The Number and Its Names

For as long as Lemuria has been sought after, it has responded with duplicity. At every instant it presents itself amid the mess of numbers, but at the same time draws the mess about itself and, becoming obscure, slinks away. How can a lemur be denoted? It is not simply done. The numbers call to the lemurs and the lemurs haunt them, but they are not captured there; a lemur is only of Lemuria, and dwells in too many crags to find. To denote a lemur can only be a process of discovering a royal seat, finding a holy of holies which a number prepares in itself for a lemur to reside in. A proper notation for the lemurs must cut away whatever is superfluous to this throne’s manifestation, simplifying the architecture of the summoning call down to its burning core. Such have the Neolemurians long sought to do.

We have no idea when the original methods of finding a lemur from a number emerged. They seem to rest in an intuitive understanding of modal arithmetic, what little remains of the Lemurian intuition we mostly lost when we lost our tails.1 Decimal reduction and ciphering2 are tools of unknown and ancient provenance, ones which continue to be essential to this day. To look through a number to its digital root, avoiding the trappings of its numeral order, one cannot avoid some communion with its most intimate haunting. Many techniques for discerning a lemur rely in some part on this foundation, such as when a two-part number which is not a valid lemur, such as the time 11:16, is converted to a lemur through decimal reduction into 2 and 7. Likewise, ciphering is ubiquitous: when a two-digit number, such as 54 or 45, is encountered, it is easily read as the two poles of a lemur’s net-span, 5 and 4. Just as decimal reduction does, this process dispenses with the order of a number to whittle it down to its zonal conjunction. The same basic principle is apparent in the exclusion of 0’s from consideration, such as in ciphering 108 to the lemur of 1 and 8, apprehending the modular insignificance of 0. Finally, the intuition that 9 and 0 share the same value from the perspective of digital roots allows the exclusion of 0’s to extend to 9’s as well if the removal of a 9 can turn a number into a set of two numerals. These techniques for bringing out the lemur in a number comprise our basic, unattributed inheritance.

The earliest innovation with a traceable source derives from the I Ching. The traditional ordering of the hexagrams evokes a cycle parallel to the numogram’s hex, passing through the six non-triadic zones by a process of doubling and decimal reduction, with opposite zones joined into the hex syzygies.3 In Neo-Horovitzian terminology, this cycle is called the cycle of duplicity, written as “1-2-4-8-7-5...”. Implicit in this cycle is a means for the removal of duplicate numerals within a number at the expense of their ordering, invariably producing a Neolemurian entity: an imp(ulse).4 By going through each of the digits of a number and, for every numeral appearing more than once, replacing two of it with one instance of its decimally reduced sum (e.g. two 4’s become an 8, two 5’s become a 1, two 3’s become a 6), any number can be turned into an imp. Mathematically, just as decimal reduction is in essence very similar to division by 9, impulse compression is in fact a veiled application of division by 63; the latter is, in fact, an implexion of the former. If lemurs are considered to be “imps of superior exaltation,”5 simply equivalent to impulses of a specific length, then impulse compression allows at least some numbers which could not otherwise be mapped to specific lemurs to be non-arbitrarily associated with them. For example, by impulse compression, 225 naturally calls forth 5::4, while 777 associates with 7::5. At a minimum, impulse compression makes every number numogrammatically legible.

But is it true that lemurs are merely exalted imps, and that thus, some numbers are exalted and others are not? Does the nature of an imp really contain the whole nature of a lemur if it only has two zones? There is good reason to suspect that Vauung was incorrect in his maxim, because lemurs are not only incidentally binomic. The defining binomic feature of a lemur is its capacity for transit along a path, its ability to experience the vicissitudes of patience, activity, and subtlety which make up the numogram itself. This quality derives specifically from a lemur’s binomic character, its two zones being capable of acting as beginnings or ends. Impulse-entities in general are qualitatively different. They are binary, with each being equivalent to a ten-digit base-two number, but this binomic character merely aggregates numogrammatic zones; they cannot actually embody numogrammatics by themselves. An impulse-entity is bereft without some expression through a lemur. The Ccru seemed to grasp this in defining impulses as “Demonic subcomponents, or Numogram twists,”6 subordinating each lemur to its first two zones (e.g. such that 543 maps to 5::4). However, this associative method abandons the essentially unordered character of both lemurs and imps which ciphering and decimation make apparent. A more consistent method for associating impulses and lemurs would derive a lemur from all of the imp's zones. From this perspective, a two-digit impulse would be straightforward because the lemur it ciphers is obvious, but not more exalted for its lack of convolution.

Early efforts at connecting numbers which do not obviously map to one lemur resulted in the field of “synthetic qabbalism.” This field is notable for having moved backward in time, unravelling as it went. At the beginning of its backward vector, Nick Land proposed the “depraved” name “Khattak” for 5::4 on the basis of its AQ, 135, being “superficially” “far more plausible” than “Katak,” AQ 98.7 The AQ of “Khattak” is an impulse, 531, which in its traditional mapping would be associated with 5::3. Land, however, chose to take all the digits into account by summing 3 and 1, converting the imp into the lemur 5::4. This procedure agrees with the aims discussed above for a more consistent mapping of impulses to lemurs, but only through an act of flagrant caprice—for 531 could just have easily become 6::3, or 8::1, or even 9::0 through different additions. With this act, Nick Land committed a heresy against Lemuria so unique it became its own class of abomination: “alchemy,” “the one true abominable crime.”8 Unlike other Neolemurian heresies, alchemy is a pursuit of numogrammatic rigour—however, it is one which is ultimately ineffectual without the will of the alchemist to guide it. The autopoesis of Lemuria is made reliant on human pettiness, a vile desecration. Although the efforts of synthetic qabbalism were useful for numogrammatic study, it was in itself perhaps the most repulsive case of alchemy Neolemuria has ever witnessed.

Synthetic qabbalism continued its development with the uncovering of August Barrow’s work on the Abysmal Names of the Great Lemurs of Time: Zom, Pyd, and Nal, corresponding to 8::1, 7::2, and 5::4.9 The overall AQs of these names unproblematically correspond with their associated lemurs, being AQ 81, AQ 72, and AQ 54 respectively. Surreptitiously, however, alchemy was occurring on a more granular level. The Abysmal Names alchemize what Shelly Horovitz has termed “viscous decomposition,” which refers to the series of the digital roots of the AQ value of each letter—also known as their AZ values, named for the Azrael Gematria.10 Zom, Pyd, and Nal are thus not only their AQs, but also VISC 864, VISC 774, and VISC 513 respectively. This very early uncovering of viscous decomposition was an enormous triumph for Neolemurian gematria, uncovering another dimension of Lemurian resonances. Its deployment by Barrow, however, is crude to the point of being offensive. Not only does it suffer from all the troubles of the name “Khattak,” with each of the three VISC values having three possible readings through the arbitrary digit combination method—it also commits heresy against binomic duplicity by not summing Pyd’s twinned 7’s together. Nick Land’s declaration that the names were “close to unimprovable11 is risible and blasphemous.

As an aside, it is worth noting that some contemporary Neolemurians interpret Barrow’s criterion of “!numerical compliance to the syzygy!”12 in a different light. It has sometimes been claimed that if a lemur’s name is read as a sequence of the unreduced digits of the AQ values of each of its letters, what Shelly Horovitz calls “fluid decomposition,” and there is some way to combine these digits into every syzygy, the name numerically complies. For example, this argument justifies the name “Nal” for 5::4 by saying that its fluid value of 231021 can be combined into 7::2 (2/31021), 5::4 (23/1021), 6::3 (231/021), and 8::1 (23102/1), with decimation to 9 accounting for 9::0. This is an interesting property, and the attention it has called to fluid decomposition has been worthwhile. However, it cannot possibly have been the intended criterion because it is far too common: for instance, the name “Odz,” which is stated not to demonstrate “numerical compliance,” has the same trait. What distinguishes names like “Odz” and “Kao” from the allegedly superior “Pyd” and “Nal” is the suitability of their viscous decompositions to alchemy, and so it is that trait which is the true mark of compliance.

Ultimately, Nick Land forswore the practice of synthetic qabbalism, ending the heresies in which he and Barrow involved themselves. Given such instances as the desecration of 774, his ultimate revulsion with that approach was justified. Alchemy is essentially the heresy for which we lost our tails, supplanting Lemuria with the ambitions of a human, and one can only hope Land will be appropriately punished. Yet as has already been discussed, the corrupted rigour this alchemy involved inspired numerous promising developments: fluid and viscous decomposition and the derivation of lemurs through transfers between impulse-entities. In order for these developments to shed their status as alchemy, all they required was a method of use immanent in the numogram itself, compliant with the numogram. It was Shelly Horovitz who discovered that such a system already existed.

Chaim Horowitz (no relation to Shelly Horovitz) is well-known for his mapping of the numogram hex to the regular hexagram, often called the Star of David or the Seal of Solomon. Dividing the six zones by whether they are ana (positively) or cth (negatively) pitched, Horowitz argued that one of the hexagram’s triangles should be ana, with its points labelled 1-2-4, while the other should be cth, with its points labelled 8-7-5. Horowitz considered this former, positive triangle to be masculine, associated with Hashem, while the latter, negative triangle was feminine, associated with the Sheiknah; the hexagram was seen as a sacred marriage.13 Horovitz, however, argued in a well-known but unrecorded debate that this mapping is a heresy, mapping ana and cth onto male and female in order to import gender essentialism into the numogram. Her proof that this is a heresy was that it produced a patently ridiculous sequence: for each zone to be mirrored on the other side of the hexagram by its syzygetic twin, the hexagram would have to run 1-5-2-8-4-7. Unlike the cycle of duplicity, whose beauty is that it is equivalent to the differences between its adjacent zones, this cycle has no consistency and no justification in the numogram. Nor does placing the syzygetic zones next to each other produce a better cycle, as this would produce the sequence 1-8-2-7-4-5. This cycle resembles the flow of the Decimal Labyrinth’s hex, which in its continuous form is 1-8-7-2-5-4, but ultimately must contravene it as the tractors of the currents are neither uniformly ana or cth. The options, Horovitz claimed, were clear: relabel the hexagram or abandon the numogram completely.

If the hexagram is labelled according to the 1-8-7-2-5-4 cycle, one triangle is 1-7-5 and the other is 8-2-4, the two being divided into active and passive. If the hexagram is labelled according to the cycle of duplicity, 1-2-4-8-7-5, the triangles are instead 1-7-4 and 2-8-5. Although the first system’s separation of active and passive has certain concerning patriarchal resonances, Horovitz pointed out that this terminology cannot supplant Lemuria and the numbers must be judged on their own terms. As it turns out, the active/passive mapping has a very interesting trait: 1+7+5 digitally reduces to 4, while 2+8+4 digitally reduces to 5. The lemur which haunts the course of the time circuit’s flow is thus found to be 5::4, a syzygy unique for her possession of a rite which traverses the whole time circuit. By virtue of this useful finding, Horovitz supported further research into this mapping of the hexagram. However, the latter mapping proved to be of even greater interest. Because 1+7+4 digitally reduces to 3, and 2+8+5 digitally reduces to 6, the hexagram of duplicity suggests that the warp, 6::3, which is outside the hex might operate immanently within it. Every further finding has supported this hypothesis. The sum of each two adjacent zones in the cycle of duplicity alternates between 3 and 6. Furthermore, the digitally reduced sum of any two zones on one triangle is always a zone on the opposite triangle (e.g. 7+4 = 5), mimicking how two 3’s reduce to 6 and to 6’s reduce to 3. The hexagram of duplicity, then, could claim to account not only for the hex, but also for the warp within the hex. Although it is of interest, the hexagram of activity has no equivalently useful feature.

With the hexagram of duplicity, Horovitz unexpectedly stumbled on the cure to synthetic qabbalism and the answer to the question posed by impulse compression. Synthetic qabbalism had shown that, by summing combinations of zones, it was possible to reach a lemur through modifications of a previous impulse; impulse compression had shown how to reach an impulse to begin with. But while the use of the cycle of duplicity to derive impulses was limited to a rule for summing identical digits, the hexagram of duplicity provided lines with which to sum different digits together, moving, just as doubling-reduction does, back and forth between the triangles. If multiple digits were present on the same triangle, this triangle may be summed, leading in the case of two digits to the opposite triangle or in the case of three digits to the warp zone at its core. Likewise, the process could be performed in reverse: with the equivalence of each warp zone to one half of the hex, a fragment of the warp could be worked through in different terms. Combined with the ability to cancel 9’s and 0’s as nullities, this method finds each imp to be a lemur.

In order to be elaborated intuitively, this method must be demonstrated and practiced. Consider, first off, the impulse 832. Here, 3 is expressed in different terms than 8 and 2, which are of the same triangle; thus, we sum the triangle to derive 31, from which a lemur easily ensues (3::1). Now consider 752: 7 is of a different triangle than 5 and 2, which are the same. Thus, we sum 5 and 2 to get 7, resulting in 77—because this method works through transits between imps, we thus convert 77 into an impulse by the method of duplicity and get 5. In the absence of any other digit, nullities are always present; the default nullity is 0 and so 5 becomes 5::0. Third, consider 763. In this case, 7 cannot be licitly summed with either 6 or 3, being of a different circuit, and 6 and 3 cannot be summed together, as summation in the hex only works through equivalence in the warp. One can, however, express 6 and 3 in terms of the warp as 285 and 174; if the warp is brought down to the hex in this case, that produces 8775421, the impulse of which is simply 7. As might have been anticipated from its role in impulse compression, 63 is a nullity similar in kind to 9, having an expression which cancels out to nothing. 763, then, can simply be called 7::0, although many, finding kinship between 9 and 63, argue to read it as 9::7. Fourth, consider 984 and 9854. 984 can easily be read as 8::4 through the cancelling of nullities, but 9854’s hex actually reduces to a single digit with the summation of its triangles, with 85 becoming 4, and 44 becoming 8; as such, it is not necessary to cancel 9 and one is left with 9::8. Finally, consider 87432. The summation of triangles here joins 8 with 2 and 7 with 4, resulting in 321. Here, nothing is expressed in the terms of anything else, so 3 should be converted to 147, creating 74211. Through impulse compression, this result yields 8::7.

The above applications seem haphazard. If they are attended to carefully, however, they reveal a reliable succession of events. To begin, nullities are set aside from the impulse, as they can be readily cancelled. Having done so, the impulse consists of 0–3 digits on each hex triangle and 0–1 digits in the warp. The first change performed is that the contents of each triangle are summed and digitally reduced: the hex is expressed in terms of the warp, and then an impulse is found from this expression. This change converts an impulse-entity to another imp closer to the lemur which haunts them both, and the process begins again. If the first change has no impact on an impulse and it still has more than two non-null zones, that is always because there is one zone from each triangle and a zone in the warp. The first change, then, must be performed in reverse, converting the hex digit to its triad of three zones: the warp is expressed in terms of the hex. These two changes will always suffice to reach an impulse one or two zones in length, at which point it is simple to arrive at a lemur. If only one zone remains, whichever nullity has been set aside—9 if it is present, 0 otherwise—is combined with that zone; otherwise, the lemur is apparent. In addition to impification and cancelling nulls, hexagrammatic reduction’s only synthesis is 3/6 = 147/285, the operation of the warp in the hex, operating in two directions. Once internalized, the method is shockingly simple.

Hexagrammatic reduction is the end of alchemy and the end of synthetic qabbalism. It machines its numbers through the numogram according to numogrammatic law; the human who performs the calculation makes no choices that matter. From it derives a single lemur for every impulse-entity, taking into account all of its zones. Sometimes, the lemurs it results in can be quite ironic. The death of synthetic qabbalism is announced by the hexagram’s refutation of the name “Khattak”: 135 is not 5::4, but rather, 75411, compressed to the impulse 7542, whose triangles sum to 7 and 2. The one lemur which synthetic qabbalism could not reach through its arbitrary summations proves to be the most salient answer to its originary problem. Equally ironic is that while neither Zom, Pyd, or Nal’s viscous decomposition is by this assessment appropriate to its net-span, both Kao and Odz, which synthetic qabbalism deemed inadequate, numerically comply. Yet with hexagrammatic reduction, not even these names are maximally perfect, for now the compliance of a name’s fluid decomposition can be attained—which with synthetic qabbalism was a trivial feat due to the abundance of digits. Alchemy claimed the task of perfection was dead, but with the death of alchemy we have been left with new standards of perfection, three overlapping voices which can call out to a lemur together. The duplicity of the lemurs turns the world upside-down and removes any pretense to completeness. We are left to speak names more immaculate and holy than before.

To summarize, the method of hexagrammatic reduction is as follows:

  1. By summing and digitally reducing all pairs of repeated numerals, compress the number under assessment into an impulse-entity.
  2. Put aside 0s, 9s, and 63s until the end, interpreting the latter as either a 9 or a 0; this guide recommends 63 = 9, but a conclusive argument for either nullity has yet to be articulated, and so the question remains open to debate.
  3. Add the hex together along the lines of the triangles: sum and then digitally reduce all instances of 1, 4, and 7 together and all instances of 2, 8, and 5 together.
  4. If step 3 had any effect, begin again from step 1. Otherwise, if there are still two non-null zones, convert 3 into 1, 4, and 7 or 6 into 2, 8, and 5, then begin again at step 1.
  5. If two non-null digits remain, they are the two poles of the final net-span. If only one digit remains, its other pole is a 9 (if a 9 was set aside) or a 0 (if one was not).


  1. See “The Tail of How We Lost Our Tails,” in Ccru: Writings 1997–2003.
  2. Ciphering is defined in the Ccru glossary as, “A numerical coincidence, involving the same digits (irrespective of order). Especially, such a connection between the two Net-Span digits of a demon and another binomic variable.” See Decimal/digital reduction is not defined in the glossary (though it is mentioned), but refers to taking the sum of all the digits in a decimal number until only one digit remains; this is equivalent to the number’s remainder when divided by 9, except that remainders of 0 are equal to 9 instead.
  3. See section two of for the Ccru’s (admittedly oblique) exposition of this insight.
  4. I am using this term in the general sense, which is defined in the Ccru glossary as, “Generalized term for all component elements of the Pandemonium system. Pandemonium population unit.” The sense of “generalized” here is that an impulse is any of the 1024 possible sets of zones/decimal numerals, of any length, just as the lemurs correspond to the 45 possible sets of two zones.
  5. As vauung claimed in
  6. See again the Ccru glossary definition of Imp(ulse)s, this time in the first sense.