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<nettime> Freaks of Number
matthew fuller on Mon, 22 Mar 2004 13:15:44 +0100 (CET)

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<nettime> Freaks of Number

Freaks of Number

There is very intriguing book from 1893, with a second edition in 1905.  
Maurice d'Ocagne, a Professor at the l'Ecole des Ponts et Chaussées's 'Le
Calcul Simplifié par les Procédés Mecaniques et graphiques''1 subtitled 'a
history and description of instruments and machines of calculation,
tables, abacuses and nomograms.' Much of the book is exactly that a set of
descriptions for increasing the speed and accuracy of numerical
calculation.  The text is notable for a number of things.  First, it is
perhaps one of the first examples of software criticism.  D'Ocagne makes
developed comparative portraits of each of the kinds of calculating
machines and techniques available in 1905 (indeed the book is bang up to
date with several last minute addenda on new machines).  All the heroes of
computation and their amazing gadgets are there: Pascal, Babbage, Leibniz,
Napier.  But there also appear a set of more everyday pieces of equipment,
cash registers, arithmometres, and so on.

Alongside the super-accurate ironmongery, one of the techniques promoted
by the book is that of Nomography.  This lost art is essentially that of
producing gridded visual diagrams showing the results of what would
otherwise be mental calculations.  In a reverse of today's expenditure on
processor power, these are graphics for the purpose of calculation,
computer graphics.  In his Universal History of Numbers, Georges Iffrah
describes, d'Ocagne's work: "...The first major step towards modern
concepts was taken in 1893 when Maurice d'Ocagne discovered the famous
collection of calculating machines in the Conservatoire des Arts et
Métiers as well as the equally important collection belonging to General
Sebert (now owned by IBM).  Since he could not relate these machines to
any contemporary mechanical theory, d'Ocagne had the highly original idea
of placing them into categories for which he developed his own hierarchy.  
To achieve this, he borrowed his classification criteria from biology.  
>From 1905, the date of the of the new edition of his Calcul Simplifié
appeared, he always referred to "the comparative anatomy of calculating
machines".  This stripped mechanical calculators of the uniqueness they
had previously enjoyed and which conferred on each its peculiar
bizarreness or curiosity.  Without question, d'Ocagne's approach paved the
way for an axiomatic theory of mechanical calculating machines.  After
that, the study of machines was viewed as a discipline that could be
rational, objective and therefore scientific."2

Actually, the book is not quite as rigidly scientistic as Iffrah has it.  
D'Ocagane acknowledges in the introduction that a number of things appear
in more than one category for the purposes of comparison.  The book is
more aimed at increasing the understand and availability of techniques of

	Another thing that is fascinating about this work is that it
begins, after the general assurance that arithmetic is important to a
number of trades and professions, with a list of what can only be called
freaks of number.  D'Ocagne makes an inventory of individuals for whom the
power of calculation reaches a prodigious intensity. "The history of
calculation has conserved the names of several of them.  We can cite: the
young Lorrain Mathieu Le Coq who, in Florence at eight years old, filled
Balthasar de Monconys, in his third voyage to Italy (1664) with wonder;
Mme de Lingré, who, in the salons of the Restoration, made, according to
Mme de Genlis, the most complicated mental operations in an atmosphere
full of the noise of conversations; the negro slave Tom Fuller, of the
state of Virginia, who, at the end of the 18th Century, died at the age of
twenty-four without being able to read or write; the Wurtemburgeois
shepherd Dinner; the Tyrolian shepherd Pierre Annich; the Englishman
Jedediah Buxton, a simple thresher from a barn;  the American Zerah
Colburn who was successively an actor, Methodist deacon and teacher of
languages; Dase who applied his faculties of calculation, the only ones
that he had, to the table of prime divisions of Burkhardt for the numbers
7 000 000 to 10 000 000; Bidder, the constructor of the Victoria Docks in
London, who became president of the Institute of Civil Engineers and who
transmitted in part his gifts for calculation to his son Georges; the
Sicilian shepherd Vito Mangiamelle, who possessed, besides, a great
facility for learning languages;  the young Piemontais Pughiesi; the
Russians Petrof and Mikhail Cerebriakhof; the shepherd of Touraine Henri
Mondeux, who came into great reknown during the reign of Louis-Philippe;
the young Bordelais Prologeau; the human-trunk Grandemange placed in the
world without arms or legs; Vinckler, who was the object of a remarkable
experience at the University of Oxford.  Finally we have today the
marvelous arithmetical tours de force of the Piemotais Jacques Inaudi, who
was also a shepherd at the beginning and who has found an emulator in the
person of Grec Diamandi."3

D'Ocagne ascribes much of the facility of calculation found so often in
this list amongst shepherds because of the way in which, even in
childhood, calculation can provide a way of passing the time whilst
guarding the flock.  To him, such powers of calculation are extremely
rare, and often won at the expense of other faculties. The fascination
with numerical prodigies continues today, although it is often more
radically clinicalised as for instance romantically described in the film
'Rain Man'.  Indeed in a number of recent films the quadrivium or four
arts of mathematics of ancient Greece (arithmetic, music, geometry,
astronomy) have appeared as existing on the border of neurological
disorder.  What is interesting though is that this list of numerical
freaks appears at the beginning of a sober text on the means of automating
mathematical operations.  It is as if it were something that has to be
acknowledged, marveled at, but disowned.  The chemist describes the
alchemists.  This shudder of recognition and of admiration passes.  The
thing is safely out of their clammy hands, but the continuum between these
persons and these machines is established.

	There is however something in this freakishness that is amplified
by calculation machines.  It is something that provides a figure of the
monstrous, the numerical grotesque.  Whilst the shepherds, the slaves, the
human trunks are marginalised, in the case of the former literally at the
edges of habitability up the hills grubbing for grass, they are also, once
their talent or curse is recognised, wrenched into the centre of attention
as a talismanic weird cousin.

For the comparative anatomy of calculation devices, these are freaks,
because they have this power lodged into their heads.  Such power should
be built only as the result of an anatomy that makes itself comparable by
means of abstraction by a machine. That such a continuum exists is the
result of a key quality of mathematics as a media - that it is immensely
abstract, but at the same time, utterly concrete.

I make this detour into the nineteenth century because this period
provides a veritable thunderstorm of cloudburst upon cloudburst of
arithmetico-material drives.  We have Charles Darwin, who spoke of the
'geometrical powers of increase' inherent in reproduction and variation of
species.  "There is no exception to the rule that every organic being
naturally increases at so high a rate, that if not destroyed, the earth
would soon be covered by the progeny of a single pair."4 It is also the
century of Karl Marx, who mapped the chaotic, ruinous and massively fecund
explosion of the factory system and of capitalism.  In his book 'The
Taming of Chance'5 Ian Hacking uses the term, 'the avalanche of numbers'
to describe the birth of statistics and the attempt to map and control
populations in terms of health, criminality, births, deaths, marriages,
physical non-human phenomena occurring at the same time. On the scale of
numbers, post-industrial society is perhaps something that occurs when the
'avalanche of numbers' of Hacking, an enormous and self-generating torrent
of factualisation, tabulation and recording meshes with numericalised
labour, mechanization and product and informational standardization and

Arithmetico-material drives occur as a result of the application of the
very fruitful perspectival trick that Newtonian (1642-1727) science pulls.  
This form of science, "Consisted in isolating some central, specific act,
and then using it as the basis for all further deductions concerning a
given set of phenomena"6 In its strongest form it led champions such as
Pierre Laplace, (1749-1837) whose determinism was such that he made the
well-known claim that if the position of every particle could be but
known, "Nothing would be uncertain, and the future, as the past, could be
present to out eyes."  But one can be determinist and be rather more
modest. Arithmetico-material drives are firstly generated in the moment
when matter is formed according to the mathematical model of it given by
such science.  One result of such objectivisation is the Standard Object,
the modular component typical of globalised trade, but with its roots
deep, for instance, in the licenses afforded the monopolistic guilds of
the Middle Ages, and the history of trading generally.  Everything from
ships to pizzas are quality assured, subject to rigorous treaties and
processes of standardization.  These are typical results of industrial
production.  The second stage is when this process of standardization
becomes so abstracted it becomes amenable to massive acceleration in
production.  The human work put into the production is scanned, abstracted
and multiplied by means of machinic energy.  Once turned into numbers,
registered as a pattern, the actor of the work can be discarded and the
pattern accelerated.  When hooked up to processes of production we get the
discovery that, according to Walter Benjamin, "...the speed of traffic and
the ability of machines to duplicate words and writing outstrips human
needs.  The energies that technology develops beyond this threshold are
destructive.  First of all, they advance the technology of war and its
propagandistic preparation."7 Overproduction, the massive churning of
ordered matter and of markets: one might also say that any development
beyond this threshold might be captured by forces other than war, for
redistribution, for the reshaping of work, for burning.  One of the aims
of art is to capture this excess away from the apparatus of war.

Opposed to the Platonism of mainstream computing which finds its beauty in
the most apparently simple, the most purely expressed of formal
resolutions to a problem, the recognition of arithmetico-material drives
reaches its current apotheosis in software.  The logically mighty Turing
machine might be trapped in the weakling body of a PC, but it provides an
environment in which is computationally almost unimaginable.  Every
household and every workplace with a computer contains its own avalanche
of numbers.  That many are now networked allows arithmetico-material
patterns of turbulence or gentle weather to move from hard drive to hard
drive in modes including the various forms of voluntary or involuntary
file-sharing such as peer-to-peer networks or viruses.

We can see too that much digital art is often the turning loose of these
powers into the contexts of established art genres.  Thus the most typical
'digital' reversioning of a portrait is the morph, the simultaneous
assault on and reconfirmation of identity by the availability of processor
cycles and of algorithms to compute various kinds of medium terms,
variables in between states; to find edges; to match patterns of light
intensity. 8 What does it mean to throw the core digital archetypes:
loops, variables, arrays, conditionals, and so on into the context of art?  
By the sheer onrush of available permutations the historically established
art genres are shredded, but at the same time they become the loci around
which activities are fixated.  I mean this in the sense of the most
willfully tedious work, typical of, say, the grimmer corners of Siggraph,
but also about work which aims to deploy this reconstituting turbulence in
ways that use generic limits to test out and mutate calculational
monstrosity itself. Equally it is not just self-consciously computational
art which allows ways of sensing into these processes.  Keith Tyson shows
these spaces in the various ways in which they are constructed, as
jargons, as diagrams, as routines, as the art gestural jargon of splashes
and drips as recordings of certain kinds of material bodily dynamism.  I
like the way he uses theorems and equations as part of pop culture, as
cosmic doodles.  At once schematic and sploshy they are enormously vivid
and multidimensional. Further into the numerical grotesque, and thus
beyond the boundaries of contemporary art good taste, M.C. Escher creates
landscapes of ink on paper, possible yet impossible according to the
'laws' of perspective, these laws which exist only as a loophole hackable
by excessive feats of draughtsmanship.  Equally as deft an exponent of the
geek sublime, but in text, J.G. Ballard's story 'Report on an Unidentified
Space Station'9 of an endless space station being explored by a crew who
will never reach its end.  Both of these are made possible by the simplest
linking devices of realist representation, a linear narrative with a
narrator or a line dividing one space from another.  Telephone
call-centres too, created by means of digital exchanges, a structured
progress through an ordered sequence in which potentially thousands of
people are held in suspension waiting their turn in the multi-choice
queue.  Digital abundance creates buffer zones as well as turbulence,
pockets of delay, holding patterns

Here, I think it is useful to recall one of the early critics of this easy
facility of achievement in computing.  Jospeh Weizenbaum is noted as a
computer scientist and famed for the Eliza program, the core conceptual
work behind many of today's efforts towards natural language programs and
also the grandmother of all chatbots. "Almost anyone with a reasonably
orderly mind can become a fairly good programmer with just a little
instruction and practice.  And because programming is almost immediately
rewarding, that is, because a computer very quickly begins to behave
somewhat in the way the programmer intends it to, programming is very
seductive."10 Are such programmers today's freaks?  The isolated shepherds
of their data-flocks?  It has become commonplace to identify Asperger's
Syndrome with hackers and programmers but these are the most recognisable
examples of such drives.  How many little numerical disorders exist in our
habits?  Stepping on the cracks in the pavement an equal number of times
with each foot.  Remembering numbers.  Being in a couple.  There are vast
populations of numerical patternings running through the populations of
our heads Weizenbaum goes on to note that the educational system is
ideally structured, and present at a moment in a person's life, when they
are easily enraptured and absorbed by such facility, usually without any
fundamental questioning.  Here we see the seductive power of
mathematico-material drives, the imaginal space they open up, especially
in the fast, low friction world of computation, a world where one standard
object acts upon another, acting upon another and another, in an
infinitely seductive and rapidly changing infinite regress through layer
upon layer from interface, through strata of code to circuits and beyond.  
Under digital abundance each generation of programmers is a processor
cycle, the completion of a loop of instructions, more fuel for the
explosion mapped by figures of perpetual geometric increase such as
Moore's Law.  If, for Darwin, 'death is the blind sculptor' of geometric
increase in life what is it that provides friction, a test of fitness for
arithmetico-material drives under conditions of digital abundance?  In
order to understand the aesthetics by which this sculptor
perspectivally-delimited artist operates a politics of numbers, and of the
mechanisms of calculation and life is required.  In other words, what are
the nomograms that describe or synthesise contemporary
arithmetico-material drives?

First of all, viruses and worms.  One could almost transpose the glorious
terms in which Marx, reading from the British Governments blue books of
industrial statistics, tripping on the stock market, straight into the
tales of the massive escalation of viruses.  2003 saw the Slammer
infecting 75,000 servers in ten minutes;  the Blaster worms followed for
PCs; Sobig.F had, at one point nearly four percent of all email traffic as
its vector of propagation.  The various versions of MyDoom, at the
beginning of 2004 took that to five percent.  Netsky.D 'has broken the
records for the speed at which it has spread, having infected over 200,000
computers within hours of its detection.'11

	It takes statistics, the creatures of the avalanche of numbers to
describe these plagues of logic.  One can only experience them, as a user,
at the interface of a pc, or as a sysadmin as traffic logs.  That is to
say that the perceptual tools available to understand and sense into the
passage of viruses and the materiality of networks are limited.  We are
left with as much sense of things as a viewer of glitch art12 an
accidental scalarly defined aperture into a process occurring outside of
the interface we are assigned.  A question is whether the position of the
human or the user is a perspectival scale which is able actually to grasp
such processes except as a kind of residue.13

	Some work such as the Human Cellular Automaton14, or that of
socialfiction.org works directly to make arithemetico-material drives
palpable by moving software outside of the casing of the computer.  Elias
Cannetti attempted to provide a typology of such cloudbursts of behaviour
in urban crowds, with an emphasis on the abuse possible by their actors'
at least partially unconscious involvement.  These works and to some
extent phenomena such as the wave of Flash Mobs generated in 2003 provide
formations in which a literacy of open combination of loosely uniform
behaviours produces a palpably different consistency of interactions.

But let us recoup, scientific idealism achieves historical agency.15 It
works.  As it does so it gains the capacity to forge elements - at a
certain scalar level - to a schema which enables them to reproduce the
qualities and behaviours of ideal objects.  (It is the reproduction of,
not full conformity to, such schemas that is suggested here.)  It does so
by means of numbers and relations between them.  This achievement - and
its is a significant one, achieved in part by a massive determination to
pay careful and comparable attention to the world - has however, two
problems, or more accurately - openings:  that of scalar perspectivalism,
in which dimensions of relationality of an object are occluded or
functionally shorn off; the relative incapacity to describe non-metrical
activity by the interaction of metrically defined parts, that is, the
relation between intensity and extensity.

	The context of software amplifies on a massive scale the condition
of multiple layers of standard objects interacting at calculationally
accelerated speeds and which indeed provides the mechanism by which
further arithmetico-material cloudburts are engendered and delivered.

There is a small group of Perl poems by the artist and programmer Harwood,
a member of the group Mongrel, that I think capture some of what it is to
provide a nomogram, a sensorial device into these cloudbursts.  Freaks of
number, the paragons of the unnatural, condense calculational power into
themselves, they boil days of computation by hand into s few seconds of
technique and neurotic power.  Arithmetico-material drives burst out of
bodies, feed off them, turn them into fuel.

	In London.pl a poem usefully annotated by Florian Cramer for the
Run_Me repository,16 Harwood provides a means, through software, of
sensing into these drives.  If, for Hacking, the avalanche of numbers is a
way of describing the birth of statistics and the gradual generation of a
form of control based on the modulation of populations, here it is a means
of reversing such a process and rebuilding part of the capacity of the
bodies of those turned to fuel by capitalism and the arithmetico-material
drives of industrialization.

	The poem is a rewrite, a plagiarism, of William Blake's 'London'.  
Published in the book 'Songs of Experience' in the last decade of the
Eighteenth Century this vivid burst of rage is only sixteen lines long,
yet it manages to impress a profound set of sensations.  The predominant
sensorial impression is that of breaths, breaths combined with political,
economic and social violence, breaths as the marker of rancorous suffering
life:  cries, cries of fear, voices, bans or proclamations, cries of
chimney-sweeping children, sighing soldiers wrecked by the wars between
the competing imperiums of England and France, cursing harlots, and
screaming babies.  Blake makes a robust and defiant list of the ravages of
society governed by access to the simultaneously abstract and brutally
factual apparatus known as money.  What is charter'd, isolateable as
property, made 'proprietary' as the poem reversions it , is urban life.
	In the hashed comments to the poem we see the following:

# London - Simple Act Redress
# The American War was the last judgment on England.
# Inoculated against the sewer. Albion's Angels
# Rise up on wings of iron & steel, spreadsheet & rule:
# To gift sanitation & sulphurous fire to:
# The wheat of Europe,
# The rice of Asia,
# The potato of America,
# The maize of Africa.
# Massacre-bloated, angels crawl from the corpse of war.
# Five times fatter than when they entered.

The systems of commodity, health standardization via immunization, and war
is built upon the disasterous repression of the English revolution, the
massacre of potential futures by the dictatorship of Cromwell and the
introduction of new energy sources to populations via the parasitical use
of colonies.  'Spreadsheets' and rulers, metric systems, fuelled and
propitiated by the capacities of metals and the populations working them.

	In London.pl, Harwood takes statistics of average lung capacity,
height, life-expectancy of particular ages and class populations in this
era, turns them into a variable for a program to compute the volume,
length and number of screams that such a number of such a typical set of
sizes of lungs could produce.  In the words of another text 'pushing' the
resulting quantity of air, 'through a speaker system in the waveform of a

	Screams in poetry are often the representatives of an unameable
thing, a burning kernel of anguish which represents the soul and is
inaccessible to language.  London.pl by contrast, sharing this with some
of the work of Diamanda Galas on the plague of AIDS or the resolutely and
rightly obscene monuments to the massacres in Rwanda, shows how much this
screaming is caught up in systems of numericalisation and acceleration
through the operations of calculus.

	After making these calculations of numerically induced screaming,
the poem, as a program then sets an output for the results.  An as yet
unwritten Perl module PublicAddressSystem.pm The comments in the program
read: use PublicAddressSystem qw(Hampstead Westminster Lambeth Chertsey);
# PublicAddressSystem is an I/O library for the manipulation of the
wheelen # Vortex4 129db outside warning system. # # from Hampstead in the
North, to Peckham in the South, # from Bow in the East to Chertsey in the

# Find and calculate the gross lung-capacity of 
the children screaming from 1792 to the present
# calculate the air displacement needed to represent the public scream
# set PublicAddressSystem intance and transmit the output.
# to do this we approximate that there are 
7452520 or so faces that live in the charter'd 
streets of London.
# Found near where the charter'd Thames does flow.

The soot-encrusted burned skeletons of children are still lodged in the
heads, the chimney stacks of London, the screaming is still going on.  
This poem, designed to be reversioned as an actually functioning program
attached to a PA provides a way in which two scales at which this violence
simultaneously occurs can be sensed into and thought.  At the level of a
numerically recognizable 'fact' an account of voices disappeared from
history, and at the level of an arithmetico-material drive, a way of
understanding this process as systematic.  Here, we are all freaks of
number.  Calculation machines are here built into bodies, lives are
deleted, burnt up, expended, but they are also the means by which they can
be understood and, like the calculation machines of D'Ocagne, turned to
make accounts.

Matthew Fuller
fuller at xs4all dot nl

Originally written for the symposium, Programmation Orientée Art, CRECA,
Sorbonne, Paris . March 19 & 20, 2004. http://ww.creca.org

With thanks to David-Olivier Lartigaud, Anne-Marie Lartiguad and Nathalie

1 Maurice d'Ocagne, 'Le Calcul Simplifié par les Procédés Mecaniques et
graphiques', 2nd ed.  Gauthier-Villars, Paris 1905

2 Georges Iffrah, 'The Universal History of Numbers, vol. 3 The Computer
and the Information Revolution', trans. E. F. Harding, Harvill Press,
London, 2000, p.228

3 p.3-4 According to the page, 'Mathematicians of the African Diaspora'
maintained by Dr. W.  Scott Williams, Professor of Mathematics of SUNY,
Buffalo, Tom Fuller,
http://www.math.buffalo.edu/mad/special/fuller_thomas_1710-1790.html died
at the age of eighty in 1790.  Further brief speculation about Fuller can
be found in, E.W.  Scripture, Arithmetical Prodigies', American Journal of
Psychology, vol.4, no.1.  April 1891.  A more developed survey of
mathematical prodigies of the period, and giving further information about
many of the people cited by d'Ocagne is, Frank D. Mitchell, 'Mathematical
Prodigies', American Journal of psychology, vol.  18, no.1, April 1907
both papers can be found on the same page on memory techniques, games,
card sharping and magic tricks maintained by Oleg Stepanov at:  

4 Charles Darwin, 'The Origin of Species', Penguin, London 1985, p.117

5 Ian Hacking, 'The Taming of Chance', Cambridge University Press, 1990

6 Ilya Prigogine and Isabelle Stengers, 'Order out of Chaos, man's new
dialogue with nature', Flamingo, London 1985

7 Walter Benjamin,' Edward Fuchs, collector and historian', in, Selected
Works, vol. 3, Harvard University Press , p.266-67

8 A useful survey of electronic portraiture, including a number of uses of
facial morphing and computer-generated personalities is given in a lecture
by Jasia Reichardt at the Tate gallery site

9 in, J.G. Ballard, 'War Fever', Farrar Strauss Giroux, New York, 1990

10 Jospeh Weizenbaum, 'Computer Power and Human Reason, from judgement to
calculation', Pelican, London, 1984, p.277

11 'Internet Havoc', New Scientist, 6 March 2004, p.5

12 Glitch Art, http://www.beflix.com/index.html

13 see for two texts clarifying scalar perception, Edwin A. Abbott,
'Flatland a romance of many dimension's, Dover Publications and, Ret Marut
aka B.Traven, 'The Scarf', in, 'To The Honourable Miss S and other
storie's, Lawrence Hill and Co. Westport and Cienfuegos Press, Sanday,

14 A performance script from 1999 which has participants acting as a cell
in a game of Life.

15 Though of course, not all, or even most scientific idealisms do so: the
notorious example is that of Lysenko, documented in detail in Dominique
Lecourt, 'A Proletarian Science?', trans. Ben Brewster, New Left Books,
London, 1977

16 http://www.run_me.org/

17 'Lungs' at www.scotoma.org

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