[D66] Number: Its Origin and Evolution

[R.O.]

(Ne we weer om de oren geslagen worden met getallen, getallen, getallen 
moeten we eens kijken wat een getal eigenlijk is...)

LONG READ

https://theanarchistlibrary.org/library/john-zerzan-number-its-origin-and-evolution


John Zerzan
Number: Its Origin and Evolution

The wrenching and demoralizing character of the crisis we find ourselves 
in, above all, the growing emptiness of spirit and artificiality of 
matter, lead us more and to question the most commonplace of “givens.” 
Time and language begin to arouse suspicions; number, too, no longer 
seems “neutral.” The glare of alienation in technological civilization 
is too painfully bright to hide its essence now, and mathematics is the 
schema of technology.

It is also the language of science—how deep we must go, how far back to 
reveal the “reason” for damaged life? The tangled skein of unnecessary 
suffering, the strands of domination, are unavoidably being unreeled, by 
the pressure of an unrelenting present.

When we ask, to what sorts of questions is the answer a number, and try 
to focus on the meaning or the reasons for the emergence of the 
quantitative, we are once again looking at a decisive moment of our 
estrangement from natural being.

Number, like language, is always saying what it cannot say. As the root 
of a certain kind of logic or method, mathematics is not merely a tool 
but a goal of scientific knowledge: to be perfectly exact, perfectly 
self-consistent, and perfectly general. Never mind that the world is 
inexact, interrelated, and specific, that no one has ever seen leaves, 
trees, clouds,animals, that are two the same, just as no two moments are 
identical. As Dingle said, “All that can come from the ultimate 
scientific analysis of the material world is a set of numbers,” 
reflecting upon the primacy of the concept of identity in math and its 
offspring, science.

A little further on I will attempt an “anthropology” of numbers and 
explore its social embeddedness. Horkheimer and Adorno point to the 
basis of the disease: “Even the deductive form of science reflects 
hierarchy and coercion...the whole logical order, dependency, 
progression, and union of [its] concepts is grounded in the 
corresponding conditions of social reality” —that is, the division of labor.

If mathematical reality is the purely formal structure of normative or 
standardizing measure (and later, science), the first thing to be 
measured at all was time. The primal connection between time and number 
becomes immediately evident. Authority, first objectified as time, 
becomes rigidified by the gradually mathematized consciousness of time. 
Put slightly differently, time is a measure and exists as a reification 
or materiality thanks to the introduction of measure.

The importance of symbolization should also be noted, in passing, for a 
further interrelation consists of the fact that while the basic feature 
of all measurement is symbolic representation, the creation of a 
symbolic world is the condition of the existence of time.

To realize that representation begins with language, actualized in the 
creation of a reproducible formal structure, is already to apprehend the 
fundamental tie between language and number. An impoverished present 
renders it easy to see, as language becomes more impoverished, that math 
is simply the most reduced and drained language. The ultimate step in 
formalizing a language is to transform it into mathematics; conversely, 
the closer language comes to the dense concretions of reality, the less 
abstract and exact it can be.

The symbolizing of life and meaning is at its most versatile in 
language, which, in Wittgenstein’s later view, virtually constitutes the 
world. Further, language, based as it is on a symbolic faculty for 
conventional and arbitrary equivalences, finds in the symbolism of math 
its greatest refinement. Mathematics, as judged by Max Black, is the 
“grammar of all symbolic systems.”

The purpose of the mathematical aspect of language and concept is the 
more complete isolation of the concept from the senses. Math is the 
paradigm of abstract thought for the same reason that Levy termed pure 
mathematics “the method of isolation raised to a fine art.” Closely 
related are its character of “enormous generality,” as discussed by 
Parsons, its refusal of limitations on said generality, as formulated by 
Whitehead.

This abstracting process and its formal, general results provide a 
content that seems to be completely detached from the thinking 
individual; the user of a mathematical system and his/her values do not 
enter into the system. The Hegelian idea of the autonomy of alienated 
activity finds a perfect application with mathematics; it has its own 
laws of growth, its own dialectic, and stands over the individual as a 
separate power. Self-existent time and the first distancing of humanity 
from nature, it must be preliminarily added, began to emerge when we 
first began to count. Domination of nature, and then, of humans is thus 
enabled.

In abstraction is the truth of Heyting’s conclusion that “the 
characteristic of mathematical thought is that it does not convey truth 
about the external world.” Its essential attitude toward the whole 
colorful movement of life is summed up by, “Put this and that equal to 
that and this!” Abstraction and equivalence of identity are inseparable; 
the suppression of the world’s richness which is paramount in identity 
brought Adorno to the “primal world of ideology.” The untruth of 
identity is simply that the concept does not exhaust the thing conceived.

Mathematics is reified, ritualized thought, the virtual abandonment of 
thinking. Foucalt found that “in the first gesture of the first 
mathematician one saw the constitution of an ideality that has been 
deployed throughout history and has questioned only to be repeated and 
purified.”

Number is the most momentous idea in the history of human nature. 
Numbering or counting (and measurement, the process of assigning numbers 
to represent qualities) gradually consolidated plurality into 
quantification, and thereby produced the homogenous and abstract 
character of number, which made mathematics possible. From its inception 
in elementary forms of counting (beginning with a binary division and 
proceeding to the use of fingers and toes as bases) to the Greek 
idealization of number, an increasingly abstract type of thinking 
developed, paralleling the maturation of the time concept. As William 
James put it, “the intellectual life of man consists almost wholly in 
his substitution of a conceptual order for the perceptual order in which 
his experience originally comes.”

Boas concluded that “counting does not become necessary until objects 
are considered in such generalized form that their individualities are 
entirely lost sight of.” In the growth of civilization we have learned 
to use increasingly abstract signs to point at increasingly abstract 
referents. On the other hand, prehistoric languages had a plethora of 
terms for the touched and felt, while very often having no number words 
beyond one, two and many. Hunter-gatherer humanity had little if any 
need for numbers, which is the reason Hallpike declared that “we cannot 
expect to find that an operational grasp of quantification will be a 
cultural norm in many primitive societies.” Much earlier, and more 
crudely, Allier referred to “the repugnance felt by uncivilized men 
towards any genuine intellectual effort, more particularly towards 
arithmetic.”

In fact, on the long road toward abstraction, from an intuitive sense of 
amount to the use of different sets of number words for counting 
different kinds of things, along to fully abstract number, there was an 
immense resistance, as if the objectification involved was somehow seen 
for what it was. This seems less implausible in light of the striking, 
unitary beauty of tools of our ancestors half a million years ago, in 
which the immediate artistic and technical (for want of better words) 
touch is so evident, and by “recent studies which have demonstrated the 
existence, some 300,000 years ago, of mental ability equivalent to 
modern man,” in the words of British archeologist Clive Gamble.

Based on observations of surviving tribal peoples, it is apparent, to 
provide another case in point, that hunter-gatherers possessed an 
enormous and intimate understanding of the nature and ecology of their 
local places, quite sufficient to have inaugurated agriculture perhaps 
hundreds of thousands of years before the Neolithic revolution. But a 
new kind of relationship to nature was involved; one that was evidently 
refused for so many, many generations.

To us it has seemed a great advantage to abstract from the natural 
relationship of things, whereas in the vast Stone Age being was 
apprehended and valued as a whole, not in terms of separable attributes. 
Today, as ever, when a large family sits down to dinner and it is 
noticed that someone is missing, this is not accomplished by counting. 
Or when a hut was built in prehistoric times, the number of required 
posts was not specified or counted, rather they were inherent to the 
idea of the hut, intrinsically involved in it. (Even in early 
agriculture, the loss of a herd animal could be detected not by counting 
but by missing a particular face or characteristic features; it seems 
clear, however, as Bryan Morgan argues, that “man’s first use for a 
number system” was certainly as a control of domesticated flock animals, 
as wild creatures became products to be harvested.) In distancing and 
separation lies the heart of mathematics: the discursive reduction of 
patterns, states and relationships which we initially perceived as wholes.

In the birth of controls aimed at control of what is free and unordered, 
crystallized by early counting, we see a new attitude toward the world. 
If naming is a distancing, a mastery, so too is number, which is 
impoverished naming. Though numbering is a corollary of language, it is 
the signature of a critical breakthrough of alienation. The root 
meanings of number are instructive: “quick to grasp or take” and “to 
take, especially to steal,” also “taken, seized, hence...numb.” What is 
made an object of domination is thereby reified, becomes numb.

For hundreds of thousands of years hunter-gatherers enjoyed a direct, 
unimpaired access to the raw materials needed for survival. Work was not 
divided nor did private property exist. Dorothy Lee focused on a 
surviving example from Oceania, finding that none of the Trobrianders’ 
activities are fitted into a linear, divisible line. “There is no job, 
no labor, no drudgery which finds its reward outside the act.” Equally 
important is the “prodigality,” “the liberal customs for which hunters 
are properly famous,” “their inclination to make a feast of everything 
on hand,” according to Sahlins.

Sharing and counting or exchange are, of course, relative opposites. 
Where articles are made, animals killed or plants collected for domestic 
use and not for exchange, there is no demand for standardized numbers or 
measurements. Measuring and weighing possessions develops later, along 
with the measurement and definition of property rights and duties to 
authority. Isaac locates a decisive shift toward standardization of 
tools and language in the Upper Paleolithic period, the last stage of 
hunter-gatherer humanity. Numbers and less abstract units of measurement 
derive, as noted above, from the equalization of differences. Earliest 
exchange, which is the same as earliest division of labor, was 
indeterminate and defied systematization; a table of equivalences cannot 
really be formulated. As the predominance of the gift gave way to the 
progress of exchange and division of labor, the universal 
interchangeability of mathematics finds its concrete expression. What 
comes to be fixed as a principle of equal justice—the ideology of 
equivalent exchange—is only the practice of the domination of division 
of labor. Lack of a directly-lived existence, the loss of autonomy that 
accompany separation from nature are the concomitants of the effective 
power of specialists.

Mauss stated that exchange can be defined only by all the institutions 
of society. Decades later Belshaw grasped division of labor as not 
merely a segment of society but the whole of it. Likewise sweeping, but 
realistic, is the conclusion that a world without exchange or 
fractionalized endeavor would be a world without number.

Clastres, and Childe among others well before him, realized that 
people’s ability to produce a surplus, the basis of exchange, does not 
necessarily mean that they decide to do so. Concerning the nonetheless 
persistent view that only mental/cultural deficiency accounts for the 
absence of surplus, “nothing is more mistaken,” judged Clastres. For 
Sahlins, “Stone Age economics” was “intrinsically an anti-surplus 
system,” using the term system extremely loosely. For long ages humans 
had no desire for the dubious compensations attendant on assuming a 
divided life, just as they had no interest in number. Piling up a 
surplus of anything was unknown, apparently, before Neanderthal times 
passed to the Cro-Magnon; extensive trade contracts were nonexistent in 
the earlier period, becoming common thereafter with Cro-Magnon society.

Surplus was fully developed only with agriculture, and 
characteristically the chief technical advancement of Neolithic life was 
the perfection of the container: jars, bins, granaries and the like. 
This development also gives concrete form to a burgeoning tendency 
toward spatialization, the sublimation of an increasingly autonomous 
dimension of time into spatial forms. Abstraction, perhaps the first 
spatialization, was the first compensation for the deprivation caused by 
the sense of time. Spatialization was greatly refined with number and 
geometry. Ricoeur notes that “Infinity is discovered...in the form of 
the idealization of magnitudes, of measures, of numbers, figures,” to 
carry this still further. This quest for unrestricted spatiality is part 
and parcel of the abstract march of mathematics. So then is the feeling 
of being freed from the world, from finitude that Hannah Arendt 
described in mathematics.

Mathematical principles and their component numbers and figures seem to 
exemplify a timelessness which is possibly their deepest character. 
Hermann Weyl, in attempting to sum up (no pun intended) the “life sum of 
mathematics,” termed it the science of the infinite. How better to 
express an escape from reified time than by making it limitlessly 
subservient to space—in the form of math.

Spatialization—like math—rests upon separation; inherent in it are 
division and an organization of that division. The division of time into 
parts (which seems to have been the earliest counting or measuring) is 
itself spatial. Time has always been measured in such terms as the 
movement of the earth or moon, or the hands of a clock. The first time 
indications were not numerical but concrete, as with all earliest 
counting. Yet, as we know, a number system, paralleling time, becomes a 
separate, invariable principle. The separations in social life—most 
fundamentally, division of labor—seem alone able to account for the 
growth of estranging conceptualization.

In fact, two critical mathematical inventions, zero and the place 
system, may serve as cultural evidence of division of labor. Zero and 
the place system, or position, emerged independently, “against 
considerable psychological resistance,” in the Mayan and Hindu 
civilizations. Mayan division of labor, accompanied by enormous social 
stratification (not to mention a notorious obsession with time, and 
large-scale human sacrifice at the hands of a powerful priest class), is 
a vividly documented fact, while the division of labor reflected in the 
Indian caste system was “the most complex that the world had seen before 
the Industrial Revolution.” (Coon 1954)

The necessity of work (Marx) and the necessity of repression (Freud) 
amount to the same thing: civilization. These false commandments turned 
humanity away from nature and account for history as a “steadily 
lengthening chronicle of mass neurosis.” (Turner 1980) Freud credits 
scientific/mathematical achievement as the highest moment of 
civilization, and this seems valid as a function of its symbolic nature. 
“The neurotic process is the price we pay for our most precious human 
heritage, namely our ability to represent experience and communicate our 
thoughts by means of symbols.”

The triad of symbolization, work and repression finds its operating 
principle in division of labor. This is why so little progress was made 
in accepting numerical values until the huge increase in division of 
labor of the Neolithic revolution: from the gathering of food to its 
actual production. With that massive changeover mathematics became fully 
grounded and necessary. Indeed it became more a category of existence 
than a mere instrumentality.

The fifth century B.C. historian Herodotus attributed the origin of 
mathematics to the Egyptian king Sesostris (1300 B.C.), who needed to 
measure land for tax purposes. Systematized math—in this case geometry, 
which literally means “land measuring”—did in fact arise from the 
requirements of political economy, though it predates Sesostris’ Egypt 
by perhaps 2000 years. The food surplus of Neolithic civilization made 
possible the emergence of specialized classes of priests and 
administrators which by about 3200 B.C. had produced the alphabet, 
mathematics, writing and the calendar. In Sumer the first mathematical 
computations appeared, between 3500 and 3000 B.C., in the form of 
inventories, deeds of sale, contracts, and the attendant unit prices, 
units purchased, interest payments, etc.. As Bernal points out, 
“mathematics, or at least arithmetic, came even before writing.” The 
number symbols are most probably older than any other elements of the 
most ancient forms of writing.



At this point domination of nature and humanity are signaled not only by 
math and writing, but also by the walled, grain-stocked city, along with 
warfare and human slavery. “Social labor” (division of labor), the 
coerced coordination of several workers at once, is thwarted by the old, 
personal measures; lengths, weights, volumes must be standardized. In 
this standardization, one of the hallmarks of civilization, mathematical 
exactitude and specialized skill go hand in hand. Math and 
specialization, requiring each other, developed apace and math became 
itself a specialty. The great trade routes, expressing the triumph of 
division of labor, diffused the new, sophisticated techniques of 
counting, measurement, and calculation.

In Babylon, merchant-mathematicians contrived a comprehensive arithmetic 
between 3000 and 2500 B.C., which system “was fully articulated as an 
abstract computational science by about 2000 B.C.. (Brainerd 1979) In 
succeeding centuries the Babylonians even invented a symbolic algebra, 
though Babylonian-Egyptian math has been generally regarded as extremely 
trial-and-error or empiricist compared to that of the much later Greeks.

To the Egyptians and Babylonians mathematical figures had concrete 
referents: algebra was an aid to commercial transactions, a rectangle 
was a piece of land of a particular shape. The Greeks, however, were 
explicit in asserting that geometry deals with abstractions, and this 
development reflects an extreme form of division of labor and social 
stratification. Unlike Egyptian or Babylonian society, in Greece, a 
large slave class performed all productive labor, technical as well as 
unskilled, such that the ruling class milieu that included 
mathematicians disdained practical pursuits or applications.

Pythagoras, more or less the founder of Greek mathematics (6th century, 
B.C.) expressed this rarefied, abstract bent in no uncertain terms. To 
him numbers were immutable and eternal. Directly anticipating Platonic 
idealism, he declared that numbers were the intelligible key to the 
universe. Usually encapsulated as “everything is number,” the 
Pythagorean philosophy held that numbers exist in a literal sense and 
are quite literally all that does exist.

This form of mathematical philosophy, with the extremity of its search 
for harmony and order, may be seen as a deep fear of contradiction or 
chaos, an oblique acknowledgement of the massive and perhaps unstable 
repression underlying Greek society. An artificial intellectual life 
that rested so completely on the surplus created by slaves was at pains 
to deny the senses, the emotions and the real world. Greek sculpture is 
another example, in its abstract, ideological conformations, devoid of 
feeling or their histories. Its figures are standardized idealizations; 
the parallel with a highly exaggerated cult of mathematics is manifest.

The independent existence of ideas, which is Plato’s fundamental 
premise, is directly derived from Pythagoras, just as his whole theory 
of ideas flows from the special character of mathematics. Geometry is 
properly an exercise of disembodied intellect, Plato taught, in 
character with his view that reality is a world of form from which 
matter, in every important respect, is banished. Philosophical idealism 
was thus established out of this world-denying impoverishment, based on 
the primacy of quantitative thinking. As C.I. Lewis observed, “from 
Plato to the present day, all the major epistemological theories have 
been dominated by, or formulated in the light of , accompanying 
conceptions of mathematics.”

It is no less accidental that Plato wrote, “Let only geometers enter,” 
over the door to his Academy, than that his totalitarian Republic 
insists that years of mathematical training are necessary to correctly 
approach the most important political and ethical questions. 
Consistently, he denied that a stateless society ever existed, 
identifying such a concept with that of a “state of swine.”

Systematized by Euclid in the third century B.C., about a century after 
Plato, mathematics reached an apogee not to be matched for almost two 
millennia; the patron saint of intellect for the slave-based and feudal 
societies that followed was not Plato, but Aristotle, who criticized the 
former’s Pythagorean reduction of science to mathematics.

The long non-development of math, which lasted virtually until the end 
of Renaissance, remains something of a mystery. But growing trade began 
to revive the art of the quantitative by the twelfth and thirteenth 
centuries. The impersonal order of the counting house in the new 
mercantile capitalism exemplified a renewed concentration on abstract 
measurement. Mumford stresses the mathematical prerequisite of later 
mechanization and standardization; in the rising merchant world, 
“counting numbers began here and in the end numbers alone counted.” 
(Mumford 1967)

But the Renaissance conviction that mathematics should be applicable to 
all the arts (not to mention such earlier and atypical forerunners as 
Roger Bacon’s 13th century contribution toward a strictly mathematical 
optics), was a mild prelude to the magnitude of number’s triumph in the 
seventeenth century.

Though they were soon eclipsed by other advances of the 1600’s, Johannes 
Kepler and Francis Bacon revealed its two most important and closely 
related aspects early in the century. Kepler, who completed the 
Copernican transition to the heliocentric model, saw the real world as 
composed of quantitative differences only; its differences are strictly 
those of number. Bacon, in The New Atlantis (c.1620) depicted an 
idealized scientific community, the main object of which was domination 
of nature; as Jaspers put it, “Mastery of nature...’knowledge is power,’ 
has been the watchword since Bacon.”

The century of Galileo and Descartes—pre-eminent among those who 
deepened all the previous forms of quantitative alienation and thus 
sketched a technological future—began with a qualitative leap in the 
division of labor. Franz Borkenau provided the key as to why a profound 
change in the Western world-view took place in the seventeenth century, 
a movement to a fundamentally mathematical-mechanistic outlook. 
According to Borkenau, a great extension of division of labor, occurring 
from about 1600, introduced the novel notion of abstract work. This 
reification of human activity proved pivotal.

Along with degradation of work, the clock is the basis of modern life, 
equally “scientific” in its reduction of life to a measurability, via 
objective, commodified units of time. The increasingly accurate and 
ubiquitous clock reached a real domination in the seventeenth century, 
as, correspondingly, “the champions of the new sciences manifested an 
avid interest in horological matters.”

Thus it seems fitting to introduce Galileo in terms of just this strong 
interest in the measurement of time; his invention of the first 
mechanical clock based on the principle of the pendulum was likewise a 
fitting capstone to his long career. As increasingly objectified or 
reified time reflects, at perhaps the deepest level, an increasingly 
alienated social world, Galileo’s principal aim was the reduction of the 
world to an object of mathematical dissection.

Writing a few years before World War II and Auschwitz, Husserl located 
the roots of the contemporary crisis in this objectifying reduction and 
identified Galileo as its main progenitor. The life-world has been 
“devalued” by science precisely insofar as the “mathematization of 
nature” initiated by Gallo has proceeded—clearly no small indictment. 
(Husserl 1970)

For Galileo as with Kepler, mathematics was the “root grammar of the new 
philosophical discourse that constituted modern scientific method.” He 
enunciated the principle, “to measure what is measurable and try to 
render what is not so yet.” Thus he resurrected the Pythagorean-Platonic 
substitution of a world of abstract mathematical relations for the real 
world and its method of absolute renunciation of the senses’ claim to 
know reality. Observing this turning away from quality to quantity, this 
plunge into a shadow-world of abstractions, Husserl concluded that 
modern, mathematical science prevents us from knowing life as it is. And 
the rise of science has fueled ever more specialized knowledge, that 
stunning and imprisoning progression so well-known by now.

Collingwood called Galileo “the true father of modern science” for the 
success of his dictum that the book of nature “is written in 
mathematical language” and its corollary that therefore “mathematics is 
the language of science.” Due to this separation from nature, Gillispie 
evaluated, “After Galileo, science could no longer be humane.”

It seems very fitting that the mathematician who synthesized geometry 
and algebra to form analytic geometry (1637) and who, with Pascal, is 
credited with inventing calculus, should have shaped Galilean 
mathematicism into a new system of thinking. The thesis that the world 
is organized in such a way that there is a total break between people 
and the natural world, contrived as a total and triumphant world-view, 
is the basis for Descartes’ renown as the founder of modern philosophy. 
The foundation of his new system, the famous “cogito ergo sum,” is the 
assigning of scientific certainty to separation between mind and the 
rest of reality.

This dualism provided an alienated means for seeing only a completely 
objectified nature. In the Discourse on Method...Descartes declared that 
the aim of science is “to make us as masters and possessors of nature.” 
Though he was a devout Christian, Descartes renewed the distancing from 
life that an already fading God could no longer effectively legitimize. 
As Christianity weakened, a new central ideology of estrangement came 
forth, this one guaranteeing order and domination based on mathematical 
precision.

To Descartes the material universe was a machine and nothing more, just 
as animals “indeed are nothing else but engines, or matter sent into a 
continual and orderly motion.” He saw the cosmos itself as a giant 
clockwork just when the illusion that time is a separate, autonomous 
process was taking hold. Also as living, animate nature died, dead, 
inanimate money became endowed with life, as capital and the market 
assumed the attributes of organic processes and cycles. Lastly, 
Descartes mathematical vision eliminated any messy, chaotic or alive 
elements and ushered in an attendant mechanical world-view that was 
coincidental with a tendency toward central government controls and 
concentration of power in the form of the modern nation-state. “The 
rationalization of administration and of the natural order were 
occurring simultaneously,” in the words of Merchant. The total order of 
math and its mechanical philosophy of reality proved irresistible; by 
the time of Descartes’ death in 1650 it had become virtually the 
official framework of thought throughout Europe.

Leibniz, a near-contemporary, refined and extended the work of 
Descartes; the “pre-established harmony” he saw in existence is likewise 
Pythagorean in lineage. This mathematical harmony, which Leibniz 
illustrated by reference to two independent clocks, recalls his dictum, 
“There is nothing that evades number.” Leibniz, like Galileo and 
Descartes, was deeply interested in the design of clocks.

In the binary arithmetic he devised, an image of creation was evoked; he 
imagined that one represented God and zero the void, that unity and zero 
expressed all numbers and all creation. He sought to mechanize thought 
by means of a formal calculus, a project which he too sanguinely 
expected would be completed in five years. This undertaking was to 
provide all the answers, including those to questions of morality and 
metaphysics. Despite this ill-fated effort, Leibniz was perhaps the 
first to base a theory of math on the fact that it is a universal 
symbolic language; he was certainly the “first great modern thinker to 
have a clear insight into the true character of mathematical symbolism.”

Furthering the quantitative model of reality was the English royalist 
Hobbes, who reduced the human soul, will, brain, and appetites to matter 
in mechanical motion, thus contributing directly to the current 
conception of thinking as the “output” of the brain as computer.

The complete objectification of time, so much with us today, was 
achieved by Issac Newton, who mapped the workings of the 
Galilean-Cartesian clockwork universe. Product of the severely repressed 
Puritan outlook, which focused on sublimating sexual energy into 
brutalizing labor, Newton spoke of absolute time, “flowing equably 
without regard to anything external.” Born in 1642, the year of 
Galileo’s death, Newton capped the Scientific Revolution of the 
seventeenth century by developing a complete mathematical formulation of 
nature as a perfect machine, a perfect clock.

Whitehead judged that “the history of seventeenth-century science reads 
as though it were vivid dream of Plato or Pythagoras,” noting the 
astonishingly refined mode of its quantitative thought. Again the 
correspondence with a jump in division of labor is worth pointing out; 
as Hill described mid-seventeenth century England, “...significant 
specialization began to set in. The last polymaths were dying out...” 
The songs and dances of the peasants slowly died, and in a rather 
literal mathematization, the common lands were closed and divided.

Knowledge of nature was part of philosophy until this time; the two 
parted company as the concept of mastery of nature achieved its 
definitive modern form. Number, which first issued from dissociation 
from the natural world, ended up describing and dominating it.

Fontenelle’s Preface on the Utility of Mathematics and Physics (1702) 
celebrated the centrality of quantification to the entire range of human 
sensibilities, thereby aiding the eighteenth century consolidation of 
the breakthroughs of the preceding era. And whereas Descartes had 
asserted that animals could not feel pain because they are soulless, and 
that man is not exactly a machine because he had a soul, LeMetrie, in 
1747, went the whole way and made man completely mechanical in his 
L’Homme Machine.

Bach’s immense accomplishments in the first half of the eighteenth 
century also throw light on the spirit of math unleashed a century 
earlier and helped shape culture to that spirit. In reference to the 
rather abstract music of Bach, it has been said that he “spoke in 
mathematics to God.” (LeShan & Morgenau 1982) At this time the 
individual voice lost its independence and tone was no longer understood 
as sung but as a mechanical conception. Bach, treating music as a sort 
of math, moved it out of the stage of vocal polyphony to that of 
instrumental harmony, based always upon a single, autonomous voice fixed 
by instruments, instead of somewhat variable with human voices.

Later in the century Kant stated that in any particular theory there is 
only as much real science as there is mathematics, and devoted a 
considerable part of his Critique of Pure Reason to an analysis of the 
ultimate principles of geometry and arithmetic.

Descartes and Leibniz strove to establish a mathematical science method 
as the paradigmatic way of knowing, and saw the possibility of a 
singular universal language, on the model of empirical symbols, that 
could contain the whole of philosophy. The eighteenth century 
Enlightenment thinkers actually worked at realizing this latter project. 
Condillac, Rousseau and others were also characteristically concerned 
with origins—such as the origin of language; their goal of grasping 
human understanding by taking language to its ultimate, mathematized 
symbolic level made them incapable of seeing that the origin of all 
symbolizing is alienation.

Symmetrical plowing is almost as old as agriculture itself, a means of 
imposing order on an otherwise irregular world. But as the landscape of 
cultivation became distinguished by linear forms of an increasingly 
mathematical regularity—including the popularity of formal 
gardens—another eighteenth-century mark of math’s ascendancy can be gauged.

In the early 1800s, however, the Romantic poets and artists, among 
others, protested the new vision of nature as a machine. Blake, Goethe 
and John Constable, for example, accused science of turning the world 
into a clockwork, with the Industrial Revolution providing ample 
evidence of its power to violate organic life.

The debasing of work among textile workers, which caused the furious 
uprisings of the English Luddites during the second decade of the 
nineteenth century, was epitomized by such automated and cheapened 
products as those of the Jacquard loom. This French device not only 
represented the mechanization of life and work unleashed by seventeenth 
century shifts, but directly inspired the first attempts at the modern 
computer. The designs of Charles Babbage, unlike the “logic machines” of 
Leibniz and Descartes, involved both memory and calculating units under 
the control of programs via punched cards. The aims of the mathematical 
Babbage and the inventor-industrialist J.M. Jacquard can be said to rest 
on the same rationalist reduction of human activity to the machine as 
was then beginning to boom with industrialism. Quite in character, then, 
were the emphasis in Babbage’s mathematical work on the need for 
improved notation to further the processes of symbolization, his 
Principles of Economy, which contributed to the foundations of modern 
management—and his contemporary fame against London “nusiances,” such as 
street musicians!

Paralleling the full onslaught of industrial capitalism and the hugely 
accelerated division of labor that it brought was a marked advance in 
mathematical development. According to Whitehead, “During the nineteenth 
century pure mathematics made almost as much progress as during the 
preceding centuries from Pythagoras onwards.”

The non-Euclidean geometries fo Bolyai, Lobachevski, Riemann and Klein 
must be mentioned, as well as the modern algebra of Boole, generally 
regarded as the basis of symbolic logic. Boolean algebra made possible a 
new level of formulized thought, as its founder pondered “the human 
mind...and instrument of conquest and dominion over the powers of 
surrounding nature,” (Boole 1952) in an unthinking mirroring of the 
mastery mathematized capitalism was gaining in the mid-1800s. (Although 
the specialist is rarely faulted by the dominant culture for his “pure” 
creativity, Adorno adroitly observed that “The mathematician’s resolute 
unconsciousness testifies to the connection between division of labor 
and ‘purity’.”)

If math is impoverished language, it can also be seen as the mature form 
of that sterile coercion known as formal logic. Bertrand Russell, in 
fact, determined that mathematics and logic had become one. Discarding 
unreliable, everyday language, Russell, Frege and others believed that 
in the further degradation and reduction of language lay the real hope 
for “progress in philosophy.”

The goal of establishing logic on mathematical grounds was related to an 
even more ambitious effort by the end of the nineteenth century, that of 
establishing the foundations of math itself. As capitalism proceeded to 
redefine reality in its own image and became desirous of securing its 
foundations, the “logic” stage of math in the late 19th and early 20th 
centuries, fresh from new triumphs, sought the same. David Hilberts 
theory of formalism, one such attempt to banish contradiction or error, 
explicitly aimed at safeguarding “the state power of mathematics for all 
time from all ‘rebellions’.”

Meanwhile, number seemed to be doing quite well without the 
philosophical underpinnings. Lord Kelvin’s late nineteenth century 
pronouncement that we don’t really know anything unless we can measure 
it bespoke an exalted confidence, just as Frederick Taylor’s Scientific 
Management was about to lead the quantification edge of industrial 
management further in the direction of subjugating the individual to the 
lifeless Newtonian categories of time and space.

Speaking of the latter, Capra has claimed that the theories of 
relativity and quantum physics, developed between 1905 and the late 
1920s, “shattered all the principal concepts fo the Cartesian world view 
and Newtonian mechanics.” But relativity theory is certainly 
mathematical formulism, and Einstein sought a unified field theory by 
geometrizing physics, such that success would have enabled him to have 
said, like Descartes, that his entire physics was nothing other than 
geometry. That measuring time and space (or “space-time”) is a relative 
matter hardly removes measurement as its core element. At the heart of 
quantum theory, certainly, is Heisenberg’s Uncertainty Principle, which 
does not throw out quantification but rather expresses the limitations 
of classical physics in sophisticated mathematical ways. As Gillespie 
succinctly had it, Cartesian-Newtonian physical theory “was an 
application of Euclidean geometry to space, general relativity a 
spatialization of Riemann’s curvilinear geometry, and quantum mechanics 
a naturalization of statistical probability.” More succinctly still: 
“Nature, before and after the quantum theory, is that which is to be 
comprehended mathematically.”

During the first three decades of the 20th century, moreover, the great 
attempts by Russell & Whitehead, Hilbert, et al., to provide a 
completely unproblematic basis for the whole edifice of math, referred 
to above, went forward with considerable optimism. But in 1931 Kurt 
Godel dashed these bright hopes with his Incompleteness Theorem, which 
demonstrated that any symbolic system can be either complete or fully 
consistent, but not both. Godel’s devastating mathematical proof of this 
not only showed the limits of axiomatic number systems, by rules out 
enclosing nature by any closed, consistent language. If there are 
theorems or assertions within a system of thought which can neither be 
proved or disproved internally, if it is impossible to give a proof of 
consistency within the language used, as Godel and immediate successors 
like Tarski and Church convincingly argued, “any system of knowledge 
about the world is, and must remain, fundamentally incomplete, eternally 
subject to revision.” (Rucker 1982)

Morris Kline’s Mathematics: The Loss of Certainty related the 
“calamities” that have befallen the once seemingly inviolable “majesty 
of mathematics,” chiefly dating from Godel. Math, like language, used to 
describe the world and itself, fails in its totalizing quest, in the 
same way that capitalism cannot provide itself with unassailable 
grounding. Further, with Godel’s Theorem mathematics was not only 
“recognized to be much more abstract and formal than had been 
traditionally supposed,” but it also became clear that “the resources of 
the human mind have not been, and cannot be, fully formalized.” (Nagel & 
Newman 1958)

But who could deny that, in practice, quantity has been mastering us, 
with or without definitively shoring up its theoretical basis? Human 
helplessness seems to be directly proportional to mathematical 
technology’s domination over nature, or as Adorno phrased it, “the 
subjection of outer nature is successful only in the measure of the 
repression of inner nature.” And certainly understanding is diminished 
by number’s hallmark, division of labor. Raymond Firth accidentally 
exemplified the stupidity of advanced specialization, in a passing 
comment on a crucial topic: “the proposition that symbols are 
instruments of knowledge raises epistemological issues which 
anthropologists are not trained to handle.” The connection with a more 
common degradation is made by Singh, in the context of an ever more 
refined division of labor and a more and more technicised social life, 
noting that “automation of computation immediately paved the way for 
automatizing industrial operations.”

The heightened tedium of computerized office work is today’s very 
visible manifestation of mathematized, mechanized labor, with its 
neo-Taylorist quantification via electronic display screens, announcing 
the “information explosion” or “information society.” Information work 
is now the chief economic activity and information the distinctive 
commodity, in large part echoing the main concept of Shannon’s 
information theory of the late 1940s, in which “the production and the 
transmission of information could be defined quantitatively.” (Feinstein 
1958)

 From knowledge, to information, to data, the mathematizing trajectory 
moves away from meaning—paralleled exactly in the realm of “ideas” 
(those bereft of goals or content, that is) by the ascendancy of 
structuralism. The “global communications revolution” is another telling 
phenomenon, by which a meaningless “input” is to be instantly available 
everywhere among people who live, as never before, in isolation.

Into this spiritual vacuum the computer boldly steps. In 1950 Turing 
said, in answer to the question ‘can machines think?’, “I believe that 
at the end of the century the use of words and general educated opinion 
will have altered so much that one will be able to speak of machines 
thinking without expecting to be contradicted.” Note that his reply had 
nothing to do with the state of machines but wholly that of humans. As 
pressures build for life to become more quantified and machine-like, so 
does the drive to make machines more life-like.

By the mid-’60s, in fact, a few prominent voices already announced that 
the distinction between human and machine was about to be superseded—and 
saw this as positive. Mazlish provided an especially unequivocal 
commentary: “Man is on the threshold of breaking past the discontinuity 
between himself and machines...We cannot think any longer of man without 
a machine...Moreover, this change...is essential to our harmonious 
acceptance of an industrialized world.”

By the late 1980s thinking sufficiently impersonates the machine that 
Artificial Intelligence experts, like Minsky, can matter-of-factly speak 
of the symbol-manipulating brain as a “computer made of meat.” Cognitive 
psychology, echoing Hobbes, has become almost based on the computational 
model of thought in the decades since Turing’s 1950 prediction.

Heidegger felt that there is an inherent tendency for Western thinking 
to merge into the mathematical sciences, and saw science as “incapable 
of awakening, and in fact emasculating, the spirit of genuine inquiry.” 
We find ourselves, in an age when the fruits of science threaten to end 
human life altogether, when a dying capitalism seems capable of taking 
everything with it, more apt to want to discover the ultimate origins of 
the nightmare.

When the world and its thought (Levi-Strauss and Chomsky come 
immediately to mind) reach a condition that is increasingly mathematized 
and empty (where computers are widely touted as capable of feelings and 
even of life itself), the beginnings of this bleak journey, including 
the origins of the number concept, demand comprehension. It may be that 
this inquiry is essential to save us and our humanness.