We introduce the discussion of dispersion as it applies to language.
As we have mentioned several times, language is a shared system of interaction. We inherit it from previous generations and from our interaction with others. We have discussed loosely how the system propagates or disperse through a population. Let us examine more closely what the notion of dispersion, in physics term, can add to our understanding of linguistic interaction.
We define dispersion in the context of state space and equilibrium. Dispersion (of components of a system) is a microphysical phenomenon underlying some specifiable macrophenomenal relaxation of a system toward a state of equilibrium. Equilibrium is a point in state space where, in accordance to some state variable, a system comes to rest, reflecting the most probable place in state space for it to be. Of course, choosing the appropriate state variables of the state space is a matter for decision, rather than a matter of fact. As a simple example, consider the system defined by a child's play room, there are many more states in which toys are scattered across the room than there are states in which they are arranged in orderly fashion on shelves. Depending upon where in the hierarchy we position ourselves, that is, how many and which parameters we use to define the space, the distinguishable states of scatterings (teddy here, or over there) will be one point or a cluster of points in the space.
We introduce our perspective from the point of view of statistical mechanics, thus defining equilibrium. Statistical mechanics is the branch of physics that addresses the relationships between energy and forces of change, in a macroscopic system relative to microscopic constituents. It is the key to understanding thermodynamics and describes almost every change in nature from cell development to combustion in car engines. We borrow the notion of equilibrium from statistical mechanics. It defines a closed system (a system that is influenced only by forces within (no loss or gain); a hermetically sealed pot of coffee is considered closed) in terms of one or more state variables such as temperature, pressure or relative concentration. It then describes a state space, a space defined according to these state variables in which innumerable possible configurations of the system can be represented as unique points. Equilibrium then refers to a condition in which the system's current state remains proximal to some average state over time. In other words, even if other aspects of the system are changing, the selected state variables are approximately constant. Its macroscopic limits remain constant.
We use a description of the relaxation of a system to equilibrium and establish the relevance of state variables such as temperature, to illustrate our point. As a simple example consider an ice cube in a glass of warm water. Assuming the ice, water and heat to be within a closed system, the global temperature can be assigned the role of state variable. Clearly it will be difficult to define the temperature spatially, as well as temporally, as the ice melts and the hotter water cools. Eventually however, the ice will be gone, the water will be thoroughly mixed and the temperature constant throughout. Thereafter, even though the individual molecules may continue to move around owing to ambient thermal, we can say that the system has come to equilibrium. Its state variable, temperature, has assumed a constant value and will not change thereafter (aside from stochastic fluctuations around that value). Dispersion, in this example leads to equilibrium.
Now that we have defined relaxation and dispersion, how do we use it in the context of language? We have used dispersion conversationally to illustrate some of the shared aspects of vocables across a population of users. The main feature of dispersion, as we have described it in our ice cube example, is the dynamics that settles a concentration gradient into an homogenous state. Is there some aspect of human linguistic practice that can be usefully described as dispersion in the sense in which physicists use that term? Using what state variable can we plausibly claim that there is a kind of relaxation, in the theoretical sense of the term, that is specifically linguistic?
We think that dispersive effects are relevant to a description of language if we treat instances of specific vocables as statistical probabilities. We know that, in the course of their becoming dispersed (in the conversational sense of the word), vocables increasingly lose the capacity to generate highly specific effects. At the earliest stages of vocable use, the effects that are occasioned are highly particular; at later stages less so. The word but, or more properly its ancestors, had a relatively narrow range of uses: In particular, those in which it picked out a highly specific physical relationship, that of being spatially related just outside of. At later stages it was also capable of picking out a relationship of conceptual and then circumstantial outsideness, (nothing but grief, but that he was my own son ...), however in environments in which it has such uses, the original physical relationship no longer competes. Moreover when that physical relation is selected, the work of picking it out is shared with other sentence elements. In these later stages, but has lost its ability to generate so specific an effect. In probabilistic terms, its earliest uses have become the least probable of its uses. But, by the same token, it has acquired many other syntactically distinguishable uses, each of which has a relatively low probability. Moreover, among these other uses, the syntactic type that distinguishes it is itself so general that we would be hard pressed to say what its effect in such constructions amounts to.
The loss of specificity in vocable effect is verifiable but a description of the dynamics of this phenomenon is not yet accounted for. This thesis addresses that topic.
Consider in this connection the conjunctive use of but wherein it joins whole sentences. It is all but impossible to formulate in semantic terms the effect achieved by but rather than and in these constructions. But the same point is seen if less dramatically in each of the many disparate classes of use. The loss of semantic specificity is an inevitable consequence of use, even within the confines of a single syntactic class of uses. In fact, many if not most vocables both completely lose contact with the earliest classes of constructions in which they were used and also eventually find themselves used throughout a much broader range of constructions through which there is no consistent semantic thread. R.E. Jennings [32] has demonstrated that unified semantic theories for connective vocabulary are not readily available. Or, like but, has both disjunctive and conjunctive uses, though the evolutionary processes that brought about these broad semantic disparities are different for the two cases. It is a central claim of this thesis that this kind of functionalization is a particular instance of a mathematically similar process pervasive throughout all stages of the evolution of language.