The Names of God As Universal Principles
The names of God are universal principles, that is, forces which lawfully act in every octave, regardless of level.
The principle of action within any octave is always the same, because development must follow a lawful path that does not change just because a level is different. The path always recapitulates the same struggle, depicting the expression of matter as it emanates from the divine, and its wish to return.
Each octave is, in other words, a circulatory system with a set of specific demands placed upon it. The demands always begin from the lowest level of vibration, where the forces exerted upon them are primarily mechanical, and as they evolve through successively higher rates of vibration, and interact with one another, they evolve into an expression of less mechanical, or more conscious, forces.
The development of each octave is a dialogue between these universal principles. The two conscious shocks are what one would call "unique principles," since each one of them introduces an agency from a higher level into the equation. They alter the interaction of the universal principles.
Al 'Arabi, who well understood the principles but may not have been directly familiar with the diagram, describes the system in this link.
The universal principles thus go under other, but analogous, names within different levels, And their subordination to names at higher levels of vibration is inevitable. Nonetheless, their essential properties remain the same. Each of the universal principles has subordinate principles related to it; and since each principal is the do for an octave of its own, taking into account the fact that each octave (and each position occupied by a shock) has nine notes under it, we can iterate 81 names, or attributes, of God.
Intriguingly, al 'Arabi indicates that God has 99 names, but none of the known lists are reliable. He consequently sites that only 83 of the names can be known with certainty. (ibid, p.44.) If one adds the iterated names in known octaves to his own two "supreme" names, the Essence and the Divinity, we would reach his number.
Ranked in order of vibration, the names of God in the form of the universal principles are as follows:
Material
This represents the first order of vibration at its lowest level after emanation from the absolute. All matter, animate and inanimate, arises from this foundational principle, and everything that is fundamentally material, that exists objectively is something that is (incorrectly) perceived as separate from divinity originates from this universal principle and at this lowest level of order. At this level of awareness, there is no understanding of the separation from the divine, So the wish to return to it has not arisen.
Desire
This second order of vibration represents a higher level of awareness, which, the moment it becomes aware of its existence, inexorably manifests Desire. although the essential (and esoteric) wish of Desire is always to return to its origins, the moment that it realizes it exists, Desire at this level remains attached to Material, and thinks that it desires itself. This peculiar situation creates a paradox; for both Material and Desire are, in fact, a part of the Essence, and thus have no absolute need to return; they are already there. Nevertheless, the consequence of material manifestation is the perception of separation, due to the lowering of the order of intelligence by decrease in the rate of vibration, and it is this perception that must be overcome.
Unfortunately, the development of the octave — the lawful interaction of the forces—complicates the matter, before it resolves it, because lower levels of intelligence are unable to perceive, or sense, in the manner necessary to effect a return.
Power
The third order of vibration represents the acquisition of the means to return, without the proper will, or wish, to do so. Power is thus turned towards egoistic purposes, rather than toward service of the Essence.
These first three universal principles, representing the mechanical, or material, side of the enneagram, have an ego, but no real "I." They are separated from the Essence by the very nature of their interaction itself, but cannot see its existence. Hence seeing is essential in order to correct the situation, and the forces must furthermore be of an order where the forces see themselves and see where they are. This is where Gurdjieff's entire practice of self remembering comes into play; the shock of conscious labor — the universal principle whereby Being recognizes, that is, re-cognizes itself for what it is: a fragment of God — being necessary in order for the manifestation of the names to acquire real Being. Real Being represents a return to a recognition of position as that which serves, the servant. This is the position that real "I" must always rediscover itself in before any further work can take place.
The lack of awareness of position is the lack that Jeanne de Salzmann asked her pupils to stand in front of, and it occupies its position on this side of the enneagram because of the described consequences and interactions of the forces, or names, of God in the mechanical portion of the diagram.
Being
The forth universal principle represents the first manifestation of conscious forces, or, awareness of one's actual position. This level of intelligence develops what Gurdjieff called "real will," because all of its will, once it sees where it is, is dedicated to returning to its origin, the absolute, by raising its level of vibration to the necessary point. All of the sacred individuals and societies in Gurdjieff's Beelzebub who reached this level inexorably turned all their efforts toward salvation.
Until this development takes place, all the efforts aimed at salvation, returned to be essence, are false ones, manufactured by the interaction of mechanical forces to keep possession of the energy at their own level.
Indeed, Al 'Arabi also well understood this principle, which is described in some detail in The Sufi Path of Knowledge, in the chapter entitled The Divine Roots of Hierarchy and Conflict. In it, he specifically says that the levels of vibration compete with one another, in the same way that tones can either harmonize or disharmonize (see page 55.) The argument is brilliant but complex, and I will not repeat it here; suffice it to say that when a manifestation which appears to contradict an attribute of God, for example, a lack of compassion, appears, it is exactly because of this phenomenon,
Purification
This is perhaps (to me, at least) one of the most interesting characteristics, since its subordinate forms include the vitally important elements of speech and language.
Being, the fourth note or Sol, is a level that can exist in an unsullied state, so to speak, one without mind or language. It's an exalted state; but an inherently limited one, since, without language, it can't form conscious (as opposed to mechanical) relationship in community. The emergence of language, which confers a different level of meaning, takes place on this next level, which is what the yogis call the throat chakra. Prayer, expressed through speech, including all mantras, hymns, and chants, are all forms of purification, and well understood as such in monastic, dervish, and yogic disciplines. This is the physical creation of vibration, the initiation and emanation of a fundamental divine principle which has now been turned to the use of the aspirant in order to refine their vibration in order to make it acceptable for return to the fundamental source.
There are, to be sure, multiple forms of purification, but this primary meaning becomes intelligible when one sees that it is subordinate to wisdom, or, what al Arabi called Knowing, the highest level of intelligence before returning to the Godhead.
Knowing
This universal principle reigns over all of the other principles. Each principal, whole unto itself and meaningful in the hierarchy, must be informed by knowing, or wisdom, in order to function properly; and indeed, in the iterations of octaves, each other attribute of God needs to complete itself to this level of understanding. Gurdjieff made direct reference to this near the end of Beelzebub, in the ceremony in which Beelzebub's horns are restored. We can infer, from what we know of the enneagram and the notes, that the reason Beelzebub has five points on his horns is that they represent the completion to the stage of "knowing" for the octaves of Material, Desire, Power, Being, and Purification. Only one stage is remaining: the knowing of the knowing, referred to as the sacred Anklad. And the stage is, indeed, precisely appropriate for him, since he has purged himself of the factors that caused his rebellion and fall from heavenly grace; It falls, in other words, exactly where one would expect it to in the diagram.
Summary
There might be a tendency to presume, because one attribute is subordinate to the other attributes in terms of rate of vibration, that one is inferior to another, and this is decidedly not the case, as Al 'Arabi explains. This is no more the case then the inference that Yogic chakras represent a hierarchy of superiority and inferiority. In the end, they are both inseparable systems where each element has an equal, though different, value. The paradox of apparent inequality is an incorrect perception.