This is a great question!
Yes, anagrams can be, and have been, used for divinination since antiquity, although they are also popular word games.
For those who are not familiar with anagrams, they consist of rearranging the letters in either a word or phrase to create a new word or phrase that will often relate to the original. For instance, the words "debit card" can be rearranged to mean "bad credit" and "schoolmaster" can be rearranged to spell "the classroom." These are known as cognate anagrams, but there are many different kinds.
For instance, an ambigram is an anagram that is directly opposed to the original word. This website lists an example as "The Nuclear Regulatory Commission" which can be rearranged to read "Your rules clone nuclear nightmares."
The anagram is actually very ancient, dating back to the 4th Century BC according to some historians. In the time of the early Christians, anagrams were believed to have mystical or prophetic meaning. They largely fell out of practice until around the 13th century AD when Jewish Cabalists began to use them again, usually attributing some mystical significance to them.
As this site explains, Cabalists liked to apply anagrams to people’s names. Called Themuru, which means change, "the rearranging of letters in a name was believed to unveil hidden meanings and the spiritual natures correlating to that person," the site states, adding that " Pythagoras (6th century BC) is also thought to have used anagrams to discover a person’s destiny."
A famous story that reveals how the anagram was used to divine the future involves Alexander the Great who supposedly divined the outcome of the siege of Tyre after a disturbing dream about a Satyr attacking him. His sages divined that he would triumph over Tyre by anagramming the Greek word for Satyr - which spelled out "Tyre is thine".
Anagrams have also been used to hide secret information - as a kind of code, if you will - such as during the Middle Ages when scientists would use them to hide the findings of experiments that they didn't want widely known.
They have also been used throughout the centuries as popular word games.
As I see it, anagrams are like tea leaves and pebbles. Both have long been used for divination, but that doesn't mean you can't use them to make tea or pave your driveway.
Using an anagram as a word game for amusement is perfectly acceptable - just don't start reading anything into the new words or phrases you create!
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