“Silent” and “Listen” are anagrams.
An anagram is, of course, a word constructed by rearranging the letters in another word, using all the letters in the first word, each exactly once. The word “anagram” first appeared in English in the 16th century, drawn from the French “anagramme,” which is based on the Greek “ana” (up, back) plus “gramma” (letter). Creating and “decoding” anagrams has been popular at least since Ancient Greece, and there are several free anagram generators and decoders available online (my name produces 618 possibilities, including “river moans,” “overarm sin” and “arm version”). “Anagram” itself produces only 16 anagrams, the most interesting of which is probably “agar man.”
The anagram generator at wordsmith.org suggests various practical uses for anagrams (safeguarding passwords, picking a career, etc.), but to my knowledge anagrams have never played a significant role in the evolution of a standard English word. And while “silent” and “listen” may be anagrams, they come from two entirely separate sources.
“Listen” first appeared in Old English as “hlysnan” or “lysna,” drawn from the Indo-European root “klu,” which denoted the general idea of “hearing.” (It’s also the root of our English “loud.”) “Listen” has stuck pretty closely to its original meaning of “to hear attentively; to pay attention to” ever since, though it has developed some specialized uses such as “listen in,” which can mean either to listen to a radio broadcast or to eavesdrop on someone’s conversation, and “listen up,” originally a military command to pay close attention to what follows. The “t” in “listen,” by the way, is there because of a popular association with the once common but now obsolete English verb “to list” meaning “to wish, like, desire.” That “list” has nothing to do with the “list” you take shopping (which comes from the French “liste,” meaning “strip, border, hem of cloth, band, etc.”), but it is related to “lust.”
“Silent” first appeared in English in the 16th century with the basic meaning, regarding people, of “refraining from speech,” and of things, “noiseless.” The source of “silent” is the Latin “silentem,” the participle of the verb “silere,” to be silent. Unfortunately, that’s as far back as the trail goes, although some sources suggest the Germanic verb “anasilan,” which signified a wind dying down, as the source. “Silent” may also be related to the Latin verb “desinere,” meaning “to stop.” Another descendant of that Latin “silere,” the noun “silence,” actually appeared in English more than three centuries earlier than “silent.”
Given that “listen” and “silent” both have clearly-documented roots that have no connection to, and bear no resemblance to, each other, I think it’s safe to say that their anagrammatic nature is purely coincidental.
source Word Detective