Matthew FULLER, “Freaks of Number”, In> COX, G. – KRYSA, J. (eds.). Engineering
Culture: ‘The Author as (Digital) Producer’. New York: Autonomedia (DATA browser 02)
2005. Available on-line: < http://www.spc.org/fuller/texts/freaks-of-number/ > [cit. 12. 8.
2013].
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 book opens with a standard piece of puffery, noting
the substantial importance to all branches of modern science and industry of the art of calculation.
The text is notable for a number of things. First, it is perhaps one of the earliest 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 calculation.
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 the Greek 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 mathematico-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, and 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 variation.
Mathematico-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.
If numericalisation is the process of turning a live thing, a dynamic, or an object into something that
exists as a numerical representation of its properties, or that has such an abstraction of itself embedded
within it, mathematico-material drives are those forces produced in the coupling of numericalisation or
abstraction with the capacities and propensities of matter. Mathematico-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 mathematicomaterial
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 which is computationally
almost unimaginable to its users. Every household and every workplace with a computer contains its
own avalanche of numbers. That many are now networked allows mathematico -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. In his paintings, 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 mathematico -material drives under
conditions of digital abundance? In order to understand the aesthetics by which this sculptor or
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
mathematico-material drives?
First of all, viruses and worms. One could almost transpose the glorious terms with which Marx
describes his readings from the British Government’s blue books of industrial statistics, mapping the
growth of factory production, or his, by today’s standards rather modest, tripping on the stock market,
straight onto 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 propogation. 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 systems administrator viewing internet
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 aperature 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 projects such as the Human Cellular Automaton,14
or much of the catalogue of experiments
compiled by socialfiction.org work directly to make mathematico-material drives palpable by moving
software outside of the casing of the computer. In another resource for such work, Crowds and Power,
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. As
distributed and modularised patterns of behaviour and information become part of the general
imaginary, the available repertoire of understood ways of doing things, we can begin to see self-aware
and often wittily gratuitous conjugations of social forms and mathematico-material drives. Phenomena
such as the wave of Flash Mobs generated in 2003 provide contexts in which a growing general
literacy in the open combination of loosely uniform behaviours (often directly working on pop-science
concepts such as complexity and emergence) produce a palpably different consistency of interactions.
But let us recoup, scientific idealism, of which numericalisation is a form, 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 mathematico-material cloudbursts 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 a few seconds of technique and neurotic
power. Mathematico -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 mathematico-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 chimneysweeping
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:
# NAME
# 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.
Here, the systems of commodification, health standardization via immunization, and war are built
upon the disastrous 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, metrical systems are, fuelled and changed 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 scream.’17
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 West.
# 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 instance 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 mathematico-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.
With thanks to David-Olivier Lartigaud, Anne-Marie Duguet and Nathalie Magnan.
1 Maurice d’Ocagne, ‘Le Calcul Simplifié par les ProcédésMecaniques et graphiques’, 2nd
ed.
Gauthier-Villars, Paris 1905
Sincewriting this text, I note that a third edition, from 1928, ispublished in English, trans. J. Howlett
and M.R. Williams, CharlesBabbgae Institute reprint series for the History of Computing, MITPress,
Cambridge and Tomash Publishers, Los Angeles, 1986
2 Georges Iffrah, ‘TheUniversal History of Numbers, vol. 3 The Computer and theInformation
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 byd’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:http://users.lk.net/~stepanov/mnemo/
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, ‘Orderout 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 ofuses of facial morphing and
computer-generated personalities isgiven in a lecture by Jasia Reichardt at the Tate gallery
sitehttp://www.tate.org.uk/audiovideo/wnmwn/live_wnmwn.htm#reichardt
9 in, J.G. Ballard, ‘WarFever’, 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’, NewScientist,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,‘Flatlanda romance of many
dimension’s,Dover Publications and, Ret Marut aka B.Traven, ‘The Scarf’, in,‘ToThe Honourable
Miss S and other storie’s,Lawrence Hill and Co. Westport and Cienfuegos Press, Sanday, 1981
14 A performance script from 1999 which has participants acting as acell in a game of Life.
15 Though of course, not all, or even most scientific idealisms doso: the notorious example is that of
Lysenko, documented in detailin 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