Isopsephy
Encyclopedia
Isopsephy is the Greek
word for the practice of adding up the number values of the letters
in a word to form a single number. The early Greeks used pebbles arranged in patterns to learn arithmetic
and geometry
.
Isopsephy is related to Gematria
, the same practice using the Hebrew alphabet
, and 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 indeed its legacy remains in numerology
and Masonic
symbolism today (see arithmancy
).
were adopted and adapted from Indian numerals
in the 8th and 9th century 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. Indeed there is some evidence that from the very beginning the alphabet was designed in order to meet the needs of mathematics. 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 more-than-usual 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?" 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. 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 (the number of the Beast
) in the Biblical Book of Revelation
(13:18): "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 here "count", ψηφισάτω, psephisato, has the same "pebble" root as the word isopsephy).
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:
"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:
"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.
A headstone found at the Temple of Artemis at Sparta Orthia is a 2nd century 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 ΄ΒΨΛ, that is 2730, and, perhaps in case anyone does't notice, 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.
ϝ,(also used are stigma
ϛ or, in modern Greek, στ) for 6, qoppa
ϟ 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).
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
word for the practice of adding up the number values of the letters
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...
in a word to form a single number. The early Greeks used pebbles arranged in patterns to learn arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
and geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
.
Isopsephy is related to Gematria
Gematria
Gematria or gimatria is a system of assigning numerical value to a word or phrase, in the belief that words or phrases with identical numerical values bear some relation to each other, or bear some relation to the number itself as it may apply to a person's age, the calendar year, or the like...
, the same practice using the Hebrew alphabet
Hebrew alphabet
The Hebrew alphabet , known variously by scholars as the Jewish script, square script, block script, or more historically, the Assyrian script, is used in the writing of the Hebrew language, as well as other Jewish languages, most notably Yiddish, Ladino, and Judeo-Arabic. There have been two...
, and the ancient number systems of many other peoples (for the Arabic alphabet
Arabic alphabet
The Arabic alphabet or Arabic abjad is the Arabic script as it is codified for writing the Arabic language. It is written from right to left, in a cursive style, and includes 28 letters. Because letters usually stand for consonants, it is classified as an abjad.-Consonants:The Arabic alphabet has...
version, see Abjad numerals
Abjad numerals
The Abjad numerals are a decimal numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values. They have been used in the Arabic-speaking world since before the 8th century Arabic numerals...
). A Gematria of Latin-script languages was also popular in Europe
Europe
Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
from the Middle Ages
Middle Ages
The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...
to the Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
and indeed its legacy remains in numerology
Numerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...
and Masonic
Freemasonry
Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around six million, including approximately 150,000 under the jurisdictions of the Grand Lodge...
symbolism today (see arithmancy
Arithmancy
In modern numerological terminology, arithmancy is a simplified version of ancient Greek Isopsephy or Hebrew/Aramaic Gematria, as adapted to the Latin alphabet.-Etymology of the name:...
).
History
Until Arabic numeralsArabic numerals
Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
were adopted and adapted from Indian numerals
Hindu–Arabic numeral system
The Hindu–Arabic numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 5th centuries by Indian mathematicians, adopted by Persian and Arab mathematicians , and spread to the western world...
in the 8th and 9th century AD, and promoted in Europe by Fibonacci
Fibonacci
Leonardo Pisano Bigollo also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."Fibonacci is best known to the modern...
of Pisa
Republic of Pisa
The Republic of Pisa was a de facto independent state centered on the Tuscan city of Pisa during the late tenth and eleventh centuries. It rose to become an economic powerhouse, a commercial center whose merchants dominated Mediterranean and Italian trade for a century before being surpassed and...
with his 1202 book Liber Abaci
Liber Abaci
Liber Abaci is a historic book on arithmetic by Leonardo of Pisa, known later by his nickname Fibonacci...
, numerals were predominantly alphabetical. For instance in Ancient Greece
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...
, Greek numerals
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...
used the alphabet. Indeed there is some evidence that from the very beginning the alphabet was designed in order to meet the needs of mathematics. 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 more-than-usual sophistication (employing multiplication rather than addition), is from the mathematician Apollonius of Perga
Apollonius of Perga
Apollonius of Perga [Pergaeus] was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the field of conics, influenced many later scholars including Ptolemy, Francesco Maurolico, Isaac Newton, and René Descartes...
, 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?" More conventional are the instances of isopsephy found in graffiti at Pompeii
Pompeii
The city of Pompeii is a partially buried Roman town-city near modern Naples in the Italian region of Campania, in the territory of the comune of Pompei. Along with Herculaneum, Pompeii was destroyed and completely buried during a long catastrophic eruption of the volcano Mount Vesuvius spanning...
, 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
Suetonius
Gaius Suetonius Tranquillus, commonly known as Suetonius , was a Roman historian belonging to the equestrian order in the early Imperial era....
, writing in 121 AD, reports a political slogan that someone wrote on a wall in Rome:
-
-
- "Nero, Orestes, Alcmeon their mothers slew.
- A calculation new. Nero his mother slew"
-
which appears to be another example. 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 (the number of the Beast
Number of the Beast
The Number of the Beast is a term in the Book of Revelation, of the New Testament, that is associated with the first Beast of Revelation chapter 13, the Beast of the sea. In most manuscripts of the New Testament and in English translations of the Bible, the number of the Beast is...
) in the Biblical Book of Revelation
Book of Revelation
The Book of Revelation is the final book of the New Testament. The title came into usage from the first word of the book in Koine Greek: apokalupsis, meaning "unveiling" or "revelation"...
(13:18): "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 here "count", ψηφισάτω, psephisato, has the same "pebble" root as the word isopsephy).
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:
-
-
- Θυει σοι τοδε γραμμα γενεθλιακαισιν εν ὡραις,
- Καισαρ, Νειλαιη Μουσα Λεωνιδεω.
- Καλλιοπης γαρ ακαπνον αει θυος· εις δε νεωτα
- Ην εθελῃς, θυσει τουδε περισσοτερα.
-
"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:
-
-
- Εἱς προς ἑνα ψηφοισιν ισαζεται, ου δυο δοιοις,
- Ου γαρ ετι στεργω την δολιχογραφιην.
-
"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.
A headstone found at the Temple of Artemis at Sparta Orthia is a 2nd century AD example of isopsephic elegiac verse. It says:
-
-
- ΟΡΘΕΙΗ ΔΩΡΟΝ ΛΕΟΝΤΕΥΣ ΑΝΕΘΗΚΕ ΒΟΑΓΟΣ ΒΨΛ
- ΜΩΑΝ ΝΙΚΗΣΑΣ ΚΑΙ ΤΑΔΕ ΕΠΑΘΛΑ ΛΑΒΩΝ ΒΨΛ
- ΚΑΙ Μ ΕΣΤΕΨΕ ΠΑΤΗΡ ΕΙΣΑΡΙΘΜΟΙΣ ΕΠΕΣΙ ΒΨΛ
-
It is the votive stele for a boy who won a competition in singing. The words in each line add up to ΄ΒΨΛ, that is 2730, and, perhaps in case anyone does't notice, that total is also given at the end of each line. Also in the 2nd century AD, Aelius Nicon of Pergamon
Pergamon
Pergamon , or Pergamum, was an ancient Greek city in modern-day Turkey, in Mysia, today located from the Aegean Sea on a promontory on the north side of the river Caicus , that became the capital of the Kingdom of Pergamon during the Hellenistic period, under the Attalid dynasty, 281–133 BC...
, the Greek architect
Architect
An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...
and builder described by his son, the famous physician Galen
Galen
Aelius Galenus or Claudius Galenus , better known as Galen of Pergamon , was a prominent Roman physician, surgeon and philosopher...
, as having "mastered all there was to know of the science of geometry and numbers", was a master in composing isopsephic works.
Letter values of the Greek alphabet
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 24-letter alphabet was extended by using three obsolete letters: digammaDigamma
Digamma is an archaic letter of the Greek alphabet which originally stood for the sound /w/ and later remained in use only as a numeral symbol for the number "6"...
ϝ,(also used are stigma
Stigma (letter)
Stigma is a ligature of the Greek letters sigma and tau , which was used in writing Greek between the middle ages and the 19th century. It is also used as a numeral symbol for the number 6...
ϛ or, in modern Greek, στ) for 6, qoppa
Qoppa
Koppa or Qoppa is a letter that was used in early forms of the Greek alphabet, derived from Phoenician qoph. It was originally used to denote the /k/ sound, but dropped out of use as an alphabetic character in favour of Kappa . It has remained in use as a numeral symbol in the system of Greek...
ϟ for 90, and sampi
Sampi
Sampi is an archaic letter of the Greek alphabet. It was used in addition to the classical 24 letters of the alphabet to denote some type of a sibilant sound, probably or , in some eastern Ionic dialects of ancient Greek in the 6th and 5th centuries BC...
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).
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