- Email: [email protected]
Self-organization, flow fields, and information
Human Movement North-Holland
Science 7 (1988) 97-129
97
Peter N. KUCL University
of Illinois, Urbana, USA
M.T.TURVEY University of Connec:icut, Storm, USA, a,;d Haskins Jaboratories, New Haven, USA
ugler, P.N. and information.
.T. Turvey, 1988. Self-qanization, ovement Science 7, 97429.
flow fields, and
A construct for self-organizing information systems is outlined that requires (i) an ensemble of loosely constrained subsystems, (ii) an openness to external flows, and (iii) low energy field couplings among subsystems. The pattern of interaction between the subsystems can vary as a function of the amount of external openness. If the openness is small, the subsystems relate according to local linear laws. As the openness is increased, the linear relations break down and are replaced by global nonlinear relations, resulting in the emergence of large-scale patterns among subsystems. A single control parameter (regulating external openness) can be used to assemble and disassemble organizational states among subsystems, forming an efficient, selforganizing, control system. The principles of self-organization are illustrated in the context of nest building behavior by social insects. The organization of insects is sustained by a low energy pheromone diffusion field. Under open conditions a cascade of bifurcating diffusion patterns emerges that organizes the insects. The causal potency of these macroscopic patterns are discussed in terms of a realist’s theory of information.
A fundamental problem in the study or biologica; systems is the transition from disordered to ordered states. From a physical perspecow does z uniform tive the problem can be stated as follows: distribution of matter, obeying standard physical principles (laws of conservation of momentum, energy, and matter) develop spontaneously * The writing of this article 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. Correspondence address: P.N. Kugler, Dept. of Kinesiology, 113 Freer Hall, 906 S. Goodwin Avenue, University of Illinois, Urbana, IL, USA.
OI67-9457/88/$3.50
0 1988, Elsevier Science Publishers
B.V. (North-Holland)
98
B.IV. Bugler, M. T. Turvey / Self-organizing information systems
a fn~nutifr;)m distdmhn? Identification of the necessary car ditions ng transformations responsietry-bre for the occurrence of the sy is the fundamental goal of a physical theory ble for the nonunif~ fines what might be termed ‘the problem of of self-organization. origin’. curs in systems composed of multiple subsystems Self-organrzation w of energy, matter, and/or information. Under when opened to these open con ns nonlinearities can develop among subsystems leading to the emergence of (a) sharp or subtle transitions between states, (b) fluctuation-induced instabilities, qualitatively differ erm_inistic dynamics. r (c) ch>ic, hsugh ‘openness’ to conservational flows is a necessary condition for the transi%icn to endent on initial condititins determined externally, and ne er is it derived from any ‘smart’ internal subsysseparates the amount of order exhibited in the inputs and the internally stored states from the amount of order revealed in behavior, is e hallmark of self-organizing systems. r-pose of this c pter is to protide an elementary overview of cal strategies underlying self-organization, and to identify their connections with traditional pects of classical physics, such as Newtonian mechanics and therm0 namics. The strategies in question apply to both simple physical systems - where subsystem interactions etic (force) Ii ages - and complex biological s are dominated ‘by nonkinetic (kinematic, geometric, ages. Of particular interest is a anical systems whose self-motion is powered by interok In these systems energetic flows cross the system’s external boundary an are converted into useful work cycles through internal thermodynamic processes. egulation of these work cycles (such as locomotion, manipulation, ing, fighting, feeding, reproducing, etc.) is through a circular mapping of low energy (kinematic, ages into hi&r energy, force generating actucoupling of a low energy linkage with a force generating actuator can lead to a cascade of symmetry-breaking instabilities and the sub uent emergence of new cooperativities among subsystems. The re is the formation of an execution-driven, selforganizing, control system.
P.N. Kuglei; M. T Turvey / Self-organizing information systems
sica
99
es
2.1. Cfassical (Newtonian) mechanics 2.1.1. Doctrirze of simple (isolat24) atomisms
The search for a fundamental level of description for modeling behavior has been one of the principle objectives of physics. From thcr; perspective of classical (Newtonian) phvsics 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 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 jcatures. The inventory of invariant features defines a simple atom&m (see Iberall 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 turn, 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 dynamics of these elemental units, echoing throughoui the system with perfect fidelity, determines all observable (macroscopic) phenomena. The assumption uf 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 nce an atomism is identified, the (superatomistic and subatomistic).
100
P. N. Kugier, M. T. Turvey / Self-organizing information systems
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. n order words, no spatial or temporal boundaries can be assembled that segregate locally, or isolate, the ynamic from the micro d namic. Under these conditions a tion cannot be ‘forgotten’. n this classical approach to analynce a system is bounded, above or below, sis there is no moderation: nduced into the system that originates outside the nce a set of initial conditions are specified, its for eternity with no possibility for new signatures. cannot self-organize. his is the ‘doctrine of atom-km’, and interpretation of isolated systems. ewton’s mechanics program. Assumption.
ounded or isolated from external interactions e rise to new dynamic regimes: No new laws e that govern the behavior of the system at a privileged scald or region of the state space. *
octrine of mechanical (temporal) reversibility ne of the basic characteristics of trajectories defined by Newton’s master equation ( ty, No distinction is allowed between fut change in the sign of the e results in no change in the solution, that is, the equation mmet,ric with respect to time inversions. namic defines cha ges such as t -+ -t, time inversion, dnd E -+ - v, velocity inversion, as tiquivalent mathematiat one dynamic change achieves, szlch as time inversion, namic change, such as velocity i vf:rsion, can undo, and in this way restore the initial condition. ur daily experience with natural events counter to the notion of mechanical reversibi burning match never reverses itself, retur phase; a rop of ink in water always s ’ Ta aid in deconstruction of the various frlrmcworks (mcchnnicu%, thsrmodynumictrl, modeling assumptions will be explicitly identified wi~cncvcr invoked.
crrc~.)
P. N. Kugler, M. T. Turvey / Self-organizing informatron systems
101
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. Assumption.
All mechanical events are temporally reversible, for example, they do not distinguish historical beginnings from endings, births from deaths.
21.3. Doctrine of force (kinetic) interactior\w 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 atomisms. ?‘he 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 ~~r;l&tions the idealtification of all the velocities and displacements of aI1 atomisms at a sin instant of time allows for the e ifiication of all states of the
transformations
to
102
P. N. Kugler, M. T. Tumey / Self-organizing informatim systems
2.2. Reversible (equilibrium) ajzd irreversible (nunequilibrium) thermodynamics 2.2. I. 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 t e solar system (classical and relativity mechanics), subatomic particles (electrodynamics), and nuclei (chromodynamics). n be considered as descriptions of static All of these constructs machines, obtained by a ng together components in equilibrium (i.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 hile an atomistic (imicroscopic) perspective of a N-body system reveals a microcosm of unending motion, with every atom&m 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 . there is a homeomorphic mapping that relates a single macro state to multiple micro states. These macroscopic bookkeeping metrics constitute the thermodynamic variables for a system at equilibrium. Equilibrium thermodynamics is the study of laws that relate macroscopic (phenomenological) descriptions of atomistic systems under 2 While 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. ‘I’he 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/set would require a duration of time on the order of the squared estimated age of the universe.
P. N. Kugler, M. T Tumey / Self-organizing information systems
103
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 uctive passage from two bodies to N bodies was considered legitimate, even though the only rigorously solved problem was the two-body t 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 Schuster 1984; Cvitanovic 1984). Assumption.
A small number of mean (statistical) macro states map homomorphically onto many micro states.
22.2. Irreversibility
as an improbable event in an isolated system
is an empirical fact that an isolated system (e.g., closed to external flows) evolves irre .,rsibly rp 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. ecause 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. nce at equiiibrium, events no longer exhibit hisnd endings, births and deaths, since the path torical beginnings between the two states is, once again, reversibJe temporally. hen confronted with the identification of the mechanism responsible for the origin of the initial conditions that displaced the system away froAmequilibrium, 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, It
.
104
P. N. Kugler, M. T. Turvey / Self-organizing information systems
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 temporal direction to events (future or past). T thermodynamics states that the entropy of an isolated system will increase with time until it achieves asymptote as the equilibrium state, nce at equilibrium, the entropy at which time the entropy is constant. of an isolated system never decrease pontaneously, 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 terms of the organization of molecular motions, and by showing, after Boltzmann, that this increase corresponds to progressive disorganization and an evolution towards 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 law, the production of entropy is associated with a process conserved entities over available degrees of freedom. second law is viewed as a distribution process that always operates 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 is viewed traditionally as a process operatin against the theory of (organizational) evolution. he temporal evolution of the distribution process, while undefina= t the level of mechanics, can be assigned a direction, a2 historical beginning and ending, at the level of thermodynamics. The direction is assigned in terms of the entropy function. The introdusa,ron of entropy in?‘0 macroscopic descriptions makes it impossible to reduc scopic thermodynamic descriptions to purely mechanical des
echanical reductionism is forever doomed to analytical incompleteness for all systems exhibiting irreversible processes. An irreversible, macroscopic, description cannot be reduced to a reversible, microscopic, description.
Assumption.
2.2.;.
Equilibrium and nonequilibrium (linear) force laws: 1 -I- 1 = 2
regions defined by microscopic
Irreversible flows near equihbtium express an important property, captured by the principle of minimum dissipation. This principle was formulated first by nsager (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 according 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 minimize the rate of entropy production are driven by forces that are linear, weak, and l%ited 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 pat terns. Near equilibrium the forces that drive the flows relate linearly in terms of additive constants.
Assumption.
2.2.5. Nonequilibrium
regions defined by macroscopic (nonlinear) jorce
laws: I -I- 1 + 2
In the region of the linear force laws (near or at equilibrium), the system responds to perturbations and/or fluctuations with small adjuskments 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
106
P. N. Kugler, M. T Twvey / Self-organizing information systems
sufficiently far from equi force laws. These new force global thermodynamic po nonuniformities in their scopic force laws can res for example, time-depen As noted, the macrosc system is displaced furthe scopic force laws actively c driven toward system moves into a regi the attractiveness of the (
nonequilibrium attractor, its tion away from thermody the system to evolve in the
n this far from equilibriu
e same manner atomisms. And, most imp certain degree of autonom scopic laws, even though scopic laws. In sum, the m constraints that act as bou that is, the macroscopic laws the simple atomisms.
re replaced by new nonlinear, s are defined macroscopically relative to 1s that arise as a function of large scale butional configurations. These macrothe emergence of a patterned dynamic, nd/or spatially-dependent regimes. force laws come into existence as the equilibrium. In this region the macroete with the microscopic force laws. As influence the dynamic, the system is states. Starting from an initial near ated by the equilibrium attractor, the ynamic is no longer organized by mic) equilibrium state. Instead, its veness of a nonequilibrium (therr away from the equilibrium state. Once nated by the influence of the olutionary trajectory moves in the direcc equilibrium. The emergence of the ral tendency for the dynamic of ction of increasing order. An intrinsic s suddenly the previously dominant region, the new macroscopic laws thatt obal constraints that harness the microratomisms (fluid cells, flow units, and the microscopic laws act on simple ly, these macroscopic laws have a sovereignty with respect to the microemerge from the actions of the microscopic laws define the dynamic for the conditions 3n the microscopic laws s e as dynamic boundary conditions for
Assumptien. In systems ted far from equilibrium there is a thermodynamic region in the hegemony of the weak, local (microscopic) linear force laws breaks down and is replaced by the hegemony of strong, global (macros _;cfopic) nonlinear force laws. .
P. N. Kugler, M. T. Turvey / Self-organizing information systems
107
2.2.6. Order through j7uctuations 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 breakdown of the linear force laws. As a system approaches the region where the local force laws breakdown 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 (Prigogine et al. 1972) have referred to this phenomenon as order through fluctuation. Assumption. Fluctuations comprise seeking out new stable regimes.
an exploratory
mechanism
for
2.27. A selection principle for nonequilibrium 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. n one side of the local maximum, forces are organized so PS to dri the system in the direction of thermodynamic equilibrium. On the other side 01 the maximum, the forces tend to drive the system away from therm namic equilibrium in the direction of increasing organization. differently, on one side of the critical point (local maximum) the behavior is influenced by local thermodynamic potentials, on the other side, the behavior is influenced by global thermodynamic potentials. Crossing the critical point involves a shift in the scale of the laws that dominate the structuring of the forces organizing the flow patterns: On one side of tne maximum, microscopic (potential) laws apply, on the other side, macroscopic (potential) laws apply.
108
P. N. Kugler, M. T. Turvey / Self-organizing information systems
t or near the transitional boun ary a fluctuation can drive the system over the maximum; beyond this local maximum the self-damping tendency of t e particle’s motion is replaced by a self-amp ith aamplification of fluctuations, the system’s entropy o longer identifies a minimum (as prescribed by the principle of minimum entropy production). The stability of the ampliowever, is guaranteed lo fying tEljeCtOly, excess entropy o&action function (see he instability is slowe uction attams a new production halting finally as the entropy local minimum. ath from one dyna stability of tl next is a funct of the rate of of entropy pr the path minimizes the excess entro production. ssumption .
regime to the tion - that is,
enard and Taylor instabilities A convection insta ility, first identified in 1901 by the French 9 provides an example of how the instability of a se to a self-organizing process (see Koschard instability is due to a vertical temperaliquid layer is heated fro onstant, cooler temperatu at flux (temperature differential) is estabcture that tends to push the fluid’s cooler upper surface. The convective olecules is resisted by internal friction that dissipates mechanical energy en the thermal gradient is small, only heat energy is conducte radient; the molecules remain local, their motions restricted by local dissipative processes. hen the imposed gradient reaches a t shold value, the liquid’s state of rest - the stationary state in h heat is conveyed by conduction (thermal transport without mass transport) - becomes convection (mass transport) corresponding to the coherent nsembles of molecules is produced that increases the rate of heat transfer. As the critical value of heat transfer is approached (i.e., perature), the entropy production of the system identifying a mini m as prescribed by the theorem of ‘minimum entropy production. uring the transition the
P.lV. Kugler, M. T. Turvey / Self-organizing infvmation
systems
109
stability of the system is defined locally by the minimum of \he excess entropy production function - instead of the entropy pduction function (see Glansdorff and Prigogine 1971). The Taylor instability occurs when fluid is trapped betkJeen C-.*o cylinders rotating in opposite directions. The fluid is caused to rotate by the 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 cylinder. 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 order of 10S8 sm. 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) sy.mmetry is referred to as a symmetry-breaking
instability.
2.3. Prigogine’s theory of dissipative structures ‘ Classical thermodynamics was associated.. . with the forgetting of initial conditions and rhe destruction of structure. We have seen, however, that there is another macroscopic region in which, within the framework of thermodynamics, structure may spontaneously appear.” (Prigogine 1980: 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-: ange interactions can develop bet-ween groups of subsystems. The creation and annihilation of the long-range i.nteractions, e.g. symmetry breaking instabilities, are sustained principally by entropy producing, irreversible, processes. Prigogine (1957) has termed these long-range organizations dissipative
P. N. Bugler, M. T. Tumey / Self-organizing iMf~~~~~~ SJW
structures
in reco
tion of the centr
F-&Spublished by Springer; Neil1 et al. 1986; Ulanowicz I
3.1. Complex (open) atomisms
nerates constraints that can curt reducing the degrees of among the atomisms, acco
is not accounted for full tonomy. 3.2. Self-sustaining (open) atomis
interior, and from the a
ternal forces, the r&3 of relevant fcr ~~~t~~n~ , are the fundamental
ative to extern
sms and complex atomisms as
ay be, in fact, the
TPsystems am-3simple ones is, by its very nature, without a what we p~esentiy understand as “physics” is seen in this le systek. The r&don between physics and biology is thus not at to the particukzr; in fact, quite the contrary. It is not biology, but We can see ~TFCMII this perspective that biology and physics (i.e. as two divergent branches from a theory of complex systems sed only very imperfectly.’ (Rosen 1985: 424)
ded scientist has been pfanatory accounts of biological sysqua1 importance, is the e associated with massphysical pursuit of this latter challenge descriptions and puts challenge was anticursuit of a kinematic eed and Jones 1982). d functional significontinuous with the and Turvey 1987). a natural transition can be descriptions, nonmass field on to a theory of
114
P. N. Ku+-,
M. T. Turvey / Self-organizing information systems COMPLEX (BIOLOGICAL)
ATOMISMS
Fig. 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 therrnodyntic work cydes. In a complex atomism the role of the mass dimension is less relevant. in the dynamic description that suatalis the mteractions between simple atomisms. What remains relevant are the fundamental dimensions of length and time (see table I). 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 external force fields (adapted from Kugler and Turvey 1987).
Table P The field descriptions are macroscopic. They do not include microscopic descriptions such as charge, spin and other attributes of interaction at the electromagnetic and quantzn scale (adapted from Yates and Kugler 1984). LEVEL OF ABSTRACTION KINETIC
(M,L,T)
MACRO
FORCE FIELD
MICRO
FORCE
‘)
KINEMATIC FLOW
b
FIELD
GEOMETRIC SPATIAL
FLOW
ALTERNATIVE
Descriptions
Dimensions
a Kinetic (Newtonian
,L T
mechanics) b Kinematic
(L,T)
L, T
(L) b
TEMPORAL SPECTRAL
FIELD
SPATIAL
Properties Forces-violent interaction; conservations such as mv’, mv’, mv2; symmetries; potentials; singularities,
X, X phase space
Nonviolent
interactions;
singularities;
constraints;
symmetries;
X, X phase space
forms, boundary
’ Geometric
L
Geometries,
d Temporal
T
Spectra, frequencies;
functions
FIELD
SPECTRAL
FIELD DESCRIPTIONS
constraints;
(T) ”
conditions
P. N. Kugler, M. T. Turvey / Self-organizing information systems
115
self-organizing ‘information systems’. (For extended discussions by the authors on the topic of self-organizing information systems see Kugler et al. 3980, 1982; ugler 1986; Kugler and Turvey 1987). Assumption.
Interactions 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.
4.1. 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. ynamic 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). nest construction by social insects is presented to illustrate nonkinetic (flow field) linkages in self-organization. The insects of interest are social termites that periodically construct nests that caiil;0I c +-a A:* 20 feet in height and weigh upwards of 10 tons, and which involve the active participation of more than 5 million 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 conpts expressed in the example are derived from Grasse’s (1959) and insma’s (19’137) uralistic observations and a thermodynamic treatneubourge (1977). ment advanced by The control constraints that organize the building activity arise 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 is open to the causal force -+ flow --) force -+ . . , information loop emergence of creation (and annihilation) of field discontinuities. these discontinuities results in a cascade of symmetry-brea’lcing instabil-
116
P. N. Kugler, M. T. Turvey / Self-organizing information systems
ities with the subsequent emergence of cooperative nest building phases ( see ugler and 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 nest-building process are discussed below beginning with the role of percepiclal thresholds. eptual thresholds eromones injecte throughout the site accordi
mmetry-breaking mechanisms into the building materials diffuse ick’s law (rate of transport is linearly a gradient. An insect flying into the radient if the gradient exceeds the insect’s s threshold is a symmetry-breaking mechasect’s activity space into (a) gradient-depenwhere the insects are influenced by the diffusing es, and (b) gradient-independent regions, where the insects enced by the diffusi g phero,mones (see fig. 2). The former are regions of reversibility and the latter are regions qf irreversibihy. he partitioning of the space into reversible and irreversible regions is continuous with the classical theory of dynamic processes (see Kugier 1986). ssumption. The thresholds (nonlinearaties) that characterize percep-, tion-action couplings are symmetry-breaking devices that partition (categorize) d iontrol s ace into regions of reversibility and irreversib&= ity. andom deposit phase e earliest phas f nest building the insects’ depositing behavior is random (see fig. 3). ere are no pheromone gradients strong enough to influence the insects’ 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 hi t concentration identifies a critical (singular) region. en only a few insects are participating in the depositing activity, the pheromone concentration remains low and has very little orienting influence on the insects. he majority of the building sites define regions of reversibility, and the jnsects, as an ensemble, are at equilibrium. If the number of insects remains low, then the system will
P. N. Kugler, M. T. Turvey / Self-organizing information systems
DlFFUSlON -
117
FIELD
EQUIPOTENTIAL
LINES
WSECT FLIGHT PATH
Fig. 2. ‘Perceptual limit’ of the field defines a symmetry-breaking mechanism. Insects in areas where the pheromone gradient falls below the perceptual limit exhibit 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 and Turvey 19873.
remain at equilibrium, resulting in an extended period of random depositing. During this phase no long range correlations develop among participating insects. A ssumptisn .
hen the number of insects participating in nest building is small the individual motions are uncorrelated, and the system is at equilibrium.
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 time, 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 turn make the site even more attractive, defining, thereby, an autocatalytic reaction. As the gradient region amplifies, and long-range correlations begin to the insects, the corresponding insect organization develop amon
118
P.N. Kugler, M. T. Twuey / Self-organizing information systems
0
INSECT DEPOSIT (DIFFUSED) INSECT DEPOSIT (ACTIVE) li.SECT IN% 7T FLIGHT PATH PERCWTUAL
FIELD LIMIT
EQUIPOT
LINES
:WADIENT
SINGULARITY
_
Fig. 3. Ra;ldom flight phase. The behavior of the insects is at equilibrium dunng this phase - e.g., of each insect is independent of other insects, there are no long-range correlations the between the motions of insects (adapted from Kugler and Turvey 1987).
becomes displaced from equilibrium (see fig. 4). The onset of long-range correlations marks the end of the equilibrium phase, and the beginning of a succession of nonequilibrium phases. The first nonequilibrium phase involves the construction of pillars (see fig. 5). As the number of insects increases, the depositing behaves autocatalytic resulting in the emergence of long range correlations organized about a small set of preferred deposit sites: The system is displaced from equilibrium.
Assumption.
evelopment of saddlepoints and arches phase begins with the emergence of long-range correlations distributed over two pillars, resulting in the construction of an arch. nteractions of the diffusion streams from the tops of two pillars create a saddlepoint at the midpoint (see fig. 6). The saddlepoint is constructed out of a bifurcation of two one-dimensional insets (fbw streams originating at the tops of the pillars), into a single two-dimensional outset (a planar flow orthogonal to the insets, see fig. 7). An insect entering the pheromone field via the planar outset is guided by
PN. Kugler, A4.T. Turvey / Self-organizing information systems
119
Fig. 4. Development of preferred sites. The development of a preferred site marks a sudden transition in the correlational state of the insect poptdation. 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 and Turvey 1987).
an increasing gradient leading irto the saddlepoint. Once at the saddlepoint, there are two orthogonal rcxrtes 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. Assumption. Cooperation and competition between field processes (reversible and irreversible) result in the emergence of a finite number of converging and diverging flow regions, originating and terminating in critical states (singular points, saddlepoints, etc.). 4.1.5. Construction @ 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
120
P.N. Kugler, ii4. T Turvey / Selforganizing
information systems
Fig. 5. Building a pillar (adapted from Kugler and Turvey 1987).
saddlepoint and the emergence of a single attractive critical region on the top of the arch (see fig. 8). The gradient flows emanating from the new singular region interact with neighboring gradient flows resulting in the emergence of an intricate pattenr of saddlepoints. These saddle-
Fig. 6. Building an arch. The emergence of the saddlepoint further displaces the system from equilibrium. The organizing influence of the saddlepoint extends the insect correlations to a region defined over the two pillars (adapted from Kugler and Turvey 1987).
P. N. Kugler, M. T. Turvey / Se/f-organizing infomation systems
121,
MACRO (INSECT PATH) INSET PLANE
SIONAL FIELD /
OUTSET LINE MICRO (DIFFUSION
PATH)
OUTSET Pd.;?‘-c _ INSET DEFINES A I DiMENSIONAL FIELD OUTSET DEFINES A 2 DIMENSIONAL FIELD
/ INSET LINE
PILLAR SINGULARITIES VIRTUAL SADDLEPOCNT
Fig. 7. Macroscopic and microscopic perspectives on the inset and outset flows that define the saddlepoint (adapted from Kugler and Turvey 1987).
points organize a gradient layout that constrains the construction of a dome (see figs. 9 and 18). Upon completion of the dome the nonequilibrium phases end and a new construction cycle begins, starting with the random equilibrium deposit phase (see fig. 11). 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 deat
Assumption.
4.2. Perception-action writing system
cycle: An execution-driven
self-reading aizd s#f-
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 de osits. They act as thermodynamic pumps the create and maintain chemical potential reservoirs. These potentials generate diffusional patterns that, in turn,
122
P. N. Kugler, hi. ‘T. Turvey / Self-organizing information systems
INSECT FLIGHT PATH DIFFUSION GRADIENT EQUWOTEMTIAL LINES
Fig. 8. Completion
ewlving
of
the arch and annihilation of the saddlepoint Turvey 1987).
(adapted
from Kugler and
ository activities of the insects. In this regard the insect est is exemplary of a self-reading and self -writing he insect behavior is both guided by (in the sense of self- read-
Fig. 9. Emergent saddlepoints
are used TVbuild a dome (adapted from Kugler and Turvey 1987).
P. N. Kuglep, M. T Turvey / Sey-organizing information systems
Fig. 10. Development
of a dome (adapted
123
from Kugler and Turvey 1987).
Fig. 11. Upon completion of the dome the building phase returns to equilibrium, beginning again with the random flight phase (adapted from Kugler and Turvey 1987).
once
124
P.N. Kugier, M. T. Twvey / Self-organizinginform&on system
upling)
(high-
Fig. 12. Perception/action
cycle. A circular causality of self-assembled from Kugler and Turvey 1987).
flows ad
control constrain
tively as an action
and flows (kinematics), constitute the
it is open in terms of t
e only ‘memory’ re
ssumption .
perceiving-acting syste linear, open flow system in ch future states are mo current configurational states than on prior stored states.
forces (adapt
ese maerose
e resdt is the e system (see fig. 14).
ence of an efficient,
g phases. Each phase is dominated by a small set of critical the chemical flow fields. These flow portraits provide the the insects’ motions (adapted from Kugler and Turvey 1987).
126 INSECT’S t3EHAV ‘IORAL FORCE FIELD
a_
PHERQh’lONE FORCE FIELD
Fig. 14. Self-organizing
DlSSlPATlWE FORCE FIELD DEFINES A FLOW FIELD
information
system (adapted
ns were
~ewe
from Kugler and Turvey 1
M. T. Turuey / Se~-~~~a~~zing information systems
127
ble processes was viewed as a ational states. The phenomtion and self-preservationwere viewed as islands of inevitable destructive action of the second law, of some extra physical of biological and psychological intimately tied to the physical tioiogists has cipled account of the origin and out reaching outside the framedemon to derive the art internal element is construct. It is becoming increasingly sptaced from equilibriumcan develop ts capable of harnessingtemporarily an ensemble n so as to form an efficient, self-organizing, controllable ly, the mechanisms underlying the origin and constraints are intrinsic to the dynamics of the directly from an active participation of the second
G. Engelen
and
M. Sangher,
From
microscopic
amics & life: An introduction
to macroscopic
order,
to self-organization
Berlin:
of matter.
nequihbriurn statistical mechanics. New York: Wiley. 1977. An analysis of building behavior of the termite ‘rnacrotermes subhyalinus’. of the VIII Congress IWSSI, Wageningen. ed.), 1984. Universahty in chaos. Bristol: Adam Hilger. urge, J.L., 1977. AppIieation de l’ordre par fluctuation 5 la description de la construction du nid cbez Ies tern&s. Insectes Sociaux, Journal International pour I’Ctude des Arthropodes Sociaux 24,177. Gibson, J.J., 1950. The perception of the visual world. Boston, MA: Houghton Mifflin. Gibson, J.J., 1966. The senses considered as perceptual systems. Boston, MA: Houghton Mifflin. Gibson, J.J. 1979. The ecological approach to visual perception. Boston, MA: Houghton Mifflin. Glansdorff, P. and I. Prigogine, 1971. Thermodynamic theory of structure, stability, and fluctuation. New York: Wiley-Interscience. GoIdstein, H., 1958. Classiccal mechanics. Reading, MA: Addison Wesley. Grasse, P.P., 1959. La reconstruction du nid et les coordinations interindivuelles chez Bellicosies natalensis et cubitermes. La tt&xie de la stigrnergie: essai d’interpretation des termites
aaux 6,
constructems. Insectes Sociaux, Journal Jnternational pour 1’Ctude 127. 1975. Synergetics. New York: Springer. (ed.), 1981. Chaos and order in nature. New York: Springer.
In: 1. Prigogine and S.A. oschmeider, ‘Instabilities in fluid dynamics’.
d control, NATO Turvey, 1987. Information,
In:
natural
law, and the
movement. strUctUre.s as
urvey, ! 982. ‘On the control and lso and J.E. Clark (eds.), The d control and coordination. New York: Wiley. T. Turvey, C. Carello and R. Shaw, 1985. ‘The physics of t locomotion’. In: W. Warren and R Shaw @Is.), F Proceedings of the first International Conference on Event Perception, Nicolis, G. and I. Prigogine, 1977. Self-organization in non-equili.bti Wiley. M&hen: Piper-. Allen, 1986. A h.ierm ecosystem. Princeton, NJ: khaceton UXliVLiSit~Press. Qnsager, L., 1931. rocal reistions in irreversible processes. Physkal Prigogine, I., 1945. eration ek transformations n-reversibles des syste oy. Belg. Cl. Sci. 31, 600. ude thermodynamic des processus irr&ers~bles. troduction to thermodynamics of irreversible pa Kugler, P.N., J.A.S.
?., 1967. *Structure, . Amsterdam: Nort I., 1980. From bei
sipation
and life’. In:
rder out of chaos. N oyant& 1972. The 25, 23-28. eed, B. and R. Jones, 1982. Reasons for realism: Selected essays of James J. Gi 1978. Fundamentals
Academic
of measurement
and representation
sms as causal systems wh.i In: R. Rosen ted.), Theore Press. pp. 156-203.
of nat
Science 7 (1988) 97-129
97
Peter N. KUCL University
of Illinois, Urbana, USA
M.T.TURVEY University of Connec:icut, Storm, USA, a,;d Haskins Jaboratories, New Haven, USA
ugler, P.N. and information.
.T. Turvey, 1988. Self-qanization, ovement Science 7, 97429.
flow fields, and
A construct for self-organizing information systems is outlined that requires (i) an ensemble of loosely constrained subsystems, (ii) an openness to external flows, and (iii) low energy field couplings among subsystems. The pattern of interaction between the subsystems can vary as a function of the amount of external openness. If the openness is small, the subsystems relate according to local linear laws. As the openness is increased, the linear relations break down and are replaced by global nonlinear relations, resulting in the emergence of large-scale patterns among subsystems. A single control parameter (regulating external openness) can be used to assemble and disassemble organizational states among subsystems, forming an efficient, selforganizing, control system. The principles of self-organization are illustrated in the context of nest building behavior by social insects. The organization of insects is sustained by a low energy pheromone diffusion field. Under open conditions a cascade of bifurcating diffusion patterns emerges that organizes the insects. The causal potency of these macroscopic patterns are discussed in terms of a realist’s theory of information.
A fundamental problem in the study or biologica; systems is the transition from disordered to ordered states. From a physical perspecow does z uniform tive the problem can be stated as follows: distribution of matter, obeying standard physical principles (laws of conservation of momentum, energy, and matter) develop spontaneously * The writing of this article 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. Correspondence address: P.N. Kugler, Dept. of Kinesiology, 113 Freer Hall, 906 S. Goodwin Avenue, University of Illinois, Urbana, IL, USA.
OI67-9457/88/$3.50
0 1988, Elsevier Science Publishers
B.V. (North-Holland)
98
B.IV. Bugler, M. T. Turvey / Self-organizing information systems
a fn~nutifr;)m distdmhn? Identification of the necessary car ditions ng transformations responsietry-bre for the occurrence of the sy is the fundamental goal of a physical theory ble for the nonunif~ fines what might be termed ‘the problem of of self-organization. origin’. curs in systems composed of multiple subsystems Self-organrzation w of energy, matter, and/or information. Under when opened to these open con ns nonlinearities can develop among subsystems leading to the emergence of (a) sharp or subtle transitions between states, (b) fluctuation-induced instabilities, qualitatively differ erm_inistic dynamics. r (c) ch>ic, hsugh ‘openness’ to conservational flows is a necessary condition for the transi%icn to endent on initial condititins determined externally, and ne er is it derived from any ‘smart’ internal subsysseparates the amount of order exhibited in the inputs and the internally stored states from the amount of order revealed in behavior, is e hallmark of self-organizing systems. r-pose of this c pter is to protide an elementary overview of cal strategies underlying self-organization, and to identify their connections with traditional pects of classical physics, such as Newtonian mechanics and therm0 namics. The strategies in question apply to both simple physical systems - where subsystem interactions etic (force) Ii ages - and complex biological s are dominated ‘by nonkinetic (kinematic, geometric, ages. Of particular interest is a anical systems whose self-motion is powered by interok In these systems energetic flows cross the system’s external boundary an are converted into useful work cycles through internal thermodynamic processes. egulation of these work cycles (such as locomotion, manipulation, ing, fighting, feeding, reproducing, etc.) is through a circular mapping of low energy (kinematic, ages into hi&r energy, force generating actucoupling of a low energy linkage with a force generating actuator can lead to a cascade of symmetry-breaking instabilities and the sub uent emergence of new cooperativities among subsystems. The re is the formation of an execution-driven, selforganizing, control system.
P.N. Kuglei; M. T Turvey / Self-organizing information systems
sica
99
es
2.1. Cfassical (Newtonian) mechanics 2.1.1. Doctrirze of simple (isolat24) atomisms
The search for a fundamental level of description for modeling behavior has been one of the principle objectives of physics. From thcr; perspective of classical (Newtonian) phvsics 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 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 jcatures. The inventory of invariant features defines a simple atom&m (see Iberall 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 turn, 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 dynamics of these elemental units, echoing throughoui the system with perfect fidelity, determines all observable (macroscopic) phenomena. The assumption uf 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 nce an atomism is identified, the (superatomistic and subatomistic).
100
P. N. Kugier, M. T. Turvey / Self-organizing information systems
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. n order words, no spatial or temporal boundaries can be assembled that segregate locally, or isolate, the ynamic from the micro d namic. Under these conditions a tion cannot be ‘forgotten’. n this classical approach to analynce a system is bounded, above or below, sis there is no moderation: nduced into the system that originates outside the nce a set of initial conditions are specified, its for eternity with no possibility for new signatures. cannot self-organize. his is the ‘doctrine of atom-km’, and interpretation of isolated systems. ewton’s mechanics program. Assumption.
ounded or isolated from external interactions e rise to new dynamic regimes: No new laws e that govern the behavior of the system at a privileged scald or region of the state space. *
octrine of mechanical (temporal) reversibility ne of the basic characteristics of trajectories defined by Newton’s master equation ( ty, No distinction is allowed between fut change in the sign of the e results in no change in the solution, that is, the equation mmet,ric with respect to time inversions. namic defines cha ges such as t -+ -t, time inversion, dnd E -+ - v, velocity inversion, as tiquivalent mathematiat one dynamic change achieves, szlch as time inversion, namic change, such as velocity i vf:rsion, can undo, and in this way restore the initial condition. ur daily experience with natural events counter to the notion of mechanical reversibi burning match never reverses itself, retur phase; a rop of ink in water always s ’ Ta aid in deconstruction of the various frlrmcworks (mcchnnicu%, thsrmodynumictrl, modeling assumptions will be explicitly identified wi~cncvcr invoked.
crrc~.)
P. N. Kugler, M. T. Turvey / Self-organizing informatron systems
101
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. Assumption.
All mechanical events are temporally reversible, for example, they do not distinguish historical beginnings from endings, births from deaths.
21.3. Doctrine of force (kinetic) interactior\w 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 atomisms. ?‘he 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 ~~r;l&tions the idealtification of all the velocities and displacements of aI1 atomisms at a sin instant of time allows for the e ifiication of all states of the
transformations
to
102
P. N. Kugler, M. T. Tumey / Self-organizing informatim systems
2.2. Reversible (equilibrium) ajzd irreversible (nunequilibrium) thermodynamics 2.2. I. 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 t e solar system (classical and relativity mechanics), subatomic particles (electrodynamics), and nuclei (chromodynamics). n be considered as descriptions of static All of these constructs machines, obtained by a ng together components in equilibrium (i.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 hile an atomistic (imicroscopic) perspective of a N-body system reveals a microcosm of unending motion, with every atom&m 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 . there is a homeomorphic mapping that relates a single macro state to multiple micro states. These macroscopic bookkeeping metrics constitute the thermodynamic variables for a system at equilibrium. Equilibrium thermodynamics is the study of laws that relate macroscopic (phenomenological) descriptions of atomistic systems under 2 While 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. ‘I’he 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/set would require a duration of time on the order of the squared estimated age of the universe.
P. N. Kugler, M. T Tumey / Self-organizing information systems
103
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 uctive passage from two bodies to N bodies was considered legitimate, even though the only rigorously solved problem was the two-body t 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 Schuster 1984; Cvitanovic 1984). Assumption.
A small number of mean (statistical) macro states map homomorphically onto many micro states.
22.2. Irreversibility
as an improbable event in an isolated system
is an empirical fact that an isolated system (e.g., closed to external flows) evolves irre .,rsibly rp 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. ecause 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. nce at equiiibrium, events no longer exhibit hisnd endings, births and deaths, since the path torical beginnings between the two states is, once again, reversibJe temporally. hen confronted with the identification of the mechanism responsible for the origin of the initial conditions that displaced the system away froAmequilibrium, 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, It
.
104
P. N. Kugler, M. T. Turvey / Self-organizing information systems
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 temporal direction to events (future or past). T thermodynamics states that the entropy of an isolated system will increase with time until it achieves asymptote as the equilibrium state, nce at equilibrium, the entropy at which time the entropy is constant. of an isolated system never decrease pontaneously, 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 terms of the organization of molecular motions, and by showing, after Boltzmann, that this increase corresponds to progressive disorganization and an evolution towards 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 law, the production of entropy is associated with a process conserved entities over available degrees of freedom. second law is viewed as a distribution process that always operates 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 is viewed traditionally as a process operatin against the theory of (organizational) evolution. he temporal evolution of the distribution process, while undefina= t the level of mechanics, can be assigned a direction, a2 historical beginning and ending, at the level of thermodynamics. The direction is assigned in terms of the entropy function. The introdusa,ron of entropy in?‘0 macroscopic descriptions makes it impossible to reduc scopic thermodynamic descriptions to purely mechanical des
echanical reductionism is forever doomed to analytical incompleteness for all systems exhibiting irreversible processes. An irreversible, macroscopic, description cannot be reduced to a reversible, microscopic, description.
Assumption.
2.2.;.
Equilibrium and nonequilibrium (linear) force laws: 1 -I- 1 = 2
regions defined by microscopic
Irreversible flows near equihbtium express an important property, captured by the principle of minimum dissipation. This principle was formulated first by nsager (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 according 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 minimize the rate of entropy production are driven by forces that are linear, weak, and l%ited 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 pat terns. Near equilibrium the forces that drive the flows relate linearly in terms of additive constants.
Assumption.
2.2.5. Nonequilibrium
regions defined by macroscopic (nonlinear) jorce
laws: I -I- 1 + 2
In the region of the linear force laws (near or at equilibrium), the system responds to perturbations and/or fluctuations with small adjuskments 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
106
P. N. Kugler, M. T Twvey / Self-organizing information systems
sufficiently far from equi force laws. These new force global thermodynamic po nonuniformities in their scopic force laws can res for example, time-depen As noted, the macrosc system is displaced furthe scopic force laws actively c driven toward system moves into a regi the attractiveness of the (
nonequilibrium attractor, its tion away from thermody the system to evolve in the
n this far from equilibriu
e same manner atomisms. And, most imp certain degree of autonom scopic laws, even though scopic laws. In sum, the m constraints that act as bou that is, the macroscopic laws the simple atomisms.
re replaced by new nonlinear, s are defined macroscopically relative to 1s that arise as a function of large scale butional configurations. These macrothe emergence of a patterned dynamic, nd/or spatially-dependent regimes. force laws come into existence as the equilibrium. In this region the macroete with the microscopic force laws. As influence the dynamic, the system is states. Starting from an initial near ated by the equilibrium attractor, the ynamic is no longer organized by mic) equilibrium state. Instead, its veness of a nonequilibrium (therr away from the equilibrium state. Once nated by the influence of the olutionary trajectory moves in the direcc equilibrium. The emergence of the ral tendency for the dynamic of ction of increasing order. An intrinsic s suddenly the previously dominant region, the new macroscopic laws thatt obal constraints that harness the microratomisms (fluid cells, flow units, and the microscopic laws act on simple ly, these macroscopic laws have a sovereignty with respect to the microemerge from the actions of the microscopic laws define the dynamic for the conditions 3n the microscopic laws s e as dynamic boundary conditions for
Assumptien. In systems ted far from equilibrium there is a thermodynamic region in the hegemony of the weak, local (microscopic) linear force laws breaks down and is replaced by the hegemony of strong, global (macros _;cfopic) nonlinear force laws. .
P. N. Kugler, M. T. Turvey / Self-organizing information systems
107
2.2.6. Order through j7uctuations 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 breakdown of the linear force laws. As a system approaches the region where the local force laws breakdown 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 (Prigogine et al. 1972) have referred to this phenomenon as order through fluctuation. Assumption. Fluctuations comprise seeking out new stable regimes.
an exploratory
mechanism
for
2.27. A selection principle for nonequilibrium 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. n one side of the local maximum, forces are organized so PS to dri the system in the direction of thermodynamic equilibrium. On the other side 01 the maximum, the forces tend to drive the system away from therm namic equilibrium in the direction of increasing organization. differently, on one side of the critical point (local maximum) the behavior is influenced by local thermodynamic potentials, on the other side, the behavior is influenced by global thermodynamic potentials. Crossing the critical point involves a shift in the scale of the laws that dominate the structuring of the forces organizing the flow patterns: On one side of tne maximum, microscopic (potential) laws apply, on the other side, macroscopic (potential) laws apply.
108
P. N. Kugler, M. T. Turvey / Self-organizing information systems
t or near the transitional boun ary a fluctuation can drive the system over the maximum; beyond this local maximum the self-damping tendency of t e particle’s motion is replaced by a self-amp ith aamplification of fluctuations, the system’s entropy o longer identifies a minimum (as prescribed by the principle of minimum entropy production). The stability of the ampliowever, is guaranteed lo fying tEljeCtOly, excess entropy o&action function (see he instability is slowe uction attams a new production halting finally as the entropy local minimum. ath from one dyna stability of tl next is a funct of the rate of of entropy pr the path minimizes the excess entro production. ssumption .
regime to the tion - that is,
enard and Taylor instabilities A convection insta ility, first identified in 1901 by the French 9 provides an example of how the instability of a se to a self-organizing process (see Koschard instability is due to a vertical temperaliquid layer is heated fro onstant, cooler temperatu at flux (temperature differential) is estabcture that tends to push the fluid’s cooler upper surface. The convective olecules is resisted by internal friction that dissipates mechanical energy en the thermal gradient is small, only heat energy is conducte radient; the molecules remain local, their motions restricted by local dissipative processes. hen the imposed gradient reaches a t shold value, the liquid’s state of rest - the stationary state in h heat is conveyed by conduction (thermal transport without mass transport) - becomes convection (mass transport) corresponding to the coherent nsembles of molecules is produced that increases the rate of heat transfer. As the critical value of heat transfer is approached (i.e., perature), the entropy production of the system identifying a mini m as prescribed by the theorem of ‘minimum entropy production. uring the transition the
P.lV. Kugler, M. T. Turvey / Self-organizing infvmation
systems
109
stability of the system is defined locally by the minimum of \he excess entropy production function - instead of the entropy pduction function (see Glansdorff and Prigogine 1971). The Taylor instability occurs when fluid is trapped betkJeen C-.*o cylinders rotating in opposite directions. The fluid is caused to rotate by the 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 cylinder. 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 order of 10S8 sm. 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) sy.mmetry is referred to as a symmetry-breaking
instability.
2.3. Prigogine’s theory of dissipative structures ‘ Classical thermodynamics was associated.. . with the forgetting of initial conditions and rhe destruction of structure. We have seen, however, that there is another macroscopic region in which, within the framework of thermodynamics, structure may spontaneously appear.” (Prigogine 1980: 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-: ange interactions can develop bet-ween groups of subsystems. The creation and annihilation of the long-range i.nteractions, e.g. symmetry breaking instabilities, are sustained principally by entropy producing, irreversible, processes. Prigogine (1957) has termed these long-range organizations dissipative
P. N. Bugler, M. T. Tumey / Self-organizing iMf~~~~~~ SJW
structures
in reco
tion of the centr
F-&Spublished by Springer; Neil1 et al. 1986; Ulanowicz I
3.1. Complex (open) atomisms
nerates constraints that can curt reducing the degrees of among the atomisms, acco
is not accounted for full tonomy. 3.2. Self-sustaining (open) atomis
interior, and from the a
ternal forces, the r&3 of relevant fcr ~~~t~~n~ , are the fundamental
ative to extern
sms and complex atomisms as
ay be, in fact, the
TPsystems am-3simple ones is, by its very nature, without a what we p~esentiy understand as “physics” is seen in this le systek. The r&don between physics and biology is thus not at to the particukzr; in fact, quite the contrary. It is not biology, but We can see ~TFCMII this perspective that biology and physics (i.e. as two divergent branches from a theory of complex systems sed only very imperfectly.’ (Rosen 1985: 424)
ded scientist has been pfanatory accounts of biological sysqua1 importance, is the e associated with massphysical pursuit of this latter challenge descriptions and puts challenge was anticursuit of a kinematic eed and Jones 1982). d functional significontinuous with the and Turvey 1987). a natural transition can be descriptions, nonmass field on to a theory of
114
P. N. Ku+-,
M. T. Turvey / Self-organizing information systems COMPLEX (BIOLOGICAL)
ATOMISMS
Fig. 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 therrnodyntic work cydes. In a complex atomism the role of the mass dimension is less relevant. in the dynamic description that suatalis the mteractions between simple atomisms. What remains relevant are the fundamental dimensions of length and time (see table I). 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 external force fields (adapted from Kugler and Turvey 1987).
Table P The field descriptions are macroscopic. They do not include microscopic descriptions such as charge, spin and other attributes of interaction at the electromagnetic and quantzn scale (adapted from Yates and Kugler 1984). LEVEL OF ABSTRACTION KINETIC
(M,L,T)
MACRO
FORCE FIELD
MICRO
FORCE
‘)
KINEMATIC FLOW
b
FIELD
GEOMETRIC SPATIAL
FLOW
ALTERNATIVE
Descriptions
Dimensions
a Kinetic (Newtonian
,L T
mechanics) b Kinematic
(L,T)
L, T
(L) b
TEMPORAL SPECTRAL
FIELD
SPATIAL
Properties Forces-violent interaction; conservations such as mv’, mv’, mv2; symmetries; potentials; singularities,
X, X phase space
Nonviolent
interactions;
singularities;
constraints;
symmetries;
X, X phase space
forms, boundary
’ Geometric
L
Geometries,
d Temporal
T
Spectra, frequencies;
functions
FIELD
SPECTRAL
FIELD DESCRIPTIONS
constraints;
(T) ”
conditions
P. N. Kugler, M. T. Turvey / Self-organizing information systems
115
self-organizing ‘information systems’. (For extended discussions by the authors on the topic of self-organizing information systems see Kugler et al. 3980, 1982; ugler 1986; Kugler and Turvey 1987). Assumption.
Interactions 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.
4.1. 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. ynamic 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). nest construction by social insects is presented to illustrate nonkinetic (flow field) linkages in self-organization. The insects of interest are social termites that periodically construct nests that caiil;0I c +-a A:* 20 feet in height and weigh upwards of 10 tons, and which involve the active participation of more than 5 million 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 conpts expressed in the example are derived from Grasse’s (1959) and insma’s (19’137) uralistic observations and a thermodynamic treatneubourge (1977). ment advanced by The control constraints that organize the building activity arise 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 is open to the causal force -+ flow --) force -+ . . , information loop emergence of creation (and annihilation) of field discontinuities. these discontinuities results in a cascade of symmetry-brea’lcing instabil-
116
P. N. Kugler, M. T. Turvey / Self-organizing information systems
ities with the subsequent emergence of cooperative nest building phases ( see ugler and 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 nest-building process are discussed below beginning with the role of percepiclal thresholds. eptual thresholds eromones injecte throughout the site accordi
mmetry-breaking mechanisms into the building materials diffuse ick’s law (rate of transport is linearly a gradient. An insect flying into the radient if the gradient exceeds the insect’s s threshold is a symmetry-breaking mechasect’s activity space into (a) gradient-depenwhere the insects are influenced by the diffusing es, and (b) gradient-independent regions, where the insects enced by the diffusi g phero,mones (see fig. 2). The former are regions of reversibility and the latter are regions qf irreversibihy. he partitioning of the space into reversible and irreversible regions is continuous with the classical theory of dynamic processes (see Kugier 1986). ssumption. The thresholds (nonlinearaties) that characterize percep-, tion-action couplings are symmetry-breaking devices that partition (categorize) d iontrol s ace into regions of reversibility and irreversib&= ity. andom deposit phase e earliest phas f nest building the insects’ depositing behavior is random (see fig. 3). ere are no pheromone gradients strong enough to influence the insects’ 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 hi t concentration identifies a critical (singular) region. en only a few insects are participating in the depositing activity, the pheromone concentration remains low and has very little orienting influence on the insects. he majority of the building sites define regions of reversibility, and the jnsects, as an ensemble, are at equilibrium. If the number of insects remains low, then the system will
P. N. Kugler, M. T. Turvey / Self-organizing information systems
DlFFUSlON -
117
FIELD
EQUIPOTENTIAL
LINES
WSECT FLIGHT PATH
Fig. 2. ‘Perceptual limit’ of the field defines a symmetry-breaking mechanism. Insects in areas where the pheromone gradient falls below the perceptual limit exhibit 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 and Turvey 19873.
remain at equilibrium, resulting in an extended period of random depositing. During this phase no long range correlations develop among participating insects. A ssumptisn .
hen the number of insects participating in nest building is small the individual motions are uncorrelated, and the system is at equilibrium.
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 time, 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 turn make the site even more attractive, defining, thereby, an autocatalytic reaction. As the gradient region amplifies, and long-range correlations begin to the insects, the corresponding insect organization develop amon
118
P.N. Kugler, M. T. Twuey / Self-organizing information systems
0
INSECT DEPOSIT (DIFFUSED) INSECT DEPOSIT (ACTIVE) li.SECT IN% 7T FLIGHT PATH PERCWTUAL
FIELD LIMIT
EQUIPOT
LINES
:WADIENT
SINGULARITY
_
Fig. 3. Ra;ldom flight phase. The behavior of the insects is at equilibrium dunng this phase - e.g., of each insect is independent of other insects, there are no long-range correlations the between the motions of insects (adapted from Kugler and Turvey 1987).
becomes displaced from equilibrium (see fig. 4). The onset of long-range correlations marks the end of the equilibrium phase, and the beginning of a succession of nonequilibrium phases. The first nonequilibrium phase involves the construction of pillars (see fig. 5). As the number of insects increases, the depositing behaves autocatalytic resulting in the emergence of long range correlations organized about a small set of preferred deposit sites: The system is displaced from equilibrium.
Assumption.
evelopment of saddlepoints and arches phase begins with the emergence of long-range correlations distributed over two pillars, resulting in the construction of an arch. nteractions of the diffusion streams from the tops of two pillars create a saddlepoint at the midpoint (see fig. 6). The saddlepoint is constructed out of a bifurcation of two one-dimensional insets (fbw streams originating at the tops of the pillars), into a single two-dimensional outset (a planar flow orthogonal to the insets, see fig. 7). An insect entering the pheromone field via the planar outset is guided by
PN. Kugler, A4.T. Turvey / Self-organizing information systems
119
Fig. 4. Development of preferred sites. The development of a preferred site marks a sudden transition in the correlational state of the insect poptdation. 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 and Turvey 1987).
an increasing gradient leading irto the saddlepoint. Once at the saddlepoint, there are two orthogonal rcxrtes 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. Assumption. Cooperation and competition between field processes (reversible and irreversible) result in the emergence of a finite number of converging and diverging flow regions, originating and terminating in critical states (singular points, saddlepoints, etc.). 4.1.5. Construction @ 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
120
P.N. Kugler, ii4. T Turvey / Selforganizing
information systems
Fig. 5. Building a pillar (adapted from Kugler and Turvey 1987).
saddlepoint and the emergence of a single attractive critical region on the top of the arch (see fig. 8). The gradient flows emanating from the new singular region interact with neighboring gradient flows resulting in the emergence of an intricate pattenr of saddlepoints. These saddle-
Fig. 6. Building an arch. The emergence of the saddlepoint further displaces the system from equilibrium. The organizing influence of the saddlepoint extends the insect correlations to a region defined over the two pillars (adapted from Kugler and Turvey 1987).
P. N. Kugler, M. T. Turvey / Se/f-organizing infomation systems
121,
MACRO (INSECT PATH) INSET PLANE
SIONAL FIELD /
OUTSET LINE MICRO (DIFFUSION
PATH)
OUTSET Pd.;?‘-c _ INSET DEFINES A I DiMENSIONAL FIELD OUTSET DEFINES A 2 DIMENSIONAL FIELD
/ INSET LINE
PILLAR SINGULARITIES VIRTUAL SADDLEPOCNT
Fig. 7. Macroscopic and microscopic perspectives on the inset and outset flows that define the saddlepoint (adapted from Kugler and Turvey 1987).
points organize a gradient layout that constrains the construction of a dome (see figs. 9 and 18). Upon completion of the dome the nonequilibrium phases end and a new construction cycle begins, starting with the random equilibrium deposit phase (see fig. 11). 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 deat
Assumption.
4.2. Perception-action writing system
cycle: An execution-driven
self-reading aizd s#f-
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 de osits. They act as thermodynamic pumps the create and maintain chemical potential reservoirs. These potentials generate diffusional patterns that, in turn,
122
P. N. Kugler, hi. ‘T. Turvey / Self-organizing information systems
INSECT FLIGHT PATH DIFFUSION GRADIENT EQUWOTEMTIAL LINES
Fig. 8. Completion
ewlving
of
the arch and annihilation of the saddlepoint Turvey 1987).
(adapted
from Kugler and
ository activities of the insects. In this regard the insect est is exemplary of a self-reading and self -writing he insect behavior is both guided by (in the sense of self- read-
Fig. 9. Emergent saddlepoints
are used TVbuild a dome (adapted from Kugler and Turvey 1987).
P. N. Kuglep, M. T Turvey / Sey-organizing information systems
Fig. 10. Development
of a dome (adapted
123
from Kugler and Turvey 1987).
Fig. 11. Upon completion of the dome the building phase returns to equilibrium, beginning again with the random flight phase (adapted from Kugler and Turvey 1987).
once
124
P.N. Kugier, M. T. Twvey / Self-organizinginform&on system
upling)
(high-
Fig. 12. Perception/action
cycle. A circular causality of self-assembled from Kugler and Turvey 1987).
flows ad
control constrain
tively as an action
and flows (kinematics), constitute the
it is open in terms of t
e only ‘memory’ re
ssumption .
perceiving-acting syste linear, open flow system in ch future states are mo current configurational states than on prior stored states.
forces (adapt
ese maerose
e resdt is the e system (see fig. 14).
ence of an efficient,
g phases. Each phase is dominated by a small set of critical the chemical flow fields. These flow portraits provide the the insects’ motions (adapted from Kugler and Turvey 1987).
126 INSECT’S t3EHAV ‘IORAL FORCE FIELD
a_
PHERQh’lONE FORCE FIELD
Fig. 14. Self-organizing
DlSSlPATlWE FORCE FIELD DEFINES A FLOW FIELD
information
system (adapted
ns were
~ewe
from Kugler and Turvey 1
M. T. Turuey / Se~-~~~a~~zing information systems
127
ble processes was viewed as a ational states. The phenomtion and self-preservationwere viewed as islands of inevitable destructive action of the second law, of some extra physical of biological and psychological intimately tied to the physical tioiogists has cipled account of the origin and out reaching outside the framedemon to derive the art internal element is construct. It is becoming increasingly sptaced from equilibriumcan develop ts capable of harnessingtemporarily an ensemble n so as to form an efficient, self-organizing, controllable ly, the mechanisms underlying the origin and constraints are intrinsic to the dynamics of the directly from an active participation of the second
G. Engelen
and
M. Sangher,
From
microscopic
amics & life: An introduction
to macroscopic
order,
to self-organization
Berlin:
of matter.
nequihbriurn statistical mechanics. New York: Wiley. 1977. An analysis of building behavior of the termite ‘rnacrotermes subhyalinus’. of the VIII Congress IWSSI, Wageningen. ed.), 1984. Universahty in chaos. Bristol: Adam Hilger. urge, J.L., 1977. AppIieation de l’ordre par fluctuation 5 la description de la construction du nid cbez Ies tern&s. Insectes Sociaux, Journal International pour I’Ctude des Arthropodes Sociaux 24,177. Gibson, J.J., 1950. The perception of the visual world. Boston, MA: Houghton Mifflin. Gibson, J.J., 1966. The senses considered as perceptual systems. Boston, MA: Houghton Mifflin. Gibson, J.J. 1979. The ecological approach to visual perception. Boston, MA: Houghton Mifflin. Glansdorff, P. and I. Prigogine, 1971. Thermodynamic theory of structure, stability, and fluctuation. New York: Wiley-Interscience. GoIdstein, H., 1958. Classiccal mechanics. Reading, MA: Addison Wesley. Grasse, P.P., 1959. La reconstruction du nid et les coordinations interindivuelles chez Bellicosies natalensis et cubitermes. La tt&xie de la stigrnergie: essai d’interpretation des termites
aaux 6,
constructems. Insectes Sociaux, Journal Jnternational pour 1’Ctude 127. 1975. Synergetics. New York: Springer. (ed.), 1981. Chaos and order in nature. New York: Springer.
In: 1. Prigogine and S.A. oschmeider, ‘Instabilities in fluid dynamics’.
d control, NATO Turvey, 1987. Information,
In:
natural
law, and the
movement. strUctUre.s as
urvey, ! 982. ‘On the control and lso and J.E. Clark (eds.), The d control and coordination. New York: Wiley. T. Turvey, C. Carello and R. Shaw, 1985. ‘The physics of t locomotion’. In: W. Warren and R Shaw @Is.), F Proceedings of the first International Conference on Event Perception, Nicolis, G. and I. Prigogine, 1977. Self-organization in non-equili.bti Wiley. M&hen: Piper-. Allen, 1986. A h.ierm ecosystem. Princeton, NJ: khaceton UXliVLiSit~Press. Qnsager, L., 1931. rocal reistions in irreversible processes. Physkal Prigogine, I., 1945. eration ek transformations n-reversibles des syste oy. Belg. Cl. Sci. 31, 600. ude thermodynamic des processus irr&ers~bles. troduction to thermodynamics of irreversible pa Kugler, P.N., J.A.S.
?., 1967. *Structure, . Amsterdam: Nort I., 1980. From bei
sipation
and life’. In:
rder out of chaos. N oyant& 1972. The 25, 23-28. eed, B. and R. Jones, 1982. Reasons for realism: Selected essays of James J. Gi 1978. Fundamentals
Academic
of measurement
and representation
sms as causal systems wh.i In: R. Rosen ted.), Theore Press. pp. 156-203.
of nat