CONTENTS - ouroboros ponderosa

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ushered in an attendant mechanical wlu'ld-vicw that was (,uin(idl' nlal wilh
a tcnd ney to:vard central government controls and concentratioll or
power In the form of the modern nation-state. "The rationalization of
admlnlstralion and of the natural order was occurring simultaneously "
In the words of Merchant." The total order of math and its mechaic1
phIlosophy of reahty proved irresistible; by the time of Descartes' death
In 1650 It had become virtually the official framework of thought
throughout Europe.
Lcibniz, a near-contemporary, refined and extended the work of
Descartes; the "pre-established harmony" he saw in existence is like
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.
wise
f agorcan to Illcage. This mathematical harmony, which Leibniz
illustrated by reference to two independent clocks recalls h's d' t
ere IS nothmg that evades number."" Responsible also for the
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"Th .
.
we II -k nown p h rasc "T'
,
cartes, was decply mterestcd in the design of clocks.
I Ie urn,
more
lmc IS money,"" Leibniz, like Galileo and Des-
In the binary arithmetic he devised, an image of crcation was evoked;
he lmagmed 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 calculs, a project which he too sanguinely
expected would bc completed In bve years. This undcrtaking was to
provide all the answcrs, mcludmg 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 univcrsal symbolic languagc'
he was certaInly the "first great modern thinker to have a clear insigh;
mto the true character of mathematical symbolism.""
Furthenng the quantitative model of reality was the English ro alist
Hobbes, who rcduced the human soul, will, brain, and appetites to :atter
' mechalllcal motton, thus contributing directly to thc current concep­
hon of thmkmg as the "output" of the brain as computer.
The complete objectification of time, so much with us today, was
achlevcd by Isaac Newton, who mapped the workings of the Galilean­
Cartesian clockwork universc. Product of the severely repressed Puritan
outlook, which focused on sublimating sexual energy into brutalizing
labor, Newton spoke of absolute rime, "flowing equably without regard
to anythmg external."" Born in 1642, the year of Galileo's dearh Newton
capped the Sc:entific Revolution of the seventeenth century by
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develop­
mg a complete mathematIcal formulatlOn of nature as a perfect machine
a pcrfect clock.
Whitehead judged that "thc history of seventeenth-century science
reads as though It were some vivid dream of Plato or Pythagoras,""
notmg the astolllshmgly rcfmcd mode of its quantitative thought. Again
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Ihr ftllTCSpOlltkun° wil\1 a jump ill divisi01l or lahor is w()rtlt Jllliting
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1 1 \11: as Ilil! lkscl'ihlo.d rlIidscvcntL:enth ct.:ntury England " : o .slgl11hca ,
" I HTiali/aliol1 "c:gal1 to sct in. The last polyo:aths were dymg OUL . .
nit" songs alld dances of the pcasants slowly dlcd, and to a rather Itteral
Illathcmatization, the common lands were enclosed 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 thc centrality of quantitication to the entire rangc of human
sensibilities, thereby aiding the eighteenth-century consolidation of the
breakthroughs of the preceding era. And whereas Descartcs had asserted
that animals could not feel pain because they arc soulless, and that man
is not exactly a machine bccausc he has a soul, LeMettrie, in 1777, went
the whole way and made man completely mechameal ll1 hiS L Homme
Machine.
Bach's immense accomplishments in the first half of thc eightccth
century also throw light on thc spirit of math unlcashed a century earher
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."" 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 ocal
polyphony to that of instrumental harmony, based always upon a smgle,
autonomous tone fixed by instruments, instead of somewhat vanable With
human voiccsoR9
Later in the century Kant stated that in any particular theory there is
only as much real science as there is mathematics, and d voted a
considerable part of his Critique of Pure Reason to an analYSIS 01 the
ultimate principlcs of geometry and arithmetic. 1
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Descartes and Lcibniz 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 numerical symbols, that
could contain the whole of philosophy. The eighteenth-century Enltghten­
ment thinkers actually worked at realizing this latter project. Condillae,
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, mathematlzcd sy bohc
\evel madc thcm incapable of seeing that the origin of all symboltzmg IS
alienation.