**Introduction**
Numerology is the belief that numbers represent far more than quantitative signs: each one of the primary numbers is thought to be a qualitative, archetypal essence, possessing a distinct, living

*personality*. Popular numerology books, and tarot books usually have a list of what the primary numbers mean.

The question we need to ask ourselves is

*why* do the numbers mean what a writer claims they mean. Nine out of ten times, the list of meanings will just be regurgitating some other writers list, which itself may have been a regurgitation. As with everything, we should know where an idea comes from, and from where the meaning is derived. The place to start is Vincent Foster Hooper's

*Medieval Number Symbolism*. This is THE essential primer for understanding number symbolism from antiquity to Dante.

Generalizing greatly, we can summarize the basic sources for the numbers symbolic meanings come from-

**The arithmetical nature of number** (number in itself)

**The geometric nature of number** (number in space)

**The harmonic nature of number** (number in time)

**Number symbolism connected to nature** — the number of fingers, the months of pregnancy, etc.

**Number symbolism connected to astronomy and astrology** — seasons, lunar cycles, planets, signs, etc.

**Number symbolism related to language** — for example the Pythagoreans called the number 1 *Apollo* because of its lack of multiplicity. This is actually a pun, for *a-pollon* in Greek means literally "not of many." Also, Isopsephy, a practice whereby numerical values of each Greek letter are added up so as to turn a phrase, name, or word into a single number.

**Number symbolism connected to religious doctrines** — number of apostles, stations of the cross. Isopsephy was a big part of much of later Abrahamic religious mysticism.

The largest surviving source of information on Pythagorean number mysticism is the work

*Theology of Arithmetic*, attributed to Iamblichus. It is my main, though not exclusive source for my approach to number. But even this work must be approached with a discriminating eye. The problem is, it seems to have been someone's lecture notes or something, with little snippets from various famous Pythagoreans, all mixed up in a totally disorganized mess. Sometimes you'll find interesting things about the 3 over in the section on the 4... sometimes the snippets from Anatolius contradict the snippets from Nichomachus, etc. The trick is finding the 'thread' that pulls the whole thing together. Clearly, the meanings that derive merely from 'puns' in Greek are meaningless for us.

Admittedly,

*The Theology of Arithmetic* is a work that lends itself to a certain amount of interpretation, and three different people reading it, may come to three different conclusion to what a given number really means.

Aetius (1st cent. AD) said that Pythagoras,

*"...assumed as first principles the numbers and the symmetries existing among them, which he calls* harmonies,

*and the elements compounded of both, that are called* geometrical."

This gives us at least three perspectives on how numbers can illustrate the workings of "higher reality,"

*arithmetic, harmonic and geometric*.

Hopper points out that,

*"The geometric approach to mathematics provided a link between abstract number and concrete reality."* He also points out that Euclid's summary of Greek mathematics testifies to the predominance of geometric thinking over arithmetical.

Geometry plays a very strong role in my interpretation of number. I apply the sequence of 1 through 10 to the three basic geometric forms — the square, the triangle, and the circle, to see how they work as a 'narrative of meaning'. I use these models to analyze the validity of what I find in ancient texts.

Just how well that these models reflect the true nature of number will be up to you to decide. Keep in mind Guénon's insights into the symbolism of models,

*"It should be carefully noted these geometrical representations are always to some extent imperfect, as must indeed be the case with any representation or formal expression. The representation is necessarily imperfect, simply by being enclosed within narrower limits than that which it represents, and indeed it would otherwise be useless."*

"...the higher can never in any way symbolize the lower, but on the contrary is always symbolized by it. Obviously if the symbol is to fulfill its purpose as a 'support', it must be more accessible, and therefore less complex or extended than what it expresses or represents."
I believe these models are revealing of the properties of the first ten numbers, which are themselves revealing of the nature of all numbers, which are indeed revealing of the very pattern of the whole universe.

**Number 1 - The Monad**
The 4th Century Pythagorean Mystic Iamblichus, on the Monad (1)

*"Just as without the monad there is in general no composition of anything, so also without it there is no knowledge of anything whatsoever, since it is a pure light, most authoritative over everything in general, and it is sun-like and ruling, so that in each of these respects it resembles God, and especially because it has the power of making things cohere and combine, even when they are composed of many ingredients and are very different from one another, just as He made this universe harmonious and unified out of things which are likewise opposed."*
We start at the unity of the 1, which is like the divine source. The Monad is the

*prima materia*, the seed of all. The process from 1 through 4 show how this divine 'oneness' separates and emanates downward into matter - impulse, separation, process, completion. In this process of emanation, the energies are expansive, and practically we can draw useful parallels to evolution, and to the transpersonal.

The One also is an undifferentiated unity, and all-encompassing so it isn't self aware, as self awareness requires a separation of the self from itself to be able to have awareness (Plotinus).

**Number 2 - The Dyad**
The Dyad represents the separation, differentiation from unity, and the beginning of strife. It is the principle of all change. With the Dyad arises the duality of subject and object, the knower and the known.

It may be a surprise to some that the ancients called the dyad 'inequality', as it is the source of all differences, and in terms of what precedes it, it is more (2 is more than 1).

**Number 3 - The Triad**
The Triad (3) being the principle that joins the duality of the Monad and Dyad, a mediation, a synthesis of opposites. Iamblichus calls the triad

*"a mean between the others"*. It restores balance after the separation of the 2, and it is also a mean between the 1 and the 4. It is both equal to and successive to the Monad and the Dyad, hence the Triad symbolizes the unifying of opposites.

**Number 4 - The Tetrad**
The Pythagoreans say the 4 contains the 10 (1 + 2 + 3 + 4 = 10). In

*The Theology of Arithmetic* it says, "Everything in the universe turns out to be completed in the natural progression up to the tetrad." The Tetrad is the consolidation of the synthesis which brings completeness and stability, and ultimately petrification and stagnation. The process from 1 ~ 4 represents materiality's descent from the divine -

*how matter arises from emptiness*. It is showing us how things, situations, develop. We might compare this process to

*evolution*, in the broader sense of the word. In the cycle from 1 to 10 the next critical point, after the Dyad, is the 4. Here the danger is in stagnation. 1 to 4 is in itself a natural cycle, and the stability and comfort of the material solidity of the 4 can be an obstacle to moving to the next level.

The Monad is the

*prima materia*, an undifferentiated unity, the seed of everything. It evolves through stages - the Dyad (2) being separation, differentiation, the principle of change, the Triad (3) being the principle that joins the duality of the Monad and Dyad, a mediation, a synthesis of opposites, the Tetrad (4) is the consolidation of the synthesis which brings completeness and stability, and ultimately petrification and stagnation.

The symbolism of the 4 shows it to be the end of the descent. In

*The Theology of Arithmetic* it says, "Everything in the universe turns out to be completed in the natural progression up to the tetrad (4)."

Hence 1 ~ 4 come to represent the process of materiality's descent from the divine -

*how matter arises from emptiness*. It is showing us how things, situations, develop. We might compare this process to

*evolution*, in the broader sense of the word.

Iamblichus describes the sequence like this:

"...it is seen as an eternal continuum or as a created composition -

- 'the
*by* which'

- 'the
*from* which'

- 'the by
*means of* which

- 'the with
*what end*'

that is,

- God

- Matter

- Form

- Result "

**Number 5 - The Pentad**
The five is called 'marriage' as it is the union of the first female number (2), and the first male number (3). The 5 itself being odd is male, hence the Pentad is the male marriage number.

The 5 is traditionally ruled by the planet Mercury. As Mercury, the Pentad is the masculine connecter, as rationality and logic is, in essence, making connections.

The 5 is also a

*spherical* or

*circular* number. A circular number is one which reproduces itself in its last digit when raised to its powers.

If the simple numbers are arranged as a cube, no matter where you start the sequence, the 5 is centered within them:

1 2 3

4 5 6

7 8 9

fig. 1

The Pentad also is the center figure on the

*Tetractys*:

......1

....2...3

..4...

5...6

7...8...9..10

fig. 2
This show us that the Pentad is a mean to all the other numbers. It can literally be seen as the "middle man" of the simple numbers. If ill dignified, it can be viewed as a 'hidden' number. It falls center in the sequence of simple numbers, away from clear view;

It is also like the center of a scale within the simple numbers.

.................................................. l

.................................................. l

.................................................. l

...................................2...3...4...

5 ...6...7...8...

................................l................. ...................l

................................l................. ...................l

...............................1.................. ..................9

.............................____................. ..............____

fig. 3
Therefore the Pythagoreans said it was the number of Justice.

**Number 6 - The Hexad**
The Hexad is the first perfect number. Iamblichus says of it,

*"The Universe is ensouled and harmonized by it and, thanks to it, comes by wholeness and permanence, and perfect health..."*
The 6, like the 5 is called a

*marriage number*. They are both produced by a 'wedding' of the first female number, 2, and the first male number, 3 (2 + 3 = 5) (2 x 3 = 6) . Both numbers are praised by the Pythagoreans as being 'means' in various capacities. So they also function as 'marriage' numbers as they bring together the other numbers, and form a 'bond' between the two phases of numbers.

They are both related to each other, and separate from the other numbers in decad (1~10), as they are both

*spherical* or

*circular* numbers.

The 6 is traditionally ruled by Venus. Venus is the feminine connector, who makes emotional connections. From a certain perspective the 5 & 6 function as a 'connective unit' which is neither male nor female (Hermaphroditus, the son of Hermes and Aphrodite, aka. Mercury and Venus), bridging the masculine descent phase (solar, formative, expansive, evolution, external knowledge) and the feminine ascent phase (lunar, contractive, involution, inner knowledge).

The general geometric symbolism of the decad sees these numbers as a midpoint between the ascent and the descent stages of the decad. I view them as a sort of 'recharging' of energy between the two phases, a chance to pick up momentum before making the ascent. I represent this idea thus:

Imagine a roller coaster car starting at the 1 and rolling down to the 4, then flying into the smaller loop, up past the 5 and 6, and down to the 7 where it goes back on the big loop, rolling up to the 10.

~ 'Wheeeeee'

**The Number 7 - The Heptad**
The Heptad gathers together all the random energies generated thus far (1 ~6) and forges them into a new unity, a concentrated energy that enables the Decad to reach its natural completion. It is the beneficiary of the harmony and union of the Pentad and Hexad. It is the Monad born anew from their union.

**Iamblichus** says,

*"Moreover, the hebdomad seems to be an acropolis, as it were, and a 'strong fortification' within the decad, just like an invisible monad. For it alone admits no breath, since it is a rectilinear number and admits only a fractional part with the same denominator as itself; and, by mingling with any of the numbers within the decad, it does not produce any numbers within the decad, nor is it produced by the intercourse of any of the numbers within the decad, but, with a principle which is all its own and is not shared, it has been assigned the most critical place."*

The Heptad is the

*mean* between the 1 and the 10. It is a critical moment in the cycle, hence it is called

*"crisis point", "chance",* and

*"critical time"* by the Pythagoreans. The 7 launches us up on our ascent toward the 10. The 7 is the critical moment to breakthrough to the upward ascent. It is an opportunity easily missed.

The Greeks called the Heptad

*"Agelos"*, meaning "flocks", for it is a cluster of multiple forces that gather at this crucial point in the Decad and ignite the ascent toward the return to the Monad via the 10. From

*The Theology of Arithmetic*:

*"It is called 'forager', because its structure has been collected and gathered together in a manner resembling unity, since it is altogether indissoluble, except into something which has the same denominator as itself, or because all things have brought their natural results to completion by its agency..."*

In traditional astrology, all fate is ruled by the 7 (planets). This astrological analogy fits with the eclectic nature of the Heptad. It is both a beginning and an end, and the literal middle (as mean) in the Decad.

The Pythagoreans say the 4 contains the 10 (1 + 2 + 3 + 4 = 10). Similarly the 7 is thought be like the 1, and is called Pallas Athena, the Virgin, neither generated nor generating within the decad. So from a certain perspective, 7 ~ 10 is merely 1 ~ 4, but on a higher octave.

**The Number 8 - The Octad**
The tradition calls the 8

*'Embracer Of All Harmonies'*,

*'Safety'*, and

*Foundation*. It is literally a CUBE ~ safe, stable, and balanced. Yet in

*The Theology of Arithmetic* it is written,

*"Among the Muses, they said that the name 'Euterpe' was most suitable for the ogdoad, because it is the most changeable of the numbers within the decad, since it is even-times-even and is divisible up to the monad itself, which is naturally indivisible."*

How can something be both 'a foundation' & 'safe', yet be the 'most changeable'? If we look at the implications of the sequence of the numbers in the Decad, we can find a possible answer.

First, imagine the cycle of the Decad as positions on a square.

The fiery 7 launches us up on our ascent toward the 10. Once launched the 8 is on a coasting flight on the 'straight and narrow'. It ascends by its own

*momentum*, effortlessly, but has little option to do otherwise. The Octad (8) is of a Watery nature. It fits to the vessel determined by the Heptad (7). The nature of the Heptad determines what shape the Octad will take. Hence it is 'changeable'. Once launched into the ascent, and the 'cube' of the Octad has been formed, it rises by the momentum and acts as a 'safe' container for the intent of the Heptad, until it becomes the 9. The Octad is the realization of the intent of the Heptad. More than any other number in the Decad, the nature of the 8 is determined by the 7 that proceeds it.

**The Number 9 - The Ennead**
The Ennead (9) falls just short of the perfection of the 10, it was called by the Pythagoreans,

*'Failure'*, the

*'Near Perfect'*, and

*'Shortcoming'*. More positively it is also called

*'That Which Brings Completion'*.

Again, imagine the numbers arranged around a square. The Ennead sits on a corner. If we imagined this as driving, the 9 is the sharp, sudden turn we should not miss. If we miss the turn at the 9, we'll never make it back to the Monad (10 = 1+0 =1).

Similarly, using a 'rocket launch' allegory, the coasting flight ascent of the 8 comes to a halt at the 9. If our flight trajectory was good, and our rocket clears that corner, the 9 will be 'what brings completion' and we will have arrived at the 10. If we are off however, we will fall back down to earth. It is that 'last hurdle'. Even if we have jumped all the previous hurdles, if we trip on the last one, we fail. The Ennead is the last challenge before our goal can be reached.

**The Number 10 - The Decad**
Iamblichus on the Decad (10) -

*"Hence the Pythagoreans in their theology called it (10) sometimes 'universe, sometimes 'heaven', sometimes 'all', sometimes 'fate' and 'eternity', 'power' and 'trust' and 'necessity', 'Atlas' and 'unwearying', and simply 'God' and 'Phanes' and 'the sun'."*
The well known equating of the 10 with the 1 (1 + 0 = 1), defines the Decad (1 ~ 10) as a cycle, which we can represent as a circle. Both are often referred to by the Pythagoreans as 'God'. Iamblichus calls the 1, "the seed of all" and says it "encompasses everything within itself. On the 10, he says it "brings everything to fulfillment", and calls it a "receptacle", as all numbers return back to it.

As both 1 and 10 represent the divine, the cycle of 1 ~ 10 can also be seen as a process of leaving and returning to the divine. Traditionally this is represented as a decent and ascent. Iamblichus compares the 10 to the starting point of a race in which all the numbers "run their course by wheeling and turning around it"

From John Opsopaus' Pythagorean Tarot -

*1 & 7 = Impulse*

2 & 8 = Object

3 & 9 = Process

4 & 10 = Completion

This analogy only goes so far though, as the dynamics of an ascent will naturally differ from a descent. This comparison is equally important -

*1 & 10 = The Divine*

2 & 9 = The Crisis of separation or reunion

3 & 8 = The means

4 & 7 = The points farthest from the Divine

7 through 10 show us how matter ascends into the divine, from a higher impulse (7) to a higher consolidation (10). Here the energies are contractive, and can represent involution, and the personal. From the Heptad to the Decad (7 - 10) matter ascends to the divine and in the Decad (10) we have circled back to the unity of the monad (1 + 0 = 1). The Pythagoreans called the Heptad (7) the second monad, and the Decad (10) is a second tetrad (1 + 2 + 3 + 4 = 10), so 7 through 10, is basically 1 through 4 on a higher level - Impulse, Separation, Completion, Consolidation.

You'll notice, just as the 1 and 10 occupy the same point on the circle, so do the 4 and 7. These four are all centered in the middle of their respective ends of the loop model.

Iamblichus explains the relationship of these four numbers -

*"Not only do 4 and 7 mediate between the monad (1) and the decad (10) by arithmetically equal relationship, and when added together their sum is equal to the some of extremes, and 4 exceeds 1 by the same amount that 7 is less than 10, and conversely 4 is less than 10 by the same amount that 7 exceeds 1 - not only this, but also the numbers from the monad (1) to the tetrad (4) are potentially ten, while the decad is this very thing in actuality, and 7 is the arithmetic mean between the tetrad and the decad (i.e. in a sense between two decads, one potential, the other actual), since it is half of the sum of both."*