January 12, 2005

Qabbala 101, Part 3.

Primitive Numerization
Among the primary test-beds for qabbalistic analysis are the numerolexic systems inherited from cultures overcoded by the modern Oecumenic alphabet. These include the Hebrew and Greek alphabets (with their Neoroman letter names and mathematico-notational functions) and the Roman numbers (inherited as Neoroman letters and still numerically active in various domains). In this respect, the absence of names for Neoroman letters are an index of their pseudo-transcendence – as ‘unnameable’ - within the present Oecumenic order.

A discontinuity is marked in the alphanumeric series (0-Z) by the fact that the numerals composing the first 10 figures in this series do have names, grouping them with the letters of previous alphabetical numbering systems from a certain qabbalistic perspective. This might be taken as the residual indication of an ‘alien quality’ still characterizing the numerals in relation to the Oecumenic cultural order they now indisputably occupy, a legacy of the cultural trauma attending their introduction.

The qabbalistic provocation posed by this English number names is conceptually comparable to that of any other numerolexic system, while surpassing any other in the intimacy of its challenge. If the numerals have names, shouldn’t the qabbalistic processing of them as words yield – at the least – compelling suggestions of nonrandom signal? If the standard numeral names emit nothing but noise when qabbalistically transcoded, the attempt to establish relatively persuasive criteria for the evaluation of qabbalistic results suffers an obvious and immense reverse.

What, then, would count as a minimally controversial first step in such an examination?

Surely the most basic of all qabbalistic (or subqabbalistic?) procedures is simple letter counting – Primitive Numerization (PN). As a reversion to sheer ‘tallying’ PN has a resonance with the most archaic traces of numerical practice, such as simple strokes carved into mammoth bones and suchlike palaeo-ethnographic materials. If anyone was to bother systematizing PN procedure for the purpose of mechanization or simply for conceptual clarity, it would be most efficiently done by transcoding (‘ciphering’) each letter or notational element as ‘1’ and then processing the result numerically.

PN’s extremely tenuous relation to issues of modulus-notation ensures that it can only ever be a highly dubious tool when intricate qabbalistic calculation is required. Yet this utter crudity also makes it invaluable as a test case, since it minimizes axiomatic arbitrariness and precludes any plausible possibility of symbolic conjuration (‘sleight of hand’) while fully sharing the qabbalistic ‘deficiency’ of sufficient anthroposocial or communicative motivation. Common reason – sanity - insists upon noise as the only PN output consistent with the general intelligibility of signs (a pre-judgement applying rigorously to all qabbalistic procedures).

No message should inhere in the length of a word, excepting only the broad pragmatic trend to the shortening of commonly used terms. It is immediately obvious why this exception has no pertinence to the case in question here, unless stretched to a point (for instance, expecting the smaller numerals to exhibit the greatest lexical attrition) where it is straightforwardly contradicted by the actuality of the phenomenon.

So, proceeding to the ‘analysis’ -
PN of the English numeral names:
ZERO = 4, ONE = 3, TWO = 3, THREE = 5, FOUR = 4, FIVE = 4, SIX = 3, SEVEN = 5, EIGHT = 5, NINE = 4.
Is there a pattern here?
Several levels of apparent noise, noise, and pseudo-pattern can be expected to entangle themselves in this result, depending on the subsequent analytical procedures employed.

To restrict this discussion to the most evident secondary result, not only is there a demonstrable pattern, but this pattern complies with the single defining feature of the Numogram - the five Syzygies emerging from 9-sum twinning of the decimal numerals: 5:4, 6:3, 7:2, 8:1, 9:0.

In the shape most likely to impress common reason (entirely independent of numogrammatic commitments) this demonstration takes the form:
- revealing perfect numerolexic-arithmetical / PN-‘qabbalistic’ consistency.

PN confirmation of the Numogrammatic Novazygons (9-Twins).

ONE + EIGHT = NINE + ZERO. (PN 3 + 5 = (4 + 4 =) 8)
TWO + SEVEN = NINE + ZERO. (PN 3 + 5 = (4 + 4 =) 8)
THREE + SIX = NINE + ZERO. (PN 5 + 3 = (4 + 4 =) 8)
FOUR + FIVE = NINE + ZERO. (PN 4 + 4 = (4 + 4 =) 8)

The approximate probability of this pattern emerging ‘by chance’ is 1/243, if it is assumed that each decimal digit (0-9) is equiprobably allotted an English name of three, four, or five letter length, with 8-sum zygosys as the principle of synthesis. 7-sum or 9-sum zygosys are inconsistent with any five or three letter number-names respectively, and thus complicate probabilistic analysis beyond the scope of this demonstration (although if everything is conceded to the most elaborate conceivable objections of common reason, the probability of this phenomenon representing an accident of noise remains comfortably below 1/100).

Partisans of common reason can take some comfort from the octozygonic disturbance of the (novazygonic) Numogrammatic reference. How did nine become eight (or vice versa)?
Lemurophiliac numogrammaticists are likely to counter such queries with elementary qabbala (since digital cumulation and reduction bridges the ‘lesser abyss’ in two steps, 8 = 36 = 9, as diagrammed by the 8th Gate connecting Zn-8 to Zn-9).

[This is a step on the path to a discussion of time-travel – honestly!]

Posted by nick at January 12, 2005 03:55 PM




Slightly irrelevant question: Did anyone ever unearth any further information about the greek attic-numeric catastrophe?

Posted by: u/c at January 12, 2005 04:07 PM



u/c - not irrelevant, just a mite premature ...
(actually, might have been a mega-mite - you volunteering?)
Ifrah is great on this kind of thing, he's incredibly down to earth and comes up with wonderful stuff through sheer dogged pursuit.
Anyway, agree that it has to be crucial, given that it's a case of cultural autolobotomization of numerical competence. (Imagine savage market-based cultural darwinism has ruled that sort of weird shit right out of court since, based on your fascinating discussions recently - says something interesting about the Greeks that it was still possible for them).

Posted by: nick at January 12, 2005 04:29 PM



I did wonder whether there might be some indiana-jones style renegade classicist lurking somewhere in the world who has access to this mystery. On the whole though, no-one seems interested, whic his strange given the sort of minimicrodetails such academics spend their lives dissecting.

Posted by: u/c at January 12, 2005 04:37 PM



u/c PS. To tediously repeat an insert you might have missed:
Is this not strange?
And if it has never been demonstrated before (given the prominence of the octave within Western culture), is that not really strange?

Remember you had a big octave-numeracy thing at one point (long, long ago, so apologies if this sounds like 'do you remember that party we went to in 199x' - the very definition of annoying as previously given) - forgotten the source - Mr. Geodesic domes wasn't it? Also seem to recall having a lot of isomorphic zing with this, through twinning/folding (Vysparov's 'pitch' system also connected)

Posted by: nick at January 12, 2005 04:41 PM



u/c - we're in a major time-slippage zone, but the absence of this theme, not only in academia but also on the web, utterly stuns me.
Tried googling elementary search patterns around digital reduction today and kept being sent straight back to hyperstition - assuming mathematics has really shut down the whole popular numeracy topic (which is why i love your recent posts, and have major gripes with Badiou)

Posted by: nick at January 12, 2005 04:45 PM



the only site that has much on the attics (and sundry other matters) is http://www.jesus8880.com/chapters/gematria/greek-numerals.htm
Don't clearly remember the octave-numeracy although its clear that octavian period-doubling is a topic straight from the heart of the pythagorean brotherhood.

And (slipping further into distant connections) later on in history the transition to the tempered musical scale is really interesting as a numeric catastrophe: instead of a working system of harmony with anchoring in the real (ie in one particular key) and a corresponding system of different keys each with a peculiar characteristic tonality, we get a generalised, less-than-optimal approximation to pythagorean harmony that allows the scale to "start" at any point and sound 'the same', eventually making 'real' harmony intolerable or at least bizarre to our ears.

Posted by: u/c at January 12, 2005 04:56 PM



ps I'm just awating Badiou's "Le Nombre et les nombres" from amazon, hopefully this will give some hardcore insight into his fundamental in/numeracy.

Not sure whether I can add any metacommentary to the eight-twinning that wouldn't be otiose. That's the (my) trouble with the numogram really, what do you do with it apart from act impressed...?

Posted by: u/c at January 12, 2005 05:01 PM



u/c - "http://www.jesus8880.com/chapters/gematria/greek-numerals.htm" - thanks for that piece of sickness - can already see it's horribly compelling (any way we can hide this from northanger?)

musonomic geeking also highly appreciated - definitely need more of this stuff - any comments on transcultural comparisons of musical 'common sense' and the arbitrariness of the octave? (going to check out the Chinese angle before sticking my neck out, but it's totally alien)

Posted by: nick at January 12, 2005 05:07 PM



I would have thought that the existence of octave-as-period-doubling was pretty hardwired into acoustical reality. The question why it has to be an octave rather than a nonave or whatever is different; this connects to the doubling-periods 1,2,4,8 (also=binary place values) as being more 'fundamental' than the cardinals (although this, in turn, could be simply a contingent result of math's perennial entanglement with music [but you could argue that this entanglement is a condition of possibility rather than a coincidence]).

Posted by: u/c at January 12, 2005 05:12 PM



888 HUGE over here
(HUGE = 77 irrelevant to that comment)

Posted by: nick at January 12, 2005 05:13 PM



12 pitches in the Chinese 'octave'

Posted by: nick at January 12, 2005 05:17 PM



PS. http://www.cechinatrans.demon.co.uk/ctm-psm.html
- has that cool musonomic geeky feel, and addresses the issue (confirming your intuitions, while diagonalizing them into some kind of refractionalization trajectory)

Posted by: nick at January 12, 2005 05:20 PM




According to Needham, sound is a form of chi and the chinese thinkers were generally more interested in sonic contagion (sympathetic resonance) and the 'miraculous' immanent relationships this suggested than in mathematical analysis. And compared to greek musical thought there was far more interest in timbre or texture of sound over 'musical' relationships (presumably because different sounds were different types of breath or mood - whereas in greece such things are only understood in terms of the notes used - modes.)

However, there is a "five-fold division of sound", relating to the pentatonic scale (blues scale, major scale minus fourth and seventh). But also a heptatonic scale that was supposedly invented by the Duke of Chou (of I Ching fame?) then later, a 12-note series:

And...(Ok, are you ready for this, try to stay calm....)

"The easiest way to appreciate the elegant simplicity of the Chinese method is to glance first at the Greek method...A musical scale based on [pythagoras'] mathematical relationships was devised, although another Greek school still favoured tuning by ear...The Chinese gamut of pitches, on the other hand, requires only the simplest mathematics and does not use the octave as starting point..or at all....The Chinese simply took a fundamental note and then multiplied by two-thirds and three-quarters alternately, thus embarking on a process which evolves an unending spiral of notes. [In O]ur oldest source for any actual lengths... the manner in which they are expressed - by use of a decimal system in conjunction with a system based on thirds - has a distinctly Babylonian flavour."

OK, notebooks out, then. Maybe should prepare a HS post on this.

Posted by: u/c adrenoresearch dept. at January 12, 2005 05:31 PM



definitely exceeds current processing capacities ..

Posted by: nick at January 12, 2005 05:34 PM



Use of two incommensurate measures to create a spiral most appealing.

I bought this four-volume paperback of 'science and civilization in china' (the abridged version, that is!) out of a bargain bin in a bookshop in Cambridge, around a decade ago. I knew it'd come in handy _one day_, LOL!

Posted by: u/c at January 12, 2005 05:41 PM



So much going on in the adrenoresearch comment its difficult to know where to begin - mesopotamian connection ("distinctly Babylonian flavour") certainly doesn't contribute to a restriction of the research environment (if Reza has dug up any musical implements used by star-headed abominations we're really screwed into obscure spirals ...)

Posted by: nick at January 12, 2005 05:50 PM



two last points for now:

The next line or the text says something to the effect that greek and chinese systems most likely have a _common_ origin in Babylonian, which makes it important to find out what it was the two models diverged from (interesting from pov of move from babylonian to greek conceptions of mathematics).

Second, of course it should be noted that the 'western' scale is a 7 _or_ 12 tone system (7 whole tones unevenly distributed in 12 semitones.) that could be understood as base-8 or -13 with octave ascension as place-value. This is notationally complicated by the fact that in the realm of music software we conventionally start at C0 (center of piano keyboard), assigning a totally separate (decimal) system to the decimal ascension/descent, and locating it to the right of the 'units', which themselves are a place-shifted version of the first seven letters ABCDEFG supplemented by fractional-modifiers up or downwards (sharp/flat).

Posted by: u/c at January 12, 2005 06:20 PM



nick, where's the ccru website?

Posted by: northanger at January 12, 2005 06:30 PM



should read:

>next line OF the text

>assigning a totally separate (decimal) system to the OCTAVE ascension/descent,

Posted by: u/c at January 12, 2005 06:39 PM



and the clocks are wrong

Posted by: northanger at January 12, 2005 06:47 PM



the uk one is right, at any rate...where are you, northanger?

Posted by: u/c at January 12, 2005 06:51 PM



seconds are off

Posted by: northanger at January 12, 2005 07:00 PM




Posted by: northanger at January 12, 2005 07:01 PM



I'm strongly tempted to say something extremely rude to you

Posted by: u/c at January 12, 2005 07:26 PM




Posted by: u/c at January 12, 2005 07:27 PM




Posted by: northanger at January 12, 2005 07:31 PM




Posted by: northanger at January 12, 2005 07:36 PM



it's official! i'm certifiable

Posted by: northanger at January 12, 2005 07:44 PM



>>> Ifrah is great on this kind of thing, he's incredibly down to earth and comes up with wonderful stuff through sheer dogged pursuit.

you mean this guy?

Georges Ifrah, The Universal History of Numbers

Posted by: northanger at January 12, 2005 08:12 PM



>>> Is this not strange?

not strange. no one has never noticed this before? where are the ccru pages with all the zone information and the numogram on the front page? it's kind of relevant to this discussion, neh?

Posted by: northanger at January 12, 2005 08:15 PM



>>> tried googling elementary search patterns around digital reduction today and kept being sent straight back to hyperstition

always appreciated this comment:

Don't believe everything you read on the web. The internet is not (yet) a substitute for cracking a book. Verify your sources.

Posted by: northanger at January 12, 2005 08:21 PM



how is it possible that Tehran is 30 seconds slower? never noticed this before.


Posted by: northanger at January 12, 2005 08:34 PM



correction, 30 MINUTES slower

Posted by: northanger at January 12, 2005 08:58 PM




well, learn something new every day

Posted by: northanger at January 12, 2005 09:08 PM



if you're confusing minutes and seconds, it's probably you who has the timekeeping problem.
Yeah, tehran is in a fractional timezone, kind of cool eh.

Posted by: u/c at January 12, 2005 10:07 PM



u/c: as i recall, all half-hours (for the home page clocks) were set at the same half hour

Posted by: northanger at January 12, 2005 10:23 PM



>>> musical scale

main page:

The Song of the Great Pyramid

Scale (music)
In music, a scale is an ascending or descending series of notes or pitches, as opposed to a series of intervals, which is a musical mode. Each note in a scale is referred to as a scale degree. Though the scales from musical traditions around the world are often quite different, the pitches of the notes in any given scale are usually related by a mathematical rule. Scales are theoretical constructs which may be used to control a composition, but much music is written without any scale in mind. Scales may be described as tonal, modal, diatonic, derived or synthetic, and by the number of tones included.

Diatonic scale

The major scale begins on the first note and proceeds by steps to the first octave. In solfege, the syllables for each scale degree are "Do-Re-Mi-Fa-Sol-La-Ti-Do".

The natural minor scale can be thought of in two ways, the first is as the relative minor of the major scale, beginning on the sixth degree of the scale and proceeding step by step through the same tetrachords to the first octave of the sixth degree. In solfege "La-Ti-Do-Re-Mi-Fa-Sol."

Alternately, the natural minor can be seen as a composite of two different tetrachords of the pattern 2-1-2-2-1-2-2. In solfege "Do-Re-Mé-Fa-Sol-Lé-Té-Do."

In music and sight singing solfege is a way of assigning syllables to degrees or steps of the diatonic scale. In order, they are: Do, Re, Mi, Fa, Sol, La, Ti, and Do (for the octave). In the East, the origin of Solfege was in the Upanishads, which discuss a solfege system of seven notes. Much later in the West it was a pedagogical technique created by Guido of Arezzo; These names are still used for the notes in Latin countries while in Germanic countries the names of letters of the alphabet are used.

Posted by: northanger at January 12, 2005 11:00 PM



northanger - get some grip! pouring out the contents of your head doesnt mean a live connection with the hyperstitonists! you are like a child blurting out first thing in your mind. interesting site though, even if i don't understand anything you guys are talking about. except that chinese music you talk about is not the chinese music of today. dead culture. look now, things are different.

Posted by: sung lai wing at January 13, 2005 12:03 AM



northanger - "Georges Ifrah, The Universal History of Numbers" - Yes (theoretically understated, superb book)
Ccru site - damn! ... this could take a while ...

Posted by: nick at January 13, 2005 01:50 AM



Sung: of course you're right that ancient musical models must have been overcoded by pop music - but what does it mean for a culture to be 'dead'? Could it not be the case that certain general ways of thinking about sound and music still exist and influence today's music, or does technology completely erase them? Have these forms totally disappeared, or do they combine with pop to create a specifically chinese pop? I have heard very little but for instance Ai Jing(?) seems to combine elements of traditional chinese music along with stereotype guitar-rock (I'm sure there are more interesting examples....)

I'm just in the process of writing a piece about this in relation to D&G's "pop philosophy": This is an important subject because it's a metonym for a lot of fraught debates re. globalisation : is "pop" as a model to be regarded as a homogenising, erasing model of sameness, or simply as a mongrelising, contagious principle of distribution? Is "pop" to be thought of as simply relating to the production of lowest-common-denominator popularity, or is it a specific sociopolitical modality?

If I'm not wrong, the whole 'popular numeracy' topic indexes a general tendency to understand mechanisms of popularity conducted through sensory innovation as more liberatory than top-down imposed structures of understanding (sorry, that's a bit vague...). Given that numerology is generally written off as a similar kind of soothing illusory pastime to pop music, an opium for the masses, we should have something to say about an abstract "pop" model as such (as in Reza's comment about the apparently-benign but actually politically-corruptive influence of occultism).

Posted by: u/c at January 13, 2005 01:02 PM



more precisely, should say:

we should have something to say about this positive abstract "pop" model as a _de jure_ distinct assemblage despite its _de facto_ occurrence only in mixed milieus (ie the fact that the pop charts are always full of crap, or that starbucks coffee tastes lkie shit, shouldn't be a cue for dismissal and retreat to ideological purism).

Posted by: u/c at January 13, 2005 01:28 PM



u/c - 'is "pop" as a model to be regarded as a homogenising, erasing model of sameness, or simply as a mongrelising, contagious principle of distribution?'

Good question u/c. Though this question is launched above the specific Chinese milieu. Already by talking of "pop", without regard to local specificity you are exploring something assumed shared throughout all human cultures in which technology and globalised capital have a siginificant impact. I see it as a mongrelising of locality with homogeneity, a flattening, smearing of homogeneity across what was porous local space, in which previously music and culture (including dance, worship, tea ceremonies, other rituals) staked out some relatively isolated independence.

Posted by: Tachi at January 14, 2005 10:48 AM



>>> Is this not strange?

I don't get it. Are you surprised that moving an object from one pile to another does not change the total number of objects?

Posted by: DigitalDjigit at January 15, 2005 10:02 PM



Please ignore my previous comment. This is what happens when you read the comments but not the actual post.

Posted by: DigitalDjigit at January 15, 2005 10:05 PM



"This is what happens when you read the comments but not the actual post" - well i guess that's original (you're hanging onto your nic by your fingernails right now).

Tachi - you still having technical problems?

northanger - where are you?

Posted by: nick at January 15, 2005 10:56 PM



tachi, like your characterisation of pop - think it is key that it doesn't "come from" anywhere but is virtually present and activated in various ways. I'm still thinking about this....would like to find a way to prolong this line of enquiry. [many thanks for your comments at the other place, too]

Posted by: u/c at January 16, 2005 11:31 AM



"where are you?" - BOO!

Posted by: northanger at January 16, 2005 03:53 PM



Hi Nick, seem to be over the technical hitch, though just not able to dedicate enough dedicated time to engage with stuff arising in the blogspace.

u/c - cheers, agree pop doesnt really 'come from' anywhere. Would like a second run-up to your previous interesting questions, though not sure where is best to address these except here:

u/c: "is "pop" as a model to be regarded as a homogenising, erasing model of sameness, or simply as a mongrelising, contagious principle of distribution?"

This question lacks a noun relating to the key verbs 'homogenise' and 'mongrelise' - sorry to appear linguistically uptight, but think it is important - since I do not think (and guess nor do you) that there is some stuff already there to be acted upon.

Don't mean we should look for a noun that is 'doing' the homogenising and/or mongrelising, but think that it is interesting to ask whether *pop* can be seen as the *production* of a simultaneous homogenizing and mongrelizing aspect of culture (eg. music) precisely through a facilitation of the local by a bastard alliance with the global. The 'parochially local' gives way to the 'globally local'.

> Mongrelization - production through synthesis of the local and global (and/or local and local?)
> Globalization - production of/within a global model of distribution ...

u/c: "Is "pop" to be thought of as simply relating to the production of lowest-common-denominator popularity, or is it a specific sociopolitical modality?""

Again interesting q. Think I can see where you are driving at. Effacement, homogenization, simplification in a sense, vs. Effusion, dispersion, distribution?

Why not: Pop = effacement of the parochially local forms of culture through the production of the locally global.

Ahh. Help!

Posted by: Tachi at January 18, 2005 11:13 AM



Just letting you know - your site is fantastic! , to forecast table you should be very big

Posted by: Patrick Chapman at March 30, 2006 10:41 AM



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