Arkady Plotnitsky, author of the
The Knowable and the Unknowable and many preceding books, recognizes that the issue is not simply the 'naturalizing of phenomenology' but more fundamentally the phenomenalizing of our understanding of nature. Here is an extract from a review of
The Knowable and the Unknowable and a link to the whole review following the extract.
Extracted from
Gullivers, Lilliputians, and the Root of Two Cultures
Claudia Brodsky Lacour
(c) 2003
PMC 14.1
Review of:
Arkady Plotnitsky, The Knowable and the Unknowable: Modern Science,
Nonclassical Thought, and the "Two Cultures." Ann Arbor: U of Michigan
P, 2002.
"8. The interpretive antagonisms and contradictions composing the progress of
science were taken to another power--squared, or contradicted as contradictions
themselves--when 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: Anti-Epistemology
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 "double-slit
experiment"--by which particles such as electrons or photons passing through
screens with slits in them produce or do not produce a wave-like pattern depending
on whether a detector of their movements, external to the movements themselves, is
used in the experiment (61-66)--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)'
9. 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 object--as a thing with certain attributes in itself or a "whole"
constituted of experimentally conditioned, individual, phenomenal "effects"--that
Bohr's view changes. Quantum mechanics--on Bohr's "interpretation"
(68-69)--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)'
10. 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
quantum-physical dis continuity 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. (70-71)'
11. 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, puzzle-like, 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 sense--but 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 Saussure--surely, the Bohr of language study--signifier). 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
mold--the 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
patterns--any 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 self-consciously
rhetorical, or "novel," formulation of complementarity instead spells out a
thoroughly anti-representational 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)
12. Like a war which is not one, in that, one-sided, 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.
13. 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 line--the
diagonal--delimited by a regular geometric figure. An extension defined by other
extensions that together describe a self-containing figure is an entity
independent of traditionally symbolic, let alone "novel" complementary relations.
Its reality is self-evident, 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
say--nobody would--what 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 fraction--by 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 numbers--or (they would not see it as a number) mathematical
objects--discovered 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
discovery--both 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
used--was at the time of its discovery also used in its direct sense. (117-18)' . . . . .
http://pmc.iath.virginia.edu/text-only/issue.903/14.1lacour.txt
See also:
https://www.press.umich.edu/pdf/0472097970-fm.pdf
