“The current CP of CD (squiggle) collection furnishes a kind of consulting tool, an aid to study that can help one better understand the various concepts, principles, and phenomena of coordination dynamics. It also provides a nonmathematical, but no less valid access to coordination dynamics.”
TCN p218″ — Kelso, J.A.S & Engstrøm, D.A.
Introduction
The list of squiggles below is an extension and elaboration of the one initiated on pages 217-225 of TCN. In TCN, we tried hard to repeat the message that the sense and study of squiggles (complementary pairs) is ancient~modern: humans have always sensed some profound connection between contraries, opposites, poles, pairs, at least as old as yin~yang, though it is likely to have been present in our most ancient ancestors. “You can’t have attraction without repulsion, and vice versa…” We know this. We live this. We are this.
While there is much to say about the squiggles, the bottom line, the really crucial point to make about them is that they all have very specific meanings in the science of coordination dynamics. Just as time~space, energy~matter, particle~wave and particle~antiparticle have very specific meanings in physics that connect directly with the mathematical and phenomenological theory~experiments of quantum mechanics (QM), the following squiggles connect directly with the mathematical and phenomenological theory of coordination dyanamics.
This is one example of “grounding the philosophy of complementary pairs with the science of coordination dynamics.” Note that squiggles of the ‘base-set’ obviously have a unique status, for they will be found anywhere coordination dynamics is applicable. The range and scope of coordination dynamics is growing rapidly. This is actually a topic of its own here at The Squiggle Sense blog for you to explore~discover. But the point here is that of all the squiggles out there to reflect upon we feel most comfortable talking about those found in coordination dynamics itself.
The complementary prospect, or the coordination dynamics of complementary pairs (CD of CP), deals with how the science of coordination dynamics helps us understand squiggles wherever they are found, (i.e. whether they have any obvious connection to the field of coordination dynamics or not!)
We now present, extend and enhance our initial list of the complementary pairs or squiggles of coordination dynamics, which bear special status because they happen to be vital to the science that is able to explain them, we call squiggle of the base set, or alternatively ‘base set squiggles’. Different ways to refer to the same collection of phenomena~concepts. So imagine you have a ‘cheat-sheet’ of aggregated scientific wisdom from a 30 year line of scientific research:
“The current CP of CD collection furnishes a kind of consulting tool, an aid to study that can help one better understand the various concepts, principles, and phenomena of coordination dynamics. It also provides a nonmathematical, but no less valid access to coordination dynamics. Of course, one is always free to proceed by directly employing the scientific language of coordination dynamics and its mathematical underpinnings. Our point is that regardless of whether one takes one path or both, the complementary pairs (squiggles) of coordination dynamics are going to be right there in the game. Having the CP of CD collection in hand should enhance one’s own comprehension of coordination dynamics as well as help explain coordination dynamics to others.”
When considering how CP of CD might act as a tool to advance research~development, it is worth keeping in mind the possibility, even the strong likelihood, that some squiggles of coordination dynamics have yet to be discovered. As we present this brief ‘‘conceptual scaffold’’ for the science of coordination dynamics, a few further caveats are in order. First, not all the squiggles are unique to coordination dynamics. Also notice that although each complementary pair can be expressed in its reversed or ‘complementary’ direction, here only one ordering is presented:”
Relevance of Base Set
Using our squiggle sense and a little imagination, one could study the following list side-by-side with a study of coordination dynamics and precisely where and in what context each squiggle is applicable. Such efforts are already underway. Could we use the squiggles of coordination dynamics to discover something like a Periodic Table of Elements only rather than physical elements we have squiggles of Coordination Dynamics?
Well, in that case, it would have to be something like The Metastable Table of Squiggles, since complementary pairs wouldn’t be completely periodic in principle. (It goes against their complementary nature!)
The possibilities are enticing, indeed. But what is needed first is more effort to work with the base set itself. A place to begin is to study the list as a whole, and at the same time look at each squiggle individually and try to describe what we know about each so far. To this end, the squiggles with links (this is an on-going process remember) will take you to posts for each one, which includes our original summary statements from TCN as quotes. Eventually, we will begin to add other relevant pieces, like other TCN excerpts, quotes from the literature, and new thoughts and insights of our own regarding the CD base set.
SQUIGGLES OF CD TO HELP YOU LEARN CD
Would you like to know more about coordination dynamics and how it might help you comprehend the complementary nature, your nature? Here’s a hint: Instead of ploughing straight into the mathematical underpinnings, the scientific graphs, and journal articles, you can begin to get an idea of what coordination dynamics is about by just studying the base set. Note the one’s that might be interesting to you…
DON’T STOP AT YIN~YANG & DIALECTIC
Beyond yin~yang and dialectic, beyond the idea that contraries are complementary and dynamics, there is something more. The squiggle symbol says says that coordination dynamics is happening. It tells you that bistability~bifurcations happen. It tells you that multistability~metastability is happening. And that’s just the tip of the iceberg. It tells you that you are dealing with a system~level, that has ongoing pattern dynamics. And perhaps most satisfying of all, it gives human beings the ways~means of comprehending, anticipating, and when things are going really well, of predicting and designing with that same coordination dynamics–how it comes about, how it alters the system~level. And on and on it goes…
The ‘Base Set’
agency~self-organization A distinguishing feature of coordination dynamics is that self-organizing processes are the source of agency and that agency is capable of steering the dynamics.
attraction~repulsion All nonlinear dynamical systems contain mathematically described objects called attractors and repellers. Coordination dynamics also describes behavior in terms of attractors and repellers. In its metastable regime, it also achieves attraction and repulsion with no attractors and no repellers—only tendencies for attraction and repulsion. In coordination dynamics, these tendencies arise when an attractive and a repelling fixed point ‘‘kiss’’ at a so-called saddlenode bifurcation, giving rise to the phenomenon of metastability. The latter has been called the Principle of Attraction Sans Attracteurs (the ASA principle).
between~within Coordination dynamics captures the coupling between individual elements and processes and also within individual elements and processes. To capture the latter, one most quantify the coupling between individual elements and processes on another level of description.
bifurcation~path The path a system follows can be smooth and linear, or, like a tree, it can have many branches. ‘‘Bifurcation’’ means the path splits into two as a result of the system crossing a threshold. This is sometimes called a ‘‘pitchfork bifurcation.’’ Bifurcation can also occur in the reverse direction, in which case it’scalled a ‘‘reverse pitchfork bifurcation.’
birth~death Experiments and theory in coordination dynamics show that under certain conditions, an existing stable fixed point can die at the same time as a new one is born. Dynamically, this means that an attractor turns into a repeller and a repeller turns into an attractor. This may sound strange, but it’s true.
bistability~monostability When circumstances (e.g., in the form of control parameters) change continuously, monostability can give rise to bistability, and in general, multistability, and vice versa. In coordination dynamics, the latter regime gives rise to the Principle of Coexisting Equally Valid Alternatives (the CEVA principle). The mechanism of change is called a bifurcation by mathematicians and a nonequilibrium phase transition by physicists.
bottom-up~top-down Coordination dynamics reconciles purely top-down approaches to understanding and purely bottom-up approaches to understanding. Coordination dynamics stresses the importance of choosing a level of description or scale of observation. A complete account of the chosen level relies on looking one level up (to the boundary conditions, constraints, parameters, etc.) and one level down, to the individual components.
context-dependent laws~context-independent universality The laws of coordination dynamics are context-dependent. The same law may describe and explain how different kinds of things are coordinated, but may also be shaped by the things themselves. Context-dependent laws of coordination dynamics attest to the enormous diversity of nature. They are complementary to the contextindependent ‘‘first principles’’ of physics that aim to unify nature. CP of CD says that the complementary nature cannot be understood without both.
control parameter~coordination variable Control parameters may be specific, as in stabilizing coordination states that would otherwise become unstable, or nonspecific, as in moving a system through its coordination states. At places of qualitative change, control parameters reveal coordination variables and coordination variables reveal control parameters. In coordination dynamics, a control parameter at one level may be a coordination variable at another, and vice versa.
convergence~divergence In coordination dynamics, and in excitable media in general, the tendency of the flow of the dynamical system to converge coexists with the tendency of the flow to diverge. In the metastable regime of the coordination dynamics, these two opposing tendencies coexist, giving rise to the Principle of Coexisting Opponent Tendencies (the COT principle).
cooperation~competition In coordination dynamics, the relationship between cooperative and competitive processes determines the form self-organization takes, and hence the particular coordination patterns observed. In the metastable regime of the coordination dynamics, cooperation (the tendency for the parts to work together) and competition (the tendency for the parts to express their own individual character) coexist at the same time. This is another manifestation of the COT principle.
correlative inference~population inference The experimental designs used in coordination dynamics examine correlated changes in relevant variables as parameters are continuously varied in order to test key predictions underlying stability and change, e.g., critical slowing, fluctuation enhancement, etc. This complements conventional scientific experimental design, which randomizes the independent variable in order to draw inferences about the population.
coupling~components For coordination to occur and manifest the many forms it takes, coupling between components is necessary. In coordination dynamics both individual components and their couplings are context-sensitive. A component or coordinating element at one level may be a coupled dynamical system at another. Coordinating elements can be as large as the environment (organism~environment coupling) or as small as a molecule that binds to another (receptor~target). On any given level of description, coordinated patterns arise in a selforganized fashion as a result of nonlinear couplings among coordinating elements. In evolving living systems, the components themselves may carry some of the coupling or at least a remnant of previous interactions.
creation~annihilation (of information) In the metastable regime of coordination dynamics, functional information may be both created and destroyed by virtue of the system crossing a threshold. This is a basic selection, choice, or decisionmaking mechanism.
deterministic~stochastic In coordination dynamics, how a system behaves is based on deterministic and stochastic processes. All real systems have elements of both. Accident and necessity, choice and chance are inextricably connected.
discrete~continuous Discrete and continuous behaviors may arise not only as a result of activating different systems or mechanisms (the usual assumption) but as different parameterizations of the same underlying coordination dynamics (same~different).
dwell~escape In the metastable regime of the coordination dynamics, how long a system resides in the vicinity of a fixed point (its dwell time) and how quickly it escapes from this neighborhood (its escape velocity) are a function of how strongly the parts are coupled relative to how different the parts are from each other.
dynamic patterns~pattern dynamics In coordination dynamics, dynamic patterns are generated by self-organizing processes. These evolving patterns adapt, persist, and change according to context-dependent rules or laws, their pattern dynamics.
emergentism~reductionism Coordination dynamics sees no need to shift from an Age of Reductionism to an Age of Emergentism. Reductionism (e.g., breaking down into elementary parts) and emergentism (e.g., collective effects) are complementary strategies for understanding complex systems. The two may be reconciled by virtue of nonlinear interactions among components that may themselves carry some of the coupling.
fluctuations~states Fluctuations are a sign of dynamic instability and typically precede or anticipate switching among states depending on timescale relations. In coordination dynamics, fluctuations probe the stability of states and allow the system to discover and select new states. This is called the Principle of Selection via Instability (the SVI principle). SVI confers a kind of basic choice or decisionmaking capability on the system.
functional information~self-organization In coordination dynamics, spontaneous self-organizing processes create meaningful or ‘‘functional’’ information, and functional information guides (modifies, steers, directs, constrains, sets boundary conditions for) self-organizing processes. This crucial complementary pair locates coordination dynamics relative to other theories of self-organization. Each complementary aspect of this complementary pair constitutes a primary root of coordination dynamics. Both are crucial for the coordination of living things.
gradual~abrupt Due to its inherent nonlinearity, coordination dynamics may exhibit changes that are gradual (continuous) or abrupt (discrete) depending on where the system is located in its parameter space. In learning, the competitive~cooperative relationship between new information and the preexisting repertoire, landscape, or intrinsic dynamics determines whether change will be seen as a gradual adaptive shift or as an abrupt phase transition. These are the two routes to learning discovered by studies of coordination dynamics.
homogeneous~heterogeneous In coordination dynamics and living things in general, the individual coordinating elements may be all the same (e.g., as in the idealized case treated by the HKB model). More generally, they differ. In coordination dynamics the degree to which the individual coordinating elements differ is an important parameter~variable that affects the phenomena observed.
horizontal~vertical In coordination dynamics, interactions may occur side to side (within a level) and vertically (across levels in both directions). The resulting coordinative organization is heterarchical and coalitional, not only hierarchical.
individual~collective In coordination dynamics, a part is a whole and a whole is a part. Individual entities may retain their autonomy and independence within the collective at the same time as binding together to form a cohesive group. Individuals create the collective, and the collective, as it forms, affects how the individuals behave.
information~intrinsic dynamics Intrinsic dynamics refers to coordination tendencies and dispositions that exist as a kind of network memory at a given point in time. Once created via bifurcations and metastable dynamics, new information both modifies and is modified by the existing intrinsic dynamics. This principle applies at all levels and is especially relevant to situations where adaptation, learning, and change are at issue.
intention~dynamics In coordination dynamics, intention acts in the same space as the intrinsic dynamics, attracting the system toward an intended pattern. Intentions constrain and are constrained by the intrinsic dynamics. They may both stabilize and destabilize patterns of behavior.
integration~segregation In the metastable regime of the coordination dynamics, tendencies to integrate the parts coexist at the same time as tendencies for
the parts to remain segregated, thereby retaining their individual autonomy. This has been called ‘the complementarity of the twenty-first century.’
learning~memory In coordination dynamics, learning modifies the preexisting landscape or repertoire and the latter influences how new information is assimilated. Memory refers to the stabilization of functional information over time and can be stored both locally, e.g., in synaptic connections, and globally, as in a broadly distributed network.
linear~nonlinear Depending on surrounding circumstances, i.e., where the system is located in the space of its parameters, behavioral change may be smooth and linear or abrupt and nonlinear. Nonlinearity is a requirement for multistability and its biological manifestation, multifunctionality.
local~global In coordination dynamics, component elements such as specific areas of the brain may be coupled both locally (e.g., through neighborhood-based intracortical connections) and globally (e.g., over large distances through intercortical connections).
Local~global and intra~inter complementary pairs are essential for information processing in complex systems.
macro~micro In coordination science, macro and micro are relative terms. What is micro at one level may be macro at another. This is called the Principle of Relative Levels (PRL).
metastability~information creation Self-organizing tendencies in the metastable regime of the coordination dynamics create~destroy functional information. multifunctionality~functional equivalence Multifunctionality—the capacity for the same material structure to express multiple functions—and functional equivalence—the capacity for the same function to be realizable by multiple structures—are inherent aspects of coordination dynamics. The complementary pair multifunctionality~functional equivalence is manifest at all levels of biological organization and may be understood in terms of multistable and metastable coordination dynamics. The coexistence of multiple dynamic steady states and tendencies in coordination dynamics provides a scientific underpinning for the philosophy of complementary pairs.
multistability~metastability In coordination dynamics, as symmetry is broken and couplings are altered, multistability—in which several functional states may coexist for the same parameter values—gives way to metastability, in which only tendencies coexist. The generic mechanism is a saddle node or tangent bifurcation.
>organism~environment Though by no means unique to coordination dynamics, this complementary pair is nevertheless central to it. In coordination dynamics, organisms do not exist independent of their environment and vice versa. One may be said to entail the other as an informationally coupled self-organizing dynamical system. Organism~environment is a general complementary pair of coordination dynamics which entails informationally coupled self-organizing dynamical systems at multiple levels, e.g., perception~action, stimulus~response, genotype~phenotype.
part~whole In coordination dynamics, the parts are not free of the context of the whole and vice versa. A whole is a part and a part is a whole. perception~action In coordination dynamics, what an organism perceives is a function of how it acts, and how it acts is a function of what it perceives. Part and parcel of every action is perception, and part and parcel of every perception is action. The same applies to sensing and motion, which in living things are a complementary pair.
persistence~change The more things change, the more they stay the same. In coordination dynamics, whether a process is observed to persist or change depends on the timescale on which the process lives and the timescale of observation.
planning~execution Planning and execution, like mind and matter, sensory and motor, are but two complementary aspects of a single activity written in the language of biologically meaningful coordination variables and their dynamics.
preferences~exploration In the metastable regime of the coordination dynamics, a system exhibits tendencies or preferred locations in the phase space where it tends to reside, while also being able to explore the entire space of possibilities. How long the system dwells in a given preference before escaping to explore the phase space depends on how strong the parts are coupled relative to how different or heterogeneous the parts are. Dwell times and escape times are important empirical measures of coupling in systems that exhibit transient tendencies and dynamics.
qualitative~quantitative In coordination dynamics, quantitative consequences accompany and anticipate qualitative change (e.g., critical fluctuations, critical slowing down). Quantitative causes may or may not produce qualitative changes in behavior.
reaction~anticipation Whether a system reacts to or anticipates environmental information depends on parameters of the coordination dynamics (e.g., the rate of stimulation).
recruitment~annihilation In coordination dynamics, the ability to selectively recruit and annihilate degrees of freedom to accomplish a function is a crucial source of flexibility. These processes may go on at the same time as circumstances vary.
reduction~construction This complementary pair captures the strategic approach of coordination dynamics toward connecting levels of description. One of the mantras of coordination dynamics is, find the relevant pattern or coordination variables and their dynamics on a given level of description, then derive the latter from nonlinear interactions among components. This strategy allows one, scientifically speaking, to reduce down and construct up.
simple~complex In coordination dynamics, a complex system may crack itself into simple behavioral modes whose pattern dynamics may be rich. This complements the usual notion of nonlinear dynamics that simple nonlinear laws may give rise to surface complexity.
source~sink In the dissipative systems of coordination dynamics, the flow of energy from a source to a sink creates a cycle (Morowitz’s theorem). The cycle is the archetype of all time-dependent behavior (Yates-Iberall conjecture).
space~time Coordination refers to functions that evolve in both space and time in the phase space of informationally relevant coordination variables.
stabilization~destabilization In coordination dynamics, functional information can both stabilize and destabilize patterns of behavioral coordination depending on context.
stability~instability In coordination dynamics, stability and instability are both indispensable attributes of pattern formation and change. One does not exist without the other. Selection among stable states occurs via instability (the SVI principle).
stable~unstable Fixed points of the coordination dynamics may be both stable and unstable. One can transform to the other. They can also collide or ‘kiss’ and give rise to metastability.
states~tendencies In coordination dynamics, asymptotically stable states represent polarized ideal aspects. In between these asymptotic extremes lie metastable tendencies that are neither stable nor unstable states, but that possess remnants, ghosts, or traces of previously stable states. The coexistence of multiple tendencies and the convergent~divergent flow of their coordination dynamics undergird the philosophy of complementary pairs.
structure~function Structure and function are distinguished only by the multiple timescales on which they live. For example, in the developing organism, cells that fire together wire together, and cells that wire together fire together. In general, invariance of function under change of material structure (e.g., reconfiguration of connections among elements) is an intrinsic feature of coordination dynamics.
symbolic~dynamic After H. H. Pattee, symbolic, rate-independent descriptions and continuous dynamic descriptions are equally valid complementary aspects of complex systems. As a scientific strategy, coordination dynamics says exploit the dynamics to a maximum and trim the symbolic to a minimum.
symmetry~dynamics Symmetries refer to properties of a system that remain invariant under transformation (e.g., mirror, left-right symmetry; forward~backward time symmetry, etc.). In coordination dynamics, symmetries allow for the classification of possible coordination patterns or states. What you see in the real world, however, depends crucially on the coordination dynamics, that is, which patterns are more or less stable under current conditions.
symmetry~broken symmetry Symmetries allow for the classification of patterns in nature. Curie’s principle, that symmetric causes produce symmetric effects, is not necessarily true in living things. Pattern diversity occurs when symmetries are broken. In coordination dynamics, symmetry breaking is a necessary condition for the emergence of metastable, converging~diverging tendencies. When differences between coordinative elements are eliminated, symmetry is restored or created.
togetherness~apartness Tendencies for togetherness coexist with tendencies for apartness. This is likely an inherent property of all complex organizations. For example, successful groups are loosely bound both by a commitment to a common goal and by the diverse needs and capabilities of their members. This is the essence of metastable coordination dynamics.
within~between As the science of coordination in living things, coordination dynamics seeks the laws, principles, and mechanisms underlying coordinated behavior in different kinds of system and at different levels of description. It aims to characterize the nature of the coordination within a part of the system (e.g., the firing of neurons in the brain), between different parts of the system (e.g., parts of the body, areas of the brain), and between different kinds of system.
