The relevance of dynamic systems theory for cognitive linguistics.ppt

1、The relevance of dynamic systems theory for cognitive linguistics,Interdisciplinary Themes in Cognitive Language Research Symposium University of Helsinki and FiCLA November 25 26, 2005,Wolfgang Wildgen,Wolfgang Wildgen,2,Contents,1 Basic oppositions 2 Some features of dynamic models for language 3

2、Talmys “force- dynamics” 4 Lakoff and Johnsons metaphorical mappings 5 The problem of compositionality (construal) in cognitive grammar (Langacker) 6 The dynamics of composition in grammar 7 Conclusions,Wolfgang Wildgen,3,Basic oppositions,Thom was guided by his discussion with Waddington on biologi

3、cal morphogenesis and expanded this thought to linguistics. In his holistic strategy Thom preferred a gestaltist, geometrical, morphogenetic view on biology and not so much a mechanistic one, which takes the brain as the central (and finally) only “organ” responsible for thought, language and cultur

4、e. The research line of cognitive linguistics in general since the 50s may be situated in an interdisciplinary but rather technically minded world: that of information theory (Shannon), and cybernetics (Wiener). It was developed in the philosophical atmosphere of logical empiricism (Quine) and forma

5、l syntax (Carnap). Whereas Chomsky elaborated this field and created a compact mentalistic theory, Lakoff (since 1975) and with him Langacker and Talmy combined insights of gestalt-psychology and modern computer vision with ideas stemming from issues of generative semantics.,Wolfgang Wildgen,4,Some

6、features of dynamic models for language,Figure 1: List of elementary catastrophes.,Wolfgang Wildgen,5,Figure 2: Two basic types of dynamics: stability (attractor) and instability (repellor).,Figure 3: A hierarchy of dyna-mical conflicts typical for the compact catastrophes “cusp” (A3), “butterfly” (

7、A5) and “star” (A7).,Wolfgang Wildgen,6,The process type called “capture”,Figure 4: Derivation of a process-schema (right) from a path p in the vector-field of the cusp (A3).,Wolfgang Wildgen,7,Figure 6: Feigenbaum-scenario (the constant k increases from 2 to 4 horizontally, whereas the vertical dim

8、ension concerns the state x. At k = 3 the curve splits; at k = 3,58 the “tree” has infinitely many branches.,Figure 5: Rssler-attractor (in the case: a = 0,035; b = 0,46; c = 4.5; cf. Plath and Wildgen, 2005).,Wolfgang Wildgen,8,Restrictions on qualitative dynamic models,The topological nature of el

9、ementary catastrophe theory asks for a “rough” modelling by which only general features of the field in question can be captured. The “dynamics of language”, must in the beginning consider mainly: critical transitions, bimodal, trimodal oppositions, etc. Specific predictions or an exact reproduction

10、 of descriptive details cannot be the goal of these models, because it is by definition a topological (and not a geometrical) model and all description have to be interpreted modulo smooth deformations (diffeomorphisms); i.e., one cannot simply transfer them to the level of metrical measures. This m

11、eans that only very general questions may be assessed with the help of qualitative dynamics,Wolfgang Wildgen,9,Talmys “force- dynamics”,The material on which Talmys analyses is based are two sets of examples with a closed class term at their centre, either a preposition (a) or a connector (b). The b

12、all sailed past his head. The ball sailed through the hoop. He ran around the house. He walked across the field. (Cf. Talmy, 1975: 201-205) The ball kept rolling because of the wind blowing on it. The shed kept standing despite the gale wind blowing against it. (Cf. Talmy, 1988: 5),Wolfgang Wildgen,

13、10,The pictures in Talmys article demonstrate, that the examples in (a) use notions of space, border, transition, and motion that may be modelled in dynamic system theory. Fig. 7 sketches such an elaboration. In the sentence “He walked across the field”, the field is a topologically coherent surface

14、 with a boundary, ideally a circle or a regular polygon. We have two dynamics: slow (stable) and quick (transitory) dynamics, the latter corresponds to one of the two types in Figure 2; i.e., an attractor is found or a repellor is avoided. The verb “walk” focuses on the stable (slow) motion, with an

15、 implicit ingressive (start) and egressive (stop) phase, whereas “across” focuses on the quick dynamics of change, called a “catastrophe”.,Wolfgang Wildgen,11,Be captured by the attractor ENTER,Let free from the attractor LEAVE,Attractor “field”,Walk (path) slow dynamics,across,Figure 7: Catastrophe

16、 theoretical description of the major dynamic meaning components in the sentence.,Wolfgang Wildgen,12,The ball kept rolling because of the wind blowing on it. intrinsic force tendency of the Agonist (right): towards rest (), the Antagonist (left) is stronger (), intrinsic force tendency of the Antag

17、onist: action (), result of the force interaction: action ( ).,Figure 8: Schematisation of force-dynamics by Talmy (1988).,Wolfgang Wildgen,13,roll : motion (attracted by a position of rest); consequence for motion is the end (death) of motion; i.e. a fold-catastrophe (A2). B. blow: energy gain C. b

18、ecause: link between energy gain and natural (diffusive) loss of energy D. keep: equilibrium between loss of energy and (added) gain of energy.,Versal unfolding of the attractor,End of motion as fold-catastrophe,Rest as attractor,Figure 9 : A dynamic analogue of Talmys description,Wolfgang Wildgen,1

19、4,Coupled dynamic systems,The coupling of two dynamic systems has been analyzed in the case of physical systems (the classical case are coupled oscillators and resonance phenomena). The dynamic systems approach produced the interdisciplinary field called “synergetics” by Herman Haken. It has been ap

20、plied to cognitive systems. Haken, Kelso, a. o. studied the coupling of finger movements, of animal gaits etc. Haken (1996) applied the methods of synergetics also to effects of synchronization and desynchronization shown in EEG and MEG patterns. Oullier et alii (2004) expanded this paradigm to imag

21、ined sensorimotor coordination.,Wolfgang Wildgen,15,Semantic coupling in language,In the case of two sentences coupled by a connector or an adjunct (adjective) coupled with a head noun one could imagine an application of this methodology, if there was a proper dynamic model of single word meanings.

22、At least the notion of prototype introduced by Eleanor Rosch and others in the 70s shows that simple concepts like those of color-terms have an attractor like shape. The major difficulty is that many simplex word-concepts are semantically already complex (as they involve different sensorimotor param

23、eters, abstraction, metonymy, metaphor). The syntactic composition of words must therefore first consider a kind of frozen complexity at the word level and build a syntactic operation of meaning composition on this basis.,Wolfgang Wildgen,16,Although the pictorial illusion of simplicity in Talmys mo

24、del is destroyed, the dynamical model-sketch pinpoints basic problems hidden in Talmys description. There is a mapping between physical dynamics (the wind, the ball), the perception or the imagined enacting of the process, its memory trace (with abstraction) and the linguistic expression. The first

25、levels are hidden in Talmys description, although his terminology and pictures presuppose their existence. Thus part of the “cognitive aspect” is veiled by his description. The semantics of these complex sentences blend different types of dynamics: spatio-temporal dynamics with attractors and catast

26、rophes (cf. a) energy functions and the coupling of subsystems (cf. b),Wolfgang Wildgen,17,Lakoff and Johnsons metaphorical mappings,If one considers the list of all metaphors mentioned in Lakoff and Johnson one sees that their relational networks are very shallow. Almost all metaphors have relation

27、al length 1; examples for a relational net of length 2 are (a) and (b): a) field war lovewar is a field / love is war b) path journey argumenta journey is a path / an argument is a journey In some cases the relation is transitive; thus in (a) one could deduce (by transitivity) “love is a field” and

28、in (b) “argument is a path”.,Wolfgang Wildgen,18,Two basic types,a. Those metaphors (A, B) where more fillers for B are mapped on one filler of A. Example: A: ideas are B: objects, commodities, organisms (people, plants), resources, products, fashions, light-sources b. Those metaphors (B, C) where o

29、ne filler of C is mapped on more fillers of B: Example: B: vision, action, event, activity, state is C: a field,Wolfgang Wildgen,19,Figure 9: Scale of metaphorical transitions.,Wolfgang Wildgen,20,A more “cognitive” explanation of metaphor,The orientational metaphors are rooted in non-linguistic cog

30、nition (complex perception and action programmes). The processes of metonymic mapping use part-whole separations and are basically relational. They presuppose a dual focus. Current research on the attentional blink and relevant time lags which allow for the two consecutive stimuli may be relevant he

31、re. Again a rhetorical principle must be reduced to a more basic perceptual and mnemonic process. Metaphoric mappings exploit differences in semantic density. The general rule says that expressions which are more concrete (have more semantic density) may replace less concrete ones (with less semanti

32、c density) if some basic similarities are given.,Wolfgang Wildgen,21,Questions (in a dynamic perspective),How stable are such mappings? What happens, if the mapping is iterated? Does it go to chaos? How complex (in terms of dimensionality, number of components) can a source space be in order to be m

33、apped in a stable fashion? Do maps preserve a basic structure? Do they reduce the dimension of the object mapped?,Wolfgang Wildgen,22,Chaos attractors of iterated mappings,It is known from chaos theory (cf. Peitgen et alii, 1992: 277 ff. and for an application to language Wildgen, 1998) that even in

34、 the case of a two-dimensional input, like that on a video-screen, an imperfect map to itself produces chaos after some steps only. In classical cases it has an attractor intrinsic to the system itself and totally independent from the input. The input information is lost and the iterative process is

35、 “frozen” into a standard pattern.,Figure 10: The Sierpinski triangle as a standard attractor of a chaotic mapping process , which involves: reduced copy, threefold composition.,Wolfgang Wildgen,23,The problem of compositionality (construal) in cognitive grammar (Langacker),Figure 11: Langackers ana

36、lysis of the verb ENTER.,Wolfgang Wildgen,24,Figure 12: The constituent analysis of the sentence: A man finds a woman (proposition: FIND-WOMAN-MAN) in Langackers analysis.,Wolfgang Wildgen,25,The difference to traditional phrase-structure-models consists in the fact that pictures are inserted into l

37、exical positions. At first sight one could presume that the cognitive “meaning” of this procedure lies in the fact that meanings may be imagined quasi-spatially, but Langacker explicitly rejects such an interpretation. He says (Langacker, 1990: 12-15) : “The symbolic resources of a language generall

38、y provide an array of alternative images for describing a given scene, and we shift from one to another with great facility, often within the confines of a single sentence. The conventional imagery invoked for linguistic expression is a fleeting thing that neither defines nor constrains the contents

39、 of our thoughts.” The second possibly cognitive notion introduced is the distinction between trajectory (figure) and landmark (ground), which is more or less taken from gestalt-psychology.,Wolfgang Wildgen,26,Langackers “cognitive” programme is theoretically ambiguous,If images are only vague and f

40、luctuating after-effects observed in the analysis of linguistic structures, how can we ever know anything specific about these volatile creatures? What are the empirical techniques which allow for the capturing of these phantoms? If we look at the large corpus of image analyses presented in Langacke

41、r (1987 and 1991) the answer is almost shocking: The individual introspective insight of the linguist, supported by heuristic techniques taken from current linguistic models are the only empirical method used.,Wolfgang Wildgen,27,Catastrophe theoretical description,Figure 13: The topological schema

42、of “enter” and “leave”.,Wolfgang Wildgen,28,The dynamics of composition in grammar,In a simple case which avoids the complexity of verbal valence, and rather takes nominal syntax as a basic example, one may consider a noun related to the form of an object, say a “square”, an adjective of colour, say

43、 “red”, and a present participle of motion, say “moving”: red moving square How does the brain compose a head-noun referring to form with two satellites referring to colour and motion?,Wolfgang Wildgen,29,Andreas Engel (2004) distinguishes three major areas for sense related information: The visual

44、system (subdivided into the areas V1 V5), the occipital areas and the parietal ones. The major binding process is one of temporal synchronization of assemblies, which form wholes (gestalts) from parts and desyn-chronization which distinguishes figure and ground. The syn-chronization of two perceived

45、 stimuli can be measured in the Gamma-band (60-70 Hz) and the Beta-band (15-20 Hz) of an EEG. The fronto-parietal centres select features that are then passed to working memory and planning. This type of analysis concerns only the composition in perception, attentiveness and memory, but one may conj

46、ecture a parallel process for words (related to perceptual information) and their composition in syntactic constructions involving nouns and adjectives. The role of determiners, who have an indexical function, is probably another story, which needs other experiments and measures.,Wolfgang Wildgen,30

47、,Verbal valence patterns,Here the application of catastrophe theory to semantics (cf. as a recent summary Wildgen, 2005) has its classical field. The complex but nevertheless structurally stable valence patterns seems to lie beyond the current experimental reach of neurological experiments. Therefor

48、e the plausi-bility of dynamic semantics must still rely on a rough iso-morphism between patterns in the real world (physical process patterns) and linguistic forms (sentences in different languages). One can presume that the brain as the mediating apparatus has the means to map the eco-logically re

49、levant aspects of physical processes into stable linguistic patterns. For the moment I do however not have any evidence how such complex achieve-ments can be observed or measured with the techniques of brain imaging available to date.,Wolfgang Wildgen,31,Conclusions,We need an intermediate level tha

50、t generalizes the specific findings and constitutes a neurodynamic model of semantic processing. Such a model will build on the topology of the brain, synchronization and desynchronization, coupling of subnetworks with self-organization (filtering, choice of dominant modes), self-reference and monit

51、oring in consciousness, etc. The class of models emerging in this field will certainly belong to dynamic systems theory, although such qualita-tive and simple models as catastrophe theory will be insuf-ficient, insofar as chaos-attractors, transitions between order and chaos, and stochastic processes (with diffusion) have to be considered.,