Varela F. J. (1988) Structural coupling and the origin of meaning in a simple cellular automation

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In this paper I wish to address what I consider one of the central conceptual issues underlying the Immunosemiotics meeting: the origin in meaning in cellular communication. Semioticists have done immunology a great service by framing the role of molecular interactions as a system of signs and their significations. This is hardly what immunologists normally do, involved as they are with the nitty-gritty of molecular mechanisms, far too close to visualize the entire forest.

Took a while to track down an open source of this – formatting not nice but here it is!

Source: Varela F. J. (1988) Structural coupling and the origin of meaning in a simple cellular automation


Cite as: Varela F. J. (1988) Structural coupling and the origin of meaning in a simple cellular automation. In: Secarz E., Celada F., Mitchinson N. A. & Tada T. (eds.) The semiotics of cellular communication in the immune system. NATO ASI Series, Volume 23. Springer-Verlag, New York: 151–161. Available at
1. Introduction: Classification vs. generation
In this paper I wish to address what I consider one of the central conceptual issues underlying the Immunosemiotics meeting: the origin in meaning in cellular communication. Semioticists have done immunology a great service by framing the role of molecular interactions as a system of signs and their significations. This is hardly what immunologists normally do, involved as they are with the nitty-gritty of molecular mechanisms, far too close to visualize the entire forest.
In my view, however, current semiotics is not a satisfactory framework to advance understanding of cellular communication because so far it has only signs and their systems.[Note 1]Note 1. NOTETEXT-1 There is nothing by the way of a mechanism as to how a sign one: there is no explicit mechanism for the origin of meaning. It is somewhat like reading a taxonomy text before natural selection was proposed as a mechanism for the origin of diversity. This contrast – taxonomic (or structuralist) vs. generative – was, in my opinion, at the center of many discussions during the meeting.
Accordingly, my intention in this paper is to address this issue directly through the use of a simple I hope that this will do more to illustrate what I have in mind that a dry theoretical presentation. Some conceptual background is nevertheless necessary, and that is the topic of the next section.
2. Operational closure and structural coupling
Meaning can only arise for those systems which assert their own identity vis-a-vis their environment, that is, for systems with a degree of This class of autonomous systems stands out in contradistinction to those systems which are defined through relations. For these latter class of systems, the way in which they relate to their environment is not an issue: they are specified through input/output conditions which completely clarify how their environmental coupling occurs. The familiar digital computer is the clearest example of this class of systems: the meaning of a given keyboard sequence is always assigned by the designer.
In contrast, cells and organisms are far from being in the same category. Under very restricted circumstances we can speak as if we could specify the operation of a cell or an organism through input/output relationships. In general, however, a living system its own world of relevance, and is not given in advance. The meaning of this or that interaction is not given by an outside designer, but is the result of the organization of the system itself and its history. This point is intuitively quite evident to any working biologist, but more often than not, eschewed because of its seeming difficulty.
The question is, then, how to account for the emergence of meaning from a milieu of interactions for a system which cannot be specified through a list of input/outputs. The answer I have been developing for some years is basically this: follow the consequences of characterizing the system, not as input/output, but as having that is, as defined through a network of processes of some kind. Once a system is adequately defined in this fashion, its self-organizing qualities will become apparent. In particular, a with an environment will lay down what is and what is not relevant for the system: the history of coupling will inevitable bring forth a world of signification.[Note 2]Note 2. NOTETEXT-2
My experience in trying to convey these ideas is that although many people accept with some ease the notion of operational closure (self-organization in a network -like system), the complementary notion of the origin of meaning through structural coupling remains veiled in a cloud of mystery. The reason for this is not intrinsic complexity, but simple lack of occasion to be exposed to such an analysis. This is why I wish to provide an example that is so transparent that it can serve as a paradigm or exemplar.
3. The system
The example I wish to present is based on very simple cellular-like automata which receive inputs from two immediate neighbors, and communicates its internal state back to them. Each cellular automaton can only be in two alternative states (i.e. 0 and 1, active or inactive). Assume that the rule governing the change in each automata is simply a boolean function of the two arguments it receives from its neighbours at each discrete moment of time. Typical boolean function are, for instance, the well-known logical operation And or ‘Exclusive or’. We can associate such a boolean function to each one the two states in which the cellular automaton is in; this says that the way the cellular automaton will respond to its surrounding neighbours will change depending on its own state. Thus, the functioning of each automaton is completely specified by a of boolean functions. In our figures this is expressed as an 8-digit binary number if we express each boolean function in terms of their 4-digit transition tables, which indicates the output of the automaton as a function the four possible combination of its two inputs.
The closure of the system is now introduced simply by connecting it as a circular array, so that there no inputs and outputs from the entire system ring, but only internal actions. For the purpose of display, however, it is easier to cut this ring open and to present it linearly, with the cells in the 1 state indicated by a black square, and the opposite state indicated by a blank space. Accordingly, in the display shown here, cellular position runs from left to right (modulo the ring’s length) (Fig. 1).
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Figure 1: Schematics for the definition of the cellular automata studied here (see text).
This ring of cellular automata acquires a temporal dynamics by starting it at some random state and letting each cell reach an updated state at each discrete moment of time in a synchronous fashion (i.e. all of them together). In the display we represent the initial instant at the top-most row, and successive instants of time going downwards. Thus the successive state of the same cell can be read as a column, and the simultaneous state of all cells can be read as a row.
In the cases we study here all cells in the ring are defined by the same pair of boolean functions, and it appears inscribed on top of the display. Further, we consider only symmetrical boolean functions (i.e. with identical entries in the diagonal of their transition matrix, so that strictly speaking we need only six digits to define the dynamics of the ring). In all the simulations presented here the ring was composed of 80 cells, and its initial starting state was chosen at random.
4. The dynamics of the closure: Self-organizing qualities
These rings of boolean cellular automata have very interesting and surprising self-organizing capacities. An extensive discussion of these capacities has been conducted recently by S. Wolfram.[Note 3]Note 3. NOTETEXT-3 It is not my intention to recapitulate his work here. Suffice it to say that the closure dynamics of these rings fall into four major classes illustrated in Fig. 2. A first class exhibits a simple dynamics dominated by a single attractor, leading all cells to become homogenously active or inactive. For a second more interesting class of rings, the rules give rise to spatial periodicities, that is, some cells remain active while other do not. For a third class the rules gives rise to spatio-temporal cycles of length two or longer. Finally, for a few rules, the dynamics seem to give rise to chaotic regimes, where one does not detect any regularities in space or time.
We shall not dwell on the interesting diversity of the internally generated dynamics of these boolean rings. Our interest is to move beyond their closure to examine what happens when they enter into a history of coupling.
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Figure 2: Representative self-organizing dynamics for different choices of defining rules (the 8-digit binary number on top). Initial states in all cases is randomly assigned. The differences in the global behavior Is immediately visible in the pattern of the display. Arrow to the left indicates the arrival of a perturbation following the mode of coupling depicted in Fig. 3.
5. Histories of structural coupling
Of the many forms in which we could endow our rings with a coupling with an environment, I have chosen the following. Imagine that we dump the ring in a milieu of random O’s and l’s, much like a cell is plunged in a chemical milieu. Imagine further that the encounter of a cell with one of these two alternatives (0’s and l’s) leads to the state of the cell being replaced by the perturbation that it encountered (Fig.3). For the sake of brevity, let us call Bittorio this particular ring of cellular automata this form of structural coupling with the chosen milieu.
In Fig. 2 the arrow to the left indicates the moment where one perturbation reaches one particular cell at one particular instant. The dynamics that follows indicates the way Bittorio compensates this perturbation, i.e. the ensuing change (or lack of it). As it is apparent, if Bittorio’s rule belongs to the first or fourth class (i.e. a simple or a chaotic attractor) the consequence of the perturbation is simply invisible: Bittorio either goes back to its previous homogenous state, or it remains in a random-like state.
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Figure 3: Schematics for the mode of coupling defined for the cellular automata of Fig. 1. A chance encounter with a I or 0 changes the internal state of the perturbed cell for that of the perturbation encountered. For simplicity, perturbations at only one location are displayed here.
It follows that only the second and third class of rules can provide us with a dynamics capable of producing Interesting consequences for the kind of structural coupling we have chosen for Bittorio. As also shown in Fig. 2, for these kinds of Bittorios, a single perturbation induces a change from one to another spatio-temporal configuration, both of them stable and distinguishable.
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Figure 4: An instance of discrimination of odd sequences of perturbation. Automata with the same rule but different initial configurations are displayed. Top row: encountering one perturbation at arrow. Bottom row: encountering two successive perturbations.
The base of Bittorio of rule 1001000, illustrated in Fig. 4, is worth commenting in more detail. As can be seen, the encounter with just one perturbation changes the spatial periodicities from one to another stable configuration. However a second perturbation at the same cell undoes the previous change. Hence, any sequence of perturbations at the same locus will lead to a change in the state configuration for Bittorio, while any even sequence of perturbations will be invisible, since it leaves Bittorio’s global state unchanged. Thus, of all the innumerable sequences of possible perturbations, this Bittorio picks up or singles out from the milieu a very specific subset: finite odd sequences; only they induce a repeatable change in configuration. Stated in other words, given its rule, and given its form of structural coupling, this Bittorio become an ‘odd sequence recognize.’
Another example of this emergent signification is shown in Fig.5 for Bittorio of rule 01101110. A sequence of perturbations is the only trigger capable of leading to a change In the state configuration of Bittorio. This is readily seen in Fig.5 where I have superimposed several encounters at different cellular loci to facilitate comparison. Everything other than double perturbations in one location leave this Bittorio unchanged.
I have explored what happens to these ring automata with simultaneous perturbations and more complex forms of structural coupling. They reveal very many rich and interesting behaviors. I will not enter into the detail of these observations for the purpose of illustration: our simple Bittorio is enough.
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Figure 5: An instance of discrimination of pairs of perturbations. Here, in contrast to Fig. 4, several sequences of perturbations are induced at different locations on the same automata, since each one only has local effects.
6. Bringing forth meaning
In the two specific cases described above, we have not provided Bittorio with a program to distinguish ‘odd sequences’ or ‘two successive perturbations’. What we have done is to define a form of closure on the one hand (its internal dynamical alternatives), and the way in which this system will couple with a given milieu on the other hand (the contingence of its encounters). The result is that the brings forth or selects from a random world what is relevant for the system itself. The system recognizes out of its own autonomy what is significant and how it is so.
I have used the words significance, relevance, and meaning advisedly. Meaning involves necessarily a form of in an encounter. My claim is that Bittorio performs precisely this form of a minimal interpretation in its encounters, thus pointing to us, as observers, what does and what does not lead to changes in its internal dynamics.
This is similar to the study of cellular or animal behavior. We must see what the animal singles out as relevant in reference to changes in internal dynamics; its world cannot be constituted as a set of predefined inputs independently of its particular history. This is the capacity upon which the creativity of life hinges. In general, then, my claim is that once closure and coupling are described for a system, the emergence of a world of relevance becomes apparent to an observer.
The example presented here is extremely simple, in some sense minimal, so that we can follow the entire process in detail. That was its intention; it should not be read as a model of any specific phenomena of cellular recognition. However It seems that even with the very simple form of operational closure and of coupling given to Bittorio if we can already recognize the emergence of a minimal form of signification, then this will be all the more so for living cells or cellular networks such as the brain and the immune system.
Notice, however, that what I have proposed is a mechanism and not a recipe. To investigate how it is actually embodied in each situation, one needs to pursue the details of that situation. In particular, one must have at least some idea of:
the operational closure of the system and its dynamical landscape, and
the fundamental dimension of the structural coupling with the milieu.
Both these points are central for the network perspective in immunology.[Note 4]Note 4. NOTETEXT-4 In fact, since its inception this perspective has emphasize the self- organizing dynamics that must constantly arise in such a network system, in contrast to the local character of the clonal selection dynamics. Furthermore, the network perspective has always raised the issue of the dependency between internal dynamics and antigenicity, in contrast to the antigen-centered clonal perspective. In a word, the traditional immunological views are closer to input/output descriptions, and it is not surprising that the emergence of molecular significations remains difficult to handle within that framework. In contrast, a network perspective is already a step in the right direction to understand immune phenomena as a system of signs and significations produced by the immune system itself.
My thanks to Alfonso Gómez, Patricio Huerta and Marcelo Miranda for participating at various stages in the computer presentation of these ideas. My interest in immunology is due to the patient and friendly influence of Nelson Vaz and Antonio Coutinho. I hope it will continue.
FV is the holder of the Fondation de France Chair of Cognitive Science and Epistemology at Ecole Polytechnique. Thanks also to the Prince Trust Fund for financial support.
1 I am using as a reference here U. Eco, A Theory of Semiotics, Indiana U. Press, 1978.
2 I’m painfully aware that these key notions – operational closure and structural coupling – remain quite vague here. I only intend to evoke some of their signification and to use them through the example. For a full discussion see: F. Varela, Principles of Biological Autonomy, Elsevier/North Holland, New York, 1979, and for an introductory account see H. Maturana and F. Varela, The Tree of Knowledge: The Biological Roots of Understanding, New Science Library, Boston, 1987.
3 See in particular: S. Wolfram, Statistical mechanics of cellular automata, Revs. Modern Physics 55: 601-644, 1983, and: Cellular automata as models of complexity, Nature 311: 419, 1984.
4 The classical paper by N. Jerne, Towards a network theory of the immune system, Ann. Immunol. (Paris) 125C: 373-395, 1974 emphasized the “eigen-behaviors” (or self-generated) states of the immune systems. The idea is also discussed in N. Vaz and F. Varela, Self and non-sense: An organism- centered approach to immunology, Med. Hypotheses 4: 231-257, 1978 together with the notion of a cognitive domain. See also A. Coutinho, L. Forni, D. Holmberg, F. Ivars, and N. Vaz, From an antigen-centered clonal perspective of immune responses to an organism-centered network perspective of autonomous activity in a self-referential system, Immunol. Revs. 79: 151-168, 1984.