· What happens when we apply complex systems theory to systems in which meanings are made and matter?

· What happens when we apply semiotic theory to the study of complex systems?

Let me sketch out first some principles from complex systems theory that I believe are useful in analyzing human social-cultural ecosystems, including the key question of how they are integrated across multiple levels of internal organization and what role semiotic artifacts and practices play in that integration.

**Some principles from complex systems
theory: **** **

· Ecosocial systems are dynamic and metastable, with emergent organization

This means, familiarly, that the properties of each level of organization emerge from interactions among units and processes at the level below, and that the whole system continues to persist as a system only to the extent that it maintains an energy flow through itself by its interactions with an external environment

· Ecosocial systems have a hierarchy of multiple levels of organization on multiple spatial-extensional, mass-energy, and time-rate scales

Part of what makes a complex system complex is that each level of organization embodies additional descriptive and dynamical information needed to either construct or describe the system sufficiently for some purpose. This organizational structuring begins with the initial emergence of any ‘system’ with a degree of autonomy or autocatalytic closure from what then counts as its ‘environment’. Highly evolved complex systems are presumably those in which this process of emergence has repeated itself again and again internally, leading to multiple levels of organization. Each level is characterized by a typical size or distance scale, a typical mass of units and energy per unit or process cycle, and a typical time or rate for processes and cycles of processes to occur.

· Emergent organization at any focal level depends on constraints from the level above, affordances from the level below; interactions among units and couplings between processes

This is the basic ‘three-level model’ of emergence formulated by Salthe (1985, 1993) for hierarchically organized complex dynamical systems. I believe it is more complete than more common two-level accounts. In effect it points out (as does Prigogine 1961) that higher level, relatively persistent and slowly changing, ‘external’ constraints (here interpreted as merely at the next higher level (N+1) within the system; only at the ‘top’ of the levels hierarchy are the constraints properly ‘external’) are always necessary to maintain the organization of focal level (N) dissipative structures. In effect they also select from among all the possible self-consistent patterns of interaction on the level of constituents (N-1), those which satisfy boundary conditions necessary for co-existence with structures at the next higher (N+1) level. Units at the (N-1) level interact to produce emergent structures at the focal (N) level, subject to constraints from the next higher level (N+1) of overall system organization. A corollary of this is that:

· New emergent levels occur at intermediate scales between those of higher level constraints and those of lower level constituents

This principle is therefore also a thesis about the evolution, development, and histories of hierarchically organized complex systems. New levels of organization are always interpolated in between already existing levels of organization; they are not added to the ‘top’ or ‘bottom’ of the stack.

· Emergent levels of organization filter and buffer higher levels against fluctuations on lower levels, and preserve many-to-one degrees of freedom within constraints

There are always many possible ways in which (N-1) level constituents can interact consistently with (N+1) level constraints; emergent structures are underdetermined, except perhaps for the dynamically simplest systems. Any particular pattern or structure at the focal level (N) is tolerant to some degree of fluctuations on the next lower level (cf. Thom’s ‘structural stability’ criterion). This very fact, however, also means that noise or information below some threshold at (N-1) is filtered out by (N), which effectively buffers (N+1) against its influence. All that matters to (N+1) is that the patterns at level (N) remain quasi-stable on an appropriate timescale; what is happening down at (N-1) is effectively invisible so long as (N) is behaving normally.

·
Processes at significantly different time/rate scales do not
exchange energy or information directly [*Adiabatic separation*]

There is a second principle which insulates non-adjacent organizational levels. Processes on each level have a characteristic timescale or rate scale. These differ across non-adjacent levels typically by at least two orders of magnitude (often more), and in such cases dynamically, thermodynamically (and quantum-mechanically) the efficiency of energy transfer falls off rapidly. Very brief signals from lower levels do not last long enough to transfer enough total energy to by noticeable above the background noise by higher levels. Higher level processes deliver energy signals so slowly that these signals appear only as relatively constant fluxes over the lifetime of lower level structures.

· Emergent organization occurs when there is autocatalytic and/or cross-catalytic closure in the systems of interdependencies among processes

What is it that happens in the interactions among constituents at level (N-1) that leads to the emergence of new patterns of organization at level (N)? Most fundamentally, it is an entrainment of available energy fluxes into closed cycles of interdependent processes, such that some far-from-equilibrium steady-state can be maintained after it is initially reached (e.g. by fluctuations, or by changes in constraints, external gradients, or flows).

All these principles appear to apply and indeed to be
heuristically highly useful in the analysis of ecosocial systems.

But clearly they are also not enough, since they apply to a much more generic class of systems than we are interested in here (cf. Lemke 1993, 2000b on the specification hierarchy from general dissipative structures to ecosocial systems).

We need to combine these principles for complex multi-level dynamical systems with those from semiotic theory:

**Some principles from semiotic theory:
**

· Semiosis occurs when a system (SI) exhibits a response (I) to an interaction with a material phenomenon (R), such that (I) is adaptive in some larger context to the possible or actual presence of a second phenomenon (X), and where there is no material causal determination of (I) by (R)

This is an adaptation of the basic account of semiosis due to C.S. Peirce. It places a more explicit emphasis on the system of interpretance (SI) in the dual sense of both the material system in which ‘interpretation’ (in the precise sense above) takes place, and also in the formal sense of the system of rules for interpreting (i.e. for associating some set of (I, R, X) in some local context). Peirce calls the system response its Interpretant, the phenomenon which is taken to be a sign of something else is the Representamen, and the phenomenon for which it is taken to be a sign is the Object. As a simple biological example, when an organism (SI) interacts with a ‘telltale’ molecule and then produces a response which is adaptive, not to the molecule as such, but to the presence of food or predator in the vicinity, its response (say directional movement, or release of internal enzymes) can be said to be an interpretant (I) of taking the molecule (R ) as a sign of the food or predator (X). This is strictly semiotic to the extent that there is no determinate causal chain from the interaction with the molecule to the response (I). So, for example, if (I) is produced under some conditions but not under others where the telltale is detected, or if multiple intermediate levels of the system buffer the level at which (I) is produced from that at which (R ) is detected.

· The response (I) by (SI) to (R) is in general a function of not only the material properties of (SI) and ( R), but also of other phenomena in the environment and the history of (SI)

The meaning of a sign is not in one-to-one correspondence with its object. Sign meanings rather depend on both the so-called syntagmatic context (other signs which are co-present) and the paradigmatic context (other signs in the same meaning-class which might have occurred in place of the one which did occur); they depend also, certainly in human semiosis, on the history of the SI, that is, on which rules of interpretance it has acquired.

· The pairings (R,X) are not determined by the properties of R and X for a given SI, but only by (possibly many-to-many) correspondences among R’s relations to other members of a class of R’s, and X’s relations to other members of a class of X’s, as constructed by the history and behaviors of SI.

The system of interpretance responds as if the triples (R, X, I) depend on the relations of any given R to some set of possible alternative R’s, and likewise for X’s and I’s. These paradigmatic sets (which may be continuous as well as discrete) are presumably learned through a history of participation in a community of sign-users where similar classifications and principles for interpretation occur. For more details, see Lemke 2000a.

· Variations in either degree (continuous) or kind (discrete) among R’s may correspond for a given SI to variations in either degree or kind among X’s.

One of the key difficulties initially in integrating semiotic principles with those of complex system dynamics is that traditionally only discrete sets of R’s were associated with discrete X’s (this is more true in continental semiotics than in Peirce’s original theory). But we know that much of what happens dynamically in the material systems that enact semiotic processes, and certainly in the ecosystem as a whole, depends on quasi-continuous responses to quasi-continuous variation in a whole host of key dynamical variables. Fortunately, much of the history of physics, and the associated mathematics that grew up with it, is a lesson in how to do semiosis quantitatively, and how to integrate discrete linguistic concepts or mathematical symbols with representations of continuous variation in graphs, number systems, and a variety of visual and material representations. We will return to this issue below.

So what shall we take as the basis for a synthesis of these two sets of principles? I offer the following hypotheses, which so far look rather promising:

** Joint
Dynamical-Semiotic hypotheses:**

* *·
SI is a multi-scale complex dynamical system

That is, any system which can do semiosis has a multi-scale dynamical organization. This is elaborated below and represents a mapping of the (SI, I, R, X) formalism onto the 3-level paradigm of Salthe for hierarchically organized complex dynamical systems.

· SI interacts materially with R on some subscale

That is, as in our example of the telltale molecule, the interaction with R is at some sub-maximal scale of internal organization of the SI as a material system.

· SI exhibits its response I on a higher scale, typically that of SI itself (maximal)

·
SI integrates contextual factors across scales, up to its own
(maximal)

These next two hypotheses are quite critical to the overall picture, for they link the notion of (syntagmatic) context to the scale of the SI. The SI must both persist long enough and extend, or move, across a wide enough range to take into account the lower-scale interactions of its multiple constituents with telltales of various relevant sorts. One can imagine a cell integrating the information accumulated over some time interval and throughout its volume or across its surface area from multiple ligand-scale molecular interactions. The scale on which the integration takes place may be an intermediate scale (a particular membrane structure) or the total cellular scale, depending on the timescale and spatial extension scale needed. The response likewise must be on the integrating scale or above, even though it may then cascade downwards again to smaller scales.

· SI is itself a unit in a larger-scale system and its (R,X,I) patterns are constrained by its participation in that higher-scale system.

This hypothesis is clearest for the case of human semiosis, where the SI is taken as the human organism and the larger scale system is that of the ecosocial community (or some subsystem that includes multiple human organisms in interaction). It may apply as well to sub-organismic SI’s.

· A new level in the hierarchy of semiotic interpretance emerges IFF a new level emerges in the scale-hierarchy of dynamical organization (both are intermediate between pre-existing levels)

This is a very strong hypothesis, that may have heuristic value even if true only in limited domains. In one logical sense it requires that semiosis depend on the dynamical relations among multiple scales of organization within a system, as in the 3-level paradigm model of those relations. In the converse sense, it implies that all multi-scale dynamical systems do in fact perform some sort of at least rudimentary semiosis, or perhaps more realistically that they have the capacity to do so.

While it is quite clear what it means for a dynamical level to be intermediate between two others, we should point out that for a semiotic level to be intermediate means that there is a chain of interpretations, such that the interpretant response (I) of the level below is now taken as itself a sign (R ) for interpretation by the level above. Whether, as Peirce maintained, the ultimate ‘object’ (X) necessarily remains the same through this chain is not quite so clear. My sense is that in some sense it can remain the same, but that it need not. In any case this view of multiple levels of semiosis leads to another rather striking hypothesis:

·
A new intermediate level N organizes (quasi-) continuous variation
at level N-1 as discrete variants of meaning for level N+1; and/or discrete** **variation
at level N-1 as continuously variable meaning for level N+1.

When we come to interpret the buffering or filtering effect of a focal level of organization in semiotic terms, we must confront the issue of what makes a level of organization emergent in the sense of having qualitatively new, sui generis, properties. The above hypothesis is both a generalization from observed cases and a possible criterion for the qualitatively distinct ‘feel’ of a new level of organization. If an intermediate level simply re-coded discrete units as discrete units, or mapped one continuum of variability into another, I do not think we would see this as an emergent level of organization. It is only when variation in degree is reorganized as difference in kind, or differences of kind are averaged out so as to function as a new sort of continuum, that we get the sense of something genuinely new emerging.

·
Insofar as a strict scale-hierarchy can be defined, continuous and
discrete semiotic transductions strictly alternate across triples of
organizational levels

This ‘principle of alternation’ is meant to apply to the biological
hierarchy, if it applies at all. It does seem to be striking how often the
reorganization of variety across levels follows this pattern. At each stage
variability below (at N-1) is filtered through a tolerance within the pattern at
(N), and only the state of this pattern matters for (N+1).

As rudimentary examples consider:

The discrete variation from one amino acid to another along a protein chain (N-1) matters to a membrane structure to which the protein ligand binds or does not bind (discrete response) only through the conformational folding of the chain, which produces a shape whose variation occurs in a quasi-continuous three-dimensional space.

Individual small-molecule interactions in a region of a cell produce discrete variation in the presence or absence of reactants of discrete molecular species, but larger scale responses (themselves discrete, threshold-dependent phenomena) integrate over the region and respond only to the quasi-continuous volume-averaged density of a species (e.g. pH).

Discrete neuron firings are integrated at a higher scale to produce the continuous variability of fine-motor articulation of speech, but the meanings of speech sounds in a community depend only on discrete threshold differences between contrasting phonemes. (For more examples see the appendix to Lemke 2000a.)