i'm on a hunger strike

i'm not eating until someone can explain this and make it so clear that you granny could explain it to her grandkids. leave a comment if you can do that!

6. Space/Time

Key Concepts:

Modernist: three-dimensional space; integral; homogeneous; striated space;
Newtonian mechanics; Euclidean geometry; Cartesian coordinates;
quantitative; differential equations and continuities; reversibility of
time.

Postmodernist: multidimensional; smooth; fractal; imaginary; quantum
mechanics/relativity; implicate (enfolded) order; non-Euclidean geometry;
holographic; topology theory; qualitative; twister space (imaginary);
cyberspace; nonlinear; nonreversible time.

Commentary:

a. Modernist Thought. Modernist thought rests on Newtonian mechanics. This
classical view in physics rests on notions of absolute space and time. This
in turn is connected with the existence of determinism within systems: if we
know the positions, masses, and velocities of a particle at one time we can
accurately determine their positions and velocities at all later times
(Bohm, 1980: 121).

Newtonian physics and Euclidean geometry, with its use of Cartesian
coordinates, is the map or blueprint of space on which modernists construct
the social world. It is what Deleuze and Guattari refer to as striated space
(1987: 488): it consists of space with whole-number dimensions where
constant direction can be describable and end-states predictable. Drawing
from Descartes' coordinate grid of an x-axis perpendicularly intersecting
with a y-axis, a point could be located anywhere in two-dimensional space
(similarly with 3-D space, with an added z-axis). Thus the equation, y = 3x,
can be identified on this graph. At one stroke geometry and algebra are
linked. And Newton refined this further with his calculus with its
differential equations. Now a continuous change in one variable can be shown
to produce a calculable change in the other. And just as time flows forward,
it can flow backward in a predictable way: the romantic past, the "good old
days," can be re-created.

This model has been incorporated in the social sciences. A person's life
course, for example, could be plotted with precision if we could discover
appropriate determinants. This is the basis of positivism. It is by a
striated space (Deleuze and Guattari, 1987) that science progresses and by
which desire can be territorialized on the body (1986) by a political
economy. But striated space needs its discrete variables with whole-number
dimensions.

b. Postmodernist Thought. Postmodernists see things differently. Quantum
mechanics, non-Euclidean geometry, string theory, twister space, topology
theory, and chaos theory, to name a few of the most prominent approaches,
have offered alternative conceptions. The question of a dimension and
prediction becomes problematic.

Nuclear physicists, for example, faced with trying to reconcile general
relativity theory with quantum mechanics, have come up with infinities. By
adding space dimensions to their equations, these begin to drop out of the
equation. At 10-D in one model and 26-D in another, they disappear (Peat,
1988; Kaku, 1994). The 3-D model we see is perhaps just an explicate order
with the rest of the dimensions rolled up tightly (compactified). This
compactified order is the enfolded or implicate order (Bohm, 1980), said to
have its origins moments after the Big Bang.

Chaos theory has developed the idea of fractal dimensions. Rather than
having whole dimensions we can refer to a space with 1½ dimensions, 1¾, etc.
(A point has a dimension of zero, a line a dimension of one; a plane, two; a
volume, three.) A coastline, for example, can have a fractal dimension
between one and two. So, for example, contrary to the Boolean logic of
doctrinal legal analysis, truths are always fractal in form. Deleuze and
Guattari have developed the idea of a smooth space, which is continuous, not
discrete. The notion of fractals is in accord with smooth space (1987), and,
as we shall show below, fields. It is within smooth space that becoming
occurs; but progress and conventional science is done in striated space (p.
486; see also Bergson, 1958; Serres, 1982a, 1982b).

Yet others, such as the noted mathematician Penrose, have constructed a view
of space in terms of imaginary numbers, a twister space (Peat, 1988: Chapter
8; Penrose, 1989: 87-98). Chaos theorists, such as Mandelbrot, made use of
complex numbers in the form of z = x + iy, where i is an imaginary number
(the square root of -1). By further plotting z = z 2 + c and by taking the
result and reiterating by the use of the same formula, they were to find
enormously complex and esthetically appealing figures (see Penrose, 1989:
92-4). Yet others have relied on the hologram to indicate how inscriptions
of phenomena are encoded and how they can be revealed with their
multidimensional splendor (Bohm, 1980: 150; Pribram, 1977). Finally, we note
the field of topology, the qualitative math which offers alternative ways of
conceptualizing phenomena without the use of math. Here, in what is often
called the "rubber math," figures are twisted, pulled, and reshaped in
various ways. Breaking and gluing are not legitimate operations. Breaking
produces entirely new forms. Much current thinking in nuclear- and
astrophysics relies on topology theory (Peat, 1988; Kaku, 1994).

Lacan has made use of topology to explain such things as the structure of
the psychic apparatus by using borromean knots, Mobius bands, the torus, and
projective geometry (the cross-cap) (see also Milovanovic, 1993b, 1994c;
Granon-Lafont, 1985, 1990; Vappereau, 1988; for an introduction to topology
theory, see Hilbert and Cohn-Vossen, 1952; Weeks, 1985; for non-Euclidean
geometry, see Russell, 1956). In fact, in 4-D space the borromean knot of
Lacan is no longer knotted. The cross-cap, which topologically portrays the
working of schema R and how desire is embodied as a result of the effects of
the Symbolic, Imaginary, and Real Orders, can also be presented in 3-D or
4-D space (Milovanovic, 1994c; Hilbert and Cohn-Vossen, 1952). It is not
without effect when we move from 3-D to 4-D space (Rucker, 1984; Banchoff,
1990; for the contributions of non-Euclidean geometry and 4-D space on
cubism in art, see Henderson, 1983). Much needs to be done in the analysis
of the effects of these novel conceptions.

Thus, for the postmodernists, several notions of space are currently being
explored and incorporated in their analysis of the subject, discourse,
causality, and society: multiple dimensional (Peat, 1988), fractal
(Mandelbrot, 1983), holographic (Talbot, 1991; Bohm, 1980: Pribram, 1977),
enfolded/implicate order (Bohm, 1980; Bohm and Peat, 1987), cyberspace
(Gibson, 1984), hyperreal (Baudrillard, 1981), smooth space (Deleuze and
Guattari, 1987), twister space (Penrose, 1989; see also Peat, 1988), and
topological (Lacan, 1976, 1987a; Peat, 1988; Granon-Lafont, 1985, 1990;
Vappereau, 1988; Milovanovic, 1993b, 1994c; Lem, 1984). T.R. Young has been
succinct in indicating the relevance of these notions in that an alternative
space is open for the development of conceptions of "human agency in ways
not possible in those dynamics privileged by Newtonian physics, Aristotelian
logic, Euclidean geometry and the linear causality they presume" (1992:
447). And there can be no return to the nostalgic "good old days": time is
irreversible; since initial conditions are undecidable, then, with the
passage of time and iteration, there can be no return to some decidable
state.

7. Causality

Key Concepts:

Modernist: linear; proportional effects; positivism; determinism; classical
physics; I. Newton; "God does not play dice"; certainty; grand theorizing;
predictability; future fixed by past; particle effects.

Postmodernist: nonlinear; disproportional effects; genealogy; rhizome;
chance; contingency; quantum mechanics; uncertainty; iteration; catastrophe
theory; paradoxical; discontinuities; singularities; field effects.

Commentary:

a. Modernist Thought. Modernist thought rests on the determinism of
Newtonian physics. It appears most often in the form of positivism.
Modernist thought would assume that given some incremental increase in some
identified cause or determinant, a proportional and linear increase in the
effect will result. The basic unit of analysis is particles (i.e., assumed
autonomous individuals, social "elements," and discrete categories) and
their contributory effects. The use of cartesian coordinates, whole-number
dimensions, calculus, etc., in a few words, striated space, is what makes
possible a highly predictive mathematics. Even Einstein refused to accept
much of quantum mechanics that came after him, particularly the notion that
God plays dice.

b. Postmodernist Thought. Postmodernists see things differently. Chaos
theory, Godel's theorem, and quantum mechanics stipulate that proportional
effects do not necessarily follow some incremental increase of an input
variable. Uncertainty, indeterminacy, and disproportional (nonlinear)
effects are all underlying assumptions and worthy of inquiry in explaining
an event (genealogy). In the extreme, a butterfly flapping its wings in East
Asia produces a hurricane in Warren, Ohio. Key thinkers here are Edward
Lorenz, Benoit Mandelbrot, and Stephen Smale (see the excellent overview by
Gleick, 1987; Briggs and Peat, 1989). In fact, in the extreme, something can
emerge out of nothing at points identified as singularities; this is the
sphere of order arising out of disorder.

Two current approaches within chaos theory are making their impact: one,
focused more on order that exists in an otherwise apparently disorderly
state of affairs (Hayles, 1991: 12; see Feigenbaum, 1980; Shaw, 1981); the
second, focused more on how, in fact, order arises out of chaotic systems—
order out of disorder or self-organization (Hayles, 1991: 12; 1990: 1-28;
see also Prigogine and Stengers, 1984; Thom, 1975). A growing number of
applications is taking place. See particularly Unger's application in his
prescription for an empowered democracy (1987).

The notion of iteration is a central concept of postmodernism. Simply, it
means recomputing with answers obtained from some formula. Continuous
feedback and iteration produces disproportional (not linear) effects.
Derrida has applied it to how words obtain new meaning in new contexts
(1976; see also Balkan, 1987); in law, for example, the "original intent" of
the "founding fathers" undergoes modification over time and can not be
reconstructed. The point being made is that because of minute initial
uncertainties—however small, consider Godel's theorem—, when iteration
proceeds these are amplified, producing indeterminacies (Hayles, 1990: 183;
Lyotard, 1984: 55). Thus, rather than celebrating global theory, chaos
theorists and postmodernists look to local knowledges, where small changes
can produce large effects (Hayles, 1990: 211). In other words,
postmodernists see otherwise small contributions as having profound
possibilities. Yes, one "small" person's actions can make a difference! One
person's involvement in a demonstration, petition signature, act of civil
disobedience, or "speaking up," can, in the long run, have greater effects
than anticipated.

Causation can be attributed to field rather than particle effects (Bohm,
1980; Bohm and Peat, 1987). Borrowing from Bohm's insights concerning the
quantum potential and the enfolded order where all is interconnected, rather
than focusing, as the modernists do, on particles, points and point events,
all of which are narrowly spatiotemporally defined (analogously, consider
the subject in traditional positivistic sciences: an object, located
socioeconomically, who has engaged in some act at a particular time and
place), the unit of analysis, for postmodernists, should be a field with its
moments, duration, intensities, flows, displacements of libidinal energy.
Moments, unlike point events, have fluctuating time-space coordinates that
defy precise measurement (Bohm, 1980: 207). Within this field, heterogeneous
intensities can affect movement, even if they are not immediately
discernible or linear and/or local. Nonlinear and nonlocal factors,
therefore, even at a distance, can have a noticeable effect (Bohm and Peat,
1987: 88-93, 182-3). Research awaits in drawing out the implications of
moving from 3-D to 4-D space, i.e., what is knotted in the former becomes
unknotted in the latter (Rucker, 1984; Kaku, 1994; consider Lacan's
borromean knot in 4-D space, as discussed in Milovanovic, 1993b).

In the postmodern view, certainties that do appear are often the creation of
subjects: Nietzsche has shown, for example, how a subject in need of
"horizons" finds semiotic fictions that produce the appearance of a centered
subject; Peirce, anticipating chaos, has shown how free will is often
created after the event as the "facts" are rearranged to fit a deterministic
model and individual authorship (1923: 47); legal realists, in the early
part of this century, have shown that what creates order in legal
decision-making is not syllogistic reasoning and a formally rational legal
systems, but ex post facto constructions; and so forth. For postmodernists,
especially Nietzsche and Foucault, it is the "fear of the chaotic and the
unclassifiable" (Dews, 1987: 186) that accounts for the order we attribute
to nature.