Isopsephy (/ˈaɪsəpˌsɛfi/; ἴσος isos meaning "equal" and ψῆφος psephos meaning "pebble") or isopsephism is the practice of adding up the number values of the letters in a word to form a single number.^{[1]} The total number is then used as a metaphorical bridge to other words evaluating the equal number,^{[2]} which satisfies isos or "equal" in the term. The early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, which corresponds to psephos or "pebble" and "counting" in the term.
Isopsephy is related to gematria: the same practice using the Hebrew alphabet. It is also related to the ancient number systems of many other peoples (for the Arabic alphabet version, see Abjad numerals). A gematria of Latin script languages was also popular in Europe from the Middle Ages to the Renaissance, and its legacy remains in codebreaking, numerology, and Masonic symbolism today (see arithmancy).^{[3]}
Until Arabic numerals were adopted and adapted from Indian numerals in the 8th and 9th centuries AD, and promoted in Europe by Fibonacci of Pisa with his 1202 book Liber Abaci, numerals were predominantly alphabetical. For instance in Ancient Greece, Greek numerals used the alphabet. It is just a short step from using letters of the alphabet in everyday arithmetic and mathematics to seeing numbers in words, and to writing with an awareness of the numerical dimension of words.
An early reference to isopsephy, albeit of morethanusual sophistication (employing multiplication rather than addition), is from the mathematician Apollonius of Perga, writing in the 3rd century BC. He asks: "Given the verse: ΑΡΤΕΜΙΔΟΣ ΚΛΕΙΤΕ ΚΡΑΤΟΣ ΕΞΟΧΟΝ ΕΝΝΕΑ ΚΟΥΡΑΙ ('Nine maidens, praise the glorious power of Artemis'), what does the product of all its elements equal?"^{[4]} More conventional are the instances of isopsephy found in graffiti at Pompeii, dating from around 79 AD. One reads Φιλω ης αριθμος ϕμε, "I love her whose number is 545." Another says, "Amerimnus thought upon his lady Harmonia for good. The number of her honorable name is 45." Suetonius, writing in 121 AD, reports a political slogan that someone wrote on a wall in Rome:
which appears to be another example.^{[5]}^{[6]} In Greek, Νερων, Nero, has the numerical value 50+5+100+800+50=1005, the same value as ιδιαν μητερα απεκτεινε (idian metera apekteine) — "He killed his own mother", (10+4+10+1+50) + (40+8+300+5+100+1) + (1+80+5+20+300+5+10+50+5). A famous example is 666 in the Biblical Book of Revelation (13:18): "Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six." The word rendered "count", ψηφισάτω, psephisato, has the same "pebble" root as the word isopsephy.^{[7]}^{[8]} The Greek Neron Kaisar (Nero Caesar in Latin/English) when transliterated into Hebrew gematria equals "six hundred sixtysix".
Also in the 1st century AD, Leonidas of Alexandria created isopsephs, epigrams with equinumeral distichs, where the first hexameter and pentameter equal the next two verses in numerical value. He addressed some of them to Nero:
Which translates to: "The muse of Leonidas of the Nile offers up to thee, O Caesar, this writing, at the time of thy nativity; for the sacrifice of Calliope is always without smoke: but in the ensuing year he will offer up, if thou wilt, better things than this." Here the sum of both the first and second distich is 5699. In another of his distichs, the hexameter line is equal in number to its corresponding pentameter:
Which translates to: "One line is made equal in number to one, not two to two; for I no longer approve of long epigrams." Here each line totals 4111.^{[9]}
A headstone found at the Temple of Artemis at Sparta Orthia is a 2ndcentury AD example of isopsephic elegiac verse. It says:
It is the votive stele for a boy who won a competition in singing. The words in each line add up to ΄Β΄Ψ΄Λ, that is 2730, and that total is also given at the end of each line. Also in the 2nd century AD, Aelius Nicon of Pergamon, the Greek architect and builder described by his son, the famous physician Galen, as having "mastered all there was to know of the science of geometry and numbers", was a master in composing isopsephic works.^{[4]}
In Greek, each unit (1, 2, ..., 9) was assigned a separate letter, each tens (10, 20, ..., 90) a separate letter, and each hundreds (100, 200, ..., 900) a separate letter. This requires 27 letters, so the 24letter alphabet was extended by using three obsolete letters: digamma ϝ (also used are stigma ϛ or, in modern Greek, στ) for 6, qoppa ϙ for 90, and sampi ϡ for 900.
This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 241 is represented as σμα (200 + 40 + 1).
