The tetractys ( el, τετρακτύς), or tetrad, or the tetractys of the decad is a
triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
. As a
mystical
Mysticism is popularly known as becoming one with God or the Absolute, but may refer to any kind of ecstasy or altered state of consciousness which is given a religious or spiritual meaning. It may also refer to the attainment of insight in u ...
symbol, it was very important to the secret worship of
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, ...
. There were four seasons, and the number was also associated with planetary motions and music.
Pythagorean symbol
# The first four numbers symbolize the ''
musica universalis
The ''musica universalis'' (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets – as a ...
'' and the
Cosmos
The cosmos (, ) is another name for the Universe. Using the word ''cosmos'' implies viewing the universe as a complex and orderly system or entity.
The cosmos, and understandings of the reasons for its existence and significance, are studied in ...
as:
## (1) Unity (
Monad)
## (2)
Dyad – Power – Limit/Unlimited (peras/
apeiron
''Apeiron'' (; ) is a Greek word meaning "(that which is) unlimited," "boundless", "infinite", or "indefinite" from ''a-'', "without" and ''peirar'', "end, limit", "boundary", the Ionic Greek form of ''peras'', "end, limit, boundary".
Origin ...
)
## (3) Harmony (Triad)
## (4) Kosmos (Tetrad)
# The four rows add up to ten, which was unity of a higher order (The Dekad).
# The Tetractys symbolizes the
four classical elements
Classical elements typically refer to earth, water, air, fire, and (later) aether which were proposed to explain the nature and complexity of all matter in terms of simpler substances. Ancient cultures in Greece, Tibet, and India had simila ...
—
air,
fire
Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction products.
At a certain point in the combustion reaction, called the ignition point, flames ...
,
water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
, and
earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
.
# The Tetractys represented the organization of
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consi ...
:
## the first row represented zero
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...
s (a
point)
## the second row represented one dimension (a
line
Line most often refers to:
* Line (geometry), object with zero thickness and curvature that stretches to infinity
* Telephone line, a single-user circuit on a telephone communication system
Line, lines, The Line, or LINE may also refer to:
Art ...
of two points)
## the third row represented
two dimensions (a
plane defined by a
triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colline ...
of three points)
## the fourth row represented
three dimensions
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called '' parameters'') are required to determine the position of an element (i.e., point). This is the inform ...
(a
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all ...
defined by four points)
A
prayer
Prayer is an invocation or act that seeks to activate a rapport with an object of worship through deliberate communication. In the narrow sense, the term refers to an act of supplication or intercession directed towards a deity or a deifie ...
of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.
As a portion of the secret religion,
initiates
Initiation is a rite of passage marking entrance or acceptance into a group or society. It could also be a formal admission to adulthood in a community or one of its formal components. In an extended sense, it can also signify a transformation ...
were required to swear a secret oath by the Tetractys. They then served as novices, which required them to observe silence for a period of five years.
The Pythagorean oath also mentioned the Tetractys:
:By that pure, holy, four lettered name on high,
:nature's eternal fountain and supply,
:the parent of all souls that living be,
:by him, with faith find oath, I swear to thee.
It is said that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of
4:3 (perfect fourth), 3:2 (
perfect fifth
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval from the first to the last of five ...
),
2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison
1:1 and the octave
2:1. Note that the
diapason, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to the tetractys of the decad, but that the diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.
Kabbalist symbol
In the work by anthropologist
Raphael Patai
Raphael Patai (Hebrew רפאל פטאי; November 22, 1910 − July 20, 1996), born Ervin György Patai, was a Hungarian-Jewish ethnographer, historian, Orientalist and anthropologist.
Family background
Patai was born in Budapest, Austria-Hung ...
entitled ''
The Hebrew Goddess'', the author argues that the tetractys and its mysteries influenced the early
Kabbalah
Kabbalah ( he, קַבָּלָה ''Qabbālā'', literally "reception, tradition") is an esoteric method, discipline and Jewish theology, school of thought in Jewish mysticism. A traditional Kabbalist is called a Mekubbal ( ''Məqūbbāl'' "rece ...
. A Hebrew tetractys has the letters of the
Tetragrammaton
The Tetragrammaton (; ), or Tetragram, is the four-letter Hebrew theonym (transliterated as YHWH), the name of God in the Hebrew Bible. The four letters, written and read from right to left (in Hebrew), are ''yodh'', '' he'', '' waw'', and ...
inscribed on the ten positions of the tetractys, from right to left. It has been argued that the
Kabbalistic Tree of Life, with its ten spheres of emanation, is in some way connected to the tetractys, but its form is not that of a triangle. The occultist
Dion Fortune writes:
:The
point is assigned to
Kether
Keter ( he-a, כֶּתֶר, Keter.ogg, link=yes, ''Keṯer'', lit. " crown") also known as Kether, is the topmost of the sephirot of the Tree of Life in Kabbalah. Since its meaning is "crown", it is interpreted as both the "topmost" of the Se ...
;
:the
line
Line most often refers to:
* Line (geometry), object with zero thickness and curvature that stretches to infinity
* Telephone line, a single-user circuit on a telephone communication system
Line, lines, The Line, or LINE may also refer to:
Art ...
to
Chokmah;
:the two-dimensional
plane to
Binah;
:consequently the three-dimensional
solid
Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structur ...
naturally falls to
Chesed
( he, חֶסֶד, also Romanized: ) is a Hebrew word that means 'kindness or love between people', specifically of the devotional piety of people towards God as well as of love or mercy of God towards humanity. It is frequently used in Psalms i ...
.
The relationship between geometrical shapes and the first four
Sephirot
Sefirot (; he, סְפִירוֹת, translit=Səfīrōt, Tiberian: '), meaning '' emanations'', are the 10 attributes/emanations in Kabbalah, through which Ein Sof (The Infinite) reveals itself and continuously creates both the physical realm an ...
is analogous to the geometrical correlations in Tetraktys, shown above under
#Pythagorean symbol, and unveils the relevance of the Tree of Life with the Tetraktys.
Tarot card reading arrangement
In a
Tarot reading
Tarot card reading is a form of cartomancy whereby practitioners use tarot cards to purportedly gain insight into the past, present or future. They formulate a question, then draw cards to interpret them for this end. A traditional tarot deck con ...
, the various positions of the tetractys provide a representation for forecasting future events by signifying according to various occult disciplines, such as Alchemy. Below is only a single variation for interpretation.
The first row of a single position represents the Premise of the reading, forming a foundation for understanding all the other cards.
The second row of two positions represents the cosmos and the individual and their relationship.
* The Light Card to the right represents the influence of the cosmos leading the individual to an action.
* The Dark Card to the left represents the reaction of the cosmos to the actions of the individual.
The third row of three positions represents three kinds of decisions an individual must make.
* The Creator Card is rightmost, representing new decisions and directions that may be made.
* The Sustainer Card is in the middle, representing decisions to keep balance, and things that should not change.
* The Destroyer Card is leftmost, representing old decisions and directions that should not be continued.
The fourth row of four positions represents the four Greek elements.
* The Fire card is rightmost, representing dynamic creative force, ambitions, and personal
will
Will may refer to:
Common meanings
* Will and testament, instructions for the disposition of one's property after death
* Will (philosophy), or willpower
* Will (sociology)
* Will, volition (psychology)
* Will, a modal verb - see Shall and wi ...
.
* The Air card is to the right middle, representing the mind,
thought
In their most common sense, the terms thought and thinking refer to conscious cognitive processes that can happen independently of sensory stimulation. Their most paradigmatic forms are judging, reasoning, concept formation, problem solving, an ...
s, and strategies toward goals.
* The Water card is to the left middle, representing the
emotion
Emotions are mental states brought on by neurophysiological changes, variously associated with thoughts, feelings, behavioral responses, and a degree of pleasure or displeasure. There is currently no scientific consensus on a definitio ...
s, feelings, and whims.
* The Earth card is leftmost, representing physical
realities of day to day living.
Occurrence
The tetractys occurs (generally coincidentally) in the following:
* the
baryon decuplet
* an
archbishop
In Christian denominations, an archbishop is a bishop of higher rank or office. In most cases, such as the Catholic Church, there are many archbishops who either have jurisdiction over an ecclesiastical province in addition to their own archdio ...
's
coat of arms
A coat of arms is a heraldic visual design on an escutcheon (i.e., shield), surcoat, or tabard (the latter two being outer garments). The coat of arms on an escutcheon forms the central element of the full heraldic achievement, which in its ...
* the arrangement of
bowling pins in
ten-pin bowling
Ten-pin bowling is a type of bowling in which a bowler rolls a bowling ball down a wood or synthetic lane toward ten pins positioned evenly in four rows in an equilateral triangle. The objective is to knock down all ten pins on the first roll ...
* the arrangement of
billiard ball
A billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various particular ball ...
s in
ten-ball pool
* a
Chinese checkers board
* the
"Christmas Tree" formation in
association football
Association football, more commonly known as football or soccer, is a team sport played between two teams of 11 players who primarily use their feet to propel the ball around a rectangular field called a pitch. The objective of the game is ...
In poetry
In English-language poetry, a tetractys is a syllable-counting form with five lines. The first line has one syllable, the second has two syllables, the third line has three syllables, the fourth line has four syllables, and the fifth line has ten syllables. A sample tetractys would look like this:
:''
Mantrum''
:''Your /''
:''fury /''
:''confuses /''
:''us all greatly. /''
:''Volatile, big-bodied tots are selfish. //''
The tetractys was created by
Ray Stebbing, who said the following about his newly created form:
:''"The tetractys could be Britain's answer to the haiku. Its challenge is to express a complete thought, profound or comic, witty or wise, within the narrow compass of twenty syllables.''
Search result for Tetractys
/ref>
See also
* Pascal's triangle
References
Further reading
*von Franz, Marie-Louise. ''Number and Time: Reflections Leading Towards a Unification of Psychology and Physics''. Rider & Company, London, 1974.
*Fideler, D. ed
The Pythagorean Sourcebook and Library
Phanes Press, 1987.
The Theoretic Arithmetic of the Pythagoreans – Thomas Taylor
External links
Examples of Tetractys poems
{{Ancient Greek philosophical concepts
Dot patterns
Genres of poetry
Greek mathematics
History of mathematics
History of poetry
Kabbalah
Mathematical symbols
Poetic forms
Pythagorean symbols
Pythagoreanism
Tarotology
Theories in ancient Greek philosophy