Suppose we were to take five words from Modern English (ME): animal, fur, head, I, sun. In standard German the corresponding words are Tier, vier, Kopf, ich, Sonne. Since the first and third words are not related, we find a 60% agreement between the two languages. Our next step is to compare this percentage with the expected rate of loss.
To permit ready determination of the time depth of two related languages, Robert Lees devised a formula. t is equal to the logarithm of the percentage of cognates c, divided by twice the logarithm of the assumed percentage of the cognates retained after a millenia of separation r. So...
t = (log c) / 2(log r)
Using our five words from ME and German, we determine t to be:
t = log 60% / 2 (log 85%)
Which is
t = -0.511 / 2 * -0.163
To give us a number 1.563. By the formula, English separated from German around 1000 * 1.563 years ago, that is around the year AD 430. The Anglo-Saxons, in fact, moved into the British isles around AD 435.
In such a short list the range of error may be great. To reduce the chance of error, one would prefer a long, carefully designed list. The two most frequently used lists are one of 100 words, and another of 200 words.
Now, glottochronology is not without a great deal of controversy and problems. Lehmann mentions that when an emperor died, the ancient Chinese would cease to use any old religious words and replace them with synonyms. But the overall method and aim are, I think, very important.
So how do glottochronology and language economy relate to each other? Glottochronology is an historical pursuit designed to date that which has already occurred. Language economy is an effort at tracking contemporary change and predicting future language exchange.
