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Chaos, complexity and gustave guillaume
Chaos, Complexity and Gustave Guillaume
Perhaps the greatest merit of any theory is its ability to withstand the passage of time and
the advent of new data or general theoretical findings, together with its capacity to encompass
these new elements - or to be encompassed by them - without having to suffer major changes.
The new elements can come from fields totally unrelated to that of the theory in question - in
which case it is the more substantiated through the adaptation. In this dawning era of science
where inter-disciplinarity spreads more and more, yielding almost every day fascinating results,
the bell tolls for such theories as cannot accept outside evidence. This, of course, holds also
true for linguistics.
In the realm of multidisciplinary studies, the finest example, the one which promises the
most extraordinary results, is the study of chaos and complexity. Although it could be said to
have had a long history - the first scientific research into some aspects of chaos seems to have
begun in Russia in the early 1920's - it has only recently received much attention with the
advent of powerful computer (and graphics, used especially for the representation of fractals)
and the creation, some ten years ago, of the Santa-Fe Institute in the sciences of complexity
This study of complex systems is not, however, a new science as such. More precisely, it is a
tool based on a set of principles and concepts - culminating in the "complex adaptive system" -
with which one can obtain a better view of the object of research. By looking at the global
properties of complex systems - and these may be found in many places - one can better see
the specifics of particular ones. It is a new way for us to have the perception savante
(1968:300ff) talks about.
Whether this new array of concepts is to be of use in the field of linguistic study, or even
applicable to it, will depend on whether language is part of the notional frame of complex
systems; in other words, if language can be considered a complex dynamic system. If this be
the case, we must furthermore re-evaluate our ideas about language, our linguistic theory, in
the light of the evidence which comes from complexity studies. I would not propose that
linguistics be reconstructed from a complexity standpoint, rather that we verify our current
hypotheses - and maybe eventually some of theirs, we have to remember that the "sciences"
of complexity and chaos are still in their infancy. It would however be a great achievement forany linguistic theory to easily accept these new ideas and contribute to them in its own specialway.
But first we have to know if language is a complex, adaptive system, and if so, in whatspecific fashion. After which we will be able to examine the correlations of one particular theory,which seems quite suitable for such a comparison, namely the psychomechanics of GustaveGuillaume.
2. Complex, adaptive systems
The notion of complex, adaptive systems evolved out of mathematics and fluid dynamics; in
the language of these disciplines, they are systems resolved through non-linear equations1 -
for example, the weather. But that is not all, in order to fall into this category, complex systems
need to be able to adapt; as Gell-Mann puts it:
"Turbulent flow in a liquid is a complex system, but it can't be called adaptive.
(.)There's information in the system, no question. But it doesn't produce a schema,a compression of information with which it can predict the environment. In biologicalevolution, experience of the past is compressed in the genetic message encoded inDNA." (Quoted in Lewin 1992:15)
Non-linear complex systems are found everywhere, from the embryo to the economy. Theiradaptivity and information compression implies certain observable features like the apparentcreation of order out of chaos; indeed, one of their most remarkable traits is that of "globalproperties flowing from the aggregated behaviour of individuals." (Lewin 1992:13). Theseproperties cannot be predicted from the information on the individuals. There seems to be aconstant feedback from these properties to the individuals, that is, they can react to them. Thesystem is the whole: the interacting part and the emergent properties, and both are taken intoconsideration in the study of complexity.
One of the most readily observable occurrences of this phenomenon can be found in theecosystem; there, every individual in the different species tries its best to survive (andprocreate); as they do so, the ecosystem thrives by their efforts, and, without knowing it, theyall work for the best of the system. For example, there is always a certain part of cooperation(be it "conscious" or not) between the individuals within a species - or between species.
Furthermore, in a predator-prey system, the good of the predator goes through, paradoxically,the good of the prey (cf. Thom 1991 for a discussion of this relationship). Patterns ofcooperation and, in a non-darwinist way, evolution occur. And in turn, on a smaller scale, eachof these species is a complex, adaptive system on its own, as is, to some extent, everyone of
its member (in the way its body is constituted).
The answer lies in the way the information about the environment is recorded. Incomplex adaptive systems, it is not merely listed in what computer scientists would calla look-up table. Instead, the regularities of the experience are encapsulated in highlycompressed form as a model
. Such a schema is usuallyapproximate, sometimes wrong, but it may be adaptive if it can make useful predictionsincluding interpolation and extrapolation and sometimes generalization to situationsvery different from those previously encountered. (Gell-Mann 1992: 10, italics in thetext)
The most important characteristic of these systems - probably the hardest to grasp orcomprehend - is that they are, as Lewin tells us, poised "on the edge of chaos." What does itmean? Imagine a heart monitor, there are four possibilities in what it can exhibit. First, nothinghappens: there isn't any system as such. Second, a regular heartbeat: a stable, linear system.
The third possibility is fibrillation: the system is chaotic, the heart goes wild. The fourth stagelies between 2 and 3, at first things look chaotic, but on closer inspection patterns of stabilitydevelop, and this at many different levels. If the system is stable (2), it will not adapt, if, onthe other hand, it is chaotic (3) it will not work - at least not properly; between these two lies(or lives) complexity, where adaptation, progress and survival thrive (this, according to Gell-Mann, is where the greatest information processing occurs). It is, to use an oxymoron, a stablechaos.
A particular phrase which often appears in discussion of chaos or complexity is "strangeattractor". The usual representation is a spacial dimensionalization of the variables of a system,i.e. the variable are translated into coordinates, so that the movement of a point can trace theevolution of the system in a multi-dimensional graphic. What emerges is a bound trajectory,often revolving around one or two poles, but where the point never takes twice the exact samepath. The boundary cannot be exactly determined, but it is never crossed, except in shortextraordinary cases. Take for instance, the weather2: never will exactly the same sequenceoccur twice, but it will never snow in the Sahara desert (if it does, things will be back to normalin no time, the system will have "recuperated" the variable.) This reflects Gell-Mann'scomment, "complex adaptive system are pattern seekers." (Lewin 1992:16) Another of their characteristics is the reaction to external and internal forces (the famousbutterfly effect
): a little prompt may have incredible repercussions throughout the system3,only a small effect or none at all. The reactions are in what is called a "power law distribution":from an identical source, the smaller the effect the commoner it will be.
Let us turn to language, if we accept Saussure's hypothesis that language is a system -
which, in view of its structured appearance and use, seems sensible - we must consider it a
complex, adaptive one. It is obviously complex, involving a large number of parts or sub-
systems (for example, the verb system, the nominal system, etc.) with a high degree of
interaction between them. At any point in space or time it is adaptable, or adapted, to the
needs of the speakers - providing a frame for new words, being able, more or less efficiently,
to express any and every experience in the mind of the speakers. This is why we may say that
it acts as a previsional system. To do so, it uses its historical inheritance (cf. Guillaume
1984:58) to provide for future needs.
Language can easily be described, at least in part, as the "aggregated behaviour4 of
individuals" from which order arises. Language would also have to be at a stage where there
is the greatest information processing, in order to give man the necessary tools to cope with
any contingency of his experience. Looking at both diachrony and language learning, one can
with little difficulty discern some of the characteristics of non-linear adaptive systems. Non-
linearity itself can be observed in a way: the play of meaning and syntax where each word's
meaning in the sentence interacts with the others - where any minor change can bring about
major effects on the resulting sense - the emergent properties (cf. Langacker 1987:??), the
iterations (see below), etc.
The behaviour of the babbler exhibits at least two characteristics of languages (in what is
commonly called language acquisition): the presence of some sort of attractor, a near-constant
of evolutionary steps in the way and order in which he learns part of the morphology of his
mother tongue - the Brown study on morpheme acquisition is a good example of this5. The
other one is the phase transition (see below, section 3.2): when, in his mind, language stops
being a mere code and becomes an extended means of representation, a tongue6 (cf. Guillaume
1984:41). This also occurs with L learners, although - because of their already present
referential system and of the way they usually learn the language (school) - to a lesser degreeIn history we also can find both properties, e.g.
the consistent gradual loss of nominal inflectionin I.E. languages, and the switch from the Latin to the French verb system.
But is there any more to it than this? To what point is language complex and to what pointstable? To answer these questions, one has to look not only at diachrony but also at diverseaspects of synchrony - the many characteristics of complex, adaptive systems would have tobe present at the many levels of synchrony. Furthermore, since the mind is involved,mind/language interactions have to be taken into consideration.
3.1 The object of study
Before we can look at any of these aspects, however, the theoretical frame for the study of
language has to be in some key respects compatible with that of complex dynamics:
One of the most important characteristics of complex nonlinear systems is that theycannot, in general, be successfully analyzed by determining in advance a set ofproperties or aspects that are studied separately and then combining those partialapproaches in an attempt to form a picture of the whole
. Instead, it is necessary to lookat the whole system, even if that means taking a crude look, and then allow possiblesimplifications to emerge
from the work. (Gell-Mann p.14, his italics)
In his Foundations
, Guillaume tells us that the linguist, if he is to be able to understand acertain form, has to previously reconstruct the system of which it is a part (1984:82). He alsomakes clear, and often repeats it, that a system always has to be seen as a whole - thisincludes both the inner systems and the outer one, language itself - before one can make anydefinitive statement about its parts. For example, linguists should study not only the mentalaspect of a system, but also its different observable uses and semiological manifestations, fromwhich the system can be "reconstructed", to use the terminology of the comparativists.
Another important point, one which Guillaume and his disciples are perhaps the only onesto take into consideration - to postulate, in fact, as primordial in nature - is the view that, inlanguage, time "is of the essence". This postulate of operative time
as a key factor in thepsycho-mechanisms leads one to the method known as linguistique de position
, in which thetheorist studies the discursive uses as one would do the different languages in comparativelinguistics (cf. Valin 1964), after which he tries to locate them in the operative vectorrepresenting the thought process as it evolves in (micro-)time7. Time is, in non-linear dynamicsand science in general as Ilya Prigogine pointed out in a recent interview for a Montrealnewspaper (Le Devoir
, October 4, 1993; B-1), the key element to consider.
3.2 An evolving system
In diachrony, time is of course the key element, but other factors are to be considered. From
this point of view, language, according to Guillaume, is on the verge of chaos, edging between
(sterile) stability and all out disorder.
Diachronic linguistics grasps things longitudinally, in time, which makes them change,perturbs them, disorganizes them, and would destroy them
if some contrary, organizingforce did not intervene. (.) In language, systematic organization works on thedisorganization that a language inherits from instant to instant. Actually, two opposing
forces are involved here, the one descending and disorganizing, the other ascending andorganizing. (1984:59, my italics)
The disorganizing force comes from the fact that the system cannot be directly "handed on"to the next generation. The acquisition of a mother tongue comes from an analysis, on the partof the infant, of the evidence heard. The disorganizing movement also comes from the use oflanguage by humans to represent and express even new experiences. It is not rare in fact thatone uses, as he speaks, words quite beyond their intended scope. The best, and most common,example of this is the ample use of metaphors.
In a metaphor, the actualization of the word goes a little beyond its potential meaning: thespeaker often retains a sole characteristic of this meaning (cf. Hirtle 1992) as he relates it tothe other word(s). Here the line between the potential meaning and actual sense is stretched,sometimes up to a breaking point (at least for the reader/listener). "Metaphor, then, is one ofthe ways, and possibly the most important, in which the 'stretching' of the language takesplace" (1992:71).
This kind of use is not restricted to what may be called lexical words, it also occurs withdeterminers, verbal constructs, betimes whole sentences. Even the tenses of the verb are notbeyond it. In fact, it has often been suggested that metaphoric uses account for an importantpart of linguistic evolution.
The reaction to this phenomena plays on two levels, depending on the situation in which themetaphors are uttered. With adult speakers, what will usually happen is that the listener willtry and understand what is meant, what the speaker is trying to represent; he will stretch thepotential meaning (more precisely, it is the referencial capacity of the potential that isstretched) and eventually - often quite rapidly and unconsciously - figure it out, and maybekeep the expression in mind for further use. If the same metaphor occurs somewhat frequently,he may assign a new "figurative use" to the word(s). This can lead to new words or, morefrequently, change the potential meaning a little. This change, since the disturbance is mostoften lexical and limited to a small number of speakers, has little or no chance of creating ripplethroughout the whole system.
The reason for this is simple: although language is a system of systems, some parts are notsystematic, the lexemes, for example (Guillaume 1984:106). Lexical changes do not bringabout systematic modifications unless the system itself is implicated, which, is hardly possiblefor adult speakers since, for them, a system is already reconstructed, instituted in the mind.
New lexemes can and will be incorporated - every language has this faculty - but rarely newsystems.
Things do not work the same way when babblers are involved. Here the forces are muchmore salient and powerful - and this is what Guillaume had in mind. When a child learns hismother tongue, he does so by trying to reconstruct the system behind the utterances he hears.
Here an important point should be made: there is little or no "fragmentary, degenerate ornegative evidence" in that he will always be hearing whole words, no "ill-formed" ones. Onemust realize that the order of the system comes not only from the "aggregated behaviour" ofhumans as speakers but also from the mind of the infant
(Latin: "unable to speak") learninghis tongue. The child will make all the intuitive generalizations he can based on the evidence,and will form, reconstruct, the best system he can. As he grows up, he figures out through aprocess which entails both induction and deduction (and, as Pierce would say, abduction
) thedifferent categories of words and what each can and cannot do. The system is soon in place,awaiting new lexical elements.
However, although the babbler may not be exposed to "degenerate" data, the data he willget is not a perfect representation of the language of his parents. He may often be faced withuses which are, to the preceding generation, "overstretched", causing discrepancies to appearbetween his reconstructed system and the "original", that of his parents or care-givers. Whenwe speak, we never use the whole of the system, but the actualized parts give the infant agood idea of it; on the other hand, the image received, even if the number of utterances is veryhigh, is never a perfect mirror of the system. Without a restructuration on the part of theinfant, language would quite probably be doomed to crumble.
This organizing force of babblers is evident in the case of some creoles where, in the firstgeneration a pidgin is created as a somewhat artificial ad hoc
language, made up of parts oftwo or more languages, but where the second generation, which learned or acquired it as amother tongue, (re)constructed a tongue, making it systematic and thus creating a newlanguage8. And there is nothing extraordinary about it: this is normal and to be expected,humans require order in something as complex as commuting the infinite diversity ofexperience to a finite language. We have to have some kind of structured frame in order torepresent (organize) and express our experience.
In his endeavour the child is perhaps aided, paradoxically, by the language's own complexity:complex, adaptive systems are "pattern seekers", the patterns may facilitate the learning - butit is yet too soon to tell.
Like other complex systems, language is never really stable, only apparently so, ".we arenever really confronted with a system. The instant a system is established, it has virtuallybegun to remake itself9. However, in most cases the remaking is so barely incipient that the
system can be fixed, pinpointed in time, and described as if it were a stable entity." (1984:60)This, of course, applies to the whole community of speakers (containing more than onegeneration) rather than to any single one speaker.
From a wider historical standpoint, chaos and organisation are also felt to interact:
Aussi longtemps que dure le progrès architectural sous l'état structural institué, celui-cis'accuse perdurable. Il se change en un nouvel état structural lorsque cesse lapossibilité d'un progrès architectural subsident continué. Une première viséeconstructive du langage: c'est pour l'architecture subsidente de faire durer l'étatstructural, et ce n'est que lorsque cette visée a épuisé ses moyens que survient unevisée tendant au changement de l'état structural jusque-là maintenu en un étatstructural nouveau. (Guillaume 1959: f.11<bis>)10
Guillaume refers here to what he calls the periods or "areas" of language (his théorie des airesdu langage
). This clearly parallels the phase transitions where a complex system is decayingand, having no other choice, switches, sometimes quite rapidly, to a different state of being.
The most common example (which gave us the terminology) is the transition from liquid to gaswhen the molecules, excited by the temperature or pressure change, rupture their links andform new ones.
3.3 A stable system
From the standpoint of what came to be known as synchrony, we can also find properties of
non-linear systems. For Guillaume, language is,
a peripheral system consisting internally of repetitions of itself as far as the generalform is concerned. My idea of tongue is therefore that of a system of systems, with thismuch being clear: the general, containing system and the less general, containedsystems do not differ in their general form; their difference is one of substance or oflimits.(Guillaume 1984:8)
This vision echoes a comment made to Lewin by molecular biologist Brian Goodwin, ".thebasic morphogenetic events for the eye formation are simply repeats of the basic movements"that formed the animal embryo, namely the invagination and folding of sheets of cells (Lewin1992:39). To understand these statements, a more particular look needs to be taken atlanguage and non-linear adaptive systems in general. But we can already see that, in bothcases, this principle comes from a need for simplicity, although maybe not for the same reasonsor at the same level. Indeed, the best way to get something complex from a simple base is tomake use, on different levels, of the same building materials or principles.
Language has to have the ability to represent the whole of our experience. On the otherhand, it cannot be too complicated: it has to be learnable and must not use up "too muchspace" or too much time in its effection. So, as it is with the phonemic system, the rest oflanguage needs a certain simplicity. The simplest way to arrive at this situation is to useiterations: the internal sub-systems repeat one another as to their general structure. And asGuillaume tells us (1984: 81), each part of a sub-system is representative, in some way, of thewhole of the systemic process in question.
The same thing happens in complex organisms: the building blocks are limited in number andthe forms assumed are repeated all about the system, like the foetus and the eye. Thus theDNA need not specify too many possible patterns. There is also the imperative of time: thefewer possibilities you have, the more readily available each is.
In language, the imperatives are, as was pointed out earlier, twofold: learning - humans needto acquire their mother tongue quickly and easily so that they can interact more efficiently withtheir surroundings and organize their experience - and use: the "processing steps" should besimple enough for fast and efficient translation of the experience. Here, for Guillaume, the mostobvious avenue would be to make use of processes native to the human mind, already presentbefore language, something akin to primary reasoning and experience. For example, theverb/noun distinction is a reflection of our perception of a time/space dyad which has beengrammaticized, a dyad which is at the basis of the Indo-European system of parts of speech(Guillaume 1984:8). This might not have happened; some languages do not make such agrammatical distinction.
But on a deeper level, the construction of words, phrases and sentences should all rely onsimple mechanisms. Guillaume's proposition for them are movements of particularization andgeneralization or, to use terms familiar to logicians, discrimination and categorization. Thesehe takes to be at the heart of human cognition and thought, and so of language too. Hisargument is not that we should accept these movements readily, but that when constructinga theory of language one should attempt to use as few processes as possible, those likeliest tobe close, mutatis mutandis
, to native psycho-mechanisms.
3.4 The relationship with the mind
A final, and more basic, instance where we could fine complexity at work is at the bridge,
held by language, between stable representation and the chaos of experience and thoughts
(untarnished by speech), what Einstein called "the chaotic diversity of our sense experience"
Thought unaware of the extent of its own potential construction would be turbulentthought
, left in the mental turbulence of its origins - a turbulence which human thought,by its very nature, has done away with to a high degree. With the uprise
of humanlanguage, turbulent thought has been replaced by thought where turbulence is nolonger inevitable, by a type of mental activity where it is inevitable to keep a certaindistance from the original mental turbulence, to which man is no longer permitted toreturn. (.) It would not be a misuse of words to speak of the other
universe and theinner
universe, tongue, and of the unending drama of their continuedcollision
As a linguist, Guillaume ever was very much preoccupied by the relations between thought andlanguage. His solution to this problem gives us one of the finest inceptive views, not only ofprimordial linguistic processes, but also of man's inner cognitive vision. The way in whichlanguage connects experience with - one could even say it transmute experience into -(structured, categorical) thought is by its representational faculty. Language - tongue, to bemore accurate - is
representation, and representation is the most effective way of perpetratinga prehension of our mental flow.
Language is not the only means of representation we have - music and visual art are otherinstances - but it is the most effective, from a communicative point of view; it is stable in itsstructure and its semiology. Even if it is for an internal communication, according to Ellis(1993:57), language "is the basis of the most organized and systematized version of(categorized) knowledge." This stability and systematicity gives each individual the tools withwhich his essentially particular (unrepeatable) experiences can be expressed through what areessentially general representations, which are the always available, yet flexible, means ofgrasping our experience and thoughts.
Few linguists, to my knowledge, have been able to resolve, in quite such an elegant way, thismajor problem of the relationship between these near-unfathomable elements. By so doing,Guillaume showed us, before hand, that language doth lie on the edge of chaos: between thechaotic flow of sense experience and the stable means of representation. This problem alwaysfascinated Guillaume: since the beginning, man has been confronted with the problem oftransmuting his experience (l'indicible mental
) into an expressible form (le dicible mental
). Hesaw, in the successive solutions, the major phases of language evolution, "the general directionof language history (.) is for a coherent construction to develop from implicitness to anexplicitness of a higher order" (1984:140).
This partly reflects the almost teleological aspect of complexity where the systems tend to
evolve to the fittest possible status11. In language this is due not to some sort of exterior force,but simply to the re-organizing force of babblers who look for the best system possible. It isa quest for the best representational facilities; this quest (and the resulting system) makes useof the mental processes (generalization and particularization) to construct (a partly iterative)architectural structure.
From the linguistic theory of Guillaume can be extracted a few very important points which,
although they do not make up the whole of the theory, lie at the heart of most of its postulates.
They have been examined briefly here, from a complexity point of view, and, although it was
not possible to give each the full treatment it deserves, it seems reasonable to conclude that,
from what has been shown, they can readily accept, or be accepted by, chaos theory. Other
elements will, of course, have to be examined and it should be borne in mind that neither
theory is to be thought of as rigidly representing the whole truth. Other theories of language
will also have to be looked into in order to see what they can contribute. And there are many
candidates. For example, Martinet proposed that in phonology everything is interlink so that
a neutralisation of difference between two phonemes will be followed by the creation,
somewhere else in the system, of a new differentiation. In Russia, Mikhail Bakhtine
concentrated parts of his work on what can be called, in retrospect, the chaotic side of
So psychomechanics is not the only linguistic theory capable of encompassing the findings
of complexity studies; and in order for linguistic endavours to have the best chances of success,
a dialogue will have to be established between the different schools - each of those can have
its say on the matter of chaos. But the degree of corroboration between these psychomecanics
and the science of complexity leads me to think, with some assurance, that they are good
candidates for furthering our understanding of man and the universe, and I am sure that others
Had he been alive to witness the development of this new field of human research,
Guillaume, keen as he was on scientific knowledge and especially physics, would have been,
I am sure, glad to see in this new endeavour a respectable, and formidable, ally of his view of
language. And we can but hope that some day these theories will meet, in more than a short
paper, for the better good of both.
Brown, R., 1973. A First Language: The early stages. Cambridge, MA: Harvard University Press.
Einstein, A., 1956. Out of my Later Years. Secaucus, NJ: Citadel Press.
Ellis, J.A., 1993. Language, Tought, and Logic. Evanston, Il: Northwestern university Press.
Gell-Mann, M., 1992. Complexity and complex adaptive systems. In: J.A. Hawkins, M. Gell-Mann (eds.), The Evolution of Human Languages (SFI Studies in the sciences of complexity, Proc. Vol. XI), 1-19. New-York: Addison- Wesley.
Gleick, J., 1987. Chaos. New-York: Viking Press. (Translated as La théorie du chaos. Paris: Flammarion. 1989).
Guillaume, G., 1959. Leçon de linguistique du 8-1-1959. (unpublished).
1984. Foundations for a Science of Language. (Trans. of Principes de linguistique
théorique, 1973). Philadelphia:John Benjamins.
Hawks, T., 1972. Metaphor. London: Methuen.
Hirtle, W., 1992. La métaphore, une idée regardante. ALFA (Universitas Dalhousia, Halifax) 5, 137-150.
Lewin, R., 1992. Complexity: Life on the Edge of Chaos. New-York: MacMillan.
Peters, A.M. & Menn, L. 1993. False starts and filler syllables: Ways to learn grammatical morphemes. Language 69, 742-777.
Romaine, S., 1992. The evolution of linguistic complexity in pidgin and creole languages, In: Hawkins, Gell-Mann, (eds.), 210-237.
Thom, R. 1991. Paraboles et catastrophes. Paris: Flammarion.
Valin, R., 1964. La méthode comparative en liguistique historique et en psychomécanique du language. Québec: Presses de l'Université Laval.
1968. Des conditions d'existence d'une science du mentalisme. Les langues vivantes
1971. Introduction. In: G. Guillaume, Leçons de linguistique vol. 1, 9-57. Québec:
This is not to be confused with construals such as non-linear phonology,
where it is only the physical representation which is not linear.
Although the weather is not adaptive it does exhibit, as do other non-
adaptive complex systems, this feature.
Such repercussions may lead to some sort of phase transition
, this will be
I use this term in a very wide sense to include mental processes.
Here I do not take the "acquisition order" to be a fixed features, although
there is evidence showing that some sort of pattern exist. See Peters/Menn (1993)
for a most recent discussion. Remarkably enough, Brown (1973:257) made the
following remark: "In the early samples, the curves describe some wild swoops up
and down." This resembles somewhat the evidence gathered by Mandelbrot, when
working on transmission fluctuations at IBM (Gleick 1989:115f.)
I am not here undermining man's cognition; the properties of adaptive
systems flow from different sources, in this case, the human mind.
See Valin (1971:34 ff) for the distinction between micro- and macro-time.
This, however is not generally the case, cf. Romaine 1992.
9. "une réfection virtuellement engagée du système acquis."
"As long as the architectural progress lasts under the instituted
structural state, it will be perdurable. It will change into a new structural
state when the possibility of subsidient architectural progress ends. A
primordial aim of language: that the structural state last by subsidient
architecture. Only when this goal has overdrawn its means does a new one occur,
tending to change the structural state so far maintained into a new one."
This is not however deterministic in the usual sense. The "determination"
works both ways: from the individuals to the emergent structure and vice versa.
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Enrique Saínz LEZAMA LECTOR DE PLÁCIDO Leer a Plácido en nuestros días, después de tanta poesía vanguardista, tantas voces renovadoras o que han querido transformar la manera de percibir y de relatar la realidad, puede parecer a primera vista una experiencia insípida, insufrible e infructífera. Los poemas de este mulato sencillo que había nacido en Cuba bajo circunstancia