Self Organization, Flow Fields,
and Information*
Peter N. Kuglert and M. T. Turveytt
1.0 INTRODUCTION: THE PROBLEM OF ORIGIN
A fundamental problem in the study of biological systems is the transition from
disordered to ordered states. From a physical perspective the problem can be stated as
follows: How does a uniform distribution of matter. obeying standard physical
principles (laws of conservation of momentum. energy. and matter) develop
spontaneously a nonuniform distribution? Identification of the necessary conditions
for the occurrence of the symmetry-breaking transformations responsible for the
nonunifonnity is the fundamental goal of a physical theory of self organization. It
defines what might be termed 'the problem of origin."
Self organization occurs in systems composed of multiple subsystems when opened to
the flow of energy. matter. and/or information. Under these open conditions
nonlinearities can develop among subsystems leading to the emergence of (a) sharp or
subtle transitions between qualitatively different states. (b) fluctuation-induced
instabilities. and/or (c) chaotic. deterministic. dynamics.
Although "openness" to conservational flows is a necessary condition for the
transition to higher ordered states. the flows themselves do not carry or import order
into the system. The ordered behavior of the system. for example. is not dependent on
initial conditions determined externally. and neither is it derived from any "smart"
internal subsystem. This remarkable gap. separating the amount of order exhibited in
the inputs and the internally stored states from the amount of order revealed in
behavior. is the hallmark of self-organizing systems.
The purpose of this article is to provide an elementary overview of the physical
strategies underlying self organization. and to identify their connections with
traditional aspects of classical physics. such as Newtonian mechanics and
thermodynamics. The strategies in question apply to both Simple physical systemswhere subsystem interactions are dominated by kinetic (force) linkages-and complex
biological systems-where subsystem interactions are dominated by nonkinetic
(kinematic. geometric. spectral) linkages. Of particular interest is a class of
biomechanical systems whose self motion is powered by internal energy reservoirs. In
these systems energetic flows cross the system's external boundary and are converted
into useful work cycles through internal thermodynamic processes. Regulation of these
work cycles (such as locomotion. manipulation. fleeing. fighting. feeding. reproducing.
Haskins Laboratories
SR-95/96
Status Report on Speech Research
1988
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etc.) is through a circular mapping of low energy (kinematic. geometric. spectral)
linkages into high energy. force generating actuators. The circular cross coupling of a
low energy linkage with a force generating actuator can lead to a cascade of symmetrybreaking instabilities and the subsequent emergence of new cooperativities among
subsystems. The result is the formation of an execution-driven. self-organizing.
control system.
2.0 OVERVIEW OF CLASSICAL MECHANICS AND TIIERMODYNAMICS
2.1 Classical (Newtonian) Mechanics
2.1.1 Doctrine of Simple (Isolated) Atomisms
The search for a fundamental level of description for modeling behavior has been one
of the principle objectives of physics. From the perspective of classical (Newtonian)
physics the appropriate level of description for modeling a given phenomenon is that
which individuates suitable fundamental units. The selection of fundamental units
depends critically on the problem of interest. For example, in the study of the large
scale dynamics of the universe, galaxies serve as a fundamental unit: in the study of a
solar system. planets and stars serve as fundamental units: in the study of ecosystems.
organisms (and. perhaps. their reciprocally defined niches) serve as a fundamental
unit: in the study of polymer conformation. polyatomic entities serve as a fundamental
unit. and so on. The choice of a fundamental unit fixes the lower limit for the level of
detail of analysis and allows for identification of invariant structural and functional
features. The inventory of invariant features defines a simple atomiSm (see !berall.
1972).
If the phenomena under inquiry. for example. fluctuations, noise. drift. and so on.
cannot be explained by the current level of description. then the strategy is to seek a
more detailed level of description at a more microscopic scale. This strategy leads. in
tum. to the identification of new atomisms and the shifting of the lower limit of
relevance of the phenomena. This move toward the discovery of new, more
microscopic. descriptions reflects the tacit belief that the behavior of a system can, in
principle. be modeled completely in terms of some set of elemental units. The dynamic
of these elemental units. echoing throughout the system with perfect fidelity.
determines all observable (macroscopic) phenomena. The assumption of perfect
fidelity allows for the use of methods of analyses. such as Fourier decomposition. that
take advantage of the linear properties of superposition and proportionality. For these
systems, any macroscopic state description can be expressed as the Sum total of
microscopic state descriptions.
The above strategy provides a methodology for discriminating selectively between
descriptions that are relevant (atomistic) and irrelevant (superatomistic and
subatomistic). Once an atomiSm is identified. the phenomena under inquiry can be
explained without taking recourse to phenomena at more macroscopic or microscopic
scales. that is. the dynamic at the superatomistic scale or the dynamic at the
subatomistic scale. No macro scale above the atomistic level can isolate its dynamic
from the atomistic dynamic. In other words. no spatial or temporal boundaries can be
assembled that segregate locally. or isolate. the macro dynamic from the micro
dynamic. Under these conditions a perturbation cannot be "forgotten." In this classical
approach to analysis there is no moderation: Once a system is bounded. above or below.
no dynamic can be induced into the system that originates outSide the bounded region.
Once a set of initial conditions is specified. its signature will persist for eternity with no
pOSSibility for new signatures. The system cannot self organize. This is the "doctrine of
Kugler & Turvey
211
atomism." and it follows directly from the classical interpretation of isolated systems.
It is the fundamental doctrine of Newton's mechanics program.
Assumption!: Systems bounded or isolated from external
interactions cannot spontaneously give rise to new dynamic
regimes: No new laws can emerge that govern the behavior
of the system at a privileged scale or region of the state space.
2.1.2 Doctrine of Mechanical (Temporal) Reversibility
One of the basic characteristics of trajectories defined by Newton's master equation
is time reversibility. No distinction is allowed between future states and past
states. A change in the sign of the time variable results in no change in the solution,
that is. the equation of motion is fully symmetric with respect to time inversions. For
example Newton's dynamic defines changes such as t-> .t. time inversion. and v-> 'v,
velOCity inversion. as eqUivalent mathematically. What one dynamiC change achieves,
such as time inversion. another dynamiC change, such as velocity inversion. can undo,
and in this way restore the initial condition.
Our daily experience with natural events repeatedly provldes examples counter to the
notion of mechanical reversibility. For example: a burning match never reverses
itself. returning to the sulfur match phase: a drop of ink in water always spreads in a
direction of decreaSing concentration. never moving in the opposite direction of
increasing concentration: an animal grows old in time. not young. and so on. In
Newton's world. all of the above events and their reversals are equally likely. and any
generalizing of the master equation to new phenomena must first come to terms with
the requirement of temporal reversibility.
(F = ma)
Assumption: All mechanical events are temporally
reversible, for example, they do not distinguish historical
beginnings from endings, births from deaths.
2.1.3 Doctrine of Force (Kinetic) Interactions
The Newtonian model is applicable to the extent that the interior complexity of the
atomisms can be ignored-the ingredients of Newton's master equation are void of any
allegiance to the internal structure of the atomisIIlS. The Variables of interest are the
relative positions and velocities that give rise to forces acting externally between
atomisms. Put Simply. the model assumes that all interactions between atomisms are
deSCribable in terms of forces stated as explicit functions of velOCity and displacement.
Under ideal conditions the identification of all the velocities and displacements of all
atomisms at a Single instant of time allows for the complete specification of all states
of the system. both future and past. Because the behavlor of the system is determined
completely by the variables of velocity and displacement. they constitute the state
variables for the system. There is nothing unique. however. about the state variables of
velOCity and displacement. In fact. there is a long-standing tradition in theoretical
mechanics for seeking transformations to new state Variables, in which the equations
of motion take on a particularly simple form. such as action angles (see
Goldstein. 1950). What is unique about the claSSical paradigm. however. is the
privileged role played by forces. The paradigm rests ultimately upon the fundamental
dualism between states and time-dependent force laws (see Rosen. 1978, 1985).
Self Organization, Flow Fields, and Information
212
Generalizing the model rests upon the fundamental assertion that the master
description (state equation) relates states of atomisms only in terms of forces.
Assumption: The induction of all dynamic changes between
simple atomisms involves forces that are scaled to the
atomism's position and velocity.
2.2 Reversible (Equilibrium) and Irreversible (Nonequilibrium)
Thermodynamics
2.2.1 Reversible Equilibrium Thermodynamics
The challenge of describing all of nature's order and regularity in terms of the
doctrines of simple (isolated) atomisms. reversibility. and force interactions has been
taken up by Newton's physics. Predictions are made by conSidering the system's
resultant dynamic as the (mean) sum of its atomistic dynamics. These assumptions
underlie the conceptual construction of the solar system (classical and relativity
mechanics). subatomic particles (electrodynamics). and nuclei (chromodynamics). All
of these constructs can be conSidered as descriptions of static machines. obtained by
adding together components in equilibrium (1.e.• with mutual forces compensated by
reactions) and then superimposing varieties of known motions. Such is the physical
description of a crystal. a planetary system. a cosmological system. and many
mechanical (technological) devices. since rotational or alternating motions are all
particular instances of the pendulum and two-body problem. In an ensemble of
interacting atomisms. however. every atomism moves along extremely complicated
trajectories.2
While an atomistic (microscopic) perspective of an N-body system reveals a
microcosm of unending motion. with every atomism moving along an extremely
complicated trajectory. a macroscopic perspective reveals certain regularities that can
be deSCribed using a small number of state Variables. This reduction in analytic detail
is possible since a Single macroscopic state can correspond to a wide variety of different
microscopic states-there is a homomorphic mapping that relates a Single macro state
to multiple micro states. These macroscopic book-keeping mettles constitute the
thermodynamiC variables for systems at equilibrium.
Equilibrium thermodynamics is the study of laws that relate macroscopic
(phenomenological) descriptions of atomistic systems under conditions of
reversibility. The thermodynamic laws are statements about relationships linking
these mean macroscopic properties. The macroscopic laws form a self-consistent body
of empirical knowledge. They are readily observable and verifiable Without any
recourse to the details of the micro states. The formal study of the explicit mapping
between microscopic mechanical states and macroscopic thermodynamic states is the
topic of statistical mechanics (see Balescu. 1975). The inductive passage from two
bodies to N bodies was conSidered legitimate. even though the only rigorously solved
problem was the two-body problem. It is now. however. becoming increaSingly
apparent that an isolated many-body system can behave in chaotic ways that are not
predictable from pendulum dynamics and elementary two-body interactions (see
Cv1tanovic. 1984; Schuster. 1984).
Assumption: A small number of mean (statistical) macro
states map homomorphically onto many micro states.
Kugler & Turvey
213
22.2 Irreversibility as an Improbable Event in an Isolated System
It is an empirical fact that an isolated system (e.g.• closed to external flows) evolves
irreversibly in time toward a state in which all conserved entities (mass. momentum.
energy. charge. and so on) are partitioned equally over all available degrees of freedom.
Once attained. the equipartitioned state remains constant in time. and all state
transitions exhibit temporal reversibility. The attainment of equilibrium is
independent of initial conditions. All states displaced initially away from equilibrium
will converge ultimately onto the reversible equilibrium state. Because the final state
is independent of the initial state. the event is asymmetric with respect to time and.
therefore. an historical direction can be assigned to time. The event has a temporal
beginning and ending. In an isolated system. events always converge onto the
equilibrium state. Once at equilibrium. events no longer exhibit historical beginnings
and endings. births and deaths. since the path between the two states is. once again.
reversible temporally.
When confronted with the identification of the mechanism responsible for the origin
of the initial conditions that displaced the system away from equilibrium. the
atomistic perspective views these departures as fluctuational events with very low
probabilities. Irreversibility is viewed ultimately as a macroscopic random fluctuation
with an assigned probability that derives its dynamiC from the microscopic.
statistically reversible. states. It is viewed as a highly improbable statistical departure
from a mean state. The statistical approach advocates a strategy that searches for those
properties (mean states) that do not change with time below those properties
(fluctuations) that do change with time.
2.2.3 Entropy and the Second Law
Temporal irreversibility is measurable in terms of a state variable. the entropy.
whose direction of change (increase or decrease) assigns a temporal direction to events
(future or past). The second law of thermodynamics states that the entropy of an
isolated system will increase with time until it achieves asymptote at the equilibrium
state. at which time the entropy is constant. Once at equilibrium. the entropy of an
isolated system never decreases spontaneously. except for very local fluctuations
associated with thermal. microscopic. noise. It is possible to give a qualitative
interpretation of the state transitions associated with increases in entropy in two ways: .
In tenns of the organization of molecular motions. and by showing, after Boltzmann.
that this increase corresponds to progressive disorganization and an evolution toward
a "most probable state." In isolated systems the most probable state is that exhibiting
maximum disorder. This maximum disordered (equilibrium) state corresponds to a
state in which all conserved entities (mass. momentum. energy. charge. and so on) are
shared equally among all available degrees of freedom. According to the second law,
the production of entropy is associated with a process of distributing conserved entitles
over available degrees of freedom. Classically. the second law was viewed as a
distribution process that always operated in the direction of moving the distribution
from a state of less occupied degrees of freedom to more occupied degrees of freedom.
Since self organization is a process involving the transition from a state of greater
degrees of freedom to lesser degrees of freedom. the second law was viewed traditionally
as a proCess operating against the theoty of (organizational) evolution.
The temporal evolution of the distribution process. while undefinable at the level of
mechanics. can be assigned a direction. an historical beginning and ending. at the level
of thermodynamics. The direction is assigned in terms of the entropy function. The
introduction of entropy into macroscopic descriptions makes it impossible to reduce
macroscopic thermodynamic descriptions to purely mechanical descriptions. Mechan-
Self Organization, Flow Fields, and Information
214
ical reductionism is forever doomed to analytical incompleteness for all systems
exhibiting irreversible processes.
Assumption: An irreversible, macroscopic, description
cannot be reduced to a reversible, microscopic, description.
2.2.4 Equilibrium and Nonequilibrium Regions Defined by Microscopic (Linear) Force Laws:
1+1=2
Irreversible flows near equilibrium express an important property. captured by the
principle of minimum dissipation. This principle was formulated first by Onsager
(1931) and refined later by Prigogine (1945. 1947). Trajectories of irreversible flow near
equilibrium produce a minimum of entropy per unit time (i.e.• entropy production is a
local minimum). As a result. the stable state can be maintained by a smaller input of
energy than neighbOring states. Irreversible trajectories are selected acording to their
ability to dissipate energy. Steady state irreversible flows converge onto those
trajectOries. dissipating the least amount of energy per unit time.
The motions of atomisms along paths that m.iniInize the rate of entropy production
are driven by forces that are linear. weak. and limited to nearest atomistic neighbors.
The macroscopic effects these microscopic forces produce are strictly additive functions
of the microscopic forces. In regions near equilibrium. forces relate linearly to flow
rates in terms of additive constants (Onsager. 1931). Stable states in the linear region
exhibit only homogeneous spatio-temporal patterns.
Assumption: Near equilibrium the forces that drive the
flows relate linearly in terms of additive constants.
2.2.5 Nonequilibrium Regions Defined by Macroscopic (Nonlinear) Force Laws: 1 + 1 c# 2-
"In the region of the linear force laws (near or at equilibrium). the system responds to
perturbations and/or fluctuations with small adjustments in the thermodynamic
parameters. That is. no large scale (qualitative) changes occur in the distributional
properties of the conservations when the forces driving the irreversible flows are
linear. The linear force laws break down. however. when the system is displaced
sufficiently far from equilibrium. and are replaced by new nonlinear. force laws. These
new force laws are defined macroscopically relative to global thermodynamic
potentials that arise as a function of large scale nonuniformities in their distributional
configurations. These macroscopic force laws can result in the emergence of a
patterned dynamiC. for example. time-dependent and/or spatially-dependent regimes.
As noted. the macroscopic force laws come into existence as the system is displaced
further from equilibrium. In this region the macroscopic force laws. defined relative to
global thermodynamiC potentials. actively compete with the microscopic force laws,
defined relative to local thermodynamiC potentials. As the macroscopic laws begin to
influence the dynamic. the system is driven toward higher ordered states. Starting
from an initial near equilibrium condition. dominated by the equilibrium attractor.
the system moves into a region whose dynamic is no longer organized by the
attractiveness of the (thermodynamic) equilibrium state. Instead. its dynamic is
organized by the attractiveness of a nonequilibrium (thermodynamic) attractor that is
far away from the equilibrium attractor. Once the system's dynamic becomes
dominated by the influence of the nonequilibrium attractor. its evolutionary trajectory
Kugler & Turvey
215
moves in the direction away from thennodynamic equilibrium. The emergence of the
nonequilibrium attractor creates a natural tendency for the dynamic of the system to
evolve in the direction of increasing order. An intrinsic self-organizing tendency
replaces suddenly the previously dominant self-disorganizing tendency.
In this far from equilibrium region. the new macroscopic laws that come into
existence provide global constraints that harness the microscopic dynamic. They act
on superatomisms (fluid cells. flow units. and so on) in the same manner that the
microscopic laws act on simple atomisms. And. most importantly. these macroscopic
laws have a certain degree of autonomy and sovereignty with respect to the microscopic
laws. even though they emerge from the actions of the microscopic laws. In sum. the
macroscopic laws define the dynamic for the constraints that act as boundary
conditions on the microscopic laws-that is. the macroscopic laws serve as dynamic
boundary conditions for the Simple atomisms.
Assumption: In systems displaced far from equilibrium
there is a thermodynamic region in which the hegemony of
the weak, local (microscopic) linear force laws breaks down
to be replaced by the hegemony of strong, global
(macroscopic) nonlinear force laws.
2.2.6 Order through Fluctuations
Near the transitional boundary. between domination by the microscopic laws and
domination by the macroscopic laws. small perturbations in the system's dynamic can
be responded to with large scale changes in distributional patterns. The dramatic
amplification of the perturbation is the result of the break-down of the linear force
laws. As a system approaches the region where the local force laws break down the size
of the fluctuations begin to increase as a result of decreases in the damping forces. What
were small fluctuations previously. can grow into a large scale departures. driving the
system ultimately into regions influenced by the macroscopic laws. The stochastic
dynamic associated with these fluctuations constitute a form of exploratory activity
that both discovers and selects new distributional regimes. For instance. the existence
of thermal noise guarantees the presence of an incessant search strategy that seeks out
continuously more eqUitable energy partitioning regimes. The noise provides a
mechanism for exploring the stability of neighboring states.
Prigogine and his
colleagues (Prigogme. Nicolis. & Babloyantz. 1972) have referred to this phenomenon as
order through fluctuation.
Assumption: Fluctuations comprise an exploratory
mechanism for seeking out new stable regimes.
2.2.7 A Selection Principle for Nonequilib:rium Steady-States
The transition region between the local linear force laws and the global nonlinear
force laws is associated with a local maximum in the function defining the system's
production of entropy. On one side of the local maxtmum. forces are organized so as to
drive the system in the direction of thennodynamic equilibrium. On the other side of
the maximum. the forces tend to drive the system away from thennodynamic
equilibrium in the direction of :Increasing organization. Put differently. on one side of
the critical po:lnt (local maximum) the behavior is influenced by local thennodynamic
potentials. on the other side. the behavior is influenced by global thennodynamic
Self Organization, Flow Fields, and Information
216
potentials. Crossing the critical point involves a shift in the scale of the laws that
dominate the structuring of the forces that organize the flow patterns: On one side of
the maximum. microscopic (potential) laws apply. on the other side. macroscopic
(potential) laws apply.
At or near the transitional boundary a fluctuation can drive the system over the
maximum; beyond this local maximum the self-damping tendency of the particle's
motion is replaced by a self-amplifying tendency. With amplification of fluctuations.
the system's entropy production no longer identifies a minimum (as prescribed by the
principle of minimum entropy production under imposed boundary conditions). The
stability of the amplifying trajectoxy. however. is guaranteed locally by a minimum in
the excess entropy production function (see Glansdorff & Prigogine. 1911). The
instability is slowed down with a decrease in the entropy production. halting finally as
the entropy production attains a new local minimum.
Assumption: The stability of the path from one dynamic
regime to the next is a function of the rate ofchange of
entropy production-that is, the path minimizes the excess
entropy production.
2.2.8 The Benard and Taylor Instabilities
A convection instability. first identified in 1901 by the French physicist H. Benard.
provides an example of how the instability of a stationaxy state can give rise to a selforganizing process (see Koschmieder. 1915. 1977). The Benard instability is due to a
vertical temperature gradient created when a liqUid layer is heated from below while
keeping the top surface at a constant. cooler temperature. As a result of the boundaIy
conditions. a heat flux (temperature differential) is established resulting in a force
structure that tends to push the flUid's molecules in the direction of the cooler upper
surface. The convective motion of the molecules is resisted by internal friction that
dissipates mechanical energy. When the thermal gradient is small. only heat energy is
conducted along the gradient; the molecules remain local. their motions restricted by
local diSSipative processes.
When the imposed gradient reaches a threshold value. the liqUid's state of rest-the
stationary state in which heat is conveyed by conduction (thennal transport without
mass transport)-becomes unstable. A convection (mass transport) corresponding to
the coherent motion of ensembles of molecules is produced that increases the rate of
heat transfer. As the critical value of heat transfer is approached (1.e.• the gradient of
the temperature). the entropy production of the system is increased. no longer
identifying a minimum as preSCribed by the theorem of minimum entropy production.
During the transition the stability of the system is defined locally by the minimum of
the excess entropy production function-instead of the entropy production function (see
Glansdorff & Prigogine. 1971).
The Taylor instability occurs when fluid is trapped between two cylinders rotating :In
opposite directions. The fluid is caused to rotate by shear forces transmitted by the
cylinder. At rotational speeds below a critical value the fluid flow is laminar; above
that value the flow becomes turbulent progressing ultimately toward stable vortices.
From an initial unordered state. a well-organized state characterized by long range
spatial and temporal correlations emerges. These patterns are assembled and
disassembled readily by merely changing the rotational speed of the cyclinder.
The convective motions in the Benard and Taylor instabilities consist of a complex:
spatio-temporal organization with long range correlations between molecular
neighborhoods. Correlations between molecules extend over diStances of the order of a
centimeter. whereas intermolecular attractive forces act only over distances of the
Kugler & Turvey
217
order of 10-Scm. At equilibrium the uniform fluid exhibits equivalent properties at all
points. In the case of the convection cells. where adjacent cells rotate in opposite
directions. the local symmetry is broken. Equivalent points are found only if one
moves a distance of two cells in the fluid. The annihilation of local (microscopic)
symmetry and its replacement by a more global (macroscopic) symmetry is referred to
as a symmetry-breaking instability.
2.3 Prigogine's Theory of Dissipative Structures
Classical thennodynamics was associated . . . with the
forgetting of initial conditions and the destruction of
structure. We have seen, however, that there is another
macroscopic region in which, within the framework of
thennodynamics, structure may spontaneously appear
(Prigogine, 1980, p. 150).
At equilibrium energy. matter. and motion (momentum) are distributed uniformly
and interactions between subsystems are linear. reversible. and local. Under open flow
conditions. new long range interactions can develop between groups of subsystems
resulting from changes in the correlation of spatial and temporal interactions. The
creation and annihilation of the long range interactions, symmetry breaking
instabilities. are sustained principally by the entropy producing. irreversible.
processes. Prigogine (1967) has termed these long range organizations dissipative
structures in recognition of the central role played by irreversible (dissipative)
processes.
In the last thirty years the constructive role of irreversible processes has been
emphasized. most notably by liya Prigogine and his Brussels colleagues (see Allen,
Engelen. & Sanglier, 1984: Babloyantz. 1986: Glansdorff & Prigogine, 1971: Nicolis &
Prigogine. 1977. 1985: Prigogine. 1947. 1962. 1980: Prigogine & Stengers. 1984).
Recognizing the central role played by entropy production in the creation of coherence,
organization and order. Prigogine (1967) has termed these self-organizations
"dissipative structures." In 1977 Prtgogine was awarded the Nobel Prize in Chemistry
for his work on the relationship between irreversible processes and self-organization.
A major result of thiS effort is that the relationship between irreversible flows and selforganizing processes has become a prominent topic on the scientific agenda in the
biological and social sciences (see Haken.1975. 1981. and his Synergetic Series
published by Springer-Verlag: Kalchalsky. Rowland, & Blumenthal, 1974: Iberall. 1972;
O'Neill. DeAngelis. Aide. & Allen. 1986: Ulanowicz. 1986: Yates. 1987).
3.0 COMPLEX (BIOLOGICAL) ATOMISMS AND INFORMATIONAL
INTERACTIONS
3.1 Complex (Open) Atomisms
LMng systems are open to the flow of energy and matter. As noted above. opening a
physical system to the flow of energy and matter generates constraints that can curtail
the system's degrees of freedom. In redUCing the degrees of freedom. new spatlotemporal
Self Organization, Flow Fields, and Information
218
regimes arise among the atomisms, accompanied by new atomistic modes of
interaction (e.g., convection vs. conduction). Because of these evolved constraints and
their interactive consequences, an open system's behavior is not accounted for fully by
initial and boundary conditions defined strictly in the (isolated) external frame of
reference. Openness incurs autonomy.
3.2 Self-Sustaining (Open) Atomisms
Internally, a living system maintains a potential. It arises from delaying the
transport of energy and matter into and out of the interior, and from the ability to
sustain this exchange. Living systems must be served energy and matter by an external
agency, or serve themselves. Given a sustained on-board source of potential energy
(usually in the form of chemical fuel) that can be drawn upon, capabilities such as selfreparation and self-propulsion are possible. The facility to produce generalized work
cycles has the significant consequence of giving a system a certain amount of flexibility
with respect to external gradient fields. The system's trajectory need not follow
minimum energy trajectories, if the system has the capability to generate forces
comparable to those generated externally. (In contrast, trajectories of simple atomisms
must follow the external force field's geodesics.) If these departures from, and returns
to, the externally defined minimum trajectories are systematic, then a sensitivity to
gradients is implied, The abilities to discriminate selectively low-energy potential
gradients and to "self-sustain" are fundamental characteristics of living systems.
3.3 Complex Atomisms Dominated by Information Interactions
Complex (biological) atomisms can time-delay energy flows from the interior to the
exterior. The result is the emergence of thermodynamic flow processes. The timedelaying of external->internal->external-> . , . energy flows changes dramatically the
atomism's mode of interaction; the atomism is no longer a "slave" to the external force
field, The time-delaying of energy flows provides a local. internally-based, source of
forces that can compete actively with the external forces. As the internal forces
increase with respect to the external forces, the role of the mass dimension becomes
successively less relevant for sustaining interactions, What remains relevant,
however, are the fundamental dimensions of length and time. These interactions, that
are not force dominated interactions, have been termed "informational interactions"
(see Kugler, Turvey, Carello, & Shaw, 1985; Kugler & Turvey, 1987). Informational
interactions are the physical consequence of atomisms with complex interiors that can
time-delay large amounts of energy relative to external force fields.
3.4 Nonkinetically Induced Dynamics
Nonkinetic (informational) descriptions (e.g., kinematic, geometric, spectral) can be
used to regulate interactions between two complex atomisms if the description is
observable. Intuitively, the notion of observable is related to a concrete procedure for
determining properties (quantitative values and qualitative categories) carried by the
observable. The critical ingredient for defining the observable is the procedure defining
the measurement instrument. By operationally relating the problem of observable to
measurement it is possible to identify observable-induced eqUivalence relations.
EqUivalences (similarities) defined over the mapping process linking observables to
measurement can be used to relate diverse situations according to common figures of
Kugler & Turvey
219
merit, namely, the generation of dimensionless numbers or other kinds of invariants
that serve to label the measurement process. Two processes are considered similar if
and only if they bear the same quantitative value for the figure of merit.
3.5 Reciprocity of Measurement and Observables
Intuitively, a complex atomism 15 some part of the real world that defines an object of
study; a state 15 a specification of what the atomism 15 like at a particular time; and an
observable 15 some characteristic of the atomism that can, at least in principle, be
measured. More succinctly, an observable of an atomtsm is a quantity that can induce
a dynamic in some nominated measuring device. The only meaningful events for the
measuring system are those carried in the observables, for example, the dynamic
inducing descriptions. Those state descriptions that are not carried in the observables
are of no relevance to the interaction. A complex atomism, composed of multiply
embedded process scales, need only interact with another complex system through the
small set of dynamic-inducing observables.
The process of observation (measurement) can be considered as a reciprocal
induction of dynamics in both the atomism being observed (measured) and the atomism
that observes (measures). Observation (measurement) rests ultimately on the capacity
of a given system to induce a dynamic (i.e., a change in state) in an observing
(measuring) instrument (alias meter, classifier, sensor, organ, organism, and so on).
The basic problem in analysis becomes the determination of the observables through
which a particular dynamic is taking place, and the identification of the means
(transformations) by which one system 15 causing the other to change. (See Rosen, 1978.
1985, for extended treatments of the concepts of observables, meters, alternative
descriptions, and linkages, in the context of induced dynamics.)
Interactions between complex (biological) atomisms are dominated by descriptions
in which force interactions are minimal-whether hormonal, pheromonal, neuronal,
optical, acoustical, or verbal, the interaction is low in energy and momentum
exchanges. Indeed, interactions that are low in energy and momentum exchanges can
be taken as the hallmark of systemic behavior at the ecological scale at which the
entities "animal" and "environment" are defined. At the ecological scale the
interactions are largely informational. It has been traditional to view the relation
between simple atomisms and complex atomisms as the general to the particular,
biology being viewed as the result of special conditions. It is beCOming more and more
apparent, however, that the relationship between physiCS and biology may be, in fact,
the opposite: It may be that of the particular (physics) to the general (biology).
This relationship between complex systems and simple ones
is, by its very nature, without a reductionistic counterpart.
Indeed, what we presently understand as "physics" is seen
in this light as the science of simple systems. The relation
between physics and biology is thus not at all the relation of
the general to the particular; in fact, quite the contrary. It is
not biology, but physics which is too special. We can see
from this perspective that biology and physics (i.e.
contemporary physics) grow as two divergent branches from
a theory of complex systems which as yet can be glimpsed
only very imperfectly (Rosen, 1985, p. 424).
Self Organization, Flow Fields, and Information
220
3.6 The Primacy of Informational linkages
An historical challenge for the physically-minded scientist has been the removal of
vitalism from explanatoty accounts of biological systems. A less heralded challenge.
but of equal importance. is the challenge of removing the interactive violence
associated with mass-dominated interactions. A physical pursuit of this latter
challenge brings to the forefront the primacy of nonkinetic descriptions and puts a
"non-Newtonian life" back into biology. This challenge was anticipated by J. J. Gibson
(1950. 1966. 1979) in his pursuit of a kinematic flow field analysis of optical structure
(see Reed & Jones. 1982). Gibson's methodology focused on the physical and functional
significance of nonmas~ interactions in a manner that is continuous with the theoty of
collisions (see Kugler et al.• 1985; Kugler & Turvey. 1987). By focusing on nonmass field
descriptions. a natural transition can be made from the phySical theory of self
organiZation to a theoty of self-organizing Minformation systems." (For extended
discussions by the authors on the topic of self-organizing information systems see
Kugler. Kelso. & Turvey. 1980. 1982; Kugler. 1986; Kugler & Turvey. 1987.)
Assumption: Intera.ctions participated in by complex
(biological) atomisms are dominated by informational
descriptions (kinematic, geometric, spectral) that are
sustained by fields that are low in energy and momentum
exchanges.
4.0 AN EXAMPLE OF A SELF-ORGANIZING INFORMATION SYSTEM
4.1 Insect Nest Building
Biological systems are composed of subsystems that are sustained by linkages in
which kinematic. geometric. and spectral observables play the principle role in
inducing dynamic change. Dynamic fluxes (flows) of patterns within these linkages
(hormonal. pheromonal. acoustical. optical. and so on) act catalytically in the
generation of high energy responses in neighbOring subsystems (such as target organs.
motor actuators. fleeing responses. fighting responses. and so on). A model of nest
construction by social insects is presented to Ulustrate the role of nonkinetic (flow
field) linkages in self organization.
The insects of interest are social termites that periodically construct nests that can
stand 20 feet in height and weigh upwards of 10 tons. and which involve the active
participation of more than 5 mUlion insects. The insects tend to follow two simple
prinCiples (a) move in the direction of the strongest pheromone gradient; and (b) deposit
building materials at the strongest point of concentration. The principal concepts
expressed in the example are derived from Grasse's (1959) and Bruinsma's (1977)
naturalistic observations and a thermodynamic treatment advanced by Deneubourge
(1977).
The control constraints that organize the building activity originate in a low energy
pheromone field that is linked to the behavior of the insects through a chemical
affinity. The low energy linkage forms a circularly causal force->flow-> force-> ...
information loop that is open to the creation (and annihilation) of field
discontinuities. The emergence of these discontinuities results in a cascade of
symmetty-breaking instabilities with the subsequent emergence of a succession of
cooperative nest building phases (see Kugler & Turvey. 1987. for details). In the first
phase the insects fly in a random pattern. followed by a pillar construction phase. then
an arch construction phase. ending with a dome construction phase. The details of the
Kugler & Turvey
221
....nlll
/'
.....---......
SI
COMPLEX (BIOLOOICALI ATOMISMS
......
,/
.,
llOlllClY
o .'(~~~
, _......
tJ
.........
.........
SII
......
//
-........
INTERACTION
•
/
./
lIOlllQY
\
\
\ e
\
"
"
"",
"
I
\
'/
CUI.
.,--- ........
,...
'-.
0
CD
....nlll
CD
/
)
/
CIl.L
......... - - - . . . . " " ,
/' /
Figure 1: Complex (biological) atomisms store energy internally and can time-delay its release from the
interior to the exterior. The result is the emergence of thermodynamic work cycles. In a complex
atomism the role of the mass dimension is less relevant in the dynamic description that sustains the
interactions between atomisms. What remains relevant are the fundamental dimensions ?f length and
time (see Table 1 below). These nonmass (e.g. nonforce) dominated interactions are termed
informational interactions and are viewed as methodologically continuous with elastic and inelastic
interactions. Informational interactions are the physical consequence of atomisms with complex interiors
that can actively time-delay large amounts of energy relative to extemal force fields (adapted from
Kugler &: Turvey, 1987).
LEVEL OF ABSTRACTION
IKINETIC (M.L;!)
'KINEMATIC (L.TI
l(jEOMETRIC (Ll
'TEMPORAL tTl
MACRO
FORCE AELD
FLOW FIELD
SPATIAL FIELD
SPECTRAL fiELD
MICRO
FORCE
FLOW
SPATIAL
SPECTRAL
ALTERNATIVE AELD DESCRIPTIONS
Dtscriplions
I
Kinetic
(Newtonian
Dimtnsions
M.L,T
Forc:eii-violent interactions; con~rvations such
as mvo, mv l , mv 2 ; symmc:!ries; potc:ntiills;
constraints; singulasities. X. X pha~ space
L,T
Nonviolent interactions; singularitic:s;
constraints; symme:trie:s; X. Xphase: space
L
Geometries. forms. boundary
T
Spectra. frequencies; functions
Mechanic~)
'Kinematic
""emporal
Proptrties
cundition~
Table 1: The field descriptions are macroscopic. They do not include microscopic descriptions such as
charge, spin and other attributes of interaction at the electromagnetic and quantum scale (adapted from
Yates &: Kugler, 1984).
Self Organization, Flow Fields, and Information
222
nest building process are discussed below beginning with the role of perceptual
thresholds as a symmetry-breakirig mechanism.
4.1.1 Perceptual Thresholds as Symmetry-Breaking Mechanisms
The pheromones injected into the building materials diffuse throughout the site
according to Ficks's law (rate of transport is linearly proportional to density) to
produce a gradient. An insect flying into the area can become oriented by the gradient if
the gradient exceeds the insect's perceptual threshold. This threshold is a sYmmetrybreaking mechanism that partitions the insect's activity space into (a) gradientdependent regions. where the insects are influenced by the diffuSing pheromones. and
(b) gradient-independent regions. where the insects are uninfluenced by the diffusing
pheromones (see Figure 2). The former are regions of reversibility and the latter are
regions of irreversibility. The partitioning of the space into irreversible and reversible
regions is continuous with the classical partitiOning' of dynamiC processes (see Kugler.
1986).
Assumption: The thresholds (nonlinearities) that
characterize perception-action couplings are symmetrybreaking devices that partition (categorize) control spaces
into regions of reversibility and irreversibility.
III DIFFUSION FIELD
-
EQUIPOTENTIAL LINES
--+ INSECT fLIGHT PATH
Figure 2: "Perceptual limit" of the field defines a symmetry-breaking mechanism. Insects in areas
where the pheromone gradient falls below the perceptual limit exhibi.t no correlation among their
motions; they are at equilibrium. Insects in areas where the gradient is above the perceptual threshold,
exhibit correlations among their motions; they are displaced from equilibrium (adapted from Kugler &
Turvey, 1987).
4.1.2 Random Deposit Phase.
In the earliest phase of nest building the insects' depositing motions are random (see
Figure 3). There are no pheromone gradients strong enough to influence the insects'
Kugler & Turvey
223
behavior. Once a few deposits have been made. however. the pheromone diffuses into
the air. creating an attracting gradient leading to a region of highest concentration.
The point of highest concentration identifies a critical (Singular) region.
When only a few insects are participating in the depositing activity. the pheromone
concentration remains low and has very little orienting influence on the insects. The
majority of the building sites define regions of reversibility. and the insects. as an
ensemble. are at equilibrium. If the number of insects remains low. then the system
will remain at equilibrium. resulting in an extended period of random depositing.
DUring thiS phase no long range correlations develop among participating insects.
Assumption: When the number of insects participating in
nest building is small the individual motions are
uncorrelated, and the system is at equilibrium.
•
o
•
•
o
•
- .......
o
/
o
_.........
-
I
o
-/
•
o
o
INSECT DEPOSIT (DIFFUSEDI
•
INSECT DEPOSIT IACTlVE)
~
£:::OJ' INSECT
- . - INSECT FLIGHT PATH
C\
_/
o
•
PERCEPTUAL FIELD LIMIT
o
EQUIPOTENTIAL LINES
--
DIFFUSION GRADIENT
*"'
SINGULARITY
Figure 3: Random flight phase. The behavior of the insects is at equilibrium during this phase-e.g., the
motion of each insect is independent of other insects, there are no long range correlations between the
motions of insects (adapted from Kugler & Turvey, 1987).
4.1.3 Development of Preferred Deposit Sites and Pillars.
As the number of insects is increased the likelihood that an insect moves into the
vicinity of a recent deposit increases. The greater the number of random deposits
within a given interval of tiIne. the greater the probability that an insect will pass into
an active portion of the pheromone field. As the number of recent deposits make the
site more attractive. more insects contribute deposits. which in tum make the site even
more attractive. defining. thereby, an autocatalytic reaction. As the gradient region
amplifies. and long range correlations begin to develop among the insects. the
corresponding insect organization becomes displaced from equilibrium (see Figure 4).
The onset of long range correlations marks the end of the equilibrium phase. and the
Self Organization, Flow Fields, and Information
224
beginning of a succession of nonequilibrium phases. The firSt nonequilibrium phase
involves the construction of pillars.
Assumption: As the number of insects increases, the
depositing behavior becomes autocatalytic resulting in the
emergence of long range correlations organized about a
small set of preferred deposit sites: The system is displaced
from equilibrium.
o
......
....
I
/:..-"
,J 1"\
-----
.-tl~~-"
_/
. . . - INSECT TRAJECTORIES
EQUIPOTENTIAL LINES
_
DIFFUSION GRADIENT
Figure 4: Development of preferred sites. The development of a preferred site marks a sudden
transition in the correlational state of the insect population. As the size and number of preferred sites
increases correlations begin to develop among the insects' external coordinates of motion. The insect
behavior is no longer at equilibrium (independent of one another), it evolves into nonequilibrium states
exhibiting increased correlations (adapted from Kugler & Turvey, 1987).
4.1.4 Development of Saddlepoints and Arches.
A new phase begins with the emergence of long range correlations distributed over
two pillars. resulting in the construction of an arch (see Figure 5). Interactions of the
diffusion streams from the tops of two pillars create a saddlepoint at the midpoint (see
Figure 6). The saddlepoint is constructed out of a bifurcation of two one~dfmensional
insets (flow streams originating at the tops of the pillars), into a single twodimensional outset (a planar flow orthogonal to the insets. see Figure 7). An insect
entering the pheromone field via the planar outset is gUided by an increasing gradient
leading into the saddlepOint. Once at the saddlepOint. there are two orthogonal routes
out of further increasing gradients that lead directly to the inner edge of the tops of the
two pillars. A fluctuation at the saddlepoint determines which route the insect follows.
The significance of the saddlepoint is that it introduces a symmetry-breaking
mechanism for biasing deposits away from the center of the pillar. The result is the
construction of an arch that curves upward toward the saddlepoint. It is an analogue
solution to a catenary problem.
Kugler &
Turvey
225
Assumption: Cooperatwn and competUwn between field
processes (reversible and irreversible) result in the
emergence of a finUe number of converging and diverging
flow regions) originating and terminating in critical states
.(singular points) saddlepoints) etc.)•
....-- DIFFUSION GRADIENT
Figure 5: Building a pillar (adapted from Kugler &: Turvey, 1987).
-
OIP'USION GRADIENT
- - . INSECT FLIGHT PATH
Figure 6: Building an arch. The emergence of the saddlepoint further displaces the system from
equilibrium. The organizing influence of the saddlepolnt extends the insect correlations to a region
defined over the two pillars (adapted from Kugler &: Turvey, 1987).
Self Organization, Flow Fields, and Injormiltion
226
MACRO
(INSECT PATH.
INSET PLANE
OUTSET LINE
MICRO
(DIFFUSION PATH.
OUTSET PLANE
INSET DEFINES A
1 DIMENSIONAL FIELD
OUTSET DEFINES A
2 DIMENSIONAL FIELD
INSET LINE
•
•
PILLAR
SINGULARITIES
VIRTUAL SADDLEPOINT
Figure 7: Macroscopic and microscopic perspectives on the inset and outset flows that define the
saddlepoint (adapted from Kugler & Turvey, 1987).
4.1.5 Construction of a Dome.
The completion of the arch is associated with the coalescing of the two pillars at the
saddlepoint. The result is the annihilation of the saddlepoint and the emergence of a
single attractive critical region on the top of the arch (see Figure 8). The gradient flows
emanating from the new singular region interact With neighboring gradient flows
resulting in the emergence of an intricate pattern of saddlepoints. These saddlepoints
organize a gradient layout that constrains the construction of a dome (see Figures 9 and
10). Upon completion of the dome the nonequilibrium phases end and a new
construction cycle begins. starting with the random equilibrium deposit phase (see
F1gure 11).
Assumption: Actions of complex systems are assembled out
of reversible (gradient.independent) and irreversible
(gradient·dependent) transport processes that compete for
spatial and temporal boundaries-that is the action has well·
defined spatial and temporal boundaries, for example,
beginnings and endings, births and deaths.
Kugler 6' Turvey
227
---+
-
INSECT FLIGHT PATH
DIFFUSION GRADIENT
-
EQUIPOTENTIAL LINES
Figure 8: Completion of the arch and annihilation of the saddlepoint (adapted from Kugler &: Turvey,
1987).
_
EaUIPOTENTIAL LINES
DiffUSION GRADIENT
,.-") SADDLEPOINT REGIONS
~
..... _"
Figure 9: Emergent saddlepoints are used to build a dome (adapted from Kugler &: Turvey, 1987).
~lf
Organization, Flow Fields, and Information
228
Figure 10: Development of a dome (adapted from Kugler &: Turvey,1987).
- - . INSECT FLIGHT PATH
II'"
EQUIPOTENTIAL LINES (
_
DIFFUSION GRADIENT
.....
Figure 11: Upon completion of the dome the building phase returns to equilibrium, beginning once
again with the random flight phase (adapted from Kugler &: Turvey,1987).
4.2 Perception-Action Cycle: An Execution-Driven Self-Reading and SelfWriting System
.
The behavior of the insects both contributes to and is constrained by the structural
properties of the pheromone field. Insects contribute to the pheromone field through
their frequent deposits. They act as thermodynamic pumps that create and maintain
chemical potential reservoirs. These potentials generate diffusional patterns that. in
tum. constrain the depository activities of the insects. In this regard the evolVing
Kugler & Turvey
229
insect nest is exemplary of a self-reading and self-writing system. The insect behavior
gUided by (in the sense of self-reading) and a contributor to (in the sense of selfwriting) the structure of the pheromone field. There is a circular causality of the
follOwing kind: force field (muscular activity)-> flow field (pheromone control
constraints)-> force field (muscular activity)-> flow field (pheromone control
constraints)-> ... and so on. which can be described alternatively as an action-->
perception--> action--> ... and so on. cycle (see Figure 12).
is both
(
FLOW FIELD\
ACTION
PERCEPTION
(high-energy coupling)
(low-energy coupling)
FORCE FIELD)
Figure 12: Perception/action cycle. A circular causality of self-assembled flows and forces (adapted from
Kugler & Turvey, 1987).
While the cycle is closed in terms of complementary forces (kinetics) and flows
(kinematics), it is open in terms of the properties that constitute the descriptors that
can emerge from interactions. New informational primitives for nest-building can
arise in the force-> flow-> force . . . cycle. Nest-building is a self-complexing
phenomenon that is driven by the expedient behavior of the insects coupled to the
dissipative behavior of pheromone flows. In the (self) organization of this system
future states are more dependent on the system's current configurational states than on
prior (stored) states. Only crude initial conditions are reqUired to initiate the process;
once started. the process becomes parasitic upon. and driven by, reactlon-dUIusion
processes. The only "memory" requirement is of the Simple expedients. These identify:
(a) the chemical affinity to the pheromone and (b) the termination point at the highest
concentration.
Assumption: A Perceiving-acting system is an executiondriven nonlinear, open flow system in which future states
are more dependent on current configurational states than
on prior stored states.
Self Organization, Flow Fields, and Information
230
4.3 A Self-organizing Ring of Modes
The insect nest-building example defines a closed periodic orbit of macroscopic
organizational modes. The closure is a function of a "ringing together" of a succession
of symmetry-breaking instabilities that begin and end with a random (equilibrium)
phase. This succession of symmetry-breaking instabilities exemplifies the
developmental sequence of a self-organizing system.
The closed cycle of building modes is associated with the creation and annihilation
of critical regions (Singular states) in the topology of the diffusion field. Each
topologically distinct layout of Singularities ("morphologies") is associated with a
qualitatively distinct, macroscopic mode of organiZation (see Figure 13). These
macroscopic flow morphologies provide a lOW-dimensional informational description
that can be used to constrain a high-dimensional actuator system (e.g.• millions of
individual insect actuators). The result is the emergence of an efficient. self-organizing,
controllable system (see Figure 14).
Assumption: The set ofsingular states provides a lowdimensional, control space description that can be mapped
into a high-dimensional machine space description (e.g.,
neuromuscular) to form an efficient controllable system.
Figure 13: Circular ring of building phases. Each phase is dominated by a small set of critical
(degenerate) states that organizes the chemical flow fields. These flow portraits provide the control
constraints that orient the insects' motions (adapted from Kugler & Turvey, 1987).
Kugler & Turvey
231
INSECT'S BEHAVIORAL
FORCE FielD
MACROSCOPIC
INSECT
BEHAVIOR
REPLENISHES
PHEROMONE
SOURCE
<
C%~lSI
FLOW FIELD GEOMETRY
PROVIDES INFORMATIONAL
J-~
CONSTRAINTS TO GUIDE
~Q
INSECT BEHAVIOR
(t'~Q
~'tf
~
~~Cl
0"
'~
MICROSCOPIC
~Q
PHEROMONE
FORCE FielD ---------.....;.~
DISSIPATIVE FORCE
FielD DEFINES A
fLOWflELO
GEOMETRY
PHEROMONE
FLOW FielD
Figure 14: Self-organizing information system (adapted from Kugler & Turvey, 1987).
5.0 CONCLUSION: IRREVERSIBILITY AND SELF-DRGANIZATION
At the start of this century, following in the tradition of Newton's mechanics,
physical scientists were almost unanimous in proclaiming that the fundamental laws
of the universe were deterministic and reversible-doctrtne of mechanism-and that
there was a fundamental set of state descriptions (measurable properties) that applied
across all spatial and temporal scales-doctrtne of atomism. Events that did not satisfy
these conditions were viewed as exceptions, mere artifacts of random events, and were
accounted for by invoking positions of ignorance or lack of precise control over
individual vartables. By the middle of this century, however, the role of deterministic,
reversible laws and their associated state descriptions were being viewed as having
applicability only at very macroscopic and very microscopic scales. Strictly
conservative processes were being ruled out as detailed investigations revealed a wide
range of dissipative processes influenCing behavior at most middle range scales of
analySiS.
Traditionally, the role of these irreversible processes has been viewed as a destructive
agency that wears down organizational states. The phenomena of self organization and
self preservation have been viewed as islands of resistance against the inevitable
destructive action of the second law, their persistence requiring the intervention of
some extra physical Maxwellian demon. In the domain of biological and psychological
phenomena, self organization and self regulation are intimately tied to the problem of
controllability. The challenge to physical biologists has been the identification of a
principled account of the origin and evolution of the control constraints without
reaching outside the framework of the system to introduce a Maxwellian demon to
derive the answer: No deus ex machina. no elan vitaL no smart internal element is to be
invoked as an explanatory construct. It is becoming increasingly evident that an open
system displaced from equilibrium can develop new macroscopic constraints capable
of harnessing temporarily the atomistic dynamiC so as to form an efficient. selforganizing, controllable system. Most importantly, the mechanisms underlying the
origin and evolution of the macroscopic (control) constraints are intrinsic to the
Self Organization, Flow Fields, and Information
232
dynamics of the system and follow directly from an active participation of the second
law of thermodynamics.
ACKNOWLEDGMENT
The writing of this paper was supported. in part. by a Visiting Faculty Research
Fellowship at the Armstrong Aerospace Medical research Laboratory awarded to the
first author, and a James McKeen Cattell Fellowship awarded to the second author.
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FOOTNOTES
-Human Mcroement Science, in press. (Special Issue: Self organization in human movement systems)
+university of Dlinois
ttAlso, Center for the Ecological Study of Perception and Action, University of Connecticut
lTo aid in deconstruction of the various theoretical frameworks (mechanical, thermodynamical, etc.),
modeling assumptions will be explicitly identified whenever invoked.
2While it is possible, in principle, to describe the motion of the N-body states and their evolution using
the laws of mechanics-summing the elementary units of two-body interactions and pendular
rotations-the complexity and number of resulting equations make a direct analytic attack on the
problem intractable. The enormity of the task can be appreciated by considering the N-body system
comprising an ideal gas: A computer printing out only the initial positions and velocities of the
barycenters of the molecules in one mole of the gas at a rate of 300 coordinate pairs/second would
require a duration of time on the order of the squared estimated age of the universe.
Self Organization, Flow Fields, and Information