Wednesday, January 16, 2013

The Tetrad

The Tetrad

As we have journeyed through each Number, they appear to us like different states of consciousness: in the 1, I see Unity, in 2, I behold the difference between Being and Non-Being, and with 3, I see the deeper harmony of the One-and-the-Many. Of course, neither Unity, Being, nor Harmony is lacking in any of the Numbers: it is just that each Number is a key with a different dominant tone. One contains all Numbers, Two is another Monad (as well as Privation), and Three reconciles mystery with mystery.
When we reach Tetrad, we find more of the same, but differently. Are these new states of Being, or just changes in Consciousness?

1+2+3+4=10, so the Tetrad is complete: it contains the Pyramid, the four elements, and the four causes of Aristotle, and the Quadrivium – arithemetic apprehends quantity in general, music apprehends relative quantity, geometry takes in size in general (static), and astronomy apprehends size in motion in the stars. Iamblichus thinks the Quadrivium’s use of Number to apprehend Truth is less liable to error (one supposes, than religion?). He doesn’t seem to have a division between sacred/profane science – there is only Truth. He relates each science of Quadrivium to a number: Arithmetic (Monad), Harmony/Music (Dyad), Geometry (Triad), and Astronomy (Tetrad). The first and simplest three dimensional figure is the sphere, composed of center, diameter, area, circumference.

Creation proper begins with the Tetrad, as fire is symbolized by the pyramid (4 bases, 4 angles), there are 4 elements, 4 seasons, etc. Iamblichus’ use of 4 orderings in Nature is a long one. “Accretion of discrete things cannot be seen without the Tetrad, although plurality appears with the Triad”. Those who have died in virtue are not “thrice-blessed”, but “four times blessed”: they have gone beyond alteration and change.
Squares symbolize stability, and Hermes and Herakles are associated with them. Tlao means endure, so we may call it the Tetlad, for a neologism. Since its perimeter and square are equal, it is called Justice. 4 is associated with the ensoulment of Body, thanks to the various harmonic ratios established by the 1,2,3,4 sequence; so 4 (again) represents emergence out of possibility into actual existence.

In the Western tradition, we would say that the number 4 establishes the outflowing of the seminal Ideas of God into the material universe: Four is the entrance of the Triad’s energies into the actual harmonies of physical creation. In Platonic terms, matter would now be Over-Souled or given an Anima, so that the world-Soul now exists, and is a living thing. The seeds of Creation or rationes seminales (associated with Logos Spermatikos) proceed to actually unify Matter and Form into substance, shape, form, & principle. So actual things come into existence, and do not merely exist in conception as Ideas in God’s mind only.

Saturday, January 12, 2013

The Triad

The Triad

When one refers to the Triad, one must remember that:
The Triad has a special beauty and fairness beyond all numbers, because it is the very first to make actual the potentialities of the Monad – oddness, perfection, proportionality, unification, limit.
We recall that the Dyad is a second Monad, which begins the process of the primordial’s manifestation, which process reaches a form of completeness with the Triad; this is because the Triad is the first number to be “odd” (“Odd” here meaning that when divided, one part is greater than the other, or differs from the other). It is the first number to be equal to its predecessors, because 1+2=3. Recall with the Dyad that all we can say is that it does not succeed the Monad in the same way that the Triad succeeds both Monad and Dyad, because 0+1= 1, not 2; the Dyad is an “as-if” Monad, not a true successor. With the Triad, a true harmony is reached.

In the Christian tradition, the Son does not claim equality with the Father, nor does He retain dominion and lordship at the end of time: rather, He delivers all back up to the Father, or Arche, through power of the Spirit. It is with the Spirit that true balance within the Trinity is reached: The Father generates the Son, and the perfect submission and harmony from the Son to the Father, the perfect Love for the Son from the Father, is so intense it generates a Third Person, and this forms the perichoresis of both inner essence and outer energies of the Divine “Three-in-One”. The Son is associated with the Dyad, as is Queen Mary, the Queen of Heaven: Water, the most submissive element (as the Tao teaches) symbolizes the Feminine & the baptism of the Son.

The Triad is unique in that 1+1+1=3, where the middle term is the same as the two extremes. Also, in 1+2+3, the middle term is equidistant from the two extremes. So it succeeds (perfectly) two sources, and is the system of the two sources. 3 exists between 2 and 4 in a special way, additionally: 2 is the first double, and sums up the idea of being “greater than” the One (0+1=1, less than 2), while 4 is sesquialter, that is, it is less than 1+2+3 (=6). 3, as pointed out, is precisely equal and balanced, because 1+2=3.
So we see the “Son” is highly exalted, although being perfectly submissive. The “Son” (2) is not successive to the number(s) preceding it (and is therefore less), while He is greater in that He is “more” or actualized, because He “doubles” the Father. This is the way it is expressed in Christian dogma, but Iamblichus is teaching something that is at the common root of this dogma with other traditions, seeing that even in Taoism, there is a Divine Three.  We might say that Christianity is the religion of the Son, externalized, out of the bosom of the Father, but that the Monad retains the power and the glory to sustain, unmanifested and manifested, something else that shares the common root in that Monad. If this makes your head hurt, or sounds too Christian, just concentrate on the Numbers.
“The Monad is like a seed in containing within itself the unformed and unarticulated principle of every number, the Dyad is a small advance towards Number, but is not Number outright because it is like a source; but the Triad causes the principle of the Monad to advance into actuality and extension. ‘This’ belongs to Monad, ‘either’ to Dyad, and ‘each/every’ to the Triad.”
Iamblichus also uses etymology: Trein means piety, so it is called prudence & wisdom; in the Christian tradition, Divine Sophia (as well as in Gnosticism). Knowledge (true knowledge) follows the Triad. The Triad is also beginning, middle, end. This is why prayers are made three times, in formulas of threes, and why even the Triangle (the first planar figure) has three different types (equilateral, scalene, isoceles). Adding the Triad up we get 6, which is the first perfect Number. It is unyielding and cannot be worn down, because you cannot divide it into two equal parts. There are three Fates, three levels of Creation (sky, land, water), three motions of the stars (summer, winter, ecliptic), and three phases of moon (waning, waxing, full). Giving, receiving, and requital is the pattern of Generation, both divine and human. He even quotes Homer: “all is divided into three”, which becomes (with Aristotle) a meditation on virtue being the mean between two extreme vices.

What is crystal clear is that even something as simple as the relations of the very most basic Numbers is revelatory, to the meditative spirit, of the fabric of the universe. And this makes perfect sense, for how could God not be revealed in that which is most humble, the smallest of things, the very pebbles or calculi which we move around in our first attempts at numeracy?

Saturday, January 5, 2013

The Dyad

The Dyad

As we enter into the mystery of the One-and-the-Many, things begin to get more complicated. Even from Wikipedia, it is obvious (apart from the caveat that Iamblichus did not “introduce” any “notions” at all) that Iamblichus is essentially creating a parallel system that in many ways is similar to Christianity. This is why Julian the Apostate admired him so much, and why Porphyry disagreed with him so vehemently (Porphyry thought that purely notional contemplation ought to suffice for attaining divinization). From his doctrine of the One-and-the-Many, to his insistence that the lower types of men need physical theurgy, to his peopling the cosmos with various divinities and powers that are subject to Number, Iamblichus’ world highly resembles that of the Church Fathers.
He introduces his doctrine of Dyad:
“So each thing and the universe as a whole is one as regards the natural and constitutive monad, but again each is divisible, in so far as it necessarily partakes of the material dyad as well. Hence the first conjunction of monad and dyad results in the first finite plurality, the element of things, which would be a triangle of quantities and numbers, both corporeal and incorporeal. For just as the sap of a fig tree congeals liquid milk because of its active and productive property, so when the unificatory power of the monad approaches the dyad, which is the fount of flowing and liquidity it instills limit and gives form (ie., number) to the triad. For the triad is the source in actuality of number, which is by definition a system of monads. But in a sense, a dyad is like a monad on account of being like a source.”
The Dyad (therefore) is the Feminine Principle; in relation to the Monad, She is passive, as matter is to God. However, in relation to what comes after, by her productive powers, she is the Fount or Center of things, like a Monad, because in her Life originates (and multiplicity is created). This gives a good idea of the sophistication of Iamblichus’ thought: “opposition” to the Monad (for him) doesn’t mean resistance or lack of submission, but (precisely) submission through being opposite, or complementary – in other contexts (the material realms) it is the Dyad that takes on the characteristics of the Monad: the Queen stands in the place of the King (one can’t help but think of this doctrine, at this point).
I am not arguing that he is a pseudo-Christian, but rather that both Iamblichus and the Church Fathers were partaking of the same divine pattern, even (and up to) the particular manifestations of it at that time and place in history: see this article (for instance) as to how theosis and henosis differ, and how they do not. It might not be going too far to say that Iamblichus’ teachings represent a possible locus for reconciling paganism with Christianity (by purifying paganism and refining Christianity), thus creating the possibility of “white” theurgy.

These possibilities arise from the subtlety of Iamblichus’ method & manner of dealing with the One-And-The-Many, as he unfolds a doctrine of the Dyad (II – 2). Rather than posit a merely crude opposition, he shows how the Dyad is both Isis & Ison, Equal and Unequal, Generator and Destroyer.
2, mathematically, is composed of 1s, and is therefore (from arithmetic linear) a Greater or Non-Equal. When viewed as a plane (2 squared), it becomes a Lesser, since 2 itself is less than 4. The undoubted metaphysical conclusion is that the Dyad contains elements of being both Greater and Lesser within it. This is an example of the kind of paradox that Iamblichus is seeking. The number 3 (as we will see) is the first truly diverse equal (1 is equal to itself, but is not diverse): 1+2 = 3, so that the preceding sequence of numbers added together is equal to the number itself. This is not true when we come to 4: 1+2+3 does not equal 4 (Iamblichus will draw conclusions from this, as well).

The Dyad has special properties (also) because 2+2 = 4, which is the same as 2 taken to the plane (2 squared). This is the only number like this. The Dyad is another Monad (being a 1 added to a 1), but the Monad does not generate this truth of equality between arithmetic and plane extension.

Yet in another sense the Dyad cannot create a plane figure, because two angles don’t construct a plane figure: so the Triad is anticipated – it alone can create planar figures. The Dyad, on the other hand, can construct infinity, in a sense, because it can create a line running from a point, indefinitely, in two dimensions. This line may, or may not, return to its Origin.

The Dyad, therefore, is not to be mistaken for the original Monad, despite its functioning in relation to other numbers as a Monad itself. This is because the Monad stands alone – if, therefore, the Monad stands alone as Unity, something else has to take its place as the new principle of Unity to give unity to the other numbers. The Dyad, therefore, becomes “Monadic” towards the other numbers.
Numbers, therefore, inculcate the appreciation of metaphysical truths, such as the interplay between Microcosm and Macrocosm: the Moon or the Queen can become or stand in place of the Original Unity, precisely because of the primal unity of the One. Opposition can not exist, except to reinforce the One.

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