you choose you enter an ontological decision.

Is the NAA’s control:

  1. Illusory entirely?
  2. Partially illusory?
  3. Actual?

Every choice entails a different ontological picture. E.g. if 1 then we can say the NAA may not be essentially different from any other AA -it has no more or less control than a table AA. 2 and 3 are compatible with the picture suggested above. The potential actual control of 3 does entail this is how things are only that an NAA could be in actual control. 2 suggests this never possible. Already a fourth possibility appears: that an NAA can be in more or less control at different times.

NPC type theories like this kind of notion by trying to insinuate that most NAARPs are controlled by concepts whilst allocating a sense of control to a specific group (the ones labelling the others). Such groups of course should be aware that factions within the enemy agent group will be thinking similarly about them.

 

Taking a step back then from any particular ontology seems to be able to retain the notions of assimilation and accretion. Not only this but as is intimated here the notion of pneuma might also escape a particular manifestation. This pneuma though would not be that magickal pneuma but a restricted sense of information that has no bent towards any ontology. Information sounds like an ontological commitment. I’m not sure it has to be, we just have to be clear to not conflate idea and pneuma.

We might want to doubt the all encompassing claims of a purely informational ontology but to do so precisely moves us into a particular manifestation i.e. that acceptance of a materiality beyond ourselves. This isn’t particularly problematic for any phenomenology. The idea is just folded back in as a phenomena. But the nature of what it is that is disclosing all of this is entirely opaque except that things are happening that we understand in a certain way.

There is no bedrock. Of course ‘happening’ is a kind of manifestation. Things ‘are’, things ‘move’. Even that there are things at all is a manifestation undecided as a real ontological ground -their might be only one disclosed as many by the Narp field. But even that there is no bedrock is wrong. That there is no bedrock is a ‘manifestation’. There are agents for the bedrock and agents who don’t believe in the bedrock.

We need to consider manifestationism not in its nebulous form i.e. the notion that there are competing ontologies, but rather what are or does it make sense to point out the most primordial manifestations. Is it possible that the agnostic disjunction ‘magick obtains or does not obtain’ is possibly the most primordial. Maybe this is ill posed. It is not that this disjunction is primordial but rather that a world view the encompasses magick, albeit in a structured form, is primordial. The assimilation that actions, thoughts do interact with the seemingly external stuff is surely dominant until relatively recent scepticism makes inroads against it. The manifestations of ‘magick obtains’ and ‘magick does not obtain’ become a backdrop battle ground over which the other manifestations compete with each other. What we call knowledge only occurs within the latter half of the disjunction. This is empowering to it and rightly so. Yet the former side remains exactly what it is, the other side of an agnostic disjunction. These are not dialectical, they are just agnostic disjunctive. They are epistemological impasses.

Any idealism, monism, materialism, dualism, realism must ally itself to this disjunction one way or the other. If it fails to do so, it fails to be an adequate ontology for the question of magick must be pronounced upon. Every philosopher is an agent for some ontology.