Please read Part I and Part II before proceeding with this post.
Applications to cultures
Sandefur provides the following example:
Suppose at time 0, a group of people separate themselves from their culture. A group of American Indians leaves the tribe and forms its own tribe, or a group sails to a deserted island and starts its own culture. We then have two cultures, A and B. At time 0, they have the same language, so that for a given list of L words, A(0) = B(0) = 1 is the per cent of the words they both know (and have in common).
If we contact each of these cultures k years later, culture A will know A(k) = (0.805)^(0.001 k)*(0.805)^(0.001 k) = (0.805)^(0.002k) per cent of the original list. Thus the per cent of the words that both cultures know is, by the multipliation principle,
Q = (0.805)^(0.001 k)*(0.805)^(0.001 k) = (0.805)^(0.002k)
What the glottochronologist does now is to construct a list of words. From that list of words, the two cultures are studied and it is determined what per cent Q of this list of words is known by both cultures. Thus in the equation for Q above, Q is known, but k, the number of years since the two cultures separated, is unknown. Solving for k gives
k = 500lnQ/ln 0.805
To understand the significance of this ratio we need to look at some examples.
Sandefur provides several examples.
Suppose that the natives of two islands have similar language. From a list of 300 words, 180 words are understood by both groups, that is Q = 180/300 = 0.6. Then
k = 500ln 0.6/ln 0.805 = 1177.5
We then conclude that the natives of these two islands came from a common ancestry, approximately 1200 years ago.
Suppose a collection of tribes with a similar language is considered. First, group the tribes into geographical regions. Then date the time separation n for pairs of tribes in each geographical region. It can be argued that the region with the pair of tribes with the largest time separation is the homeland of the tribes. The reason for this conclusion is as follows. Suppose one tribe separates into three tribes. One tribe might move away while the other two remain in the same general region. The tribe that moved away may split again in its geographical location, but the largest time separation will always be the two that remained in the original area.
Drawbacks and Pitfalls of Glottochronology
The model presumes independence assumptions (see discussion on multiplication principle); that is, event cooccurance by chance. But we know that
If p(A1A2) = p(A1)p(A2) event cooccurance is by chance.
If p(A1A2) > p(A1)p(A2) event cooccurance is more than by chance.
If p(A1A2) < p(A1)p(A2) event cooccurance is less than by chance.
One way terms deviate from independence is through their semantics (meaning). If the meaning of words change in time, how do we know if all words from a word list change by the same amount?
As noted by Sandefur
…how do you determine if a word is the same for two culture? If the spelling of a word or the pronunciation of a word changes ‘slightly’, we will still count it as being on the list. If the meaning of a word changes ‘sigificantly’, we will delete it from the list. Thus, there is some subjectivity in determining Q which could drastically change the results. Also some words are more likely to change than the others. But in the multiplication principle, we tacitly assumed that all words were equally likely to change. This can throw the results off.
The moral of this is that you need to be careful not to make more claims about your model than are justified.