The current state of variational linguistics can be compared to a fundamental, philosophical idea from quantum mechanics, i.e. Heisenberg’s Uncertainty Principle. That principle states roughly that all physical quantities that can be observed are subject to unpredictable fluctuations, so that their values are not precisely defined. In the world of physics, this can be applied to an electron, which has a momentum (angular speed) and a position. Traditionally, the electron is presented as spinning (momentum) around a nucleus (position). However, Heisenberg said that the momentum and the position can not be determined simultaneously; either you have a precise idea of the position, or you know the exact speed. There is always a trade-off between momentum and position. This has led to the joke that Heisenberg, driving his car was stopped by a policeman who asked: “do you know how fast you were going?” Heisenberg replied: “Well, I know exactly where I was…”
The implication of the Uncertainty Principle is an incomplete physical system of probabilities. Unlike meteorology, where probabilistic predictions are due to our incomplete grasp of all the explaining dimensions, the incompleteness and uncertainty are fundamental in quantum mechanics. This was upsetting for Einstein who is claimed to have said: “God does not play dice with the universe”. Heisenberg noticed the linguistic — or rather semantic — problems that a system of probabilities implies. In the classic view, physical phenomena are accurately described in mathematics and logic (either true or false, “tertium non datur”) and a language that correlates with the logical symbols exists. However, for quantum mechanics, the situation changes. Let’s take the concept of temperature. In our classic view, we have very strict definition of what temperature is. On the level of quantum physics — the atomic level — this definition does not hold anymore. All that is left is a correlation between the measurement of temperature and certain statistical expectations about the properties of the atom.

A number of people — linguists, philosophers — have followed this semantics path, and have drifted off in the direction of the Sapir-Whorf hypothesis. Others have pointed out that the observer’s paradox links up neatly with the Uncertainty Principle. The observer’s paradox addresses the problem of a language user changing his (linguistic) behavior because he knows his language use is being observed. In the methodology of Labov, who points out that the sociolinguist should study the vernacular — the speech of someone who is not paying attention to his speech –, this is an important topic.
However, in my opinion, the Uncertainty Principle is also at work in the current state of variational linguistics. Variational linguistics is the study of grammar in relation with context. One could say that a variational linguist sees “Language” as a phenomenon with two characteristics: on the one hand, it is the production of sounds, words, clauses, sentences, text and discourse, on the other hand, it is a social phenomenon spoken by people in a certain setting. Just like in quantum physics, it is only possible to get statistical expectations of these two dimensions, and just like the momentum and position of an electron, it is not possible to predict both dimensions at the same time.
Before I give an example that might clarify this philosophical idea, let me introduce the two dimensions of variational linguistics. Each dimension is a collection of many variables. The grammar dimension contains phonology, morphology, syntax, etc. (and these are again group names for even more fine-grained variables) and the context dimension contains variables that describe the social characteristics of the language user, and the setting of the utterance (register, audience, topic, etc.). The variational linguist observed that both the grammar dimension as well as the context dimension have many configurations and assumes that a configuration on the context dimension correlates with a configuration on the grammar dimension.
The example that I’d like to give falls back on the classic socio-linguistic finding e.g. the correlation between the pronunciation of a final /r/ in New York American English and social class. If Labov were a traditional physicist, he would have quantified both the pronunciation (X) as well as social class (Y) and written out a formula of the form X = Y * l, with “l” the Labov constant. He did not do such thing because it is hard to quantify social class, and, more importantly, because such a constant can not be calculated due to the probabilistic properties of the correlation. Instead, socio-linguists have been writing “variable rules”. These rules are of the form “K ~ L + M + …”, with “K” a linguistic feature and L, M, etc. some explaining context features.

The classic socio-linguistic finding resembles the Uncertainty Principle at its best if you consider the fact that you can not predict both dimensions, grammar and context, at the same time. Although you know the context of an utterance perfectly, you can not predict the pronunciation of /r/ 100% accurately. Vice versa, if you observe a pronunciation of /r/, variational linguistics is not able to pin down the context exactly. The best you can do, is to give a probabilistic estimate.
As a conclusion, it appears that the current state of variational linguistics is incomplete: there are no fundamental laws that work in all cases. The question now is: will variational linguistics ever be a complete theory? In other words, will we hypothetically be able to oversee all possible underlying dimensions and variables and make 100% correct estimations?