Opening Up Closure: Semiotics Across Scales

For "Closure: Emergent Organizations and their Dynamics"
University of Ghent, Belgium; May 1999

I would like to offer what I believe is an interesting hypothesis about the relationship between semiotics and the dynamics of complex self-organizing systems. It assumes that the interesting complexity of such systems arises from the emergence of new levels of organization over their history. The fundamental proposal is that each new emergent level of organization in the dynamics of the system functions to re-organize variety on the level below as meaning for the level above. In this way, both the semiotic and the dynamical closure of system levels is re-opened to allow the development and evolution of greater complexity.

In order to clarify just what this proposal means, it will be necessary first to consider a number of concepts on which it is based. I will need to specify what I mean by levels of organization in a complex system, and how they relate to one another dynamically. For this I will rely mainly on the 3-level paradigm of Salthe (1985, 1989, 1993). Next, I will outline the kind of semiotic relationships that I believe can exist between levels. For this I will introduce a variant of Peirce's (1992, 1998) semiotics in which a basic distinction will be made between categorial meanings and meanings based on continuous variation. Finally, I will propose that emergent levels of organization tend to re-organize continuous variation at the level below as categorial information for the level above, and vice versa, perhaps in a hierarchy of alternating transformations between these two varieties of meaning.

It seems clear that biological systems are indeed multi-level systems of the kind to which this proposal should apply, and despite my very limited knowledge of contemporary theoretical biology, I will try to illustrate in a very rudimentary way how the proposal works in the case of the hierarchy of biological organization. I believe that examples from human sociocultural systems add further complications to the simple picture I will be sketching, and perhaps some of these also have precursors in simpler biological systems. I will mention some of these possibilities towards the end.

Certainly for biological systems, and probably for many others as well, the richness of their complexity derives in part from a strategy of organizing smaller units into larger ones, and these in turn into still larger ones, and so on. Such scale hierarchies are well recognized in modern biology (Salthe 1985, 1993). The parameter which most simply defines differences in scale, usually of a quantitative order of magnitude or more, may be taken to be the mass of a unit of organization on some level, the linear distance scale of strong correlations or interactions among the constituents of a unit, the energy scale of characteristic processes in which the units participate (typical amounts of energy exchanged in such processes), or the characteristic durational times of the cycles or processes which constitute the unit. As we move from level to level up the scale hierarchy, units get more massive, bigger, more energetic in aggregate (but with less energy used per interaction on the relevant scale), and slower in operation.

The dynamical relations among adjacent levels are what most concern us here. If we designate a level-in-focus, on which there is some emergent phenomenon constituting some units-of-interaction on a characteristic scale (level N), then in the 3-level paradigm of Salthe (1985, 1993; see Figure 1) we assume that units on level N are constituted by interactions at level (N-1) among the units at that lower level, but that of all the possible configurations which such interactions might produce at level N, only those actually occur which are allowed by boundary conditions set at level (N+1). The logic of this dynamically is that the stability of a configuration of level (N-1) units at level N depends on the putative interactions among these new units at level N. Such higher-order interactions do not generally occur in an infinite and empty vacuum, but rather in some context (a container, a medium, an environment) some of whose properties (e.g. temperature, pressure, ambient energy flows) are specified by still larger-scale dynamics (e.g. solar insolation, atmospheric pressure, salinity). Only those configurations at level N will be even meta-stable on the appropriate time-scale which are consistent with the constraints imposed from level (N+1). The properties of units and interactions at level (N-1) are constitutive for level N phenomena; those at level (N+1) are constraining for level N phenomena. (Salthe 1985 refers to 'initiating conditions' from N-1 and 'boundary conditions' from N+1.)

This is still a synchronic, or steady-state view of hierachically organized systems. More truly dynamically, the model assumes that new levels of organization always emerge between previously existing levels. New complexity arises in systems because the new level N re-organizes the relationship between level (N-1) and level (N+1). Level N units and their interactions now mediate between the levels above and below: not all variety at level (N-1) remains available for re-organization at level (N+1), there is a filtering performed by level N. Conversely, we may say that level (N+1) is buffered against variations at level (N-1) by the stabilizing mediations at level N. This principle is closely related to the model of Ehresmann and VanBremeersch (1996, 1997) in which each level of organization can be realized by a variety of combinations at the level below; thus changes at that lower level do not result in qualitative differences at level N, and may not produce any effects at level (N+1). This is also qualititatively similar to Thom's principle of structural stability (1975).

At the same time that the emergence of stable units and processes at level N reduces the flow of information from level (N-1) to level (N+1), thus in one sense simplifying the dynamics of the system (there are fewer possible dynamical combinations allowed), and so making it more specified (cf. Salthe 1985, 1993 on the 'specification hierarchy' and see Lemke 1994), the emergent level now also means that a new kind of information must be given in the description of the system; in this sense it has become more 'complicated'. We need new descriptive categories to talk about the units and phenomena of level N. Insofar as the emergence of level N may occur developmentally only following the prior emergences needed to produce its immediate precursor organization (the original level N-1 units, level N+1 conditions, and their dynamic relations), the system has also now reached a new degree of 'logical depth' (cf. Collier 1999, Collier & Hooker n.d.).

Furthermore, the new organization of the system now presents us with new options for its further development, specification, or evolution. Once some particular units and phenomena at level N have emerged, it is now possible for still newer levels to be interpolated between (N+1) and N, and between N and (N-1). Each new level of organization augments the evolutive potential of the system for increasing its organizational richness still further.

Before leaving the issue of dynamical scale, I want to add one more point that will be relevant later on. For typical biological systems, such as cells or multicellular organisms, all of the scale parameters listed above (mass, size, energy, time, etc.) tend to shift in step with one another and it does not much matter, beyond analytical convenience and the availability of data, which we use. But this is not always the case. An important critique of the application of systems theory to human communities and their technological infrastructures has been made by Latour (1987, 1996), who notes that our usual systems theories assume a particular topology: we assume that units closer in space are always more likely to interact than more remote units are. This leads to assuming a 'spherical' topology for system: we envision its levels of organization as nested spheres of larger and larger spatial scale. But it is perfectly possible for two distant units to interact more intensively or more frequently than two nearby units, if the distant units are connected by a stable channel of communication, while the nearby units are not. This leads to a 'network' topology in which units on the same network interact more than units that may be nearby in space but are 'off' the network. People on the internet but geographically distant may communicate much more frequently and influence one another's actions more than happens with their close geographical neighbors who are not on the net (or not part of a specific social network). In an ecosystem, one locus and another downstream from it may be more tightly coupled than the same locus and a nearer one that is isolated from the stream. In an aquatic or arboreal system with stratified layers, two distant sites within the same layer may be more likely to interact than either is with spatially closer sites in an adjacent layer -- at least in respect of the flow of certain kinds of information, nutrients, pollutants, etc.

In these more general cases, what happens to the neat notion of scale levels? I believe that it can be shown that what matters in the general case is not specifically spatial scale, but time scale (Lemke, in preparation). This is so to the extent that what makes a "level" in a system is its dynamical functions in relation to other levels, and insofar as the key dynamical function I am proposing is semiotic reorganization, what matters is the informational or communicational coherence of a level (and its relations to adjacent levels). If we think in terms of subnetworks within a network topology, then the way in which scale levels can be defined is in terms of the adiabatic principle, which insures that levels are relatively insulated from one another if the timescales of their characteristic and constitutive processes are sufficiently different that they cannot exchange significant amounts of energy on each other's relevant timescales. Such fastnets and slownets can each be internally communicatively coherent while remaining relatively communicatively isolated from one another, as required by the 3-level paradigm. They can only be constitutive (N-1 to N) or constraining (N+1 to N) in relation to one another, and not directly interacting. This timescale perspective promises to be especially valuable in analyzing sociocultural ecosystems, or ecosocial systems (Lemke 1994, 1995), but is also fundamental to many other kinds of analysis (e.g. entropy and information measures may also be timescale-specific).

My basic proposal is going to be that each new emergent level serves to reorganize one type of semiotic information from the level below it as another type for the level above it. What are these two basic types of semiosis? I will follow the basic model of C.S. Peirce (1998), with a few specializations of terminology, to explicate these types. Semiosis is a process of meaning-making. It is a process of construing some material entity or phenomenon as a sign, rather than simply interacting with it energetically. In Peirce's terms, the entity or phenomenon is called the representamen (R), and what we take it to be a sign of is called the object (X). But Peirce wisely recognized that no R directly points us to a corresponding X; there is work of interpretation to be done, there are principles or codes by which this interpreting is done, and so there must be, in my terms, a system of interpretance (SI). A sign is only a sign for some SI; R is a sign of X only for some SI (and not necessarily for all SI's; for some the same R may signify a different X, or the same X be signified by a different R, nor need these relations always be one-to-one).

The first step in defining a role for semiotics in the dynamics of multi-level systems is to map these defining elements of semiosis onto the 3-level paradigm of scale organization, as in Figure 1. Units or phenomena on level N are representamina, R, of object-states, X, of the interactions of units at level N-1 which dynamically constitute the phenomena at level N, for processes or structures at level (N+1), which form the system of interpretance, SI, with respect to which correspondences between R's and X's are defined and computed. Note that this implies that the SI always has both a slower timescale, and usually a more global spatial-extensional scale, than the phenomena which it interprets.

It is useful here to note the precise sense in which semiotic interpretation differs from simple physical interaction. When an organism encounters some photons or some molecules of a particular chemical species, there is a physical interaction of these entities with the organism's sensors on the corresponding scale (e.g. molecular). That is interaction. But if the organism as a whole, mediating and buffering the molecular-scale consequences of this interaction through the dynamics of other higher-scale levels of its internal organization, reacts in a way that is adaptive to the presence of food, or predators, in its environment, then it is reacting on a higher scale level than the purely physical, initial molecular-scale interaction, and it is thus acting as a system of interpretance, as if it were interpreting the encounter with the molecules or photons as a sign of the presence of food or predators (in Peirce's terms, an 'indexical' sign). The organism reacts to the molecules not just as molecules, but also as telltales of and cues for response at a higher-scale level.

There is nothing here which non-material; semiosis is a material process, but one in which typically there is a translation or re-interpretation of information from one scale level to another. This introduces the possibility of many-to-many mappings of information as we move to macroscopic scales of organization, while fundamental interactions, at the molecular or quantum scale, tend to be one-to-one. Microscale interactions are deterministic because there are very few dynamical degrees of freedom. Photons and electrons have no individuality; most small-molecule reactions have unique chemical outcomes, there is simple deterministic cause-and-effect. But when effects at the microscale are re-organized at higher scales, it becomes possible for the same molecular encounter to produce a positive tropism in one species but a negative tropism in another. The same response may be elicited by different stimuli in the same organism, the same stimulus, under different conditions of context at higher scales, can produce different responses in the same organism. Semiosis does the work of interpretation in large part by integrating contextual factors across scales (Lemke, in press-a). Now we no longer have simple deterministic causality; many causal inputs on many different scales combine in ways that lead to unpredictable and emergent behaviors, some of which prove adaptive. The extension of the anthropomorphic metaphors of 'interpretation' to simpler biological and even non-biological material systems are carefully considered in Anderson et al. (1984) and in the work of Hoffmeyer and Emmeche (1991; see also Hoffmeyer 1997).

For those who may be more familiar with Peirce's view of semiosis, it may be useful to clarify a few points. Others may wish to skip this paragraph and the next. While a sign, or more properly a representamen, R, does not determine its object, X, directly, it does, for Peirce determine its interpretant, which is another sign whose object is the relation between the initial R and its X. My own view, and probably Peirce's, is of course that R does not cause or create the interpretant: this work is done by the SI. But what enables R to function as a sign of X for the SI is that, given how the SI interprets R's, this R will be interpreted as the appropriate interpretant sign, and so as a sign of the appropriate X. It is not a causal or physical 'determination', but a logical or semiotic one. Now in my view the interpretant sign is always materially instantiated at a scale level above that of the initial R. According to Peirce, the interpretant sign normally becomes in its turn a representamen that determines some still further interpretant, and so what is for Peirce the basis of an indefinite chain of semioses is for me the basis of an indefinite (i.e. open-ended) hierarchy of scale levels of systems of interpretance. This is not the place to consider whether this 'unlimited semiosis' ultimately leads to a difficulty with the number of scale levels available, but it does pose an interesting question about the scale of the object X.

For Peirce, all along the chain, the interpretants are giving information about the same object, though they may lead us to see it in different ways or make different inferences about it. In the dynamical hierarchy view I am constructing here, each higher-scale SI at level (N+1), which interprets representamina on the level N below it, construes doubly: the material reality which is being construed by the SI as a representamen is some particular pattern of correlations of material interactions among constituents at level (N-1), but at the same time the interpretant or meaning (at level N+1) of this pattern-as-sign corresponds to an object at its own (N+1) level. So in one sense the object X of the original representamen is materially grounded at level (N-1), but in the second sense, the object X corresponding to the interpretant is some phenomenon that has material relevance at level (N+1). When I smell something, in one sense my smell-perception is a perception of the molecular interactions in the olfactory bulb, but it is semiotically (conceptually) interpreted as an index of some macroscopic food or waste or predator. A sign is meaningful for an SI because it is a sign of something on the scale of the SI. We smell the molecules of our enemy as our enemy; it is, normally, the enemy, not the molecules that are dangerous, relevant, and meaningful. Are these 'the same' object X? In the model being developed here we would need to be bit more careful in our answer than perhaps was necessary for Peirce.

In order to continue my larger argument, I need now to distinguish two broad classes of semiosis: (a) those cases in which the features of representamen that are criterial for some SI to interpret it as a sign of some X may vary continuously, so that quantitative differences of degree in a feature of R normally lead to differences of degree or kind in the interpretant, vs. (b) those in which all representamina are classified by the SI into a discrete spectrum of types, and each R-type is interpreted as a distinct X. I will call the first case 'topological semiosis'; it is a generalization of the notion of analogue signaling. By 'topological' here I really mean to invoke the topology of the continuum of the real numbers: it is continuous variation, quantitative differences of degree that matter. I will call the second case 'typological semiosis'; it is a generalization of the principle of digital signaling. By and large most of classical (Saussurean) semiotics restricts itself to typological semiosis, but this is insufficient for the analysis of general system dynamics.

The complications here arise from the fact that in principle we may map continuous variation in X onto continuous variation in R (and vice versa), the usual 'topological' case, or discrete variants of X onto discrete variants of R (and vice versa), the usual 'typological case' (Table 1), but we may also have mixed modes of semiosis in which the continuous is mapped onto the discrete and vice versa (Table 2). The mixed modes are relatively rare in human cultural conventions for symbolism and representation, but I believe they are fundamental to the inter-level relations of dynamical systems.

Thus typically, as in linguistics, what is represented (X, a semantic category) and how it is represented (R, a string of words) are both discrete. Semantic categories have a meaning potential which is defined by their contrasts with other discrete categories. A noun may be Singular or Plural, but it cannot have some continuously specifiable degree in between Singular and Plural. A verb may be Present tense or Past tense (or some one of a closed and finite list of other discrete possibilities), but there are no continuous degrees between Present and Past in natural languages. The word(s) that represent these differences are likewise discrete: a word (R) must be interpretable either as 'man' or as 'men'; pronouncing a vowel somewhere on the acoustic continuum between them does not make a new word in the English language, and cannot represent some semantic degree in between Singular and Plural. This is not how natural languages work. They are almost completely typological in their mode of semiosis. (There are some exceptions, in the case of intonation, for example.)

Type-X represented as: · spoken word · written word · mathematical symbol · chemical species	Quantitative-X represented as: · size, shape, position · color spectrum · visual intensity · pitch, loudness
	Iconic: scale models, maps
	Indexical : voltmeter, thermometer
	Symbolic: cartesian graph scientific visualization

We adopt this principle also for our mathematical and scientific symbol systems. A chemical element may be Carbon or Nitrogen; there is no continuum of elements (so far as we know) between them, and we represent them by discrete symbols: there is "C" and there is "N", we do not adopt the real number line to represent atomic species, as we do, for example, for atomic weights (even though they do not vary continuously, they may have almost any arbitrary ratio to one another). The variables in our equations are either 'x' or 'y' and we do not allow continuous variation between variable x and variable y (though we do allow for linear combinations in order to unify typological and topological logics, which is in some sense the basic historical function of mathematics, or at least of algebra, algebraic geometry, and real analysis; see Lemke, in press-b).

But we do indeed need and use the topological mode of semiosis as well. In the pure case, this means representing a continuously variable X by a continuously variable R, or equivalently, interpreting continuously variable R as continuously variable X. Thus we typically represent continuously variable dynamical parameters of a system by real numbers, or by positions on a line or in a 2- or 3-dimensional space (e.g. Cartesian graphs). We could, and with the new methods of computerized scientific visualization increasingly do, represent them by the continuous visible color spectrum, or by degrees of brightness, or by acoustic pitch or loudness. Scale models and maps represent continuously varying shapes by continuously variable shapes (iconic signs); a thermometer or barometer represents by the continuously variable height of a column the continuously variable temperature or pressure of the surrounding system (indexical signs). In Peirce's classification scheme, the arbitrary conventions of the Cartesian graph illustrate topological symbolic signs. Topological semiosis is at least as important and general as typological semiosis in the representation of nature and its dynamical systems.

As an aside, we might note that our scientific accounts of natural phenomena are conceived in terms of a mixture of typological concepts, in verbal language and the discrete variables of our theories and equations, and in the discrete types of entities that we recognize and visualize, together with topological representations of continuously variable features of systems, where that continuous variation matters to some phenomenon of interest. Mathematics is the semiotic bridge by which we bind together our primitive perception and representation of continuous variation (size, shape, spatial position, brightness, loudness, color, temperature, etc.) and our more categorial conceptual languages. Mathematics is in essence and historically an extension and specialization of the semantic categories of natural language to deal with continuously variable phenomena, or what may as well be such relative to the observer's scale.

If 'information' is, in Bateson's (1972) famous phrase 'a difference that makes a difference', then it is clear that both difference of kind, and difference of degree can make a difference. Each can be the basis of semiosis, each can be interpreted as representing a difference in the object X for which some representamen R stands for a particular system of interpretance, SI.

What happens in the mixed-mode case where we represent quantitatively variable phenomena (X) by discrete or typological representamina R? We certainly do this, as the examples in Table 2 show.

Quant-X as Type-R :

· waveform as phoneme

· painting as description

· ratios as fractions

· functions as algebraic expressions

· conformations as ligand classes

Type-X as Quant-R

· words as sonogram

· numeral as bitmap

· semantic category as fuzzy set

· event-type as probability?

In speech, there is continuous acoustical variation in sound, but for an organism that has learned a particular language, only certain distinctive feature differences count or 'make a difference' to which vowels or consonants (phonemes) and so which words are heard. When we write speech down with letters of an alphabet, we transcribe continuous variation into strings of discrete variants. We preserve the purely linguistic information (which words are said), but we lose much other information (whose voice was speaking, with what regional accent, in what degree of agitation). The SI classifies or 'types' what we hear into a finite number of discrete and mutually contrasting equivalence classes. To do so it has to have learned the language, or at least learned its 'phonology'; this learning is a process on a much longer time scale, requiring even in its momentary application to perceived sounds many more neuronal units and interlinked networks, on a much larger system scale, than the simple registering of acoustic degrees of pitch and intensity. We hear the same word even when we do not hear exactly the same sounds, e.g. from different speakers, when someone has a cold or is nervous, etc. The phoneme-analysis level of the neurological speech perception system buffers word-scale recognition from much shorter timescale, non-criterial fluctuations in perceived sound. It filters out the 'noise' that is not criterial for categorial differences between phonemes or words. The mapping of the sound-, phoneme-, and phonological system -responsive networks of the brain onto the 3-level paradigm should be obvious, as should its fit to both the dynamical scale hierarchy levels and their semiotic functions.

Consider another example at a more molecular level. When proteins fold up into their complex 3-dimensional spatial conformations, then at the scale of an amino acid what we see is discrete typological variation: each constituent unit is either this amino acid or that one, there is no continuous variation among kinds of amino acids. At the scale of the protein as a whole, interacting with something else at the same scale, what matters is the continuously variable distances and angles of its local conformational shape and electromagnetic fields. But at the still higher scale of a membrane with binding sites composed of many interlocking proteins, the complex spatial configuration of a ligand matters only insofar as it does or does not occupy a site and produce some triggering effect. The membrane reads only discrete ligand classes in many cases, and is blind to the details of the conformation, so long as they are within certain parameters. Many of our successful medical drugs are simply 'imposters' which fool the membrane, or some other complex larger-scale structure, because they are indistinguishable as members of the ligand equivalence class defined by the membrane, which is thus operatingas a higher-scale system-of-interpretance (or part of such a system).

In addition to writing systems, other human semiotic conventions also operate this particular mixed mode. When we represent the rational numbers as fractions, we are representing something that varies quasi-continuously in terms of discrete pairs (integer numerator and denominator). When we represent continuous functions by algebraic equations (e.g. polynomials), the representamina are discrete 'x' and 'y' just as if they were words in a verbal sentence (and indeed we can read algebra as if it were a sentence of English with only slight peculiarities of grammar, because of the historical origins of algebraic notation).

What of the converse mixed mode? What happens when we represent discrete phenomena by continuously variable representamina? This happens for instance when we look at a sentence of English as a 'sonogram' or acoustical graph of energy across a range of frequencies, displayed longitudinally in time on an oscilloscope or continuous feed tracing roll. You can learn to read sonograms as if they were a form of writing. It is quite difficult because there is so much 'extraneous' information represented in the sonogram, information that does not matter to deciding what words were said. The neurological networks that have already been trained to filter sound for phoneme classes do not transfer over very readily to screening these visual patterns. In fact you very quickly realize that in 'hearing words' we are often 'hearing' sound cues that are not actually there acoustically; as the sound stream is matched to the most likely or only possible word sequence, higher level networks are activated that correspond to whole words or phrases, even if parts of those words, or sometimes whole words within phrases, are not instrumentally detectable in the sonogram! This is somewhat of a linguistic analogue to Gestalt pattern completion phenomena for visual perception.

Using sonograms as a system for visually representing spoken language is not nearly as efficient as alphabetic, or even ideographic writing systems because it tries to represent a typological system of semiosis topologically. It requires the creation of a whole new system of interpretance rather than piggy-backing on an existing one. Nonetheless there may be some advantages in some cases to such a procedure. The new 'fuzzy engineering' represents semantic categories of verbally stated criteria for good machine functioning by continuously varying functions for degrees of membership in a category (the 'membership function' for fuzzy sets and fuzzy logic). By doing so it can 'smooth out' transitions in behavior and more closely approximate arbitrary functions.

Level N-1 Topology to Level N Typology

Continuum dynamics to eigenvalue typology

Bifurcations, attractors, basins

Threshhold effects

Topological variety to equivalence classes

Fuzzy sets to sharp sets ??

Level N-1 Typology to Level N Topology

· Discrete items averaged to net densities, concentrations

· Discrete units organized as polymers, lattices, networks

· Discrete lattice or network dynamics organized to coherent macro-phenomena ("propagation") and molar property effects ("elasticity")

· Discrete events organized as continuous action (neural firings --> smooth motor actions)

Considering both the logic of the 3-level paradigm, in terms of how semiotic functions are mapped onto dynamical scale levels, and many examples such as those just given of the reorganization of continuous variation into discrete variants (Figure 3, upper), and of discrete variants into continuous variation (Figure 3, lower), has led me to what seems at least heuristically an interesting conjecture:

Each new, emergent intermediate level N in a complex, hierarchical, self-organizing system functions semiotically to re-organize the continous quantitative (topological) variety of units and interactions at level (N-1) as discrete, categorial (typological) meaning for level (N+1), and/or to re-organize the discrete, categorial (typological) variety of level (N-1) as continuously variable (topological) meaning for level (N+1).

In each case, level (N+1) functions as the system of interpretance which construes entities and phenomena at level N as signs of microstates of the system at level (N-1). By extension, where these level (N-1) states correspond to the effects of interaction with the environment at level (N-1), higher levels of the system respond to them as signs at level N of phenomena in the environment at level (N+1), which may have only a very indirect causal-material relationship to the actual interactions at level (N-1) or none at all. It is not my purpose here to discuss an interactional model of how semiosis mediates learning; for an interesting effort in this direction, see Bickhard & Turveen (1995). My concern here is with the logic of the Principle of Alternation itself.

The basic mapping of semiotic functions onto organizational scales in Figure 1 has a dynamical implication, if we interpret it in terms of the evolution or development of the system:

A new level in the scale hierarchy of dynamical organization emerges if and only if a new level in the hierarchy of semiotic interpretance emerges.

This is in some sense a logical precondition for the Principle of Alternation. The exact connection between the two becomes clear if we ask ourselves whether the semiotic relationship between adjacent levels of the dynamical scale hierarchy could be a simple mapping of continuous variation at the level below to continuous variation at the next level up? Or of discrete variants at the level below to discrete variants at the next level? This is logically possible, but would we then consider that there was any point in saying that a qualitatively new level had emerged? And if it had, what would its functional advantages be? In a mapping of continuous variation onto continuous variation, there is very little room for novelty or innovation; there is only re-description. Similarly for mapping one discrete set onto another; what else is this but re-naming, especially if it is one-to-one? As Ehresmann and vanBremeersch (1996, 1997) argue in the case of a logical model of hierarchical multi-scale systems, the novelty of new levels arises in part because each higher level has many possible realizations at lower levels. It is only a many-to-one mapping that provides for classification, and filtering and buffering (from level N-1 to level N), as the 3-level dynamical scale model expects. The 3-level model of course also expects that as we go up one more level, a categorial element (at level N) can be interpreted (at level N+1) to have many possible meanings, or system responses, depending on contextual constraints from 'elsewhere' (at level N) that are integrated by the higher-scale (more global, longer timescale, N+1) level.

I believe that this dynamical logic appears to us users of human categorization as an alternation between topological and typological semiotic relationships of adjacent levels, taken in (possibly overlapping) groups of three. This is clearest in the cases where quantitative variability is reduced to discrete categorial variants. We know of many applicable mathematical models in which continuum dynamics produces discrete states, when subject to higher-scale boundary constraints: discrete spectrum eigenvalue solutions, bifurcations, discrete attractors and their (classificatory) basins, threshhold effects of all kinds. What is a bit less obvious is how the complementary half of the cycle of alternation proceeds. How do systems interpret discrete variants as continuous variation?

The answer in all cases is the same as for the continuum-to-discrete part of the cycle: by going up one level in scale. We have already seen one example of this: protein polymerization. At the small-molecule scale, the protein and its interactions in vitro are defined by the discrete typology of the constituent amino acids (level N-1). But when we consider the protein molecule as a whole, and interactions at a higher scale level (level N) that depend on, say large-molecule to large-molecule interactions, then it is the continuously variable conformational shape of the folded protein that matters. A shape which is co-determined both by the amino acid sequence (from level N-1), and by contextual-environmental constraints (level N+1) of the overall global cell chemistry (which determines, for example, the cytoplasmic pH, temperature, or similar global conditions). We should not be surprised that what at the more micro- scale look like discrete units, appears from a more macroscale perspective as continuous variation. This is the basic molecular-to-molar logic of chemistry. At the pauci-molecular scale (Halling 1989, Kawade 1996) reaction pathways depend on discrete, non-stochastic interactions of specific molecular species; but when we proceed to larger scales, such as global cellular chemistry, then we are closer to the regime of concentration-dependent effects where the Law of Mass Action applies. Concentration-dependent effects and chemical gradients are large-spacescale, long-timescale averages over discrete molecular interactions.

If we consider neurocortical activity in the brain, even in a simple model in which neural 'firing' is all or nothing (discrete variants), as we move up in scale we eventually find that there are global coherent phenomena that average over many individual 'firings' to produce the alpha and other well known EEG rhythms of continuous variation. Karl Pribram's (1991) famous 'hologram hypothesis' also posits that functionally meaningful patterns are construed more globally across neurological activity. We also know that individual firings of nerves that activate bundles of muscle fibers are globally coordinated at a higher scale (and a longer timescale) to produce smooth motor action of an entire muscle or muscle group.

Thus discrete items may be averaged to net densities and concentrations, discrete units organized into polymers and lattices (which have global coherent effects such as elastic propagation modes, which are again quasi-continuously variable phenomena), and discrete events globally coordinated to produce smooth, continuous higher-scale actions.

What the Principle of Alternation proposes is that the transformations of discrete to continuous and continuous to discrete alternate as we move from level to level of the dynamical hierarchy, and that in doing so they represent a semiotic transformation of the information content of lower levels as signs for higher levels, allowing many-to-one classifications and one-to-many context-dependent reinterpretations. A scale of dynamical processes in a system, at which such transformations occur, meets the logical conditions for novelty that define for us a genuinely emergent level of organization.

Table 3 (see also Appendix A) illustrates a possible sequence of such alternations from level to level, though clearly our, or at least my, knowledge of all the intermediate scales is too limited to present it as more than a suggestion of the plausibility, or at least the heuristic value, of looking at the dynamics of multi-scale systems from this perspective.

Quantum variety (typo) organized as molecular charge distributions (topo)

Biomolecule conformations (topo) organized as ligand class information (typo) by larger-scale membrane polymers

Pauci-molecular reaction pathways (typo) organized as molar concentration-dependent effects (topo) at global cell-chemistry scale

Molar chemistry (topo) organized as neuro-transmitter threshold effects (typo): "firing"

Firings in neural nets (typo) organized as coherent cortical effects (topo): "brainwaves" "holograms"

Cortical dynamics (topo) organized as limit cycles (typo): "percepts" "phonemes"

Neuronal attractor effects (typo) organized as smooth motor behavior (topo): "drawing" "gesticulating" "enunciating"

Smooth motor behavior (topo) organized as visual and verbal signs (typo): "gestures" "words" in ecosocial supersystem as meta-system of interpretance

Let us return, finally, to the theme of closure. In what sense are self-organizing systems closed? And what is the relevance of closure to the evolution of complexity? We must first distinguish several quite different meanings of 'closure' with respect to such systems. There is material closure, which would mean that there is neither matter nor energy flow across the boundary of the system. There is autocatalytic closure in the sense that some web of interdependent processes is self-regenerating. There is informational closure in the sense that all information critical to the system's behavior is available internally. There is semiotic closure, which entails that in some sense the system's dynamics depends on exhaustive sets of classificatory alternatives. And there is the well-known semantic closure thesis of Pattee (e.g. 1995), which posits that the semantics of classificatory symbols completes the dynamical description of such systems by specifying initial conditions on general dynamical laws.

Pattee's thesis has much in common with the argument being presented here. He emphasizes what I have been calling typological semiosis, and speaks of the type categories as 'symbols' which have both a local material structural instantiation and a function in relation to a more global system organization that 'interprets' them. His concern is not explicitly with levels of scale in this process, but he does follow von Neumann's arguments to posit "multiple-level descriptions when we need to relate structure to function." It is not clear if these are only distinct logical levels, or also scale levels, as proposed here. In any case, my principal concern will be rather with the narower issue of semiotic closure, as above, rather than with Pattee's very general notion of semantic closure, which is already an integral part of my proposals. (I might however differ with his conclusion that only natural selection can explain the symbolic dimension; across levels there is an intimate dialectic between physiological process and already-semanticized structures, leading to new symbolic functions that depend as much on material self-organization as on selectional accumulation of stored information.)

Clearly the kinds of self-organizing, dissipative multi-level structures in which we are interested are not materially closed, for they are always energetically parasitic on larger-scale energy flows, small negentropic back-loops riding piggy-back on the greater downhill degradation of order to disorder. Here, too, the issue is a matter of scale: the scale -- in mass, energy, spatial extension, and most critically in time -- of self-organization is always vastly less than the scale of the dissipative energy flows which support them. As Prigogine (1961, 1962) noted, it is both the flows through the system, and their adjoint larger-scale external constraints that together allow smaller-scale entropy reductions far-from-equilibrium. Moreover, where the dynamics is truly complex, there are many 'entropies', many modes of dissipation, and only some of them decrease in correspondence with the spontaneous emergence of order in the correlations among only some of the system's dynamical variables (Hasegawa 1985). We focus our attention on these particular variables, because their correlations have meaning for us. It is only dynamical correlations that we define to be phenomena, and about which we make our science; we privilege order because we see ourselves as the children of order, and our science is, not surprisingly, always also about us.

Of course it is also true that systems and networks are definable as units of analysis, on each scale, because their internal interdependencies and communications are more intensive than their overall dynamic dependency on interactions with their environments. The latter are the precondition of their being, but the former define their specific characteristics. In the usual 'spherical' topology of systems (as above) there may be a closed boundary separating system from environment (e.g. a membrane), and this may be a precondition for the development of delicate smaller-scale internal dependencies, buffered from the larger-scale fluctuations outside (Hoffmeyer 1997b). But in more general network topologies the buffering may be provided by the adiabatic principle itself (external fluctuations are too slow on the scale of internal processes to affect them significantly on their own characteristic timescales) or by channels of connectivity (phonelines, watersheds) which strongly link system elements internally (at high speed, or with high matter or energy fluxes) but without either enclosing the 'system' or blocking flows from outside -- they simply promote flows inside and let the adiabatic principle do the rest. Thus systems with 'network' rather than 'spherical' topologies can overlap and interpenetrate in real space; they can also interact, on a slower scale, at their 'centers' (or anywhere), rather than only at their margins or boundaries. This is a very different sort of material 'closure' once again.

The notion of autocatalytic closure (Kauffman 1993, Hoffmeyer 1997b) is a material-informational condition on self-organizing systems of sufficient complexity, and a plausible one. The system is in effect capable of synthesizing its own constituents down to some minimum level of organization (atoms, small molecules), but at and below that scale it is dependent on material flows from the environment, as also on environmentally maintained energy gradients and conditions sufficient for disposal of waste heat and other toxic by-products of the synthesizing processes. This notion has close similarity to that of semiotic closure, but in a multi-scale levels-of-organization perspective we cannot say that a system is informationally closed on autocatalytic grounds: lower levels provide informational input in the sense of smaller-scale types that are functional in the system at the scale-in-focus, and higher levels provide information in the sense that it is functional integration into these levels that determines the conditions of interaction of such systems with others on their own scale. We have perhaps too easy a habit of imagining our systems as operating solo in some much less-structured environment: one protocell in the primordial soup. But the more typical case is one in which there are other cells in the soup, and beyond the soup higher-order structures (whether tissue-like or ecological) which depend upon and constrain interactions between these units. From the cell's (organism's) point of view (internalist perspective, cf. Matsuno 1989), it is interaction with other cells (organisms) that provides the information input that we macro-observers (externalist perspective) ascribe to the next higher level of multi-cellular (ecological) organization.

In order to better formulate issues of closure across multiple levels of organization we may wish to ask in what sense our systems of interest may be semiotically closed? It would seem that self-organization does imply a degree of informational and dynamical autonomy, but to what degree and in what sense autonomous? The epigenetic principle of equifinality implicates our homeostatic, or better homeorhetic (Waddington, 1957) tendencies: larger-scale, longer-term processes and the structures they give rise to are buffered by intermediate scales of organization from fluctuations at lower levels … within some limits of tolerance defined by scale ratios (larger-scale changes in the gradients that sustain the system energetically are not buffered against, only energetically smaller-scale fluctuations, and not all of those, but only the ones already implicated in the evolution of the intermediate levels of organization). So long as this buffering is successful, the kinds of order and even the specific units, processes, and structures on each level of organization vary within narrow parameters: the informational description of these types is closed. There is nothing new under the normal sun.

Semiotically, each higher level is characterized by its own exhaustive paradigms of types, and dynamically the inter-level relations (for adjacent levels) have come to be (ontogenetically, as phylogenetically) such that normal fluctuations at lower levels do not matter because they do not, by construction, alter the 'structural stability' (in the sense of Thom, 1975) of the structures they constitute at the higher level. So far as the system-of-interpretance at the higher level is concerned, these are differences that do not make a difference; they have no information value, they are merely yet more points in phase space that all lead onto the same attractors. It is the attractors and their basins that define the higher level dynamics, closing it semiotically at the same time they presuppose its openness materially and energetically.

But semiotic closure as a typological notion can never be the whole story. We all have two eyes, but they are never the same distance apart, never the same exact shape or size. All faces look much alike at some level of typological classification, but their quantitative 'topological' differences allow us to distinguish them as individuals and to form, at a new intermediate level of interpretance, Gestalt patterns (again types) of recognition from many quantitative features, and then classify these patterns yet again. In development, the type-specific features are equifinal, but there is still plenty of room for quantitative individuation. At levels of organization where only typological difference matters, and for levels for which this is true, we can speak of semiotic closure within a level. But if the Principle of Alternation is a useful guide, then across semiotic triples of levels, there is always somewhere a lack of topological-semiotic closure, and it is this very source of potentially meaningful open variation which is reorganized at some higher level again into a new typological-semiotic closure.

We should not be surprised that in self-organizing systems quantitative variability is organized at a higher-scale level into qualitative invariants. We tend, however, in looking at cross-level relations only two at a time, rather than three at a time, to focus only on how typological closure arises from metric openness. When we consider multi-scale systems across many triples-of-scale, we also see the alternating inverse process by which larger-scale aggregations of many lower-scale types begin to appear once again as quasi-continuous distributions: the raw material for yet new orders of order to emerge at new intermediate-scale levels.

We also make more sense of closure if we look at the development (in the individual instance) or evolution (of the type-class) of a hierarchy of orders of closure at various scales of organization. According to the 3-level paradigm, new emergent levels of organization come-to-be between always pre-existing scales (primordially between smallest units and global flows/constraints that permit dissipative structure to emerge initially, and then again and again, always within supporting prior structure and residual free energy). This is a dynamical hypothesis, based on semiotic motivation. It says something about how additional levels of organization get added to an initial multi-scale dynamical system (perhaps including the primordial case of a non-semiotic two-level system). The typological order at some level, with respect to the SI level above, always has some residual quantitative variability that initially is 'ignored' by the level above. But it can (and presumably must, though 'under what conditions?' remains a key question) happen that certain correlational patterns within this residual quantitative variability become significant for the level above. This does not add new types to the original lower level, it remains semiotically 'closed'; but the correlational patterns in quantitative relations among these units now constitute a new intermediate level just insofar as they do come to matter to the level above.

These three levels now constitute a new semiotic triad, and all of them are changed by the emergent order 'in the middle' (this emergent order is really relational across all three levels; we just tend to focus on the middle level because it is the level at which the new types are defined). The top level (of these three) is changed because it has new informational input from below, it is now selectively sensitive to new kinds of pattern or order among its constituents that it was previously insensitive to. The middle level is of course entirely new. The lower level is also changed because it is now subject to new constraints from above: in the presence of the correlational patterns that define the next higher level, there are fewer degrees of freedom accessed by the lower level. Why do these particular correlational patterns, among all the possible ones, come to be selected out as signficant at a higher scale? We can say because they are 'adaptive' at the higher scale, but what we mean now is that they are the lower-scale signs of something that has reality, that makes a difference on larger scales, particularly on longer timescales, than the ones on which they themselves exist. It may be that they are the system's way of feeling ahead into its future, or at least into the future with respect to the timescale of the level in focus. One can say, with a pointlike-present view of time, that they aid 'anticipation' at some level (Rosen 1985, Salthe 1997). Or equally we can say that they are the means by which the temporal coherence, the organization and integration of processes across different timescales, is achieved level by level (or triple by triple).

We are also saying not just that these particular correlational patterns are selected for because they are adaptive in the above sense, but also that the available patterns that can be selected for, arise in large part from the attractors of the material dynamics of the constituents of the original lower level, subject to the constraints of the original higher level. Not only are they not random, but there are very few available possibilities, and different lineages can be expected to work small variations with the same available raw material. Selection becomes fine-tuning, but the instrument is largely wrought by its own self-organizing dynamics, a dynamics that in the case of biological systems has a very great evolutionary and developmental 'logical depth' (Collins & Hooker 1998).

In the story I find myself telling here (which is only a hypothetical one, of course), 'logical depth' corresponds to the unavailability of short-cuts in the ontogeny of a highly evolved, or generally a multi-level, self-organizing system: new meanings of new patterns of quantitative correlation among types on a lower scale cannot emerge until those types, along with their possible residual quantitative variations and relationships, have previously emerged. That emergence is never predictable the first time, for it is a function of unique conditions, unique to the individuation of some particular system, within the developmental trajectory of its kind before the emergence. And once it becomes somehow conserved (inevitably as a function of the longer-timescale persistence, or recreation, of those originally unique -- or at least not yet known to be persistent -- conditions) as part of the future trajectories of such systems, still newer dynamical possibilities come into being whose very terms of definition could not have been formulated one stage back, because the types whose residual quantitative variation is the basis for the new possibilities did not yet either exist or necessarily need to come to be. Some very different raw material might have become available, and some different selection adaptively shaped. Viewed as a process of computation, the results at each stage must be computed before it is possible to even define the algorithm for computation of the next stage. There are no computational shortcuts, no way to predict the instance-specific individuation component in development, only the type-specific recapitulative component, and so no way to predict evolutionary futures insofar as either long-timescale constraints may change, or the details of future evolution (and so of the late type-specific stages of future developmental trajectories) depend on shorter-timescale processes that provide the raw material to be shaped by even persistent long-timescale constraints.

That the evolutionary principle just described applies equally to human social history (i.e. to the evolution of technology, mores, and more generally 'ecosocial systems', Lemke 1994, 1995), and indeed to the history of science (or 'technoscience', Latour 1987, 1993), should be obvious. The implications, which deny the fantasies of social engineering which justify our current technocratic legitimations of power, are understandably refused by all those who hope, or will, that we can make history just as we please. We can, should, and must 'push' and 'choose' on the timescales it is given us to act within, but without the illusion that we can foresee the consequences beyond the next unpredictable emergence.

There are moreover a number of additional complications in the case of multi-scale systems, or more generally multi-scale networks (Latour 1996) of interdependent semiotic-dynamical processes in which material entities with semiotic value are produced on one scale, but are also interpretable on other scales. The topology of networks seems the most appropriate one for such systems, and, as I would argue in this case (Lemke, in preparation), timescales provide the most relevant parameter for defining cross-scale semiotic-informational relationships. A semiotic artifact may persist over very long periods of time, and itself be the product of large-scale social-institutional processes over long timescales, and may accrue and accumulate (relative to some larger-scale, longer-timescale cultural system of interpretation) many meanings, but nonetheless it may also be interpreted by human-scale actors on relatively short timescales and play a role in determining our short-timescale actions. In this way semiotic mediation can occur between processes on very different timescales, between which purely dynamical connections are forbidden by the adiabatic principle. This introduces new semiotic connectivities, with definite dynamical consequences, into the networks. What is often called 'cultural evolution' has its specific dynamical significance through these 'heterochronic' connections, perturbing a neat dynamical hierarchy toward a less well-understood semiotic-dynamical 'heterarchy'. I believe that this is the key phenomenon that must be considered in making a dynamical theory of ecosocial systems. It seems reasonable to suppose that it has precedents in biosemiotics, though whether or not DNA itself could be considered such a heterochronic material-semiotic 'artifact' is not entirely clear to me.

Regardless of these important complications in the case of human sociocultural, semiotic ecosystems, we can still, if the hypothetical story I have been telling in this paper is at all a useful guide, look to the (multi-dimensional) residual quantitative variability within and between our naturalized conceptual categories as a potential resource for opening up the closure of meanings they impose on us. Every sharp categorial distinction that we can analyze into quantitative 'fuzziness', on as many dimensions as possible; every finer-scale specification which we can backtrace to a less-differentiated, more pluripotent 'vagueness' ; every conflation that maps categories onto one another one-to-one that we can prise apart into a combinatorial matrix of relative frequencies of association … enlarges our meaning-space and multiplies our possibilities for imagination and so for action … making the future ever more unpredictable and rich in new orders of organization to be temporarily superimposed on the gradual and far larger-scale universal degradation of order, just as we ourselves are.

Quantum units at the scale of atoms or ions represent discrete, categorial, typological variety. An atom is either a Carbon type or a Nitrogen type or some other element; there are no intermediate degrees of Carbon-ness, no normal atomic or ionic species with a fractional number of protons. As we look at a biological molecule on a scale somewhat larger than the atomic scale, the variety available to be organized is the set of discrete differences from one atomic species to the next. We may increase this repertory somewhat by considering the different bonding arrangements and allowing that a nitrogen amidst one set of atomic neighbors does not behave as exactly the same intra-molecular species as a nitrogen in some other atomic environment, but still the set of possible types is finite and discrete. However, as we begin to consider the molecule as a whole as an emergent unit of organization at a new level, and we ask what properties of the molecule over longer many-atom stretches are relevant to how other molecules react to it, then we see that it is the electrical charge distributions in space, which have a quasi-continuous representation, which matter. Molecular organization represents a re-organization of the discrete, typological variety of atomic species into quasi-continuous spatial distributions of electrical charge, as a function of the interactions among the species in various combinations; and this new toplogical variation in electrical charge is what conveys information to the next higher level of organization: intermolecular interactions.

We see this most strikingly in the case of proteins, where the discrete units are compounded from atoms to repeating amino acid units (again slightly different in different neighboring AA environments, but still a finite set of types), but what matters in terms of the action of the protein as a whole in the larger-scale environment is a spatial conformation, the folded-chain, which is a collective effect and presents us with emergent properties on a larger spatial scale, which are properties that matter to a still larger scale, as below. Typological variety is emergently reorganized at a larger spatial-material scale as topological variation that is meaningful for phenomena at a still higher scale.

Biomolecule conformations (topo) organized as ligand class information (typo) by larger-scale membrane polymers

What is this next scale? The topological variety, regarded as information, represented by the conformations of macromolecules (e.g. folded proteins) and their associated (interactively functional) spatial charge distributions matter to a still higher scale, the chemistry of the cell, only by way of, for example, their interactions with intermediate-scale cellular structures such as membranes and interior reticula. The membranes, of many kinds in the cell, have in common that they respond to biomolecules as ligands, that is, as potential binders to membrane sites. These sites are formed by the interaction of the membrane-constituent molecules and represent, in their own spatial conformations and active charge distributions, an emergent level above that of the individual biomolecular species. These active sites define equivalence classes for other biomolecules, ligand classes, effectively those which will or will not bind to the site and produce some effects. In some cases binding may be partial, and some ligands may produce more pronounced effects (say the opening or closing of a membrane pore), but what has happened here is that, so far as the next still-higher level is concerned, all that matters about a biomolecule is which ligand class it belongs to relative to this membrane site.

The topological variety of the folded protein of the ligand, or of the site itself, does not matter in its quantitative detail, but only via these equivalence classes and discrete effects. Topological variety has been reorganized at a new emergent level as typological meaning for still higher levels. (Note that obviously there are still some quantitative effects that are matters of degree, but the new organizational level as such fits what is expected from the principle of alternation.)

Pauci-molecular reaction pathways (typo) organized as molar concentration-dependent effects (topo) at global cell-chemistry scale

Suppose we now move up again in scale, from a view in which we see individual molecules interacting to one in which we see only statistical distributions and average concentrations. In between, there is the interesting regime of what is coming to be known as pauci-molecular chemistry, where the assumptions of the law of mass action and macro-chemistry are not met. There may be further emergent levels of relevant organization at these intermediate scales, but they are not well understood yet. Nonetheless, it is quite clear that in this regime we are in transition from typological phenomena in which there are again quite discrete reaction pathways dependent on local conditions, to a higher level of global or gross cellular chemistry at which the law of mass action is a better or very good approximation. Global level cell chemistry has its own emergent properties, such as overall pH and other average concentrations, and these variables are now topological in nature, because to good approximation they are continuously variable. (See Halling 1989, Kawade 1996).

Molar chemistry (topo) organized as neuro-transmitter threshold effects: "firing" (typo)

The molar chemistry of cells, representing topological variety, can again be reorganized at still higher levels into typological variety, as in the well-known case of nerve cells that ‘fire’; certain quantitative thresholds are exceeded leading to global chain reactions throughout the cell, and we know that still higher level brain processes depend on configurations and sequences of this now typological variety: cells that do or do not cascade or discharge. Whole multi-cell synaptic sequences are built, which are, like molecular species built from atomic ones, again of discrete identifiable types (each recurrent pathway is a type in this sense).

Firings in neural nets (typo) organized as coherent cortical effects (topo): "brainwaves" "holograms"

But how do these synaptic cascade pathways matter to larger brain processes? in part at least they matter by way of global, coherent electrical excitation of the brain, such as the alpha wave patterns and others of similar kind. These wave patterns, while themselves discrete types, carry information in a topological form: continuously variable amplitudes. We should also note here that it appears that there are many other such global, or at least ‘volume’ effects of neurotransmitter concentrations, such that neurons may not actually ‘fire’, but only carry slow-wave changing potentials, influenced by peptide concentrations and modulating the graded release of neurotransmitters that affect many neurons in the local volume. Here too we find higher-scale topological effects of lower-scale typological variation, and vice versa. Another hypothesis of like sort is Pribram's "holograms" or holonomic functional units (1991) which in many brain systems appear to be organized non-locally across brain structures and their electrochemical activity.

Cortical dynamics (topo) organized as limit cycles (typo): "percepts" "phonemes"

It is at least possible in some models of brain functioning that topological, meso-scale brain dynamics, in the form of propagating waves of electrical activity, whose effects matter through degrees of intensity, whether of chemical concentrations or of electical polarizations, interact at a still higher scale of brain activity to produce emergent levels corresponding to elementary "percepts" or to "phonemes", which are frequently or regularly typological in their informational variety. This presumably happens through the emergence of new attractors in the dynamics of the meso-scale functioning, each attractor in effect classifying its basin into a type.

Neuronal attractor effects (typo) organized as smooth motor behavior (topo): "drawing" "gesticulating" "enunciating"

Clearly there is an intimate interdependence between perceptual and motor functional elements in such a scheme, and we can again see a transformation or re-organization in the production of smooth motor behavior, which functions in terms of its topological characteristics (timing and coordination, gross and fine movement in space), which are in turn emergent from the discrete, typological elements that correspond to dynamical attractors in the neuro-muscular system. Ennervations and innervations of particular nerve elements and muscle fiber bundles (typological and discrete) emerge as overall continuous motion in space (topological, characterized by continuous degree and change). This is surely a miracle of emergent organization at a very high level (slower processes, on larger spatial-extensional and matter-energy scales).

Smooth motor behavior (topo) organized as visual and verbal signs (typo): "gestures" "words" in an ecosocial supersystem functioning as the meta-system of interpretance

Finally, I will end here with the last step of the link from physics to language and human social semiotics that I promised, namely the smooth motor actions (topological) are re-organized by learned processes of organisms in communities to be produced and interpreted as signs, such as word-utterances and gesture-productions, which are classic instances of typological signs. The SI here is not just the organism, but the organism in a community, and not just a community of other persons, but an ecosocial system that includes all the relevant nonhuman agents or actants as well (e.g. written texts). The timescales here are not just those of cognition, but those of language- and culture- learning, and indeed implicating the next higher scale: historical change in the social meaning systems for interpreting words and gestures.