Studying the Decad for the Purpose of Refining Arithmologic Understanding

In the first millenium BCE, Pythagorean number philosophy was developed. Though the texts and theories that are attributed to Pythagoras are much later, its possible they have some provenance within the early Pythagorean movement. Of the many elements of Pythagoreanism, one of the most fascinating is arithmology, the study of Pythagorean numerology. Pythagorean numerology largely hinges on the concept of the decad, or tetrakys. “Ten, according to the Pythagoreans, is the greatest number- as well as for that is the Tetractys, as that it comprehends all arithmetical and harmonical proportions.”¹The decad corresponds to the entire cosmos. There are a number of ways to understand them, even within the Pythagorean and Platonist movements.² The attributes of each of the numbers of the decad that are given in this article can be useful to a beginner to get a very limited idea about arithmology. After looking over the terms, it is highly suggested that Nicomachus of Gerasa’s Arithmetic and Iamblichus’s Theology of Arithmetic be studied. Additionally, two modern books on Pythagoreanism, Thomas Stanley’s Pythagoras and The Pythagorean Sourcebook, are indispensable. The keyword lists would be useful to students who have a concept of arithmology after studying these texts. It should be stressed that the keywords only give a glimpse to a beginner and the study of arithmology entails much more. The qualities of numbers, linguistics, and the reasoning behind the associations given below are some of the elements of arithmology.

Short of having certain ancient texts or compilations of them, some of this information might be difficult to obtain on the internet.  The keywords that are associated with each number of the decad are included below. Hopefully, infographics will be made at a later date and shared on this website. An easy way to engage the decad can be to study and do rituals for each number of the decad per day, starting with either the decad and ending at the monad or starting at the monad and ending at the decad. Alternatively, each number of the decad could be assigned an allotment of 10 days. Numerous other approaches could be devised. Also, if it is to be included in a practice, it should accompany readings in Pythagorean and Platonist literature, and a few texts mentioned in the Bibliography section should be a good place to start. As for numeric schemes for studying the decad, if there is time, one could create a hundred days ritual to be followed by a ten days ritual. Another way to do it might be to start with the decad for ten days, then the ennead for nine days, the octad for eight days, and so forth, ending with the monad in one day. After alloting days to the numbers of the decad, they could be the subject of a ritual that takes place for ten hours of a day, with one hour given to each number. Going even smaller, one hour and 40 minutes could be allotted to the numbers of the decad as well, so that each number gets ten minutes. There are a number of approaches to use for getting familiarity with the decad in a spiritual and ritual context. The keywords are listed below.

 

The Decad

 

The Monad

Instrument of Truth

Obscure

Not-Many

A Chariot

Male-Female

Immutable Truth and Invulnerable Destiny

A Seed

Fabricator(demiurge)

True Happiness(eudaimonia)

Zeus

Life

God

The Equality in Increase and Decrease

Memory

A Ship

Essence(ousia)

The Inkeeper(pandokeus), “that which takes in all”

The Pattern or Model(paradeigma)

The Moulder

Prometheus

The First(Proteus)

Darkness

Blending

Commixture

Harmony(symphonia)

Order(taxis)

Materia

A Friend

Infinite Expanse(chaos)

Space-Producer

 

The Dyad

Inequality

Indefinite(aoristos)

The Unlimited(apeiron)

Without Form or Figure

Growth

Birth

Judgment

Appearance

Anguish

The Each of Two

Falling Short, Defect

Erato

Equal

Isis

Movement

The Ratio(logos) in Proportion (analogia)

REvolution

Distance

Impulse

Excess

The Thing with Another

Rhea(the wife of Kronos, but also “flow”)

Selene

Combination

That Which is To Be Endured; Misery, Distress

Boldness, Audacity(tolma)

Matter

Obstinacy

Nature

The Triad

Proportion(analogia)

Harmonia

Marriage

Knowledge(gnosis)

Peace

EVery Thing

Hecate

Good Counsel

Piety

The Mean Between Two Extremes

Oneness of Mind

The All

Perfection

Friendship

Purpose

The Tetrad

Nature of Change

Righteousness

Hercules

Holding the Key of Nature

The Pentad

Alteration

Immortal

Androgyny

Lack of Strife

Aphrodite

Boubastia(Egyptian divinity Boubastis)

Wedding

Marriage

Double

Manifesting Justice

Justice

Demigod

Nemesis

Pallas

Five-Fold

Forethought

Light

The Hexad

Resembling Justice

The Thunder-Stone

Amphitrite (Poseidon’s wife; a verbal pun: on both sides (amphis) three (trias)

Male-Female

Marriage

Finest of All

In Two Measures

Form of Forms

Peace

Far-Shooting(name of Apollo)

Thaleia

Kosmos

Possessing Wholeness

Cure-Ail(panacea)

Perfection

Three-Fold

Health

Reconciling

The Heptad

The Foreager(epithet of Athena)

Athena

Citadel(akropolis)

Reaper

Hard to Subdue Defence

Due Measure(kairos)

Virgin(parthenos)

Revered Seven (septas plus sebomai equals heptas)

Bringing to Completion (Telesphorus)

Fortune, Fate

Preserving

 

The Octad

Untimely Born

Steadfast

Seat or Abode

Euterpe

Cadmia

Mother

All Harmonious

The Ennead

Brother and Consort of Zeus

Helios

Absence of Strife

Far-Working(epithet of Apollo)

Hera

Hephaestus

Maiden(kore)

Of the Kouretes

Assimilation

Oneness of Mind

Horizon(because it limits the series of Memory units before returning to the Decad)

Crossing or Passage

Prometheus

Consort and Brother

Perfection

Bringing to Perfection(Telesphorus)

Terpsichore

Hyperion

Oceanus

The Decad

Eternity(aeon)

Untiring

Necessity

Atlas

Fate

Helios

God

Key-Holding

Kosmos

Strength

Memory

Ourania

Heaven

All

All Perfect

Faith

Phanes

 

Notes

1. [Note: This quote comes from Plutarch, De Placitis Philosophorum, Liber 1, Chap. 3]Thomas Stanley, Ed. James Wasserman, J. Daniel Gunther, Pythagoras: His Life and Teachings (Ibis Press, May 1, 2010).  Chapter 14.
2. Huffman, Carl, “Pythagoreanism”, The Stanford Encyclopedia of Philosophy (Summer 2024 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/sum2024/entries/pythagoreanism/><https://plato.stanford.edu/entries/pythagoreanism/#math>

 

Bibliography

Note: The authors of the Pythagorean Sourcebook recommend Thomas Taylor’s Theoretic Arithmetic of the Pythagoreans and the section on number theory in Thomas Stanley’s Pythagoras. The Theology of Arithmetic Translated by Robin Waterfield, Phanes Press, Grand Rapids, 1988.

1. Thomas Stanley. Ed. James Wasserman, J. Daniel Gunther. Pythagoras: His Life and Teachings. Ibis Press, May 1, 2010.
2. Trans. Kenneth Sylvan Guthrie. The Pythagorean Sourcebook and Library. Phanes Press. July 1, 1987.

Photo Credits