One fundamental idea of linguistics is the continuity of language and dialect; that if we were to start in some remote village of Africa and walk up all the way to Europe at a slow enough speed, along the way it would never seem like the language was changing very quickly. This model of continuity, however flawed it may be, lends to us the natural extension to linguistic calculus. That, considering linguistic differences as a function, we can safely find the rate of change of that function, and make accurate predictions about linguistic differences elsewhere.
Imagine if you took samples and found a function to model how the way an “r” is pronounced across some relatively long line (eg, all of Europe). We would get some kind of curve; perhaps a linear looking one, or perhaps an exponential one. Maybe it would be sinusoidal even, or piece-wise. Now let’s say we took samples along the same line and instead tallied, say, the words that were chosen to represent a particular symbol. That sounds very abstract, so let me give a concrete example that should make sense to most American readers. In different parts of the U.S., we use different words for a “soda”. In some places we say “soda”, others “pop”, others “soda pop”, and in many places “coke” (among other words). We could find out how the tendency to use one of these words over the other changes as we move along some curve.
Imagine the questions we could hypothesize about with just these two data sets! How does the curve of the pronunciation of “r” compare with the curve on the vocabulary? What does this say about our brain, how it communicates with and controls our voice box, how it perceives words as symbols, or how it represents a single sound compared to a whole word? How do the curves compare along the same distance, but over a different distribution of principality? For example, compare these two curves over all of Europe to over all of the US—what does this say about the difference between “languages” and “dialects”, or the sociological relationships between language and the idea of nationality? Or even the formation of nations in the first place? Is the high rate of change of language over national borders a natural consequence of how our brain processes language, or is it a result of the territory divisions? In other words, if states and countries never developed, would our language still be as different?