ΔΕΚΑΣ
The Decad (δεκάς), beyond its simple arithmetical value as ten, held for the Pythagoreans a sacred and cosmogonic significance, the Tetractys, the sum of the first four numbers (1+2+3+4=10) symbolizing the completeness and order of the cosmos. Its lexarithmos (230) suggests a connection to abundance and culmination.
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According to the Liddell-Scott-Jones Lexicon, δεκάς primarily means "the number ten" or "a group of ten things." The word is used to denote a collection of ten units, whether people, objects, or periods of time. In classical Athens, for instance, there were "ten generals" or "ten tribes," where the decad signified an organizational structure.
The significance of the decad extends beyond mere quantity, acquiring profound philosophical and symbolic content, particularly within the Pythagorean school. For the Pythagoreans, the decad was the sacred number, the "Tetractys," derived from the sum of the first four natural numbers (1+2+3+4=10). This decad was considered the source of eternal nature, the key to understanding the harmony of the world and the music of the spheres.
Furthermore, the decad was employed to denote temporal periods, such as a decade or a ten-day interval. In administrative and military organization, a "decad" could refer to a unit of ten men or a committee of ten individuals, highlighting its functional use in ancient Greek society.
Etymology
From the root of the number ten, a rich family of words is derived, signifying multiples, subdivisions, temporal periods, or organizational structures based on the number ten. Examples include the adverb «δεκάκις» (ten times), compound adjectives such as «δεκαετής» (of ten years) and «δεκαήμερος» (lasting ten days), as well as nouns describing groups or administrations, like «δεκαρχία» (rule of ten men) or «δεκάτη» (the tenth part).
Main Meanings
- The number ten — The basic arithmetical concept, the sum of ten units.
- Group of ten — A set or collection of ten persons or things, e.g., a military decury.
- Period of ten — A period of ten days or ten years (a decade).
- Pythagorean Tetractys — For the Pythagoreans, the sacred decad, the sum of the first four numbers (1+2+3+4), symbolizing cosmic harmony.
- Symbol of completeness/perfection — Due to its Pythagorean significance, the decad was often regarded as a number denoting completion and perfection.
- Administrative/Military unit — A group of ten men or a committee of ten individuals in a political or military context.
- A tenth part (tithe) — The tenth share or the tenth part of a whole, often as a tax or offering.
Word Family
deka- (root of the number ten)
The root deka- forms the basis for a series of words related to the number ten, its multiples, subdivisions, as well as temporal and organizational structures based on it. From its simple arithmetical use, this root extends to philosophical concepts, such as the Pythagorean decad, and to practical applications in politics, administration, and religion. This family highlights the central importance of the number ten in ancient Greek thought and society.
Philosophical Journey
The decad, as a number and a philosophical concept, traverses Greek thought from its simple arithmetical use to its cosmological significance.
In Ancient Texts
The philosophical and practical significance of the decad is highlighted in various ancient texts.
Lexarithmic Analysis
The lexarithmos of the word ΔΕΚΑΣ is 230, from the sum of its letter values:
230 decomposes into 200 (hundreds) + 30 (tens) + 0 (units).
The 18 Methods
Applying the 18 traditional lexarithmic methods to the word ΔΕΚΑΣ:
| Method | Result | Meaning |
|---|---|---|
| Isopsephy | 230 | Base lexarithmos |
| Decade Numerology | 5 | 2+3+0=5 — The Pentad, the number of life, harmony, and man, symbolizing the union of masculine (3) and feminine (2) or the perfection of a cycle. |
| Letter Count | 5 | 5 letters — The Pentad, the number of life and balance, associated with the human form (five extremities) and the senses. |
| Cumulative | 0/30/200 | Units 0 · Tens 30 · Hundreds 200 |
| Odd/Even | Even | Feminine force |
| Left/Right Hand | Right | Divine (≥100) |
| Quotient | — | Comparative method |
| Notarikon | Δ-Ε-Κ-Α-Σ | Dikaiosyne Eirene Kosmos Aletheia Sophia (Righteousness, Peace, Order, Truth, Wisdom) (interpretive) |
| Grammatical Groups | 2V · 3C | 2 vowels (E, A) and 3 consonants (D, K, S), indicating a balanced structure. |
| Palindromes | No | |
| Onomancy | — | Comparative |
| Sphere of Democritus | — | Divination with lunar day |
| Zodiacal Isopsephy | Saturn ♄ / Gemini ♊ | 230 mod 7 = 6 · 230 mod 12 = 2 |
Isopsephic Words (230)
Words from the Liddell-Scott-Jones lexicon with the same lexarithmos (230) as the decad, but from different roots, offering an interesting numerical coincidence.
The LSJ lexicon contains a total of 29 words with lexarithmos 230. For the full catalog and AI semantic filtering, see the interactive tool.
Sources & Bibliography
- Liddell, H. G., Scott, R., Jones, H. S. — A Greek-English Lexicon, 9th ed. with revised supplement. Oxford: Clarendon Press, 1996.
- Kirk, G. S., Raven, J. E., Schofield, M. — The Presocratic Philosophers: A Critical History with a Selection of Texts. 2nd ed. Cambridge: Cambridge University Press, 1983.
- Iamblichus — De Vita Pythagorica (On the Pythagorean Way of Life). Edited and translated by John Dillon and Jackson Hershbell. Atlanta: Society of Biblical Literature, 1991.
- Philo of Alexandria — On the Creation of the World (De Opificio Mundi). Translated by F. H. Colson and G. H. Whitaker. Loeb Classical Library. Cambridge, MA: Harvard University Press, 1929.
- Aristotle — Constitution of the Athenians. Edited and translated by P. J. Rhodes. Penguin Classics. London: Penguin Books, 1984.
- Heath, T. L. — A History of Greek Mathematics. Vol. 1: From Thales to Euclid. Oxford: Clarendon Press, 1921.
- Plato — Republic. Translated by G. M. A. Grube, revised by C. D. C. Reeve. Indianapolis: Hackett Publishing Company, 1992.