Review of: Arkady Plotnitsky, The Knowable and the Unknowable:
Modern Science, Nonclassical Thought, and the "Two Cultures." Ann
Arbor: U of Michigan P, 2002.
 In The Knowable and the Unknowable, Arkady Plotnitsky
takes on (at least) two unenviable double tasks. He endeavors to explain
to nonexperts the rationally necessitated departure from traditional
visual representation that, in part, characterizes "modern" or
"nonclassical" physics and mathematics whileequally if not more arduous
to achievedistinguishing and defending groundbreaking philosophical
reflection from the scattershot of slighter minds. In addition, rather
than succumb to the ready pleasures of polemic in carrying out these
aims, he carefully provides, in his own writing, an example of
intellectual scrupulousness so striking as to inspire the improbable hope
that The Knowable and the Unknowable might set a discursive
benchmark to which less circumspect commentators may one day rise.
Finally, Plotnitsky does all this while managing to avoid the fate to
which his theoretical expertise and abilities could easily condemn him,
that of being hamstrung by his own level of understanding, tied down, or
compelled to talk down, like a Gulliver captive among the
uncomprehending.

Such discrepancy of stature is both the inspiration for
and subject
matter of
Plotnitsky's project. While describing and addressing cognitive issues
of historic and (literally) immeasurable scope, The Knowable and
the Unknowable also represents and responds to a tempest in a
teapot, a battle in print of truly Swiftian disproportion: the recent
controversy regarding the supposed use and abuse of science by
contemporary theorists and philosophers. The socalled "Science Wars" in
which Plotnitsky intervenes were inaugurated by Paul R. Gross and Norman
Levitt's Higher Superstition: The Academic Left and Its Quarrels
with Science, but were brought to popular attention under the
spotlight of scandal with the publication of Alan Sokal's "Transgressing
the BoundariesTowards a Transformative Hermeneutics of Quantum Gravity"
in Social Text. The uproar it caused stemmed not from the
content of the "transgression" that Sokal's article nominally proposed
but from the fact that its proposal for publication received approbation
at all. Following squarely in the tradition of discursive interaction
that J. L. Austin named "speech acts," whose uncircumscribable, working
principle the author of the action entitled "Transgressing the
Boundaries..." would perforce disavow, Sokal's article was less about
what it said than what it did. And what it did was speak double talk to
great effect, perpetrating a hoax which the editors of Social
Text "failed" to recognize as such (the general failure of
quiddity in the face of effectivity, or at least their nonidentity, being
what speechact theory is all about). Sokal "successfully" presented
what, in his view, would constitute a poststructuralist view of quantum
physics, travestying both contemporary theory and quantum physics to
achieve that pragmatic end. One year later, buoyed by his imposture, he
joined forces with Jean Bricmont to publish Impostures
intellectuelles, subsequently translated into English as
Fashionable Nonsense: Postmodern Intellectuals' Abuse of
Science. In the interim, Nobelprizewinning physicist Steven
Weinberg reflected on "Sokal's Hoax" in The New York Review of
Books, followed by "Steven Weinberg Replies" and "Sokal's Hoax: An
Exchange," and Plotnitsky and Richard Crew engaged in their own
"exchange" on the "Wars" in the pages of this journal.

For the active wagers of the "Science Wars," however, the de
facto inauguration of hostilities took place long before their own
maneuvers, with a tentative answer by Jacques Derrida to a question posed
to him at a conference at Johns Hopkins University in 1969. The
proceedings of
that watershed event, compiled into the nowclassic volume The
Structuralist Controversy by editors Richard Macksey and Eugenio
Donato, include contributions from and exchanges among many of the
leading theorists of two generations working in Europe and America (then
and now). As the title of the volume indicates, these historic
discussions occurred previous to the coining of the catchall
chronological denomination "poststructuralism." Heterogeneous, neither
"structuralist" nor identifiably anything else, they in large part
exposed for the first time, at least in the U.S., the prospect of modes
of thinking as yet undesignated and unknown, work so different as to
correspond to no available proper designation.

Theoretical work that deliberately detaches itself from any governing
concept may, by force of its own unsubordinated status, occasion its
comparison with other concepts and conceptual work. In focusing on the
uncertain epistemological status of discourse committed to pursuing
adequate representations of truth without proffering new abstractions or
representations of truth in their place, such theoretical writing seems
both to pose and to beg the question of its own internal understanding.
Like the cognitive problems and impasses in the writing it analyzes,
theoretical discursive analyses may have the effect of suggesting that, by
other means, their purposeful conceptual lacunae may be filled, that the
persistent variable, or unknown, they indicate, may be defined by way of
analogy
or equation. Such suggestibility, if encountered in good faith, leads to
questions of the most basic and probing nature: if one cannot name or say
what x is, say, that x equals y, then can one
say, at least for the time being, that x is something like
y?

Such a searching question was improvised at the Johns Hopkins University Conference by an important interpreter of Hegel, the
late Jean Hyppolite, in response to the paper "Structure, Sign, and Play," presented by Derrida. Hyppolite briefly asked
that Derrida consider any similarities between his own destructuring work in the domain of philosophical systems and concepts
and Einstein's theory of relativity. Derrida's equally brief response suggests that a similarity between the two indeed
exists. Now, in the fivedecade history of Derrida's discursive workexacting, often transformative excurses on
philosophical and literary writings revealing both the indissoluble relationship of the stated and implicit purposes and
problems of these writings to "writing" as such (that is, as
nonconceptual, iterable, and recognizable material form) and the
systematic vocabularies, figures, and conceptual frameworks or limits in which these problems and purposes are posedthis
tentative answer to Hippolyte stands alone. Derrida has made no more extensive comparison between his own analyses of the
cognitive and representational difficulties posed in and by writing
aiming at knowledge (whether of the abstract, conceptual,
or philosophical, or of the "real," concrete, or referential kind), and the radical transformation by modern science and
postEuclidian mathematics of how we know and thereby what we know of the physical "world." The lone existence, in an
extraordinarily prolific career, of a single, halting statement of fewer than sixty words produced spontaneously in answer to
the suggestion of another only underscores the obvious about the adversarial posture into whose aegis it has been inverted:
that the "Science Wars," whatever that appellation means and whatever is meant to be won by them, have not exactly been joined
with any appreciable degree of reciprocity; in short, that these are "wars" waged by one side alone.

A "war" waged by one side, one may argue, is an attackin this instance
an attack that, lacking even a substantive pretext, fabricates its own
dummy text, a hoaxand Plotnitsky is unusually capable of defending
those individual developments in philosophy, now dubbed
"poststructuralist" by default, which are less antagonistic to than
allied with those developments in physics and mathematics he helpfully
calls "nonclassical" (xiii et passim). Trained as a
mathematician first and a literary theorist second, Plotnitsky's
perceptions and intellectual development reverse the direction of
untoward, misleading appropriation ascribed to discursive theorists by
the wagers of the "Science Wars"most prominently, to Derrida and Lacan,
and synecdochically, or, perhaps, simply cynically, to all contemporary
theoretical work. While scientistwarriors may view nontraditional
philosophers and theorists as poachers upon the "hard" disciplines
seeking to inflate and buttress their own insubstantial prestige,
Plotnitsky instead finds in nontraditional philosophy a wrestling, from
within the bounds of discourse, with the formal and empirical boundaries
that gave rise to nonEuclidian mathematical theory and quantum
mechanics. For Plotnitsky, the problems of the limits of cognition,
whether discursively or mathematically conceived, are problems of
rational or commensurate representation any and all disciplines
fundamentally interested in the bases and emergence of knowledge must
share.

The overlap between empirical and theoretical knowledge is rarely, if
ever, complete, and mathematical inquiry, since the invention of
geometry, has often served as a selfsustaining bridge between them.
The symbolic language of mathematics is a language of selfevidence,
which is to say, a language unlike language, and its adoption in the
study of physical data and relations frees science of some of the limits
and errors that accompany experiment and perception. Still, scientists
in even the most mathematically rich domains do engage in productive
discord among themselves; the names Einstein and Bohr stand for one such
signal development in twentiethcentury atomic physics, as do the
diverging yet, of course, interrelated paths taken by their early modern
counterparts, Descartes and Leibniz. Indeed, if one wanted to locate a
real passing referent for the unfortunate denomination "Science Wars,"
perhaps one would do well to look first to its prima facie
significance, the disputes within science itself. For what we understand
and designate as "science" at any one time is the product of an ongoing
history of differing interpretations, intellectual orientations, and
directions, the often mutually contradictory or only partly shared views
of physical reality whose full or partial, independent or contingent
approbation may be immediate or delayed, refuted or maintained.

The interpretive antagonisms and contradictions composing the progress of
science were taken to another powersquared, or contradicted as
contradictions themselveswhen Bohr proposed that, at the atomic level,
experimental results that appeared mutually exclusive should be
considered "complementary." In The Knowable and the
Unknowable, as in his earlier Complementarity:
AntiEpistemology after Bohr and Derrida, Plotnitsky follows Bohr
to the heart of the "logical contradiction" (66) that is the consequence
and insight of quantum physics, namely, that our only empirical means for
knowing "quantum objects" (67) destructure that knowledge even as they
structure it, linking the known (for example, the "particle" or "wave"
appearances of light) directly to the unknowable (how and why such dual
appearances indeed take place and pertain to a single
phenomenon). The conjunction of quantum objects and their science yields a
kind of knowledge that is neither the antithesis of ignorance nor its
cancellation and replacement, but its necessary while never observably
continuous complement. Plotnitsky's elucidating summary and discussion
of the "doubleslit experiment"by which particles such as electrons or
photons passing through screens with slits in them produce or do not
produce a wavelike pattern depending on whether a detector of their
movements, external to the movements themselves, is used in the
experiment (6166)makes this paradox of empirical, experimental, or
contingently objective knowledge clear:
if [...] there are counters or other devices that would allow us to check through
which slit particles pass (indeed even merely setting up the apparatus in
a way that such a knowledge would in principle be possible would
suffice), the
interference pattern inevitably disappears. In other words, an appearance of
this pattern irreducibly entails the lack of knowledge as to through
which slit
particles pass. Thus, ironically (such ironies are characteristic of or even
define quantum mechanics), the irreducible lack of knowledge, the
impossibility
of knowing, is in fact associated with the appearance of a pattern and,
hence,
with a higher rather than a lower degree of order, as would be the case
in, say,
classical statistical physics. (64)
 Particles which seem to know more about our behavior (whether
we've set up a detector or not) than we do about theirs (how do they
"know that both slits are open, or conversely that counters are
installed, and modify their behavior accordingly?" [66]) present, at very
least, a "situation [...] equivalent to uncertainty relations" (64), if not a
necessary suspension of logical and causal assertions of any classical
kind. Yet Bohr's Copernican shift consisted in viewing differently not
the fact of these antagonistic results, but rather the way in
which we view their (mutually exclusive) factuality. It is not what
we see but how we think of what we are seeing, the way in which we define
and understand a quantum objectas a thing with certain attributes in
itself or a "whole" constituted of experimentally conditioned,
individual, phenomenal "effects"that Bohr's view changes. Quantum
mechanicson Bohr's "interpretation" (6869)requires, in the first
place, a different mode of interpretation, and Bohr's name for that
different view of what quantum evidence means is "complementary." As
Bohr describes it in the "Discussion with Einstein":
evidence obtained under different experimental conditions cannot be
comprehended within a single picture, but must be regarded as
complementary
in the sense that only the totality of the [observable]
phenomena [produces
the data that] exhausts the possible information about the
[quantum] objects
[themselves]. (70)
 While originating in a predicament produced by physical
experiments (set up as means of clarification), Bohr's loosening of the
logician's double bind is conceptual in kind. As Plotnitsky observes,
the introduction of the term "complementary" with regard to quantum
mechanics enacts an epistemological shift from "objectivity" to
"effectivity," based upon, rather than stymied by, mutually exclusive,
experimental results:
thus, on the one hand, quantum objects are (or, again, are idealized as)
irreducibly inaccessible to us, are beyond any reach
(including again
as objects); and in this sense there is irreducible rupture,
discontinuity,
arguably the only quantumphysical discontinuity in Bohr's
epistemology. On the other hand, they are irreducibly
indissociable,
inseparable, indivisible from their interaction with
measuring
instruments and the effects this interaction produces. This
situation
may seem in turn paradoxical. It is not, however, once one
accepts
Bohr's nonclassical epistemology, according to which the ultimate
nature of the efficacity of quantum effects, including their
"peculiar
individuality," is both reciprocal (that is, indissociable
from its effects)
and is outside any knowledge or conception, continuity and
discontinuity
among them [...] Thus Bohr's concept of the indivisibility or
(the term
is used interchangeably) the wholeness of phenomena allows him
both
to avoid the contradiction between indivisibility and
discontinuity
(along with other paradoxes of quantum physics) and to reestablish
atomicity at the level of phenomena. (7071)
Like discourse, one could say, the effectivity of atomic objects is
dependent but unlimited, contingent upon the interrelated experiments of
which it is a result rather than derivative of the object in itself.
Like rhetoric as such, rather than the specific rhetorical notion of the
symbol or symbolon, according to which image and idea match,
puzzlelike, to compose a single, concretely expressive meaning, Bohr's
interpretation and use of the term "complementary" do not signify an
integral meshing of categorically distinct entities. The "aspects" or
"characteristics" of atomic "phenomena" are what we "know"in Bohr's
nontraditional phenomenological sensebut those aspects are derivative
of the different experiments to and by which atomic objects are exposed
(in rhetorical terms, these would be the different formulations or
linguistic experiments that make evident different aspects of discourse,
such as figure, noun, sign, or, following Saussuresurely, the Bohr of
language studysignifier). A notion of the complementary that is not,
or is only temporarily, contingently, closed, is, Plotnitsky points out,
"peculiar" (74). Yet such peculiar language use may indeed be exactly
appropriate to Bohr's epistemology. For, like the nonsynthetic relations
it describes, the name of Bohr's interpretive breakthrough breaks the
moldthe mold of the commensurate and thus traditionally "complementary"
parts of a whole symbolized in rhetoric by the notion of the symbol, the
equation and union of two as one. Bohr's notion of "complementarity"
instead fractures a delimited object of investigation, normally
identified through a series of equations, into experimental "phenomena"
whose perceptibility consists in a series of differing effects.
Furthermore, this fracturing occurs without limits or deducible
patternsany pattern ceases in the presence of a "counter" designed to
discern its objectivity. Nor does Bohr's notion of complementarity
suggest a shift in objective representation from the organic or living
portrait, no part of which may be inconsequentially removed, to a more
schematic outline or constellation, whose absent parts or interstices can
be supplied by the mind. Bohr's selfconsciously rhetorical, or "novel,"
formulation of complementarity instead spells out a thoroughly
antirepresentational logic by which "different experimental
arrangements," rather than cohering in any visualizable manner, bring
about visibly mutually exclusive results:
within the scope of classical physics, all characteristic properties of a
given
object can in principle be ascertained by a single experimental arrangement,
although in practice various arrangements are often convenient
for the study
of different aspects of the phenomena. In fact, data
obtained in such a way
simply supplement each other and can be combined into a
consistent picture
of the behavior of the object under investigation. In quantum
physics, however,
evidence about atomic objects obtained by different experimental
arrangements
exhibits a novel kind of complementary relationship. Indeed, it
must be
recognized that such evidence, which appears contradictory when combination
into a single picture is attempted, exhausts all conceivable
knowledge about
the object. Far from restricting our efforts to put questions to
nature in the
form of experiments, the notion of complementarity
simply characterizes
the answers we can receive by such inquiry, whenever the interaction
between the measuring instruments and the objects forms an
integral part of
the phenomena. (qtd in Plotnitsky 74)
 Like a war which is not one, in that, onesided, it opposes
without measure, a "complementarity" which is not one, in that it
represents (or in Bohr's words, "characterizes") the unrepresentable,
that which cannot both be and be measured (or known) in "a
single picture," recalls, Plotnitsky argues, the irreducible
incommensurability that arose along with the first
mathematical means for knowing the world, geometry. Perhaps the
unilateral assault conducted in the "Science Wars" on a grossly
incommensurate object should simply be called, in squarely traditional
fashion, "irrational," the negative name given to the algebraic discovery
of the immeasurable in geometry. Contradicting contradiction, we may view
the true root of the evil signaled by a "war" waged against its own
fictional pretext not as the neat opposition of one against one but
rather as the original and unsettling complementary relationship that is
the base of one with or plus one, an essential and irreducibly intricate
twoness like that of mathematics itself under the aspects of algebra and
geometry.

For the irrational arose not in opposition to but from within the basic
framework of rationality. Exposed to a certain "experimental
arrangement," it was discovered, the simplest act of calculation results
in an imponderable relation. The most fundamental equation defining
physical reality (a_ + b_ = c_), when solved for its simplest values
(a=1, b=1) yields, as one of its characteristics, an immeasurable
quantity (c= 2). The root or base number of one
with or plus
one should represent, in a single picture, an indivisible unity of two.
Derivative of that unity as such, more fundamental than the external
operation of addition, the common root of two does indeed present "a
single picture:" a finite linethe diagonaldelimited by a regular
geometric figure. An extension defined by other extensions that together
describe a selfcontaining figure is an entity independent of
traditionally symbolic, let alone "novel" complementary relations. Its
reality is selfevident, but with an insurmountable hitch: the measure,
or mathematical identity, of that reality cannot be figured. Moreover,
the necessity of such unattainable knowledge is as pragmatic as it is
epistemological. Plotnitsky states its centrality plainly"one needs it
if one wants to know the length of the diagonal of a square"before
explaining how such a novel, or immeasurable, "mathematical object," the
irrational ratio, came about:
this is how the Greeks discovered it, or rather its geometrical equivalent.
If the length of the side is 1, the length of the diagonal is 2. I would not
be able to saynobody wouldwhat its exact numerical value is. It does
not have an exact numerical value in the way rational numbers
do: that is,
it cannot be exactly represented (only approximated) by a finite, or an
infinite periodical, decimal fraction and, accordingly, by a regular
fractionby
a ratio of two whole numbers. It is what is called an "irrational number,"
and it was the first, or one of the first, of such numbersor (they
would not
see it as a number) mathematical objectsdiscovered by the Greeks,
specifically by the Pythagoreans. The discovery is sometimes attributed
to
Plato's friend and pupil Theaetetus, although earlier figures are also
mentioned. It was an extraordinary and, at the time, shocking
discoveryboth a great glory and a great problem, almost a scandal, of
Greek mathematics.
The diagonal and the side of a square were mathematically proven
to be
mathematically incommensurable, their "ratio" irrational. The very term
"irrational"both alogon (outside logos) and arreton
(incomprehensible) were usedwas at the time of its discovery also used
in its direct sense. (11718)
 In a very real sense, independent of pretexts visited upon
Social Text, it is the "scandal" of the irrational,
mathematically and rationally derived, that the socalled Science Wars
rehearse, worry, and travesty. Unlike a hoaxbased polemic, mathematics
publishes and is host to its own "transgression," one "complementary"
aspect of its operation excluding another. The discovery that the
relationship between the diagonal and side of a square, while governed by
the basic Pythagorean theorem regarding the magnitudes of lines composing
a triangle, was not translatable into rational mathematical
symbols, could not be represented as a ratio of whole numbers, and thus
as a rational relationship or (rational) number tout court, was
succeeded by the tale of the illustrative death of its progenitor.
Legend has it that a storm and resulting shipwreck buried that
revolutionary Pythagorean at sea (11819). Truth may have it that the
sound and fury of the "Science Wars," to which The Knowable and the
Unknowable tactfully, constructively responds, are an attempt to
drown this illustrative figure once more. The storm in which the mythic
discoverer of the irrational purportedly met his end may be what this
recent tempest in a teapot is attempting, more or less unwittingly, to
bring to life again.

Yet, as Plotnitsky makes clear, since the link between the irrational and
the rational, the core focus of his book, is borne out specifically by
rational processes themselves, the desire to hurl overboard those who
articulate the problem of the irrational is tantamount to curtailing
rational inquiry itself. In a chapter treating Lacan's "analogous,
but not identical" (147) references to the rationally derived
imaginary number, the square root of 1, to describe the "irreducibly
nonvisualizable" "symbolic object" of his psychoanalytic
epistemology"the 'erectile organ'" or symbolic phallus already
operating, according to Lacan, as image or "signifier" in the
psyche (141) (Plotnitsky helpfully calls this psychic object "the image
of the image of the penis" [110])Plotnitsky describes how the
nonidentities of conceptual analogies function within an epistemological
"system":
the erectile organ, or, again, a certain formalization of it, must be
seen as [...] 'the square root of 1,' (L)1
of the Lacanian system itself. It is an analogon of the
mathematical concept of the mathematical 1 within
this system, rather than anything identical, directly linked, or even
metaphorized via the mathematical square root of 1. In a word, the
erectile organ is the square root of 1, which I here designate as the
(L)1, of Lacan's system; the mathematical 1 is not the erectile organ. (147)
(Plotnitsky explicitly uses the symbol for the mathematical
concept 1, and the words "the square root of 1" or the amended
"(L)1" to designate the analogous use of that mathematical
concept
within Lacan's system [113]). In other words, just as 1 is the
"simplest complex number," which, "formally adjoined to the old domain of
real numbers, enables one to introduce the new domain of complex numbers"
(the field of numbers of which real and imaginary numbers are both
factors), so the "erectile organ" is the simplest complex concept
enabling a new domain or field of psychoanalysis, one in which real and
imaginary objects are both irreducible factors (122). Whether or not one
views this domain as thoroughly "novel" or as already latent in Freud's
epistemology, Lacan's exposition of the complex notion of the phallus (as
both imaginary and real) does indeed signal a redefinition of the
operative field of psychoanalysis. In addition, Plotnitsky emphasizes,
"analogous" means just that: "'the square root of 1' of Lacan's
statement is, I shall argue here, in fact not the mathematical
1 [...]. There is no mathematics in the disciplinary
sense in Lacan's analysis" (147). 
It is in this context of restating the fundamental rational
concept and operation of analogy itself, the proverbial wheel of reason
here not reinvented but patiently redescribed, that Plotnitsky makes the
central observation of his book, speaking not only to the inevitable
recourse made to analogy in the course of analyzing essentially
nonobjective, psychic phenomena, but to the necessary processes of
symbolization and analogy involved in every new discovery of the
irrational. Just as "the nonclassical epistemological component may be
irreducible in all mathematics" (130), so
irrationalitythe inaccessibility to rational representation (in
whatever sense)can itself be discovered rationally, for example and in
particular, by means of mathematical proof, a paradigmatic rational
argument. This emergence of the irrational (the inaccessible, the
unknowable, the unrepresentable, the incomprehensible, the inconceivable,
and so forth) at the limit of the rational
(the accessible, the knowable, the representable, the comprehensible, the
conceivable, and so forth), defines the project of philosophy throughout
its history, from Anaximander to Heidegger and beyond, or in mathematics
from
the Pythagoreans and the diagonal to Gödel and undecidability. In
the wake of Heidegger, or indeed Nietzsche, who understood this
epistemology more profoundly than anyone before him (and at least as
profoundly as anyone since him), the extraordinary critical potential of
this situation has been powerfully utilized by such nonclassical thinkers
as Bataille, Blanchot, Levinas, Lacan, Derrida, and de Man, or of course
Heisenberg and Bohr in the case of quantum
mechanics. Indeed, the nonclassical epistemology of quantum mechanics,
as considered here, gave especially remarkable shape to these relationships.
(11920)
 Plotnitsky's nonetoodelphic message is that the
irrational indicated by numerical and notational as well as discursive
epistemologies, by mathematicians and physicists as well as philosophers,
is not going to sink with any single messagebearer to the ocean floor.
And again, it is complex mathematics, rather than unilateral polemics,
which may best "illustrate" his point. As Bohr rewrites the traditional
notion of "complementarity" to indicate and encompass the notion of the
noncomplementary, the mutually exclusive realities of a single physical
phenomenon viewed under different aspects, so in mathematics the
extraordinary notion of complex numbers encompasses both real and
imaginary in a single mathematical "field." "Complex" here even appears
analogous to "complementary" when the problem of the visualization or
spatial representation of such numbers is posed. For, like the mutually
exclusive visual evidence provided by differing experimental setups in
quantum mechanics, the field of complex numbers in mathematics is
"symbolically" configurable on a twodimensional real plane, one of whose
axes, however, is being used to represent imaginary numbers. Yet this
"schematic illustration," "diagram," or "representation" (on a real plane
redefined as the Argand plane), even as it produces a kind of
visualization of its objects, and even though its relationship to the
field of alegebraic formulation is exhaustive, in no way corresponds to
the measurable lengths of real lines or vectors, or the rationally
derived points on a line, that real and rational numbers represent. The
gap between algebra and geometry, or notation and spatial representation,
is thus encompassed within the field of complex (real and imaginary)
numbers, but not bridged. The algebra involved must be plotted on two
visually analogous but mathematically different ("nonisomorphic")
structures: that of the "real plane" (or "vectorspace") and the strictly
speaking nonspatial "field of complex numbers, which would no longer
allow us to see [the real plane] [...] as a real plane" (12526).

Complex numbers thus produce a "field" irreducible to a "space." The
attempt to so reduce the field would result, one might say, in a hoax,
the representation of imaginary numbers as real. By analogy one may say
that if the real aim of the wagers of the "Science Wars" is to clear the
space of rational science of its false representation, that aim will
continue to prove itself, in the philosophical sense, "imaginary"first,
because it lacks a real object (let alone enemy), and, second, because in
the absence of such, it proves itself to belong foremost to the
complementary relations of discourse, that other field in whose
complex, nonvisualizable formulations the real and the imaginary, as in
mathematics, interact.

Riddled with their own characteristic patterns of misappropriation and
misstatement, imaginary acts of salvation may finally not be evidence of
ignorance, intellectual disingenuousness, or even analytic bad faith
(cf.16062 especially). The "failure" to "win" a war of one's own invention
may instead be analogous to the very force that war would mime: the
roiling sea in which (again, as discourse, or legend, would have it) the
rational voice of the irrational sinks. That is to say, the war waged
upon philosophy may be a certain view of science at war with another
view, a rejection of Bohr's conception of complementarity, or the
construction of the GaussArgand plane, or any articulation of
complexity in which one of many "different aspects" is not and cannot be
made present. For, in mathematics as in discourse, the irrational and
the imaginary are based in the rational and the real they negate. This real
scandal, recognized and interpreted in novel terms by traditionally
classical protomodernists (first among them Descartes) no less than
nonclassical "postmodernists," may necessarily attract discursive waves
of submergence, interpretive storms stirred upon an open sea. Its
details may be worth fighting over, but it itself is not open to debate.
And the drawing of a bull's eye on one contemporary French thinker or
another may be a greater extravagance than any that such contrived
aimtaking supposedly targets. Giving a face to the enemy is as old a
discursive procedure as the first history of (irrational) war, told with
unsparing rationality by Thucidydes. But the weight of tradition does
not make this rhetorical maneuver any more substantial, any less
imaginary, or, in its "defenses" of rationality, any less incommensurate
or irrational.

It is not that the target is moving and hard to hit; it is that it
is not what one represents it to be, that
objective absence being its very reason, its rationale, for being
thought. Such a surmise indeed "characterizes" much "nonclassical"
thinking, in which the failure of representation to meet its mark is
directly or indirectly addressed. But it is also the irreducible basis
for thinking proffered by the two central, significantly different
founders of modern classical philosophy, Descartes and Kant, whose
respective skeptical and critical limitations of rational cognition,
accompanied by a redefinition of the real status of geometry, negatively
reestablished the novel project and possibility of thought.

The irreducible evidence of the irrational, rationally recognized up
to a limit, unites modern mathematics, science, and philosophy into a
field whose different aspects may be analogous with complexity itself,
complexity which is real and rationally conceived precisely because its
elements and factors include the imaginary and the irrational. And it is
here, in its recognition of a shared complexity, that Plotnitsky's work
takes its most important turn. For, instead of "wars" waged by
ventriloquism, Plotnitsky suggests, a mutually reflexive acknowledgement
of cognitive limits, the very limits that compose complexity, can include
ethical action among its unknowable effects:
perhaps the ultimate ethics or (since the ultimate ethics may not
be possible, classically, in practice and, nonclassically, in principle)
at least a good ethics of intellectual inquiry, or of cultural
interaction,
is the following: being strangers ourselves, to offer other strangers,
strangers in our own or in other cultures, those ideas that bring our
own culturesay, science, on one side, and the humanities, on the
otherto the limits of both what is known and unknown, or
unknowable, to them. To have an expertise is to reach the limits
of
both what is knowable and what is unknowable in one's field; and
to be ethical in intellectual exchange is to offer others the
sense of
both of these limits, to tell the other culture or field both what we
know and what we do not know ourselves, and what is knowable
and what is unknowable, in our own field or culture. (240)
 Is this process of "exchange" of "expertise" more complex than
attacking an adversary of one's own devising? Doubtlessas the terms
themselves suggest, the rational analysis of the irrational cannot, by
definition, be unilateral; any such analysis must recognize both its own
limits and its relation to what it is not. Yet, as the appearance of
The Knowable and the Unknowable demonstrates, even the
(irrational) negation of exchange issues in its own negation, or
exchange. Thus it is, as Plotnitsky's double expertise confirms, that a
certain discrepancy of thinking remains, with the effect that, no more
than do Titans, do Lilliputians need fear their final overthrow.
Department of Comparative Literature
Princeton University
cblacour@princeton.edu
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