Saturday, November 5, 2011

Force Dynamics

4.1 Force-dynamics and the semantics of prepositions and (causal) connectors

In the realm of cognitive semantics, Talmy's paper on "force dynamics" (1988) was almost an invitation to apply dynamic systems theory. Nevertheless, philosophical barriers prevented such an application (cf. Lakoff 1987 and his opposition between experientalism and objectivism). In the following, I will propose several points of transition between cognitive semantics and dynamic semantics. [11]

The material on which most of Talmy's analysis is based are two sets of examples with a closed class term at their centre, either a preposition (a) or a connector (b).

The ball 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)
Whereas in the treatment of the meaning of verbs Talmy just refers to predicate constants like MOVE and CAUSE (cf. Talmy 1975 and 1976), he introduces "imaging systems" in Talmy (1983) which refer to "abstract geometric characterizations", a "mental eye" for the analysis of the examples under (a), and "force-dynamics" for the examples under (b).

It is clear, and the pictures in Talmy's article demonstrate it, that the examples in (a) use notions of space, border, transition, and motion that may easily be modelled in dynamic system theory. In the following I shall just sketch the lines of such an elaboration. In the sentence "He walked across the field", the field is a topologically coherent surface (it does not contain islands or other bounded areas) with a boundary, which may be crossed (entering/leaving the area). [12] We have two dynamics: slow (stable) and quick (transitory) dynamics. The latter corresponds to one of the two types; i.e., an attractor is found or a repellor is avoided. The verb "walk" focuses on the stable (slow) motion, with an implicit ingressive (start) and egressive (stop) phase, whereas "across" focuses on the quick dynamics of change, called a "catastrophe of bipolar change". Figure 5 shows such a scenario.



Figure 5. Catastrophe theoretical description of the major dynamic meaning components in the sentence.

Talmy's "force dynamics" use (and presuppose, as no definition is given) the notions of "rest" and "action". These labels correspond to the notions of "attractor" and "catastrophic transition" (change). The notions of "force tendency" and "result of force interaction" are, however, beyond catastrophe dynamics because one needs an energy-flow with loss and gain of energy, i.e., a thermodynamic model. Nevertheless a basic schematisation in terms of stability theory may stand for the simplest level of Talmy's pictographic description. Figure 6 shows Talmy's pictogram and descriptive additions.

 
 
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 antagonist: action,
result of the force interaction: action ().

Figure 6. Schematisation of force-dynamics by Talmy (1988).

The rather cryptic pictorial description of force-dynamics by Talmy has to be decomposed in a dynamic model. In Figure 7 only the catastrophe theoretical part is represented via diagrams, whereas the thermodynamic modelling is expressed via ordinary language descriptions, which can, however, be replaced by a mathematical modelling, which is too technical to be introduced here. In terms of qualitative dynamics, the energy goes to zero (by diffusion) and would thus correspond to a catastrophe of death (of motion). The coupling of the two systems (ball/wind) prevents the catastrophe and thus produces the process shown under C.


roll: motion (attracted by a position of rest). The picture above shows the dynamic system f(x) = x 2, the parabola describing the motion of a pendulum attracted towards its position of rest.
blow: energy gain, which causes the motion to continue although it is attracted towards a rest position.
because: causal link between energy gain and natural (diffusive) loss of energy
keep: equilibrium between loss of energy and (added) gain of energy; unfolding along a path vertical to the attractor
Figure 7. A dynamic decomposition of Talmy's description.

Both forces "roll" and "blow", underlie the thermodynamic diffusion law, are linked in order to form a coupled dynamic system ("because") and achieve (at least) equilibrium of energy loss and supply. The connector thus stands for the dynamic coupling of two 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 Hermann Haken (cf. Haken 1983). This has been applied to cognitive systems (cf. Haken and Stadler 1990 and Haken 1996). Haken (1996: chapters 5 and 6) and Kelso (1995) studied the coupling of finger movements of animal gaits, but Haken (1996: part III) applied the methods of synergetics also to effects of synchronization and desynchronization shown in EEG and MEG patterns. Oullier et alii (2005) expanded this paradigm to imagined sensorimotor coordination. In the case of an adjunct (adjective) coupled with a head noun one could imagine an application of this methodology if a proper dynamic model of single word meanings is available. [13] The major difficulty is that many simplex word-concepts are semantically already complex since they involve different sensorimotor parameters, abstraction, metonymy, and 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. [14]This is surely not a simple enterprise, but I cannot see how an interesting theory of grammatical composition can be developed without solving these problems.

If every sentence is mapped to a simple catastrophe scenario, the different connectors for "CAUSE" would couple these systems. Characteristic outcomes could be selected by the choice of a specific connector; e.g., because, despite, etc.

Although the dynamic system approach destroys the simple pictorial illusion in Talmy's models, it pinpoints basic problems hidden in Talmy's 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 levels are hidden in Talmy's description of force dynamics in Talmy (1988), although his terminology and pictures presuppose their existence. Thus part of the "cognitive aspect" is veiled by his description.
The semantics of complex sentences blend different types of dynamics:
Spatio-temporal dynamics with attractors and catastrophes
Energy functions and the coupling of subsystems
In a full-fledged cognitive analysis, a bridge to models of the external world, of perception, motor-control, memory, and senso-motoric imagination [15] must be established, which will involve the disciplines of physics, psychology and neurology. If social action and interaction, social relations and conflicts are expressed in a sentence or a text, models of social action proposed in sociology and social psychology and their mental correlates have to be considered. The "splendid" methodological isolation of cognitive semantics precludes a truly cognitive model of meaning in language.

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