Gurdjieff's enneagram is a representation of inner effort; and since inner effort takes place, in one way or another, at every level of the universe, the forces, or laws, that it represents are universal, although their nature varies according to level.
The inner effort which the entire universe is engaged in is, invariably, an effort to return to the source of its arising. The diagram outlines the laws governing the possibility of that return.
Understood in the context of the enneagram and its connection to the six fundamental elements of inner work, the multiplications shown in the diagram have specific meanings regarding the way forces affect one another, and how one energy, or influence, needs to take a definite path in order to reach an ultimate destination.
The energies or influences in us, in other words, have aims. They are not just our aims, but what one might call "universal aims," much like Gurdjieff's "Obligolnian Strivings." These are aims that all of the material properties in the universe must share in their effort to evolve back towards what Ibn al 'Arabi called the Essence, or source (God.)
Readers will note that the premises and aims of the Obligolnian Strivings mirror some of the below relationships. Since the strivings represent, in Gurdjieff's world, universal lawful impulses, they would, in theory, have to relate back to the enneagram and its presumed cosmological meaning; and they do indeed appear to. It's correlative material of this kind that we ought to be looking for when we attempt to understand these matters.
The first force in each multiplication will, if followed through to the end of the numerical sequence itself, ultimately affect the last number in the sequence after passing through the four numbers between them. So, in a certain sense, the first number always represents an aim of work; and the last one always represents a result. The multiplications are, in other words, a specific language that iterates various stages on the path of inner development. Each one represents a process in which one part attains an intelligible mastery, or understanding, of another part, and informs it.
Keep in mind that the forces, conceptually speaking, represent the following:
2— Desire (Gurdjieff's Aim)
3— Conscious labor (shock)
4— Power (Will)
5— Being (real "I")
6— Intentional Suffering (shock)
Different systems can use slightly different names for the above properties. I've included Gurdjieff's names for some of them—as they manifest if properly developed—in parentheses. In these cases, readers should understand that, for example, Gurdjieff's Will represents the action of power, but, in the case of man, power as developed to a higher level, at least that of sol.
What this means, as I have explained in the essay on the names of God, is that each energy described in the process of inner work represents an intelligible and intelligent influence, and that the influences have understandable names on our level, even though they are experienced quite differently from higher levels.
Let's take the multiplications in order and examine them from this point of view.
This multiplication begins with Materiality, and ends with Purification. The first stage in the material world is always the aim to refine, or purify, the substance of the material world so that it can raise its level of vibration. This first multiplication places a so-called alchemical process at the foundation of inner work. Without material mastery over the action of Purification, the very process that Gurdjieff described to Ouspensky in In Search of the Miraculous, nothing is possible.
The multiplication begins with Desire, and ends with Power. Desire, in its higher form, represents wish; desire at any level must acquire power if inner work is to proceed. The multiplication is related to the prayer, I am, I wish to be. Desire cannot do anything without power.
The multiplication begins with power, and ends with materiality. Once Desire has acquired Power, the aim of Power must always be to affect the material circumstances of inner work.
The multiplication begins with Being, and ends with Wisdom. The aim of Being must always be to acquire Wisdom.
The multiplication begins with Purification, and ends with Being. The aim of Purification is to increase Being. De Salzmann indicates this when she indicates “an effort of attention coming from all the parts of myself — to purify the attention in order to concentrate on ‘I.’” (The Reality of Being, p. 132.)
The multiplication begins with Wisdom, and ends with Desire. This represents the ultimate aim of inner work on a gicven level: in our case, a man's Wisdom attains mastery over his Desire.
Readers will see that the six multiplications, taken together and understood in this form, layout an intelligible progression familiar enough to say that it summarizes any general understanding of spiritual work, as understood from the point of view of a progression.
In a sense, what we have here is a very general outline of all the material Gurdjieff presented to Ouspensky in In Search of the Miraculous. Understood from this perspective, the enneagram and the multiplications alone can encapsulate the entire book.
The paths from aim to result — and the role of the shocks —are a whole study unto themselves, but each one indicates that the means by which the aim of one particular influence achieves its goal are not random, but governed by law and an orderly progression through a series of forces, as indicated by the diagram.
It would be much too facile and literal, however, to presume that one just engages in these steps one by one. Inner work engages in all of these actions simultaneously, and the inner processes in a man are in constant movement as these influences, aims, and results interact with one another. We thus find ourselves in a fluid state that requires constant attention in order to be seen; and the complexity of the situation underscores the fact that this is not an action we can control, but rather one that we participate in. The participation consists of seeing; and this is certainly, in great part, what the role of the attention we have on this level must play.