Qabbalistic Oddments 00
Primitive Method
Zero Philosophy
Apr 21, 2021
18
6
§00 — Words consist of letters, which can be simply tallied. This is the crudest method of
numbering language.
It is known, by esoteric tradition, as primitive method. Primitivization (₱) reduces words to values
determined by their letter count.
Both one and two are 3. Tally is 5. Number is 6. Primitive is 9.
Despite – or because of – its extreme crudity, the value of primitive method is easily
demonstrated. Its incisive contribution to the analysis of the English Numonyms is especially
remarkable.
In the ancient Sumerian, Roman, and Chinese counting systems, among many others, formation
of numerical signs up to the initial triad are indistinguishable from tally markings.
When counting in the Roman style, at its purest, I + I + I = III. This produces an impression
almost of logical tautology. The sum is merely the whole of what has been written. Between
summation and simple comprehension there is as yet no difference. One, and then another, and
then another, is – at the beginning – the entire procedure. A number is explicitly drawn, shown,
or directly inscribed. The numerical figure is at this level a tally sign. It is tempting to note here
the residual indices of a prehistorical numerical order (or PNO), one devoid of any capacity for
summarization. What it lacks, relative to the ANO (or Ancient Numerical Order), are numerical
denominations beyond unity.
The value of primitivization is first locked-in by odd and even.
Primitive consistency is also found in decimalize (and pentazygon).
The only primitively consistent number is four. Upon superficial estimation, this is a result so
unimpressive it attests almost to evasion. Sheer chance could have been expected to out-perform
it. Nevertheless, ‘four’ satisfies the conditions for a primitive exemplar. This abstract function will
be generalized, through application to other problems.
§01 — Primitive discrepancy can be simply tabulated. The PD of any natural numonym is derived
by subtracting its letter count from the number it names. Graphed PD exhibits an erratic upward
slope, converging asymptotically upon the named number. For example, the PD of one trillion is
999,999,999,989. Zero, one, two, and three have negative PD. Four is neutral (PD = 0). For all
naturals greater than four, PD is positive.
Primitive discrepancy crudely captures semiotic surplus value, or notational efficiency. A tally
has zero SSV. The number of units indicated exactly corresponds of the number of indicative
units. One trillion is tallied by a trillion strokes. PD compares these trillion virtual strokes to the
ten letters the word requires. Positive PD is thus a measure of economy. It counts strokes saved.
As noted in other terms, this economy scales quasi-linearly with the number considered.
§02 — Primitive method is the key to a riddle, which common arithmetical expectations set.
There was a gate whose lock was a puzzle. Follow the pattern to enter said the inscription upon it.
The gate spoke.
“Twelve,” it said to the first visitor, who answered “six” and was permitted to enter.
“Six,” it said to the second visitor, who answered “three” and was permitted to enter.
“Four,” it said to the third visitor, who answered “two” and died in front of the gate.
“It was a fatal error for the third visitor not to echo the gate,” said the first visitor,
understanding.
Ruin resulted from mistaking primitive method for arithmetical division, which it initially – and
then once again – simulated. The lesson might be thought harsh, were it not only a story.
§03 — There are five twins. Not much is more basic. What might be logically questionable is
pragmatically presumed.
Hands mirror each other. Their digits are twinned. In Kantian terms they are incongruous
counterparts. Their difference attests to the a-logical quality of space.
Anatomy not only instantiates decimal, but also factorizes it, exhausting its integral
decomposition. Two hands times five fingers is the basic plan, modeling the pentazygon.
No logical necessity underpins this. The numerical compliance of the body is exorbitant, which
is to say empirical, accidental, or coincidental. It decimalizes radically, without reason.
Bringing the hands together, finger-tip to finger-tip, is a common, unreflective gesture, while
also at times being a gestural sign of reflection. Doing this orders the digits into consistent pairs.
Each checks its complement. Digital, primordially, means all of this. Even after associative
collapse down to binary modularity, half this sense survives.
§04 — The first great achievement of primitive method in regard to the English Numonyms was
August Barrow’s Octaves (1753).
First, arrange the elementary numonyms in the Pentazygon. Thus:
Zero + Nine
One + Eight
Two + Seven
Three + Six
Four + Five
The remarkable result is self-evident. In it, Barrow saw the Pentazygon, Anglossic, and Primitive
method simultaneously vindicated.
§05 — Any number is even if, when it is added to an even number the sum is even. Zero is then
found to be even. This demonstration can be infinitely extended, but only the immediately
successive phase concerns us here. Any number is trinomic if, when it is added to a number
divisible by three, the sum remains divisible by three. Zero is thus trinomic.
It follows uncontroversially that any complement to a trinomic number is itself trinomic if their
sum is trinomic. The trinomic syzygies can in this way be defined.
§06 — Primitive method also unlocks the Iron Law of Six. Barrow undertook this task in his
Shelves (1758).
The abstract motor of the Zhouyi (or Yijing) is diplo-triadic. It consists of two trigrams, or twin
triangles, locked together in alternation. The structure emerges from the dynamic assembly of
three twins. Understood as a path, it is Möbian – double-sided but continuous.
The Star of David is composed of twin-triangles. Its model of the Hex is therefore approximate,
simplified, and static. This suffices, nevertheless, to betray its descent.
A purely numeric encryption of the Hex is found in the modern informatic ‘byte’ (eight bits of
information is 2^8 but eight is 2^3).
The cycle 1, 2, 4, 8, 7, 5, emerges from decimation of the binary powers. Accelerating growth is
succeeded by accelerating collapse (and inversely). Three doubling periods are marked in each
direction.
The same cycle emerges when the rows of Pascal’s Triangle are summed and decimated in
sequence.
Under primitivization, subtraction of the trinomic tetrad (0, 3, 6, and 9) regularizes the decimal
numonyms. The series one, two, four, five, seven, eight incrementally ascends through three
terraces (Barrow’s shelves). In this regard, each of the excised terms zero, three, six, nine is notably
anomalous. None fit, even among themselves. They disrupt the ordinal gradient. The effect of
their inclusion is something like an infection of alien numerical principles. Zero ordinal gradient
arrives with one pair (0, 9), negative gradient with the other (3, 6). The outsideness of these
numbers is thus primitively manifest. They destroy pattern, vividly.
Subtraction of the trinomic tetrad, decimal regularization, or hexation, is decisive. The importance
of this operation on the path of decimal investigation is difficult to over-estimate. The hexated
decimal residuum, or simple hex, repeatedly demonstrates its numerical consistency.
Every prime number above (or indeed other than) 3 decimates to 1, 2, 4, 5, 7, or 8.
The number 142,857 rotates under multiplication.
Powers of five cycle 5, 7, 8, 4, 2, 1 (which, as expected under decimal, is symmetrical with the
powers of two).
Division (of any non-multiple of seven) by seven produces the same digital output, but in
scrambled order. The recurring segment in each such case is 142857. The six-step cycle is
preserved. The diplo-triadic turbine thus exhibits a distinct, consistent phase.
Ten minus four reverses the final phase of the tetraktys. It has the Pythagorean sense, then, of a
terminal regression – a retreat from the end. Hexation is framed as a restoration, in which the
largest and most recent stage of development (alone) is undone.
§07 — The Numogram was already ancient for the Sumerians, even to the point of amnesic
oblivion. This is evident from their number system. Specifically, the Sumerian Ideal Year (of 360
days) is susceptible to zygonomic derivation. Its gnosis is typically entered through the Gate of
Five Angles (90°, 81°, 72°, 63°, and 54°). The demonstration proceeds: 90 + 81 + 72 + 63 + 54 = 360.