comparative method

The comparative method (in comparative linguistics) is a technique used by linguists to demonstrate genetic relationships between languages. It aims to prove that two or more historically attested languages are descended from a single proto-language by comparing lists of cognate terms. From these cognate lists, regular sound correspondences between the languages are established, and a sequence of regular sound changes can then be postulated which allows the proto-language to be reconstructed from its daughter languages. Relation is deemed certain only if a partial reconstruction of the common ancestor is feasible, and if regular sound correspondences can be established with chance similarities ruled out.

Developed in the 19th century through the study of the Indo-European languages, the comparative method remains the standard by which mainstream linguists judge whether two languages are related, with alternative lexicostatistical methods widely considered to be unreliable. Potential problems with the comparative method have also arisen as a result of a number of advances in linguistic thought, in large part due to some of the "basic assumptions" of the comparative method. However, as Campbell (2004:146-7) observes, "What textbooks call the 'basic assumptions' of the comparative method might better be viewed as the consequences of how we reconstruct and of our views of sound change."

Terminology

In the present context, related has a specific meaning: two languages are genetically related if they are descended from the same ancestor language^[1]. Thus, for example, Spanish and French are both descended from Latin. Therefore, French and Spanish are considered to belong to the same family of languages, the Romance languages.^[2]

Descent, in turn, is defined in terms of transmission across the generations: children learn a language from the parents' generation and are then influenced by their peers; they then transmit it to the next generation, and so on (how and why changes are introduced is a complicated, unresolved issue). A continuous chain of speakers across the centuries links Vulgar Latin to all of its modern descendants.

However, it is possible for languages to have different degrees of relatedness. English, for example, is related to both German and Russian, but is more closely related to the former than it is to the latter. The reason for this is that although all three languages share a common ancestor, Proto-Indo-European, English and German also share as a more recent common ancestor one of the daughter languages of Proto-Indo-European, Proto-Germanic, while Russian does not. Therefore, English and German are considered to belong to a different subgroup of the Indo-European language family, the Germanic languages, than Russian (which belongs to the Slavic subgroup).^[3] The division of related languages into sub-groups by the comparative method is accomplished by finding languages with large numbers of shared linguistic innovations from the parent language; two languages having many shared retentions from the parent language is not sufficient evidence of a sub-group.

This definition of relatedness implies that even if two languages are quite similar in their vocabularies, they are not necessarily closely related. As a result of heavy borrowing over the years from Arabic into Persian, Modern Persian in fact takes more of its vocabulary from Arabic than from its direct ancestor, Proto-Indo-Iranian.^[4]. But under the definition just given, Persian is considered to be descended from Proto-Indo-Iranian, and not from Arabic.

The comparative method is a method for proving relatedness in the sense just given, as well as a method for reconstructing the sound system and vocabulary of the common ancestral language and uncovering the sound changes the languages of a family have undergone.

Origin and development

The first known systematic attempt to prove the relationship between two languages on the basis of similarity of grammar and lexicon was made by the Hungarian János Sajnovics in 1770, when he attempted to demonstrate the relationship between Sami and Hungarian (work that was later extended to the whole Finno-Ugric language family in 1799 by his fellow countryman Samuel Gyarmathi),^[5] but the origin of modern historical linguistics is often traced back to Sir William Jones, an English philologist living in India, who in 1782 made his famous observation:

“The Sanskrit language, whatever be its antiquity, is of a wonderful structure; more perfect than the Greek, more copious than the Latin, and more exquisitely refined than either, yet bearing to both of them a stronger affinity, both in the roots of verbs and the forms of grammar, than could possibly have been produced by accident; so strong indeed, that no philologer could examine them all three, without believing them to have sprung from some common source, which, perhaps, no longer exists. There is a similar reason, though not quite so forcible, for supposing that both the Gothick and the Celtick, though blended with a very different idiom, had the same origin with the Sanskrit; and the old Persian might be added to the same family.” (Jones 1786, quoted in Lehman 1967 and Szemerényi 1996:4)

An insight often attributed to Jones is conceiving of the idea of a proto-language, and consequently of the type of "family tree" model of language development (one proto-language splitting into various daughter languages, some of those then splitting again into further languages), upon which the comparative method is based. However, Jones' role in the development of these ideas has recently been called into question. According to the comparative linguist Lyle Campbell, the widely quoted passage from Jones has been removed from its proper context, and a reading of his work reveals his ideas of linguistic development as less clear. Many of the linguistic classifications proposed by Jones were also erroneous; for instance, he connected Austronesian languages with Sanskrit, and failed to include Slavic in the Indo-European family.^[6]

The comparative method itself developed out of the attempts to reconstruct the proto-language which Jones had hypothesized about, known as Proto-Indo-European (PIE). The first attempt to analyse the relationships between the Indo-European languages was made by the German linguist Franz Bopp in 1816. Though he did not attempt a reconstruction, he tried to prove that Greek, Latin and Sanskrit were related by systematically demonstrating that they shared a both common structure and a common lexicon.^[7].

It was the German scholar Friedrich Schlegel who in 1808 first stated the importance of using the oldest possible form of a language when trying to prove its relationships;^[8] then, in 1818, the Danish philologist Rasmus Christian Rask developed the principle of regular sound changes to explain his observations of similarities between individual words in the Germanic languages and their cognates in Greek and Latin.^[9] It was another German, Jacob Grimm - better known for his Fairy Tales - who in Deutsche Grammatik (published 1819-37 in four volumes) first made use of something resembling the modern comparative method in attempting to show the development of the Germanic languages from a common origin, the first systematic study of diachronic language change.^[10]

Both Rask and Grimm were unable to explain apparent exceptions to the sound laws that they had discovered. Though the German linguist Hermann Grassmann explained one of these anomalies with the publication of Grassmann's law in 1862,^[11] it was in 1875 that a Danish scholar, Karl Verner, made a methodological breakthrough when he formulated Verner's law, the sound law which now bears his name, and which was the first sound law to use comparative evidence to show that a phonological change in one phoneme could depend on other factors within the same word, such as the neighbouring phonemes and the position of the accent:^[12] in other words, the modern concept of conditioning environments.

Similar discoveries were made by a group of young, radical German academics at the University of Leipzig known as Junggrammatiker (usually rendered as Neogrammarians in English) in the late 1800s, leading them to conclude that all sound changes were ultimately regular, and resulting in two of them, Karl Brugmann and Hermann Osthoff, making in 1878 the famous statement that "sound laws have no exceptions".^[13] This revolutionary idea is fundamental to the modern comparative method, since the method necessarily assumes regular correspondences between sounds in related languages, and consequently regular sound changes from the proto-language. It was this Neogrammarian Hypothesis which led to the comparative method being applied to reconstruct Proto-Indo-European, with Indo-European being at that time by far the most well-studied language family. Linguists working with other families soon followed suit, and the comparative method quickly became the established method for uncovering linguistic relationships.^[5]

Application

There is no concrete set of steps to be followed in the application of the comparative method, but linguists generally agree on the basic steps, which are as follows:^[14]

Assemble potential cognate lists

Genetic relationship between two (or more) languages can be established if they show a number of regular correspondences in native vocabulary, which means that there is a regularly recurring match between the phonetic structure of basic words with similar meanings.^[15] Thus, this step simply involves making lists of words which are likely cognates among the languages being compared. For example, looking at the Polynesian family^[16] linguists would come up with a list similar to the following, although in practice a real list would be much longer:

Caution needs to be exercised to avoid including borrowings or false cognates in the list, which could skew or obscure the correct data.^[17] For example, there is a similarity between English taboo ([tæbu]) and the five Polynesian forms. Though this may seem to be a cognate, showing that English is genetically related to the Polynesian languages, it is not, as the similarity is due to the fact that English borrowed the word from Tongan.^[18] This problem can usually be overcome by using basic vocabulary such as kinship terms, numbers, body parts, pronouns, and other basic terms.^[19] Nonetheless, even basic vocabulary can be borrowed. Finnish, for example, borrowed the word for "mother", äiti, from Gothic aiþei,^[20] while Pirahã, a Muran language of South America, borrowed all its pronouns from Nhengatu;^[21] likewise, English borrowed the pronouns "they", "them", and "their(s)" from Norse.^[22]

Establish correspondence sets

Once potential cognate lists are established, the next step is to determine the regular sound correspondences they exhibit. The notion of regular correspondence is very important here: mere phonetic similarity, as between English day and Latin dies (both with the same meaning), has no probative value.^[23] English initial d- does not regularly match Latin d-,^[24] and whatever sporadic matches can be observed are due either to chance (as in the above example) or to borrowing (e.g. Latin diabolus and English devil, both ultimately of Greek origin).^[25] The Neogrammarians first emphasized this point in the late 1800s, and their motto, "sound laws have no exceptions", has remained a fundamental axiom in historical linguistics to this day.

For example, although the correspondence d- : d- (where the notation "A : B" means "A corresponds to B") in English and Latin day and dies above is not regular, English and Latin do exhibit a very regular correspondence of t- : d-.^[24] For example:^[26]

Since a truly systematic correspondence is unlikely to be accidental, if alternative possibilities like massive borrowing can be ruled out, then the correspondence can be attributed to common descent. If there are many regular correspondence sets of this kind (the more the better), then common origin becomes a virtual certainty, particularly if some of the correspondences are non-trivial or unusual.^[15]

Discover which sets are in complementary distribution

During the time the comparative method was being developed (late 18th to late 19th century), two major developments occurred which improved the method's effectiveness.

First, it was found that many sound changes are conditioned by a particular context. Thus for example, in both Greek and Sanskrit, an aspirated stop evolved into an unaspirated one, but only if a second aspirate occurred later on in the same word;^[27] this is Grassmann's law, known to the Sanskrit grammarian Pāṇini^[28] and promulgated as a historical discovery by Hermann Grassmann in 1863.

Second, it was found that sometimes sound changes occurred in contexts that were later lost. For instance, in Sanskrit velars (k-like sounds) were replaced by palatals (ch-like sounds) whenever the following vowel was *i or *e.^[29] Subsequent to this change, all instances of *e were replaced by a.^[30] The situation would have been unreconstructable, had not the original distribution of e and a been recoverable from the evidence of other Indo-European languages.^[31] Thus, for instance, Latin que, "and", preserves the original *e vowel that caused the consonant shift in Sanskrit:

Ca is the attested Sanskrit form for and. This finding was made independently by several scholars during the 1870s.

Verner's Law, discovered by Karl Verner in about 1875, is a similar case: the voicing of consonants in Germanic languages underwent a change that was determined by the position of the old Indo-European accent. Following the change, the accent shifted across the board to initial position.^[32] Verner solved the puzzle by comparing the Germanic voicing pattern with data from Greek and Sanskrit accent.

This stage of the comparative method, therefore, involves examining the correspondence sets discovered in step 2 and seeing which of them apply only in certain contexts. If two (or more) sets involve identical or similar sounds, and apply in complementary distribution, then the sets can be assumed to reflect a single original phoneme. This is because "some sound changes, particularly conditioned sound changes, can result in a proto-sound being associated with more than one correspondence set".^[33]

To take another example, the Romance languages, descended from Latin, exhibit two different correspondence sets which both involve k:

What linguists do in this situation is try to see if the two sets occur in complementary distribution, in which case they reflect a single proto-phoneme, or if both occur in identical environments, in which case they must both reflect separate proto-phonemes. In this case, French ʃ only occurs before a in the other languages (which becomes ɛ in French), while French k occurs elsewhere. Both sets 1 and 2 can therefore be assumed to reflect a single proto-phoneme (in this case *k, spelled <c> in Latin).^[34]

A more complex case involves consonant clusters in Proto-Algonquian, which have been notoriously difficult to reconstruct. The Algonquianist Leonard Bloomfield used the reflexes of the clusters in four of the daughter languages of Proto-Algonquian to come up with the following correspondence sets:^[35]

Although all five correspondence sets overlap with one another in various places, they are not in complementary distribution, and so Bloomfield recognized that a different cluster must be reconstructed for each set; his reconstructions were, respectively, *hk, *xk, *čk (=[ʧk]), *šk (=[ʃk]), and çk (where ‘x’ and ‘ç’ are arbitrary symbols, not attempts to guess the phonetic value of the proto-phonemes).^[36]

Reconstruct proto-phonemes

This step tends to be much more subjective than the previous ones. A linguist here has to rely mostly on their general intuitions about what types of sound changes are likely and which are unlikely. For example, the voicing of voiceless plosives between vowels is an extremely common sound change, occurring in languages all over the world, whilst the devoicing of voiced plosives between vowels is extremely uncommon. Therefore, if a linguist were comparing two languages with a correspondence of -t- : -d- between vowels, they would reconstruct the proto-phoneme as being *-t-, and assume that it became voiced to -d- in the second language (unless they had a very good reason not to).

Sometimes, sound changes occur that are extremely unusual or unexpected. The Proto-Indo-European word for two, for example, is reconstructed as *dwō, which is reflected in Classical Armenian as erku. Several other cognates demonstrate that the change *dw- → erk- in the history of Armenian was a regular one.^[37] Similarly, in Bearlake, a dialect of the Athabaskan language of Slavey, there has been a sound change of Proto-Athabaskan *ts → Bearlake kʷ.^[38] It is very unlikey that *dw- changed directly into erk- and *ts into kʷ, but instead they must have gone through several intermediate steps to arrive at the later forms. The lesson here is that with enough sound changes, a given sound can change into just about any other sound. This is why it is not phonetic similarity which matters when utilizing the comparative method, but regular sound correspondences.^[23]

Another assumption used in determining a proto-phoneme is that the reconstruction should ideally involve as few sound changes as possible to arrive at the modern reflexes in the daughter languages. In other words, unless there is persuasive evidence to the contrary, whatever value is the most common reflex in the daughter languages should be reconstructed as the value of the proto-phoneme. For example, Algonquian languages exhibit the following correspondence set:^[39][40]

The simplest reconstruction for this set would be either *m or *b. Both *m → b and *b → m (where "*A → B" means "*A becomes B") are conceivable sound changes, so the principle of reconstructing "likely" changes over "unlikely" ones is not useful here. Instead, because the reflex of this proto-phoneme is m in five of the languages compared here, and b in only one of them, if *b is reconstructed, then it is necessary to assume five separate changes of *b → m, whereas if *m is reconstructed, it is only necessary to assume a single change of *m → b in one language in the family. Since the assumption is that reconstructions should require the fewest number of changes possible to arrive at the modern reflexes, linguists would reconstruct *m here.

Examine the reconstructed system typologically

In the final step, the linguist takes all the proto-phonemes that have been reconstructed using steps 1-4, and checks to see how the system fits with what is currently known about typological constraints. For example, if the reconstructed phonemes fit together in the following hypothetical system, the linguist would be suspicious, because languages generally (though not always) tend to maintain symmetry in their phonemic inventories:

In this hypothetical reconstructed system, there is only one voiced plosive, *b, and although there is an alveolar and a velar nasal, *n and *ŋ, there is no corresponding labial nasal. In this case, the linguist would have to return to step 4 and reevaluate their earlier conclusions. In this case, they would try to figure out if there is any evidence to suggest that what was earlier reconstructed as *b is in fact *m, or evidence that what was earlier reconstructed as *n and *ŋ are in fact *d and *g.

Even a symmetrical system can be typologically suspicious. For example, the Proto-Indo-European plosive inventory, as traditionally reconstructed,^[41] is as follows:

Since the mid-20th century, a number of linguists have argued that this system is, at best, very suspicious typologically.^[42] They state that it is extremely unlikely, or maybe even impossible, for a language to have a voiced aspirated (breathy voice) series without a corresponding voiceless aspirated series. These linguists therefore argue, on typological grounds, that it is necessary to reevaluate the traditional reconstruction of Proto-Indo-European. A potential solution was provided by Thomas Gamkrelidze and Vyacheslav V. Ivanov, who argued that the series traditionally reconstructed as plain voiced should in fact be reconstructed as glottalized — either implosive (ɓ, ɗ, ɠ) or ejective (pʼ, tʼ, kʼ). The plain voiceless and voiced aspirated series would thus be seen as just voiceless and voiced, with aspiration being a non-distinctive quality of both.^[43] This example of the application of linguistic typology to linguistic reconstruction has become known as the Glottalic Theory. It has a large number of proponents but is not generally accepted.^[44]

The reconstruction of proto-sounds and their historical transformations enables linguists to proceed further: they can compare grammatical morphemes (word-forming affixes and inflectional endings), patterns of declension and conjugation, and so on. The full reconstruction of an unrecorded protolanguage can never be complete (for example, proto-syntax is far more elusive than phonology or morphology, and all elements of linguistic structure undergo inevitable erosion and gradual loss or replacement over time), but a consistent partial reconstruction can and must be attempted as proof of genetic relationship.

Limitations

A number of difficulties with aspects related to the method are now recognized,^[45] but the comparative method is still seen as being one of the most valuable tools in comparative linugistics, and linguists continue to use it widely; other proposed approaches to determining linguistic relationships and reconstructing proto-languages, such as glottochronology and mass lexical comparison, are considered flawed and unreliable by nearly all linguists.^[46] Linguists recognize, however, that results obtained with the comparative method are not historical fact. Fox (1997:141-2), for example, concludes:

“The Comparative Method as such is not, in fact, historical; it provides evidence of linguistic relationships to which we may give a historical interpretation. ...[Our increased knowledge about the historical processes involved] has probably made historical linguists less prone to equate the idealizations required by the method with historical reality. ...Provided we keep [the interpretation of the results and the method itself] apart, the Comparative Method can continue to be used in the reconstruction of earlier stages of languages.”

Neogrammarian Hypothesis

The foundation of the comparative method, and of comparative linguistics in general, is the Neogrammarians' fundamental assumption that "sound laws have no exceptions." When it was initially proposed, critics of the Neogrammarians proposed an alternate position, summarized by the maxim "each word has its own history".^[47] The so-called Neogrammarian Hypothesis is now well-established and well-supported, though there remain some situations in which its application can yield faulty results.

Borrowings, areal diffusion and random mutations

Even the Neogrammarians recognized that, apart from the general sound change laws, languages are also subject to borrowings from other languages and other sporadic changes (such as irregular inflections, compounding, and abbreviation) that affect one word at a time, or small subsets of words.

While borrowed words should be excluded from the analysis, on the grounds that they are not genetic by definition, they do add noise to the data, and thus may hide systematic laws or distort their analysis. Moreover, there is the danger of circular reasoning — namely, of assuming that a word has been borrowed solely because it does not fit the current assumptions about the regular sound laws.

Attempts to apply the comparative method to languages which have been affected by the process of areal diffusion can also be problematic. This is, in essence, a subtle form of borrowing, which can take place when a significant number of speakers of one language have some competence in another, possibly unrelated language. This may lead to the languages acquiring phonological characteristics from one another, sometimes even without the conscious borrowing of lexical or morphological forms, with the result that the two languages may end up appearing to be genetically related when in fact they are not. It is also possible that two or more unrelated languages may appear to be related as the result of them all individually undergoing areal diffusion from a third unrelated language.^[48] It becomes especially hard when several areal features and other influences converge to form a sprachbund, making their identification all the more important; for instance, the East Asian Sprachbund threw the classification of such languages as Chinese, Korean, Japanese, and Vietnamese into several false classifications before correction.

The other exceptions to the sound laws are a more serious problem, because they occur in generic language transmission. One example of such a sporadic change, with no apparent logical reason, is the Spanish word for "word", palabra. By regular sound changes from the Latin parabŏla, it should have become parabla, but the r and l changed places by sporadic metathesis.^[49]

Analogy

A source of sporadic changes that was recognized by the Neogrammarians themselves was analogy, in which a word is sporadically changed to be closer to another word in the lexicon which is perceived as being somehow related to it. For example, the Russian word for nine, by regular sound changes from Proto-Slavic, should have been /nʲevʲatʲ/, but is in fact /dʲevʲatʲ/. It is believed that the initial nʲ- changed to dʲ- due to influence of the word for "ten" in Russian, /dʲesʲatʲ/.^[50]

Gradual application

More recently, William Labov and other linguists who have studied contemporary language changes in detail have discovered that even a systematic sound change is at first applied in an unsystematic fashion, with the percentage of its occurrence in a person's speech dependent on various social factors.^[51] Often the sound change begins to affect some words in a language, and then gradually spreads to others, a process known as lexical diffusion. While not invalidating the Neogrammarians' axiom that "sound laws have no exceptions", this does seem to show that sound laws do not always apply to all lexical items at the same time. As Hock (1991:446-7) notes, "While it probably is true in the long run every word has its own history, it is not justified to conclude as some linguists have, that therefore the Neogrammarian position on the nature of linguistic change is falsified."

Problems with the Tree Model

Another weakness of the comparative method lies in its reliance on the Tree Model (German Stammbaum).^[52] In this model, daughter languages are seen as branching out from the proto-language, gradually growing more and more distant from the proto-language through accumulated phonological, morpho-syntactic, and lexical changes; and possibly splitting into further daughter languages. This model is usually represented by upside-down tree-like diagrams. For example, here is a diagram of the Uto-Aztecan family of languages, spoken throughout the southern and western United States and Mexico:^[53]

An example of the Tree Model, used here to represent the Uto-Aztecan language family. (Families are in bold, individual languages in italics. Not all of the branches and languages are shown, for lack of space.)

Wave model

Main article: Wave model (linguistics)

Since languages change gradually, there are long periods in which different dialects of a language, as they evolve into separate languages, remain in contact with one another and influence each other. Therefore, the Tree Model does not reflect the reality of how languages change, as even once they are completely separated, languages which are near to one another will continue to influence each other, often sharing grammatical, phonological, and lexical innovations. A change in one language of a family will often spread to neighboring languages; and multiple waves of change may partially overlap like waves on the surface of a pond, across language and dialect boundaries, each with its own randomly delimited range.^[54] The following diagram illustrates this conception of language change, called the Wave Model:^[55]

The Wave Model has been proposed as an alternative model of language change.

However, Hock (1991:454) observes:

“The discovery in the late nineteenth century that isoglosses can cut across well-established linguistic boundaries at first created considerable attention and controversy. And it became fashionable to oppose a wave theory to a tree theory... Today, however, it is quite evident that the phenomena referred to by these two terms are complementary aspects of linguistic change...

What seemed at the outstart as two incompatible conceptions of how languages change had already coalesced into one single explanatory theory. As demonstrated by Labov (2007), what needed to be reconciled within one framework of thinking were the transmission and the diffusion principles of linguistic change. The transmission of change within a speech community is characterized by incrementation within a faithfully reproduced pattern characteristic of the tree model, while diffusion across communities shows weakening of the original pattern and a loss of structural features. This is the result of the differences between the learning abilities of children and adults as intercommunal contacts are primarily between the latter.

Non-uniformity of the proto-language

Another assumption implicit in the methodology of the comparative method is that the proto-language is uniform. This is problematic, as even in extremely small language communities there are always dialect differences, whether based on area, gender, class, or other factors (the Pirahã language of Brazil is spoken by only several hundred people, but has at least two different dialects, one spoken by men and one by women, for example).^[56] Therefore, the single proto-language reconstructed by the comparative method is an idealized language which never existed. This may not be as serious an issue as it at first appears, however; Campbell (2004:146-7) for instance, points out:

“It is not so much that the comparative method 'assumes' no variation; rather, it is just that there is nothing built into the comparative method which would allow it to address variation directly....This assumption of uniformity is a reasonable idealization; it does no more damage to the understanding of the language than, say, modern reference grammars do which concentrate on a language's general structure, typically leaving out consideration of regional or social variation.”

Subjectivity of the reconstruction

While the identification of systematic sound correspondences between known languages is fairly objective, the reconstruction of their common ancestral language is inherently subjective. In the Proto-Algonquian example above, the choice of *m as the parent phoneme is only likely, not certain. It is conceivable that a Proto-Algonquian language with *b in those positions split into two branches, one which preserved *b and one which changed it to *m instead; and while the first branch only developed into Arapaho, the second spread out wider and developed into all the other Algonquian tribes. It is also possible that the nearest common ancestor of the Algonquian languages used some other sound instead, such as *p, which eventually mutated to *b in one branch and to *m in the other.

Since the reconstruction of a proto-language involves many of these choices, some linguists prefer to view the proto-phonemes that are reconstructed as abstract representations of sound correspondences, rather than a literal guess about what sounds were present in the proto-language. On the other hand, there are a number of well-known cases where reconstructions have been confirmed as correct by independent evidence such as loanwords. For, example Finnic languages such as Finnish have borrowed many words from an early stage of Germanic, and the shape of the loans matches the forms that have been reconstructed for Proto-Germanic: compare, e.g., Finnish kuningas 'king' and kaunis 'beautiful' to the Germanic reconstructions *kuningaz and *skauniz (> German König 'king', schön 'beautiful').^[57]

See also

• Historical linguistics
• Comparative linguistics
• Proto-language
• Lexicostatistics
• Swadesh list

Notes

References

External links

• The comparative method applied to reconstruct Proto-Indo-European
• An introduction to the comparative method from the University of California (PDF)

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