Dynamics and the Navigation
of Time and Space in Cognition and Social Change
[rough draft soliciting comments]
Dynamics (aka “dynamical systems
theory”, popularly but improperly “chaos theory”, and “nonlinear dynamics”) is
a mathematical discipline based on a vector calculus that describes the
behavior of a system of interdependent variables over time using usually
nonlinear differential equations. It was first applied to the momentum and
position of objects in the study of the motion on earth and in the heavens. It
has liberated all of science to deal with complex open systems (versus isolated
features as closed systems), along with the computers that help us represent
this behavior geometrically. It is one of a number of related approaches that
attempts to integrate holistic with analytic ontological views. It empowers an
interdisciplinary point of view and the interconnectedness of things.
Its most basic concepts are (1) the
dynamical system whose geometric representation is the portrait of temporal
trajectories into a view of the interaction of the variables in a state space
under the influence of a vectorfield which in turn is represented by
differential equations. The patterns displayed by the trajectories are called
attractors. The portrait also displays other features, such as basins,
separatrices, saddles and repellors. (2) The dynamical scheme, which are
changes in the patterns generated by the system as a function of parameters in
the equations; the geometric representation we call the response diagram. (3)
Bifurcations, which are major changes in the portrait when critical values of
control parameters are crossed. That is major changes rather than gradual ones.
(4) Self-organization, which is when the system itself changes those control
parameters and thus dramatically alters its own behavior.
We each have described these
features (Abraham, Abraham, & Shaw, 1990), and in abbreviated form
speculated about them in the analysis of time in cognition (fda) and history
(rha) in Macey, Encyclopedia of Time (1994). Here we attempt an update
of those views, emphasizing the difficulty of such modelling, and emphasizing
the role of the psychophysics of the metrics to allow an emphasis on vectors of
change in social systems. Briefly, we suggested a dual concept of time in
cognition, where the mind navigated more rapidly in the portrait, and more
slowly in decision-making in the parameter space (fda), and that theories of
histories could be found that had properties of (a) point, cyclic, or chaotic
attractors, (b) bifurcations, and (c) fractal properties—the replication of space-time
behavior over different scales of observation (rha).
The problem is obvious. How does a
mathematic that deals with continuous Cartesian variables and symmetrical
space-time representation deal with the world of nonmetric (or a different
metric, Stevens; Combs) and symmetry-breaking found in the more complex worlds
of the mind and cultural change? We do not answer this question, but it is our
concern. A recent debate on the metric of time is currently raging on CHAOPSYC,
the listserver of the Society for Chaos Theory in Psychology and the Life
Sciences. My friend, Gus Koehler offers one classification of time:
I think the parameter
space is more complex as is the state space. First, many time
theorists see at least five different levels of time, each having its
characteristic associated processes. For example, the time of particles
and fields, particularly in relativistic settings, is very different from
biological time from organism to organism (internal clocks, diffusion
processes, morphogenesis, etc.), is very different from phenomenological or
socially constructed time (variation from culture to culture). In my
opinion, organizational time--that is the construction of social institutions
and processes-is very dynamic and driven by at least three different temporal
states: agent (biological involving aging, the formation of the social body,
etc.), clock (mechanical), and nonotemporal time (or prositioning relative to
the past, present and future often a simultanity). Each has its own characteristic
control parameters, each its own state space. The interesting issue is
how these systems nest together in the process of organizational formation.
(Koehler, CHAOSPSYC communication on the “orderings” thread, 1/15/2002).
Another
friend, Jeff Pressing replies:
I don't really think that these different types
of time have a lot of theoretical foundation. One time is enough, as time
is an emergent property of events. Rather, model the events, in my view.
(Pressing, reply to Koehler on the CHAOPSYC “orderings” thread,
1/15/2002).
It may (or may not) be that the
various “levels of time” mentioned by Koehler could be given a functional
relationship to the “one time” of Pressing, e.g., by psychophysical
experiments. Both of their statements suggest the difficulty of establishing
those relationships, or of even establishing the one “emergent” time.
Our suggestion of a dual as well as
infinite cognitive temporal representations is also evident in the theoretical
approaches of Michon (1994), with his distinction of implicit (non
consciousness) and explicit (conscious) representations. Our navigation of
parameter space versus trajectories in the state space might map into this
distinction, but that could be an oversimplification. Michon states that the
implicit does not require “symbolic representation of the temporal parameters
of the situation. But formal representation would:
. . . the temporal structure
of the situation may be mapped onto or into formal representations, that is,
logical, numerical, or mathematical structures. In such cases we speak of
models, or even theories, of time: temporal logics and the motion equations of
Newtonian or relativistic mechanics are examples. J. T. Fraser’s hierarchy of
temporalities for instance, may mapped a series of psychophysical measurement
scales. J. I have shown that these scales can be applied to the world as seen
from several perspectives: atemporality, protemporality, ecotemporality,
biotemporality, and nootemporality do correspond to nominal, ordinal, interval,
ratio, and absolute measurement, respectively. (Michon, 1994, p. 512.)
As is now well known, the
development of relativity, quantum electrodynamics, and cognition has seen not
only a considerable interaction of these fields, but also the emergence of a new
ontology in which the dynamical interactions of variables at all levels and
places of observation in the universe have become better appreciated. A
complexity of mathematics is required to represent the dynamics of these
processes, most of which were beyond understanding via ordinary experience.
This ontology led to a view of infinite potentials, reduced to one in the
singularity of the present moment, which in turn becomes a set of infinite
potentials for the future. This ontology also led to the view in which the
fractal boundary of the observer/observed, objective/subjective practically
dissolves.
We might argue that the same might
be said for the implicit as well as the explicit, but the “models” also remain
implicit! Michon also reflects the infinite potential idea in a discussion that
also conveys our sense of cognitive navigation in nonlinear dynamical
representations of time:
Evidently, a keen sense of
time, that is, a detailed repertoire of representations of time, has survival
value. It allows its owner to review past experience and to anticipate future
events effectively and efficiently. It expands the temporal horizon of the
organism, allowing it to attune itself in intricate ways to the requirements of
its dynamic environment. Given this biological significance of representing
time, it is not surprising that humans possess a rich repertoire of temporal
representations. (ibid, p. 511).
Probably the most sophisticated
nonlinear mathematical modelling in psychophysics is that of Robert Gregson. He
also resolves the Koehler-Pressing distinction and well articulates the
hierarchical and network approaches to modelling:
The idea of time features in
experimental psychology in different senses, as a central variable in
processes, as merely a counter-variable for tracking processes, and as a
phenomenological experience which is the intended psychophysical focus of
experimental studies. . . (Gregson, 1995, p.73.)
One of the ideas to which theoreticians in
mathematical psychology come back again and again, in one form or another is
that of hierarchical dominance of subprocesses by a higher-level process. By
hierarchy is meant that there are at least two levels, one of elementary
processes and another which has its own dynamics and acts as a controller,
switching the elementary processes in and out and selecting between them. Such
selection can arise externally as a result of feedback from the consequences of
previous system outputs. Note that this is not the argument about the minimum
number of levels in a distributed network which are necessary and sufficient
for learning, but to something evden more abstract. (Ibid, p. 74.)
So we are left with the difficulties
of metrics for the dynamics of cultural bifurcations. We consider this could be
important if we are to understand how to help create conditions in society that
allow them to evolve new potentialities. There seem to be two varieties of
exploration, roughly equivalent to Michon’s implicit/explicit distinction. We
will briefly discuss two representatives, In the first, the emphasis involves
the role of time in psychodynamics leading to discontent in individuals that
lead them to transcend or struggle against the constraints society places on
them. The second emphasizes explicit concepts of time between subcultures come
into conflict.
Kristeva (1980) provides an example of the implicit
approach. Julia Kristeva has an approach to social theory that is her own
unique blend of linguistic and psychoanalytic theory. Her basic psychoanalytic
distinction between pre-Oedipal and Oedipal aspects of personality development
lies at the foundation of her theorizing. Narcissistic identification and
maternal dependency, anarchic component drives, polymorphic erotogenicism, and
primary processes characterize the pre-Oedipal. Paternal competition and
identification, specific drives, phallic erotogenicism, and secondary processes
characterize Oedipal functioning.
Kristeva also characterizes the pre-Oedipal feminine
phase by a type of space for which she borrows Plato's term, chora (Timeaus),
an enveloping, amorphous, nonmetric space that both nourishes and threatens. It
also defines and limits self-identity. She characterizes the Oedipal male phase
by a more metric space, for which one could correspondingly use Aristotle's
term, topos. The self and the self-to-space are more precise and well
defined in topos.
Kristeva attributes to each of these spaces, a
differing view of time. Pre-Oedipal time is a more phenomenological, subjective
time, which Kristeva calls 'monumental' time, and is somewhat akin to Gorgias's
Kairos, Bergson's durée, Loye's timeless and spatial times (Loye,
1984). Oedipal time, Kristeva's 'cursive' time, is a linear time akin to
Hesiod's Kronos, Bergson's chronological time, and Loye's serial time.
These are like our time for trajectory evolution in state space, and like our
parameter space, which can be metric but to which the application of the
psychological metrics discussed above would most apply.
Kristeva relates linguistics to these basic
distinctions. Semiotics is associated with the pre-Oedipal realm. The speaking
subject is divided, decentered, and process-oriented. Semiotic process is
rooted in feminine libidinal, pre-Oedipal energy which needs channeling for
social cohesion. Infantile drives are indeterminate and multifaceted. A
phallically perceived mother (male maternity fantasy) dominates a feminine
phase.
"If the semiotic is pre-Oedipal, based on
primary processes and is maternally oriented, by contrast the symbolic is an
Oedipalized system, regulated by the secondary processes and the Law of the
Father. The symbolic is the domain of positions and proposition. The symbolic
is an order superimposed on the semiotic. The symbolic control of the various
semiotic processes is, however, tenuous and libel to break down or lapse at
certain historically, linguistically and psychically significant moments. It
results in an upheaval in the norms of the smooth understandable text. The
semiotic overflows its boundaries in those privileged 'moments' Kristeva
specifies in her triad of subversive forces: madness, holiness and
poetry." (Surap, 1993.)
It would be interesting to try to
make her approach more detailed with the psychophysics of time and space, and
with the nonlinear modelling of dynamical systems theory. We just pose this
task, which is left for later development. Kristeva invoked the relevance of
Thom’s catastrophe theory, which is a species of bifurcation theory, and
largely responsible for the development of dynamical systems theory as a
superset of itself. With that challenge, we now turn attention to an example
where cultural concepts of time themselves came into conflict that led to
social change.
Atkins “explores changes in the
perception of time — the shift from peasant to industrial time — as they were
experienced by these northern Nguni speakers on coming into contact with a
society undergoing early stages of capitalist growth. . .” and how they
influenced “Black/white colonial labor relations.” (Atkins, 1994, pp. 122-3.
The Nguni tribes, Bantu speaking, principally Zulu, were mainly in Natal, now
within the northern province of KwaZulu of South Africa. Atkins is exploring 19th
century Natalan culture).
Time was at the nexus of the
“Kafir labor problem.” No sooner was a work agreement mde than confusion arose
from the disparate notions of the white employer and his African employee
regarding the computation of time. Otherwise said, the record of persistent desertions
from service was in many instances related to tehe fact that the terms of
master-servant contracts, which were based on Eurpean units of measure, did not
accord with the African mode of temporal reckoning. (Ibid, p. 123.)
The Zulu used the moon and stars,
the sounds of different animals and birds, the weather, the seasons, and so on,
to keep track of time. Fear of spirits in the forest and fields tended to keep
people inside at night. Habitually the Zulu reckoned a day as from an hour
after dawn to an hour before dusk. The appearance of isiCelankobe
(evening start) signaled evening meal time. During the winter sugarcane
manufacturing process (June-September), the Kafir day thus averaged a short
10.5 hour day. The processing required night work night work, since crushing
had to be done immediately after harvesting to maintain the quality of the
sugar.
Their inyanga, the word for
moon and moon period, was lunar based and there were 13 inyanga a year,
which led to confusion with the European month. Inyanga file (the moon is dead,
signified the end of a month for the Kafir (apparently another term for the
Nguni workers.) They expected to be paid then, and would not work longer.
The complications arising from the
two systems of time notations were enormous, as this agitated correspondence
from “C.P.,” dated (and this is the pivotal clue) 29 October 1846, attests.
“This afternoon, because I would not pay a kafir whose month is up on the
last day of the month, I was abused like a thief. He shook his stick at me,
and was so violent that if I could have got assistance, I would have sent him
to the trunk (goal)” [emphasis added by Atkins, ibid., p. 124].
There was also a mail strike by ten
men carring mail between Durban and Maritzburg hired to work six months (July 2nd
to Jan 2nd) but “arrived at the conclusion that their engagement
expired on the 28th of December.” (Ibid., p 124.)
What stands forth most clearly
is that resorting to summary punishments (including such draconian measures as
floggings and extended stretches in the goal) to discipline preindustrial
workers around the question of time had the effect of driving labor from the
market. (Ibid., p. 125.)
The problems were exacerbated by
the contempt of the employers toward Zulu culture, and their stubbornness to
adapt to the indigenous cognition of time or to their language and by their
attempts to explain European time was considered as “an attempt to cheat them
of their time” by the Kafir laborers.
We can see from this example from
Colonial Africa, that Kristeva’s observations that language and the perception
of reality are inextricably tied to psychological and social life and their
evolution. We conclude that the perception and use of time is a dynamical
process involved in the interaction of conscious and unconscious psychological
social processes, but we end this all-to-brief introduction to the problem by
reminding that the various binaries we have invoked, implicit/explicit,
variable/parameter, semiotic/symbolic, preOedipal/Oedipal, mother/father, and
others are convenient heuristics, that the fractal separatrices between them
belie that dynamics patterns (attractors) constitute a reality that defies
adequate description. Our modelling can only be an approximation to holistic
open systems at all levels of discourse. Developing the psychological and
social temporal metrics necessary for dynamical modelling will be a great
challenge, especially as different metrics and vastly different time scales
will have to be involved in the integrative models.
References
[EoT is S.L. Macy (Ed.), Encylopedia of Time. New York: Garland.]
Abraham, F.D. (1994a). Chaos and Dynamical Navigation of
the Cognitive Map. EoT., pp. 89-91.
Abraham, F. D. (1994b). Chaos, bifurcations, & self-organization: Extensions of neurological positivism and ecological psychology. Psychoscience, 1, 85-118. Abraham, F.D., Abraham, R.H., & Shaw, C.D. (1990) A Visual Introduction to Dynamical Systems Theory for Psychology. Santa Cruz: Aerial.
Abraham, R.H. (1994). Dynamics. EoT., pp. 171-173.
Abraham, R. H. (1994). Chaos, Gaia, Eros.
San Francisco: Harper.
Atkins,
K.E. (1994) “Kafir Time”: Preindustrial Temporal Concepts and Labor Discipline
in Nineteenth-Century Colonial Natal. In J. Adjaye (Ed.), Time in the Black
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Gregson, R.A.M. (1994). Cascades and Fields in
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Koehler, G. (2002). Comments in the “orderings” thread, on
CHAOPSYC, the listserver of the Society for Chaos Theory in Psychology and the
Life Sciences, January, 15. URL: www.societyforchaostheory.org
Kristeva,
J. (1980). Desire in Language. (L. S. Roudiez, ed.; T. Gora, A. Jardine,
& L. S. Roudiez, trans.) New York: Columbia. A collection of ten papers
spanning from 1966 to 1976, with an excellent introduction by Roudiez,
including a guide and discussion of terminology.
Kristeva,
J. (1984). Revolution in Poetic Language. M. Waller (trans.). New York:
Columbia.
Loye,
D. (1984). The Sphinx and the Rainbow. New York: Bantam.
Michon,
J.A., (1994). [all in EoT.]
Psychological Present. Pp. 504-505.
Psychology of Time. Pp. 507-511.
Psychology: Representations of Time. Pp. 511-512.
Psychopathology and Time. Pp. 513-514.
Pressing,
J. (2002). Ibid. as in Koehler above.
Sarup, M. (1993). An Introductory Guide to Post-structuralism and Postmodernism (2nd ed.). Athens: Georgia