Mechanomics
Nick Land
Start in the State (it insists): organicist technospecialism, pedagogic
authoritarianism, and territorial sectorization that culminates in mass
innumeracy. Irrespective of its configuration as educational crisis, the
suppression of popular numbering practices is both result and
presupposition of institutionalized mathematics. State-culture - however
modern or even postmodern - is modelled upon an ideal despotic voice
(Logos). The word from on high drafts the signifying chain, with all its
essential features: unique enunciator, semantic interiority, consecutive
signs, formally anticipated conclusion, global application, and
interpretative redundancy. When the entropic semiology of senescent
States multiplies enunciation, referentially displaces interiority, remarks
graphic spatiality, localizes applicability, and infinitizes interpretation, it
does so under the sign of an unperturbed ineffable Logos; confirmed all the
more crushingly by discursive specialism, rigid professional accreditation,
allusive criteriology, and linguistic fetishism, as also by the contemptuous
mockery of an autopiloted megapower, now crystallized into exact
science.
Numeracy affines to an irreducible popularity which no literacy however global - can approach. Numbering practices emerge
spontaneously within any population that becomes an effective multitude.
Games, music, money, and time-marking practices1 all betray the
contagious influence of a primary numerical element. Calculation
mobilizes a thinking that is directly and effectively exterior, indexing the
machinic dispersion or anorganic distribution of the number. No sooner in
the head than on fingers and pebbles, counting always happens on the
outside. A population is already a number, mixed into irreducible hybrids
by counting techniques and apparatus (counting-board, abacus, currency
tokens, and calendric devices). Even when socially depotentiated by
sedentary societies number, evidences a residual affinity with concurrence,
asymmetry, and immanent criteria. A mechinically repotentiated numerical
culture coincides with a nomad war machine. 2
The number is distributed within itself between two principal poles.
On the Planomenon it exists intensively, as sheer ordinality, or nonmetric
envelopmental series.3 Semiotic consistency with this intensive side of the
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number involves nothing but sequencing ciphers, indifferent between
naming-numbering, marking degrees of heterogeneous continuum (nested
singularities). Notational elements are flat or nomadic, lacking organic
linkage to coding or zoning agencies. They are assembled
diagrammatically, from directly expressive traits distributed differentially
in a flat-space of 0-dimensionality (nomos), and comprise a nonredundant
order of differences (unsequenced sequence), immanently producing
variation of absolute speed-temperature and curvature (vortex).
In its Oecumenic aspect, number undergoes complex interlocking
modification, through which it acquires qualitative generality and
quantitative magnitude (cardinality).4 A simultaneous intensive
transformation (stratocapture) proceeds through twin extensive splitting:
cancelling difference in one registry (resolvable quantities) by constituting
a second registry (qualitatively different) which is in turn defined by the
uncancelled or problematic component. The difference in-itself of the
intensive number is converted into a residuum, allocated to a higher
number-type, whose metric regularity is established by the displacement: a
construction of the identical quantitative unit by qualitative relay of
problematic.5
Oecumenon is multiply twofold: expression and content, each
dichotomized recursively within itself. In each case, expression deals with
relatively deproblematized elements of a lower numerical type, exhibits a
higher degree of consolidated cardinality, and operates a selection of
comparatively tractable instances. Content deals with elements of greater
typal-generality and numerical complexity, for which it requires a
relatively heterogeneous semiotic, involving varieties of algebraic, indexic,
probabilistic, and anexact components. In one direction content has a
merely quasi-stable boundary; a fuzzy (uncompletable) limit that opens
onto unsorted elements crossed by diagonals. In the other it relates to a
superordinate expression, which defines it with qualitative reciprocity, and
from which it draws a principle of metric standardization, providing a
regulative norm for the quantitative determination of problems. There is a
complementary differentiation or real inter-relativization of a mathematical
and calculative pole, the former characterized by a superior power of
semiotic globalization (unity of expression), the latter by a greater
plasticity of function and diversity of method (comprehension of content).
Stratification at any level (not only anthropomorphic or ethoplastic)
requires processes effectively equivalent to this double-seizure of the
number, with production of an extensive substitutability by scale/type, split
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articulation, and displaced problematic. Stratic differentiation is at once an
intensively singular and an extensively segmented occurrence, by way of
which the Oecumenon consolidates an overall distinction from the
Planomenon by internally bifurcating itself. The abstract machine is drawn
into the Oecumenon by a stratically coherent diplo- or schizothesis,
effectively recomposing the problem of consistency (intensive difference)
at the level of content but in the terms of expression.
The number in-itself is exterior to the Oecumenon, even when
seized by it (an external relation of capture is always precursory to the
organization of internal relations). A preliminary indicator is provided by
the semiotic variability or polynotational cohesion that characterizes the
number in its Oecumenic aspect. At the anthropomorphic level, the most
inert numeric system is instituted by linguistic signs, combining a
vocabulary of number-names, and a set of rules to construct partialsentences (or complex words) isomorphic with all rationals. If these signs
are to provide even rudimentary completeness they must necessarily
undergo considerable decoding (abstraction of rules for local construction,
tokenization of signs). They are also marked by high levels of indexization
(zonal functions), formal or informal algebraism (notional problematic, or
indicative signs), and anexactitude (partitives, approximations, margins of
inaccuracy, uncertainty, and error, etc). There is a reciprocity between
logicization of the number and numerical decoding of language, entangling
regional consolidations of identity (mathematical-theorematic) with
complementary movements of disorganization through external relations
(calcular-problematic).
The general denigration of those (hazily conceived) modes of
linguistic arithmatization classified as ‘numerological’ is often assumed to
be the effective closure of an exotic but inconsequential cultural episode.
The sterile and formulaic character of most modern numerology - its
random esotericism and theatrical aura6 - reinforces this conclusion. It is in
such terms that the strange metamorphosis of Greek numeracy during the
2nd century BC, when the Attic numerals were replaced by an alphabetical
number system,7 is both radically marginalized, and overtly
uncomprehended by modern historians of mathematics. Similarly, the
ordinal numeracy instantiated by Roman8 and Modern Latin alphabets is
generally excluded from accounts of arithmetic culture, where the contest
between Roman and Hindu-Arab numerals is given overwhelming
predominance.9 This entire pattern of evaluation requires substantial
correction. The unmistakable trend towards an eclipse of cardinality
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(intrinsic arithmetical value) in alphabetic numeracy does not imply the
termination - or even a weakening - of its numeracy. That such a
conclusion is drawn owes much to the overt secular triumph of cardinality
over ordinality within Occidental civilization: the effective outcome of
programmatic metricization, associated with the relative ascent of money
and descent of the calendar as cultural factors. Far from denumerizing the
alphabet, progressive decardinalization reinforces its numeric function. By
eliminating quantitative interference it induces a superior actualization of
pure lexicographic numeracy, meticulously assembles socially distributed
ordinal competences, and increasingly installs itself in digital electronic
processes (alphabetic and alphanumeric sorting). Lexicographic ordinality
effectuates an actual nonlanguage and potential antilanguage. It is
indifferent to phoneticism and to signification, even to coding and
decoding. It consists of ordinal indices (zone-tags) that effect zonings and
dezonings - intershufflings, groupings, insertions, and extractions operated according to concrete rules for nonmetric cuttings, and
characterized by rigourous anexactitude.
This mass ordinal-numeric latency contrasts starkly with stratomathematics, which hurtles through ever subtler spheres of angelic
metanumber, and beyond . . . This ascent through higher and higher
general types of number - even into purportedly nonnumeric abstract sets
and groups - conforms to intensive amplification of stratification,
correlative to increasing metric rigidification of lower number-types.
Cardinality is no more essential to the lowest number-types than the
highest. On the contrary, it is precisely the calcular indefiniteness of highly
general numbers that leads most directly to the suppression of numerical
autonomy, by encouraging the subordinations of concrete numeracy to
superior dimensions that logicize or geometrize it. Valorizations of analog
subtlety and unrepresentability - by contrast with digital binarism and
reduction - remain yoked to a stratic program. It articulates itself within
terms that are on both sides only pseudo-autonomous, since they comprise
machinically complementary segments of an overall stratification. In its
relation to the intensive number, digital-analog differentiation operates as
an integrated syndrome. On one hand, an ever closer approximation to a
digital-ideal is realized through systematically interlinked massive iteration
and resolution of discrete minima, both regularization of qualitative
microsegmentarity, and quantification into abstract data. On the other
hand, the correlative analog-ideal of homogeneous continuum is tuned in
complementarity with deepened discretizations at a number of levels,
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organizing the separation of qualitative variation by digitally coded topic
(domain), and drawing upon compensatory formalizations of discrete
notational elements to program its application (such as algebraic
designators and generic terms used in the semiotics of real numbers,
technical vocabularies supporting the function of metres, read-outs, and
adjustments).
Mathematico-calculative segmentation of the Oecumenon mutually
stabilizes and interactively consolidates systems of expression and content,
in accordance with the divisional functions of an abstract machine that
remains unsegmented - as intensively divisional singularity - on its
Planomic pole. Mechanomic zygogenesis of the numbering number
composes a counter-mutuality, desolidarization, disengagement, and
dislocation of stratic interdependence, twinned to a flat fusional
convergence that collapses segmentarity. It mixes a decomplication in the
direction of the subnaturals (primes, and hyper-prime orders) with a
Planomic flattening of cardinality onto nonpunctual tropics (cosmic Nomomagnitudes condensing equatorially, as intensity degree-0 of the
megamolecule).
Multiplicative arithmetical operations take on a strictly ordinal
function when used within abstract pragmatic systems of nonmetric
numerical composition. Multiplex aggregation and disaggregative
factorization are the keys to an intrinsically bivalent (or zygonomous)
ordinal numbering practice, employing a small number of consistent and
reversible conversions to machinically potentiate primes as singular (or
non-substitutable) ordinal parts. The susceptibility of each natural number
to unique factorization (and reaggregation) realizes a basic modal
difference internal to it, and engages it with a heterogeneous external
system. Both procedural implex (compacted factorization schema), and
interordinal linkage (matrices of prime-natural cross-sequencing). It is this
double ambivalence that connects the number to the secret, and makes of
primes the principle components of cryptographic systems, in which they
function as keys: abstract operators for the (aggregative) locking and
(disaggregative) unlocking of multiplicities.
The distinction between the modes of the number aggregated/disaggregated - is purely semiotic (though nonsignifying). It
concerns notational ambivalence with consistent designation, switches in
compositional phase of a single heterogenous magnitude. In contrast, the
difference between prime series (traits of content) and its ordinates (traits
of expression) is real, regulated by an alogical distribution without
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correspondence or conformity, and complying with a difference in register,
between rigorously interconnected heterogeneous series. It is only by way
of its (aggregate or disaggregated) ordination(s) that the number switches
its capacity for modal conversion into a synthetic power, effected each
time a member of the prime series becomes determinable as such by
passing into the register of a different series. Such ordinal dezonings and
rezonings upon the natural number series occur each time a compositional
number disaggregates into singular parts (effecting codings and decodings
as surplus values), or a prime transfers itself to the ordinality that itemizes
it into the potential factor of another number.
Incorporeal transformation of 1931: the cultural initiation of Gödelcoding10 potential produces an instantaneous Planomic mutation slanted
towards nomadic multiplicities: virtually enveloping Oecumenic
segmentarity into a side-process of flat numerical systems. Gödelnumbering accomplishes a revolutionary redirection of kantianism according to a nomad rather than a copernican schema - by turning it
towards the operationalization of transcendental synthesis as method, and
away from the programmatic exhaustion of a self-limiting analytical
endeavour. It converts the kantian discovery of numerical synthesis from
doctrinal commitment to procedural machinery: subsuming philosophy into
transcendental arithmetic, with annihilating critique of the Hilbert
programme as surplus product.
Gödelization sets arithmetical diagram against axiomatic model,
shattering semantic interiority by infecting organizational overcodings with
numerical difference (synthesis or external relations). It anorganically
systematizes an arithmetical counterattack against axiomatization: a
methodical re-flattening of applied isomorphy (code and metacode) onto
metamorphic potential (number). From the perspective of transcendental
arithmetic, Gödel-coding nests within Gödel-numbering, where it is
produced as a coherent supplementary subsystem of numerical
polyfunction (surplus value of code).
On its sheerly numerical side, Gödelization produces, compacts, and
deploys a heterogeneous aggregate on the sequence of natural numbers,
where it enters solely into external syntheses with ordinal characteristics.
Simultaneously - and as surplus product - it installs a virtually
disaggregated assemblage of unlimited potential, composed of
consecutively decompacted numerical singularities marked in another
register (as ordinally-tagged prime factors sequenced by ascending
values). Each Gödel number is produced as an intrinsic twinning of
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aggregated numeric particle and disaggregative polysemiotic freight
(abstract virus).
How much pattern exists in the prime number series? Gödelization
renders this question Oecumenically critical, by definitely indicating that
inexplicit number pattern constitutes undelimitable surplus values
potentially realizable as synchronic decodings. It also makes the question
absolutely cryptic, by using a fragment of this surplus - a disaggregative
macroparticle functioning as decoding appendix - to trigger
Planomoseismic virtual envelopment of all Oecumenic tracings (including
any axiomatic number theory). Any number of natural numbers might
potentially disaggregate into systems of lateral antilogic that effectively
scramble axiomatizations.
When Gödelization codes the number (on the side) it is in order to
produce - or to reach - an absolute decoding and destratification (nomos).
A numerically extraneous coding-model - more precisely, an exemplary
instance of executive isomorphy (or nuclear stratosemiotics of the most
exalted kind) - induces cosmic transition at the level of the abstract
machine. It marks a passage in intensity, concurrent with the
comprehensive envelopment by surplus pattern of Oecumenic-order.
Numeric engulfing of Oecumenon, crashed segmentarity, and laterally
disrupted codings and axiomatics (at any level), fold together in a single
immense catastrophic event, fully realized in Planomic-potentials on the
Outside.
On one side the number flees from cardinality, innovating polyordinal machineries and semiotic surplus-values that outflank overcodings.
On the other side - but simultaneously - the number opens a line of flight
that escapes metrics towards cardinality: compressing it to absolute
(uncountable) magnitudes. A compositional-numeric scrambling of
expression (Gödelian transcendental arithmetic) virtually interoperates
with a diagonal-diagrammatic disruption of content (Cantorean
planotectonics). Both start from the Strata: isomorphically interlocked
segmentary metastases with complementary dynamics. Gödelization turns
isomorphism into side-process virus, unlocking metricization by
dismantling superordination of expression. Cantor-diagonals run
isomorphy the other way, down through Oecumenon into vague cataspaces
of problematic content, where it hystericizes against continuum (metric
collapse into planomic hyper-densities).
Make of cardinality itself a measure of isomorphic potential. The
result is a transfinite analysis of sets - flush with torsional nomos - where
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orders of containment are topologically disinteriorized by an absolute
warping. According to metric intuitions (conformity with finite strata), a
set that contains another within itself evidences superior cardinality. The
natural number series is the crucial case. It is clearly not the first countable
infinity, but the nth, where n is itself an infinite number. Innumerable
infinities are nested by the naturals, amongst which preeminence belongs
to the primes (demonstrably endless since Euclid).11 Since primes consist
of a proportionally diminishing selection from the set of naturals,
projective finite metrics confidently anticipates their cardinal subsumption.
Introducing isomorphy makes sense at first. Why not get infinities to
count each other? Produce abstract counting criteria by virtually
interzipping unending series. What draws things onto a line of flight is the
missing piece. A criterion is required, for differentially estimating the
cardinalities of subnatural infinities. Nothing turns up.
The problem is compounded when a definition is needed for the
threshold of infinity. How to determine the first transfinite set? The
naturals provide a model for countability: the capability to execute an
abstract count - even endless - by exhaustive steps. Use another infinity to
count through the abstract machine for you, as long as it doesn’t miss any
steps. If the end is already there, from the perspective of infinity, then
extensive prolongation loses its prominence. The first nonfinite set must
already be intensively infinitized: introducing sufficient recursion as the
principle of transfinite magnitude. For a set to avoid being outcounted relegated to finitude - a minimum of recursivity is required. The first
transfinite set must be isomorphic with a subset of itself (first recursion to
an infinite power).
Cardinality melts into schizophrenia precisely here. Every countable
set crossing into transfinite recursion threshold flattens onto a single
hypervalue: Aleph-0. Primes do it (and anything doing it does it to a
transfinite power (so an infinite number of prime subsets do it (which each
in turn (((( . . .)))))). When the transfinite happens it feeds straight into
itself, becomes instantaneously transfinitely larger that itself . . . then
diagonals click in.
Arithmetical consistency (e.g. (1 ÷ 3) x 3 = 1) implies the equation
1 = 0.999 . .,12 and thus a necessary expanded form for each number,
expressing it with as many decimal places as there are numbers in a
countable infinite series (Aleph-0). An ordered set of such numbers draws
a matrix, which has two sides, defined by diagonals which function as
cutting edges: defining a boundary by crossing it (in the direction of
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consistency). They count as Leibnizian monads, each reduplicating the
universe inside itself (the complexity of each being no less than that of the
whole). Equally, they count Spinozistic bodies, whose intrinsic latitudes
map extrinsic relations, constituting the strict parallelism between intensive
and extensive cosmos.
When cartography charts bodies by latitude and longitude it
construes them as diagonalizable. Diagonals are lines of flight. They
connect to elements outside the totality, drawing trajectories between the
absolute crossings marked by hypertense Oecumenic and Planomic
magnitude. Diagonal method activates an inexhaustible innovative
potential. It exploits capabilities no greater than those presupposed by a
prospective completion, which it then subverts, by finding an extraneous
item relative to any list, even an infinite one. It does so by constructing a
number that varies from the nth already listed number in its nth decimal (or
fractional-modular) place (at least). This is most economically exemplified
by a deterministic diagonalism, produced when all numerical values are
expressed in binary (mod-2) notation. The series of diagonal variations
will then be strictly programmed by simple alternation (flip 0 to 1, and
inversely). By recursively including each new number in the exceeded list
and rediagonalizing, the entire (transfinite) set of extranumerated items
generates itself automatically.
What has been discovered? Transfinite cardinality number-2:
Ultimate Continuum, an absolute edge, touched diagonally - as what
comes next - after Oecumenic totality has finished in intensity. At
cardinality C(ontinuum) magnitude becomes countless, disengaging
metrics from comparative countability. Cantor slides across schizophrenia,
nomos nonzone, magnitude is occupied without being counted.13 A smell
like something burning in the Superstratum.
Outside it’s Planomic Now, and the numbers are swarming. Aleph-0
vaporizes on the plane of consistency.
Notes
1
Calendric systems provide a partial and stasized model of the war
machine (which cannot enter history without collapsing it). Both work
compositionally, and involve ordinations (rather than quantities) the nth (of
the nth . . .). In both cases, the convention of ascending values indicates a
proximity to the subjectivity of the numbering number, opposed to the
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global perspective of the State expressed by the descending values of
standard place-value allocation. Calendric ordinality finds itself
increasingly cardinalized by chronometry under capitalist conditions.
The next Calendar is Millennium Time-Bomb, which dates
(AD1900 = 00, but so does AD2000).
An economical protocol for prolonging this dating system beyond
the millennium modifies and expands it to K-Time (K-Space- or Kilo-time)
by prefixing an additional zero. AD1900 = K-000, AD2000 = K-100, etc.
postponing its notational crisis until AD2900. (Dr. Melanie Newton).
2
The war machine processes destratified intensities through numerizing
multiplicities in affinity with disorganization, intercultural traffic,
biomechanical hybridity, pragmatics, and turbodynamics. It reproduces
itself by way of two complementary operations, both numerical: a
subtractive dezoning that marks its escape from State organization, and an
arithmetical decoding that maintains its fluidity against recrudescent tribal
lineages. The two together regenerate eccentric convergence of the war
machine: problem-in-process sustaining consistent disunity.
3
Even a metricized intensive scale substitutes the 0th intensity for the 1st
cardinal value of the system considered (n-1). This characteristic is shared
by the prime ordinate (1 = P-0).
4
‘Identical unity is not presupposed by ordinality, but arises through
cardinalization and the cancellation of difference in extension.’ (Deleuze,
Difference and Repetition, p. 233)
5
‘In the history of number, we see that every systematic type is
constructed on the basis of an essential inequality, and retains that
inequality in relation to the next-lowest type.’ (Deleuze, Difference and
Repetition, p. 232)
6
Occultists as insightful as Aleister Crowley and Kenneth Grant regularly
fall into a merely mechanical and pseudo-traditional use of Gematria. The
attempt to reproduce the values and consequences of Hebrew gematria
without renewing its systematic cultural function is largely responsible.
7
The Ionic or Alexandrian (alphabetical) numbers had completely
replaced the Attic numerals by the end of the 2nd century BC. The basis of
the Attic system was a more rigorously decimal precursor to that of the
Roman. Its core elements were the signs (1), (10), (100), (1000),
(10 000), although more complex signs for a small number of
intermediate values also existed.
8
The standard modern estimation of the Roman numerals as fundamentally
incompetent - interesting exclusively as the exemplary inferior antecedent
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to place-value decimal - overlooks a theoretically crucial nomad residuum.
This is best exemplified by their superior affinity with (ancient and current)
cash-money, deriving from similar exigencies, and associated with
relatively dezoned space. In the case of the Roman numerals this stems
from intense proximity to the numeric functions of the war machine,
evident from numerous historical records, and most clearly in the
numerical appellations of Roman military units and personnel. The later
allocation of a subtractive relation to series of ascending numerical values
ultimately compromises their mobility, providing an index or rigidifying
State-civilianization, with a growing predominance of bureaucratic and
financial (rather than logistical) imperatives.
9
The organicist-segmentary conclusion drawn from the semiotic
specialization of the Hindu-Arab numerals can be problematized in
numerous ways. Particularly noteworthy is the evidence of continual
interchange between numerals with linguistic signs (Gokhale 1996), the
persistent arithmetization of the Sanskrit alphabet even after it had
supposedly acquired an exclusively linguistic status, and the algebraic
usage of letters as token arithmetic elements (itself deeply intricated in the
history of Indian mathematics). An evolutionary interpretation (stages of
alphabetical numerology, then arithmetic with numerals, then algebraic
abstraction) seems no more plausible than its mechanotypic alternative (a
State-segmentarization of the initially fluid semiotic algebraism drawn
from nomad influences).
10
The code is comprised by a small set of mappings between numerical
values and nuclear overcoding notations (metamathematical theorem
jargons). The size of the numeric-coding set is nonfinite in principal, but
constrained pragmatically. The relevant values are realized in the factorial
disaggregation of a composite number, which produces them as blocks of
reiterative factors (sheer numerical difference, arithmetically isomorphic
with the series factor powers). The Gödel code makes explicit an implicit
isomorphy between arithmetical side-products and metamathematic formal
systems, thus eliminating all principled difference between logical
metastatements (expression) and the number theoretic object (content).
Numbers obtain the undelimitable virtual power of insinuation, drawn from
a reservoir of flat numeric surplus-values, and are able to actualize this
explicitly to make overcoding systems talk about themselves (in way they
cannot anticipate). The introduction of a liars paradox into the Principia
Mathematica number theory is the concrete way that version-1 Gödel code
wrecked its logical competence.
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11
Euclid’s prime number theorem inaugurates number theory by proving
the nonfinitude of the prime series. Its basic conceptual ingredient is the
factorial of n (n! = 1 x 2 x 3 _ x n), comprehending all possible divisors
under and up to n. Whichever way n! + 1 is divided (other than by 1), it
necessarily leaves 1 as a remainder. If any divisors for n! + 1 exist therefore - they must be greater than n itself, so that n! + 1 is either prime,
or a multiple of some prime greater than n. Since no number less than n
can be the last prime, and n can be any number, no number can be the last
prime. It is notable that this abstract demonstration shares a crucial feature
of diagonal argument: that of unlimitable constructive innovation through
rigorous exhaustion and permutation, producing a surplus item indicating
noncompleteness.
12
1 = 0.999... (mod-10), or (mod-2): 1 = 0.111...
13
Nomos - unsectioned space or ‘pasture’ (however scant) - supports a
population in continual transit, tolerates nothing but exploded totalities. By
destacking all organizational levels into turbular dynamics, nomos ensures
a perpetual conversion of redundancy into differential process, effecting a
collective counter-memory as vortical momentum (torque).
References
Crowley, Aleister, 777 and other Qabalistic Writings.
Deleuze, Gilles, Difference and Repetition. London (Athlone) 1994.
Deleuze, Gilles, and Félix Guattari, Capitalism and Schizophrenia Volume
1: Anti-Oedipus. London (Athlone) 1984.
Deleuze, Gilles, and Félix Guattari, Capitalism and Schizophrenia Volume
2: A Thousand Plateaus. London (Athlone) 1988.
Gödel, Kurt, On Formally Undecidable Propositions. New York (Basic
Books) 1962.
Gokhale, Shobhana Laxman, Indian Numerals. Poona (Deccan College)
1996.
Kaplan, Aryeh, ed., Sefer Yetzirah, the Book of Creation (In Theory and
Practice). New York (Samuel Weiser) 1983.
McLeish, John, Number. London (Bloomsbury) 1991.
Thapar, Romila, Time as a Metaphor of History: Early India. Delhi
(OUP) 1996.
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