Glottochronology is the study of the ages of languages, by comparing phonetic changes in a list of basic words, such as dog, foot, mountain, and green. From the difference in pronunciation between two languages, you can supposedly figure out when they diverged from a common stock. This theory was put forth by two American linguists, Swadesh and Lees.
Their premise is ridiculous, because it assumes that languages evolve at a constant rate. Lithuanian retains ancient Indo-European cases; students in Iceland can read thousand year old sagas with little difficulty. I have difficulty reading Shakespeare, who lived only four hundred years ago.
Languages change at different rates. In school (師大, National Taiwan Normal U) I was taught that, concerning Chinese dialects at least, location and geography are important factors in deciding how quickly dialects change. Change is much swifter in open plains with good transportation, much slower in mountains. Northern Chinese dialects, on the great plains of the Yellow River long ago lost many features preserved in southern dialects from the mountains and valleys of Canton, Fujien, and Taiwan; Cantonese dialects are even more conservative than Fujien/Hokien dialects.
For example, Cantonese and Hakka keep complete 入聲/entering tones, words ending in glottal ~k, ~p, ~t, but Fujien dialects have only a few, and northern dialects have lost them entirely.
aside: In college, we had to write poems with Tang dynasty rhymes. This was very challenging, because what rhymed in the eighth century does not necessarily rhyme anymore. The Cantonese speakers (mostly from Hong Kong) in class had no problem. They simply composed in Cantonese and the rhymes all fit. We often asked them to recite poems, to get a better idea of how they sounded in the Tang.
another aside: in a phonology class I analyzed the phonemes of Chinese words in Viet Namese and concluded that they retained the sounds of 盛唐初the early part of the prime of the Tang. In other words, Viet Namese pronunciation of words imported from Chinese has remained stable for well over a thousand years.
Some words have stayed the same for centuries across Chinese dialects: the great hero Lord Kuan/關公 is pretty much the same in any dialect, and he probably pronounced it like that when he lived, in the 3rd century. But his given name, 雲長, differs greatly in time and place. The reasons for this are complex and boring, so you’ll have to take my word for it; if you had any interest, you would know anyway.
Sometime just before Lord Kuan’s time, there was a great change in Chinese pronunciation. 陰陽對轉不轉了. Final ~g, ~b, ~d, the endings corresponding to ~k, ~p, ~t, disappeared completely and forever across the board, as did consonant clusters. For example, 各/ke was probably pronounced /klok/: compare 各洛. Such features are totally absent in any Chinese dialect, and have been since about the 3rd century.
These massive changes probably occurred within a century or two, and then the language congealed. In other words, the pronunciation of the Tang dynasty (say in the seventh or eight century) is much closer to modern Cantonese than the Tang was to the Eastern Han, only five hundred years earlier.
The evolution of Chinese phonology resembles closely models of punctuated evolution: stability for a long time, then willy-nilly higgledy-piggledy changes chasing across the language, followed by lasting stability.
aside, concerning punctuated evolution: Scientific American reports, Since IBM introduced the hard disk 50 years ago, the density of data storage has increased by 65 million times – with much of that rise coming in the past decade. This is a good example of punctuated evolution.
In addition, I would like to point out some problems with the basic word list for computing language change, which includes a hundred words. At random, in the first paragraph I listed dog, foot, mountain, and green. Tayal in Wulai pronounce hozin/dog, two different ways: same tribe, same village; people in the same tribe two counties over have another pronunciation again; but everybody pronounces kakay/foot the same: put that in your pipes and smoke it, Swadesh and Lees! Mountain is an English word, but I am not sure if there is an inclusive equivalent in Tayal. A mountain with jungle that people hunt on is hlahuy (thus my faithful dog Tlahuy, a form of the same word), but a sharp mountain farther away is rqyax. My Tayal is not very good, but I do not think there is one word for the English mountain. Green in Tayal sometimes includes what English speakers would call blue. In Mandarin for green we now usually say 綠, but there’s also 青 and other words. And so forth.
So all in all, I do not think glottochronology is either convincing or trustworthy.
As if anybody cares.