This one is a fairly familiar example in linguistics textbooks, but one that is probably surprising to someone not familiar with Indo-European linguistics.
Punch, in the sense of a fruit beverage, is a borrowing from the Hindi pāñć meaning “five”, from the fact that the original version of punch used five ingredients. Numbers, of course, especially small numbers, tend not to be borrowed, and tend to be pretty stable in meaning as well. They therefore provide a perfect class to look at when figuring out if groups of languages are related. The Hindi pāñć descends from Sanskrit páñcan, in turn from Proto-Indo-European *pénkʷe. In the course of evolving into Sanskrit, short /e/ /a/ and /o/ all merged as /e/, the labiovelars became plain velars (thus kʷ became k) and (before the /o/-/e/-/a/ merger), /k/ became palatized before front vowels, thus, *kʷe became *ke, became *ce, became *ca.
In an early stage of pre-Proto-Germanic, *pénkʷe became *pémpe, a sporadic form of assimilation. Then, under the normal sound changes, particularly Grimm’s Law, *pémpe became Proto-Germanic *fimf. In the Ingvaeonic languages, a small group of West Germanic languages (made up primarily of English, Frisian, and Low German), nasals before voiceless fricatives were lost, with compensatory lengthening, thus, *fimf became Old English fīf, which became Modern English five.
There were two PIE roots that appear to have been closely related to *penkʷe which have also left descendants in English. *pn̥kʷ-sti-s meaning “fist” and *penkʷ-ró-s meaning “finger” The first is the origin of Modern English “fist” and the second is the origin of “finger”. It is plausible that the original meaning of this root had something to do with “fist” or “hand”. Compare, for example, the Proto-Austronesian *lima, which meant both “hand” and “five”.
The development of “fist” from *pn̥kʷ-sti-s was this way: the syllabic non-vocalic sonorants became -uC-, thus PIE *n̥ became Proto-Germanic *un. /kʷ/ (and /kw/, which merged with /kʷ/ early on) lost its labialization (the /w/ sound) in certain contexts, one of which which was when preceded by /u/, including /uC/ sequences. /k/ before an /s/ or /t/ subsequently became /x/, thus becoming Proto-Germanic *funhstiz, which was simplified to *funstiz. This became Old English fȳst, the result of the /i/ in the last syllable fronting the /u/. The vowel was shortened and unrounded to become Modern English fist. There is, however, another possible etymology of Progo-Germanic *funstiz from the zero-grade of *pewǵ- “punch”, in which case the verbal -n- infix would appear along with the suffix *-sti-s
In *penkʷ-ró-s, Verner’s Law caused /kʷ/ to become /gʷ/. Most cases of /gʷ/, whether derived originally from *gʷʰ via Grimm’s Law or *kʷ via Verner’s Law were subsequently lost, with various reflexes depending on environment. Word-initialy, historic *gʷʰ became *b, most likely after Grimm’s Law happened (thus *gʷʰ → *gʷ → *b), but the opposite order is also possible (thus *gʷʰ → *bʰ → *b), while word-medially it generally became either *g or *w. Unstressed /e/ became /i/, thus creating Proto-Germanic *fingraz.
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