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666 or 616 (or even 665) — Why should it matter?
We know that, during the Roman era, educated Greeks were fascinated by puzzles and games based on number. In Greek, numerals are represented by letters of the alphabet: alpha =1, beta = 2 and so on up to theta = 9. Then come double figures (iota = 10, kappa = 20) and treble (rho = 100, etc, up to omega = 800).
This means that words and phrases can be assigned numbers by adding up the number-values of the letters they contain. Put another way, numbers can equal words or phrases. The isopsephic epigrams of Leonides of Alexandria are a case in point: the letters of the first distich of a four-line poem add up to exactly the same as the letters of the second distich. Leonides is discussed by Page, Further Greek Epigrams 503-41.
This popular parlour-game (Page, 504) could be given a satirical or polemical slant. If numbers can equal words and phrases, they can also equal proper names. Take the Emperor Nero (incidentally the probable addressee of an isopsephic birthday greeting from Leonides: A.P. 6.321 = I Page). In Greek, he is NERON (with an omega). Add up the values of these letters and you get 1005. Add up the letters of IDIAN METERA APEKTEINE (killed his own mother) and you also get 1005. So Nero = killed his own mother.
However, there is no way the Beast can be Nero, as some have wished to suggest. Even if we ruin his Greek name by substituting an omicron (70) and losing the final nu (50), the result - 226 - will not work. It is very easy to make mistakes in figuring out ancient numerology (as noted by Page passim, especially 504 and 509).
One possibility, suggested to me by Revel Coles, is that 666 - chi, xi, stigma - may be the initials of three words. Answers on a postcard, please. A concise summary of Greek numerals is given on p.53 of Abbot and Mansfield, Primer of Greek Grammar. The numerological use of the alphabet in magic is discussed by Franz Dornseiff, Das Alphabet in Mystik und Magie (Teubner, 1925).
Although our system of numerals does not lend itself to word-puzzles in the Greek style, we are still very Greek in our use of anagrams. Just as NERON = IDIAN METERA APEKTEINE, so Tony Blair MP = Im Tory Plan B - with similar polemical intent.