This was a short response to an interesting question about the numerical trend of the Numogram - why it avoids not only irrationals but even fractured rationals - it's posted here as a test
The Numogram avoids fuzziness. It consists of 'crisp' numbers (naturals and sub-naturals).
'Sub-naturals' consist of numbers of a more elemntary order even than the naturals, in particular:
(1) Primes and hyperprimes (primes whose ordinates are themselves prime - i.e. 31, the 11th prime, where 11 is the 5th prime, etc. in this case (5 is the 3rd prime)).
(2) Qabbalistic numbers, used 'alphabetically' for marking by type and ordinal sequencing - at the limit numerical or numerizable constellations simplified by successive digital reduction to the decimal numerals 1-9 (0 digitally reduces to 0, but no other number does so).
The numerical simplicity of the Numogram is functionally necessitated by its replication as the 'viral' propagation unit of Lemurian hyperstition - its extremely modest coding requirements directly correspond to its virulence. It demands nothing but elementary arithmetic and the globalized decimal signs.
Ultimately, the Numogram is nothing more than the disgrammatic implex of decimal numeracy - capable of spontaneous emergence out of any decimal-numeric culture. It is the virtual content of decimalism, spread by the unprecedented and unparalleled cultural virulence of the 'Hindu numbers' (although Stillwell traces things back much further).
Numogrammatic simplicity attunes it to:
(1) Qabbalism: The pre-eminence of the numerals and the operation of digital reduction, collapsing 'higher' numbers into naturals and naturals into numerals. The Numogram demonstrates its consistency with the numerical cultures instantiated in the I Ching, that of the Dogon, and in fact of every species of aboriginal numbo-jumbo to haunt the earth.
Although, when conceived rigorously from the Lemurian perspective, the Hebrew 'Tree of Life' is a Hyperstitionally Degenerated Structure, the Numogram does not critique its digital crispness (qabbalistic functionality)
(2) The Numbering-numeracy of the War Machine (Deleuze and Guattari). The War Machine counts itself in simple compositional numbers. The function of this numeracy is immanent to the assemblage, indexical and nominal, having no reference to measurement (the representation of transcendent magnitude - lying beyond the communicative plane of the machine itself). It thus has no need for 'higher numbers' (rationals, reals, complex numbers etc.) requiring only naturals - in fact simple naturals (typically mere numerals) for its semiotic.
To be crude, there is a 3rd Army, not a 3.14th Army or a Pi Army etc. - a fact holding for every compositional level of the war machine in question. Making culture operate as a war machine requires the disintegration of all semiotics into numbers and a complementary numerical simplification. (Both aspects essential to 'numerization').
The currencies - or concrete semiotics - of commercial war machines, share these characteristics of digital 'granularity' and pre-eminence of modularity (typically on a decimal base) or the compositional aspect of number.
(3) Cryptographic Number Theory: Based on Primes and Hyper-primes
(or hyprimes), a species of arithmetical sub-naturals whose ordinates are themselves primes.
The initial and most compressed hyprimes sequence runs:
(0, 1,) 2, 3, 5, 11, 31, 127 ... where each primes is the ordinate of the next
This is the dimension of efficient numerical keys within the technocommercial plane of contemporary cyberspace - digital crispness is intrinsic to the exact lockings/unlockings involved in this dimension - a system of precise keys and call-signs
However:
The Numogram 'Zones' are merely the base level of the implicit 'Pandemonium System'. It is in the systemic unfolding of this implex, rather than in a base-level 'fuzzification' of the diagram, that demands for more elaborate numerical constellations are likely to be met. The regions of numerical complexity supported by the Numogrammatic system are first of all those of the 'binomic entities', Demons or Lemurs, denizens of the interzones or the 'between' ... this is separate issue to be discussed elsewhere.
In a nuts hell, the simplicity of numogrammatic numeracy supports a series of functions, including those essential to propagation within, and inhabitation of, all decimal-numeric cultures. It codes crisply in order to hide, spread and fold (implex).
Posted by at June 24, 2004 03:51 AMExcellent enlightening piece Nick ... Although gematria works well with hyperstitional alpha-numeric distributions over each zone of the numogram but still the whole system cannot sterically (in the sense of spatial arrangement of Alpha-numeric entities and their structural sequence) correspond with the numogram perfectly. On the other hand, in the wake of WoTerror and the contamination of western Indo-European vocabulary (specially those contributing effectively in the War) by the Arabic / Farsi alpha-numeric warmachines, we need a secondary alpha-numeric system working beside and together with gematria; far more corrosive for 1 and 10 as the summits of the numogram (as you put it in your next post) while avoiding to purge them ... and far more intricate in spidering the numogram with different numeric meshworks each working with a different numeric population interconnecting with the rest of the system. Arabic / Farsi alpha-numeric system of ABJAD, directly derived from gematria, tends to grow fast over the numogram, introducing each alphabetic unit of its own to each zone of the numogram without missing one single zone of the numogram (except for Zeo) or its own alphabetic units (28 letters of Abjad and Arabic alphabet). The initial distribution begins from 1 to 9 but next propogations of Abjad around the numogram become highly multiplicative: from 10 to 100 to 1000 ... this numeric propagation perfectly diagrams a spiral around the numogram which has no summit of quitness like the Tree of Life. I think it’s a bit confusing so I’ll post a less obscure illustrated version in the next few days.
Reza - with this suggestion you are entering into fascinating but also extremely intricate and complex territory.
Assuming the Stillwell Hypothesis: Very crudely, that all numogrammatic cultures emerge out of - and converge with - an abysmally ancient Lemurian hypersource, then the application of distinct qabbalistic orientations to the Numogram necessitates the excavation of the various methodical perspectives relevant to each case (or differential 'lineage').
Assuming further that 'you' (no doubt through hyperstitional avatars yet to be specified) are bringing a further hypothesis to the question - that the 'proto-monotheistic' Z-crowd or Zoroastrian germ organizes all later Near-Eastern qabbalistic traditions (as attested for instance by the cults of Irem mentioned by Lovecraft?) - then what distinct axis of numogrammatic degeneration accounts for the step-by-step 'disappearance' (decay/concealment) of decimal insurgency into Monotheistic Totalitarianism? What distinguishes the particular meta-cultural pathway upon which the Lemurian matrix is transformed into a numerico-mystical undertow of Abrahamic revelation?
These are obviously extremely demanding questions, and perhaps it is only through experimental application of Abjad and associated qabbalistic systems to the Numogram that answers will emerge.
Anyway, double-plus interested to see how you proceed with this.