Glottochronology
Glottochronology (from Attic Greek γλῶττα "tongue, language" and χρóνος "time") is the part of lexicostatistics which involves comparative linguistics and deals with the chronological relationship between languages. The idea was developed by Morris Swadesh in the 1950s in his article on Salish internal relationships. He developed the idea under two assumptions: there indeed exists a relatively stable "basic vocabulary" (referred to as "Swadesh lists") in all languages of the world; and, any replacements happen in a way analogous to radioactive decay in a constant percentage per time elapsed. Using mathematics and statistics, Swadesh developed an equation that could determine  when languages separated and give an approximate time of when the separation occurred. His methods aid linguistic anthropologists by giving them a definitive way to determine a separation date between two languages. The formula he created finds an approximate number of centuries since two languages separated from a singular common ancestor. His methods also provided information on when ancient languages may have existed. Despite multiple studies and literature containing the information of glottochronology, it is not widely used today and is surrounded with controversy. Glottochronology tracks language separation from thousands, if not millions of years ago but many linguists are  skeptical of the concept because it is more of a 'probability' rather than a 'certainty.' On the other hand, some linguists may say that glottochronology is gaining traction because of its relatedness to archaeological dates. Glottochronology is not as accurate as archaeological data but it can provide a solid estimate. Over time many different extensions of the Swadesh method evolved; however, Swadesh's original method is so well known that 'glottochronology' is usually associated with him. Methodology. Word list. The original method of glottochronology presumed that the core vocabulary of a language is replaced at a constant (or constant average ) rate across all languages and cultures and so can be used to measure the passage of time. The process makes use of a list of lexical terms and morphemes which are similar to multiple languages. Lists were compiled by Morris Swadesh and assumed to be resistant against borrowing (originally designed in 1952 as a list of 200 items, but the refined 100-word list in Swadesh (1955) is much more common among modern day linguists). The core vocabulary was designed to encompass concepts common to every human language such as personal pronouns, body parts, heavenly bodies and living beings, verbs  of basic actions, numerals, basic adjectives, kin terms, and natural occurrences and events. Through a basic word list, one eliminates concepts that are specific to a particular culture or time period. It has been found through differentiating word lists that the ideal is really impossible and that the meaning set may need to be tailored to the languages being compared. Word lists are not homogenous throughout studies and they are often changed and designed to suit both languages being studied. Linguists find that it is difficult to find a word list where all words used are culturally unbiased. Many alternative  word lists have been compiled by other linguists and often use fewer meaning slots. The percentage of cognates (words with a common origin) in the word lists is then measured. The larger the percentage of cognates, the more recently the two languages being compared are presumed to have separated. Below is an example of a basic word list composed of basic Turkish words and their English translations. Glottochronologic constant. Determining word lists rely on morpheme decay or change in vocabulary. Morpheme decay must stay at a constant rate for glottochronology to be applied to a language. This leads to a  critique of the glottochronologic formula because some linguists argue that the morpheme decay rate is not guaranteed to stay the same throughout history. American Linguist Robert Lees obtained a value for the "glottochronological constant" (r) of words by considering the known changes in 13 pairs of languages using the 200 word list. He obtained a value of 0.805 ± 0.0176 with 90% confidence. For his 100-word list Swadesh obtained a value of 0.86, the higher value reflecting the elimination of semantically unstable words. The constant is related to the retention rate of words by the following formula: "L" is  the rate of replacement, ln represents the natural logarithm and "r" is the glottochronological constant. Divergence time. The basic formula of glottochronology in its shortest form is this: "t" = a given period of time from one stage of the language to another (measured in millennia), "c" = proportion of wordlist items retained at the end of that period and "L" = rate of replacement for that word list. One can also therefore formulate: By testing historically verifiable cases in which "t" is known by nonlinguistic data (such as the approximate distance from Classical Latin to modern Romance languages), Swadesh  arrived at the empirical value of approximately 0.14 for "L", which means that the rate of replacement constitutes around 14 words from the 100-wordlist per millennium. Results. Glottochronology was found to work in the case of Indo-European, accounting for 87% of the variance. It is also postulated to work for Afro-Asiatic (Fleming 1973), Chinese (Munro 1978) and Amerind (Stark 1973; Baumhoff and Olmsted 1963). For Amerind, correlations have been obtained with radiocarbon dating and blood groups as well as archaeology. The approach of Gray and Atkinson, as they state, has nothing to do with "glottochronology". Discussion. The  concept of language change is old, and its history is reviewed in Hymes (1973) and Wells (1973). In some sense, glottochronology is a reconstruction of history and can often be closely related to archaeology. Many linguistic studies find the success of glottochronology to be found alongside archaeological data. Glottochronology itself dates back to the mid-20th century. An introduction to the subject is given in Embleton (1986) and in McMahon and McMahon (2005). Glottochronology has been controversial ever since, partly because of issues of accuracy but also because of the question of whether its basis is sound (for example, Bergsland 1958 ; Bergsland and Vogt 1962; Fodor 1961; Chrétien 1962; Guy 1980). The concerns have been addressed by Dobson et al. (1972), Dyen (1973) and Kruskal, Dyen and Black (1973). The assumption of a single-word replacement rate can distort the divergence-time estimate when borrowed words are included (Thomason and Kaufman 1988). An overview of recent arguments can be obtained from the papers of a conference held at the McDonald Institute in 2000. The presentations vary from "Why linguists don't do dates" to the one by Starostin discussed above. Since its original inception, glottochronology has been rejected by many linguists , mostly Indo-Europeanists of the school of the traditional comparative method. Criticisms have been answered in particular around three points of discussion: Modifications. Somewhere in between the original concept of Swadesh and the rejection of glottochronology in its entirety lies the idea that glottochronology as a formal method of linguistic analysis becomes valid with the help of several important modifications. Thus, inhomogeneities in the replacement rate were dealt with by Van der Merwe (1966) by splitting the word list into classes each with their own rate, while Dyen, James and Cole (1967) allowed each meaning to have its own rate . Simultaneous estimation of divergence time and replacement rate was studied by Kruskal, Dyen and Black. Brainard (1970) allowed for chance cognation, and drift effects were introduced by Gleason (1959). Sankoff (1973) suggested introducing a borrowing parameter and allowed synonyms. A combination of the various improvements is given in Sankoff's "Fully Parameterised Lexicostatistics". In 1972, Sankoff in a biological context developed a model of genetic divergence of populations. Embleton (1981) derives a simplified version of that in a linguistic context. She carries out a number of simulations using this which are shown to give good results. Improvements in statistical methodology  related to a completely different branch of science, phylogenetics; the study of changes in DNA over time sparked a recent renewed interest. The new methods are more robust than the earlier ones because they calibrate points on the tree with known historical events and smooth the rates of change across them. As such, they no longer require the assumption of a constant rate of change (Gray & Atkinson 2003). Starostin's method. Another attempt to introduce such modifications was performed by the Russian linguist Sergei Starostin, who had proposed the following: The resulting formula, taking into account both the time dependence  and the individual stability quotients, looks as follows: In that formula, −"Lc" reflects the gradual slowing down of the replacement process because of different individual rates since the least stable elements are the first and the quickest to be replaced, and the square root represents the reverse trend, the acceleration of replacement as items in the original wordlist "age" and become more prone to shifting their meaning. This formula is obviously more complicated than Swadesh's original one, but, it yields, as shown by Starostin, more credible results than the former and more or less agrees with all the cases  of language separation that can be confirmed by historical knowledge. On the other hand, it shows that glottochronology can really be used only as a serious scientific tool on language families whose historical phonology has been meticulously elaborated (at least to the point of being able to distinguish between cognates and loanwords clearly). Time-depth estimation. The McDonald Institute hosted a conference on the issue of time-depth estimation in 2000. The published papers give an idea of the views on glottochronology at that time. They vary from "Why linguists don't do dates" to the one by Starostin discussed  above. Note that in the referenced Gray and Atkinson paper, they hold that their methods cannot be called "glottochronology" by confining this term to its original method.