XVIII-XIX)

Numbers are always connected with our ideas of wholeness. And whole­

ness is always connected with our visions of structure. There are several basic ways in which mankind has looked at these things. Gurdjieff’s use of the idea of laws is a very structural approach, since we have a whole that is divided into three or seven parts, each essential to the whole.

The tricky thing is to grasp what the whole is. We can call it the universe or something like that, but that tells us very little. When we get hold of what Gurdjiejf is talking about, we see that his trick was to let us think that the whole related to the law of three and the whole related to the law of seven are exactly the same. This is actually built into the ennea- gram and is a challenging assumption. It may well be that it is true only when it is made to be true.

The Law of Seven

Th e i d e a of the octave as a universal analogical model is based on a very general understanding of levels of organization, corresponding to different scales. If we have an organized whole, then it will exhibit typical properties and typical entities on a series of levels; it will have an organi­

zational hierarchy. Typically, we describe such hierarchies in terms rang­

ing from the smallest recognizable constituent unit to the organization as a whole, thus establishing a scale from least to greatest. Some examples are shown in figure 5.1.‘

Each of these widely known and used hierarchies happens to have a similar number of levels. They are, of course, merely human labels, and there are some widely different versions of the ones I have shown (espe­

cially of the military example). They correspond to structures in our per­

ception and thinking that, if we accept the principle of universal 68

«

Taxonomic Physiological Military

kingdom individual general

phylum organ system colonel

class organ major

order tissue captain

family cell lieutenant

genus organelle sergeant

species molecule private

5.1. Sevenfold hierarchies.

intelligence, are there for a reason. Such structures are not unambiguous nor are they fixed: they encourage perception rather than condition it.

The top level in each case appears at the threshold of something radically new^, belonging to a new level of wrholeness:^ in the case of taxonomy, that of all life-forms on earth; in the case of physiology, the life of the organ­

ism in an ecology; and in the case of the military, the political leadership (such as that embodied in the president in the United States). In more detail, we can point out that, in the case of physiology, we can move on upwards as in figure 5.2.^

We should also note that there is a shift of emphasis as we ascend any of these scales. In the military example we move from the execution of commands up into the formulation and creation of commands, or from doing to commanding. It is interesting that in real life there are strong barriers separating the realm of the soldier in the trench from the realm of the generals at headquarters!

biosphere biogeographical region

biome landscape ecosystem biotic community population (of a species)

organism

5.2. Ecological hierarchy.

The rudiments of Gurdjieff’s two kinds of shock are implicit in such organizational hierarchies. Of course, it is not possible to derive the par­

ticular format that Gurdjieff used, but the correlation is striking enough:

one kind of transition serves to bind octaves together into a higher-order scale, such as that encompassing the physiological and the ecological oc­

taves; another kind marks the changeover region between the tendencies of one kind of operation to tendencies of another kind (officers are trained separately and tend not to be promoted from the ranks).

Gurdjieff’s masterly step was in linking organizational hierarchies—

such as those he first expounded in terms of the “cosmic octave”—in temporal and the eternal, which two sides must always be kept in mind.

There is the question: Why should we have seven levels and not four

model for computer communications has finally settled on a scheme of seven functional levels. This is an entirely pragmatic scheme vnth no the­

oretical bias.'* In the seminal work of EUot Jacques, a theoretician of man­

agement and organization, there are seven levels of “time-span capacity,”

corresponding to seven levels of abstraction in logic and human action.

Contrary to contemporary fashions in dov/nsizing business to just four or three levels of responsibility, Jacques’s scheme suggests that seven lev­

els are necessary to cover the full range of possibiUties a business might encounter. His seven levels are divided into three that are relatively con­

crete and four that are relatively abstract. (See fig. 5.3.)^

False egalitarian ideals have tended to obscure and even deny such hierarchies. In present conditions of turbulence and change, they are re- emerging as a necessary feature of effective organization. The sevenfold scheme is not arbitrary but, at the moment, we have no theory to explain why.® Gurdjieff portrays the discovery of sevenfoldness as a matter of observation of the similarity of diverse natural processes, much as present-day scientists have come to discover the “patterns in chaos.”

It is possible that we have wired into us some capacity for perception in octaves, just as the linguist Noam Chomsky says that we are born with a capacity for generating language structures in ourselves. But we must remember that what is now wired into us arose by an evolutionary proc­

ess and must in some way reflect the world in which we exist and how we operate in it. It is very likely that we see “in several,” and that there is no mechanically precise number involved beyond the requirement that it be more than three, say, and less than ten. The musical analogy of the

Level Time-span Realm of Work Level of Abstraction

7 20 years global highest

6 10 years multinational creation of institutions

5 5 years national intuitive theory

4 2 years regional conceptual modeling

3 1 year 50,000 sq. ft. imaginal scanning

2 3 months 5,000 sq. ft. imaginal concrete

1 1 week 500 sq. ft. perceptual-motor

5.3. Levels of abstraction and time-span capacity.

octave helps us to see that there can be many different interpretations but that GurdjiefF’s version represents an optimum. It is halfway between an oversimplification and being caught up in the myriad of details.

As yet we do not have any precise kind of science able to measure the properties associated with the different numbers in our perception. It is interesting, however, to note the experiment which Rene Daumal puts into his fantastic novel Mount Analogue: he challenges us to follow any sequence of actions we might do in our minds and see how many steps we can hold together at once. The general finding is that we fail beyond four steps.^ It is possible to regard this result as supporting Gurdjieff’s placing of the first shock after the first three steps. It is easy to keep three steps in mind but harder to keep four. That is why we svntch from con­

crete to abstract after three.

It seems to be the case that we can perceive and understand things somewhere in this range of “the several”—^just as we do in the range associated with connections and relationships, with regard to which Gurdjieff formulated the law of three. If this notion is correct, then Gurd- jiefif’s concentration on just two fundamental laws of three and seven corresponds with the two main modes of understanding that every human being is born v«th. It is then possible to connect these two modes together—as surely they are connected anyway in ourselves—and use our powers of analysis to see how they are involved in the making of each other.

Seeing in Depth

It is because the two laws appear as intertwined with each other that we may suppose that there is an intermediary mode of understand­

ing between the three and the seven which represents their difference:

7-3 = 4. Thus would be a secondary fourfold law. We also have the possibility of the addition of the two laws: 7 -f 3 = 10. There may well be a law of ten. Indeed, this is what we find in the enneagram, which is based on the decimal system. To relate these abstract possibilities to the figure of the enneagram, we might suppose that they would appear as shown in figure 5.4. The law of ten appears above the circle because it is beyond the nine. The law of four appears opposite it, embedded in the bottom part of the figure. The law of four concerns the mixing and

blend-72 The Frame of Transformation

LAW OF TEN

5.4. Implicit laws of the enneagram.

ing which was the province of alchemy. Our playing with numbers and symbols here is more than arbitrary, since we have to take account of the progressiveness which is a feature of the movement in the enneagram, signified in the sequence from 0 to 9.® I interpret this to mean that the degree of order at each stage is an advance over the preceding, and that there is a progression of laws of greater and greater intelligence. This will form the background to all our explorations in the following chapters.

What we have to fix in our minds at this point is the general idea of combining two distinct forms of understanding. This is an important key to Gurdjieff’s intellectual method. What we have essentially is one mode of understanding connected with a small number, and another mode connected with a significantly larger number. It is only the two working in combination with each other that can provide us with an understand­

ing in depth—^just as we have a perception in depth through the conjunc­

tion of two eyes and a perception of color through the conjunction of short- and long-wave sensitivity. What we call color, depth, and under­

standing exemplify the structures of meaning that combinations of forms produce in a dynamic continuum formed in the process of their dialogue.

The law of three concerns our grasp of immediate connectivity or relations,’

while the law of seven emerges for us in such things as our fascination with narrative and with any time-factored structuring of our experience.’® .

One important thing we must keep in mind is that Gurdjieff, by his placement of the two shocks, clearly distinguished the form and sequence of descending and ascending octaves. In the octave as such, of course, we have eight notes, the last being a reiteration (though on another level) of

the first. The final note, the higher do, always represents the unity of the critical transition. Without the inner work, learning the movements

/ 4 i ne trarnt oj i ransjormation

would continue in a mechanical circle, and we would have trained danc­

ers and not a living presence. As for the second critical transition, this—as Bennett has pointed out—is when the spirit of the movement is realized."

It is then that the “movement performs itself.” It is in regard to these possibilities that Gurdjieff insisted that his sacred dances afforded the key to a real understanding of his ideas. The will-pattern of the dances, their logos, has to be realized vnthin the functional process of the dancers, and the two can only be united in being. One of the best definitions of being was given by Madame Ouspensky when she said: “Being is what you can

bear."^^

Seven into Three

In the enneagram, the law of seven is intertwined with the law of three.

This means that the two laws can map into each other or reflect each other. It should be possible to see how the sevenfold architecture we have been looking at—the structure of significant change—is reflected in three distinct parts. There are curious mathematical relationships between three and seven, but we will confine ourselves to qualitative imagery.

Reverting to the structure of the octave we have: three notes, then a shock, and then four notes before the fi^nal or second shock and the reach­

ing of the next do. We assume that the octave is made up of three triads, or three groups of relations. We already have the first triplet in the first three ascending notes. Next comes a shock. Let us consider the next three notes as another triplet: what does that leave us with? We have another note, then a shock, and then the do of the next octave. If we consider si-shock-do as a triplet, we now have three triplets as desired (fig. 5.5).

In fact, Gurdjieff always links si-shock-do together, by saying that—in a descending octave—the “will of the higher do fills the interval and produces si.” Further, his first three notes (do-re-mi) are always described as having a certain kind of momentum in common, a kind of movement that cannot of itself reach any higher. Thus, the first three notes are also bound together in their ovm way. This leaves the middle three notes, which signify a triplet equivalent to the first on the other side of the mi- fa barrier. The first transition brings together the first three notes into a whole. This is a step of progressive integration: without this transition.

76 The Frame of Transformation do

SI

la sol fa

three

two

mi re do

one

5.5 The octave in triplets.

these three would continue to repeat in succession, a condition that Gur- djiefF called a deviation of the octave which results in going around in circles. (See fig. 5.6).

The three triplets make up a higher order triplet, each of them carrying a specific quality of the triad, such as passive, active, or reconciling. We are anticipating ourselves, because we have yet to go into the nature of the law of three, which we will do in the next part of the book.’^ I have added the terms mechanical, intentional, and spiritual also in anticipation of our later explorations.

do

si

la sol fa

RECONCILING spiritual

ACTIVE intentional

mi re do

PASSIVE mechanical

5.6. The octave as a form of the triad.

Notes

1. See Odum, Ecology and Our Endangered Life-Support Systems, p. 27. The exam­

ples are just as they are given by Odum, who has no particular vested interest in looking for sevens! Gurdjieff, in his Meetings with Remarkable Men, describes a visit to a Sarmoun monastery where he sees a striking artifact made of seven branching limbs that indicate postures to be taken in sacred dances. As he points out in his introduction to the book, his intention throughout was to create strong emotional images related to the Work. It is not confined to rare and exotic peo­

ple. Once you have the idea of events on different scales, you can analyze your day and see it as an intricate branching structure of behaviors that define your life. But first you have to be convinced that there is an underlying structure.

2. See chapter 4. I am treating the relation between higher and lower do’s as that between different degrees or kinds of wholeness. The simplest picture of this I can make treats the lower do as an atom and the higher do as an organism. Every level has its characteristic elements, which may be taken as atoms relative to some higher level of organization.

3. See Odum, Ecology and Our Endangered Life-Support Systems, for explanations of the terms in the figure.

4. Private communication from Chris Thompson. There is no existing theory which accounts for this kind of structuring. Very likely, however, we vnll come across such structures when there is a strictly linear-hierarchical arrangement.

But contemporary business organizations, which actually concentrate on tasks and make rapid adjustments to changing economic forces, tend to flatten to three or four levels.

5. This table is adapted from the table “Summary of Strata and Levels of Abstrac­

tion,” which appears in Elliot Jacques, R. O. Gibson, and D. J. Isaac, Levels of Abstraction in Logic and Human Action, p. 294. Jacques and J. G. Bennett ex­

changed ideas at one time, and Bennett is referred to in Jacques’s book, a unique and extraordinary collection of studies that should be more widely known. What is not touched upon is how organizations only work well if they include nonhier- archical relationships as well as hierarchical ones.

6. Whereas in science we have laws largely expressed in mathematical equations, in the realms of will and consciousness there are patterns largely expressed in sym­

bols and numbers.

7. Others have pointed out that the maximum number of distinct elements we can keep in mind, without reference to sequence, is seven. Putting these two prag­

matic findings together gives an astonishingly close approximation to the basic ideas of the octave.

8. The sequence of integers is obviously one of the easiest ways of indicating a stepwise progression. Structure arises when we take only a limited set of num­

bers. Again, in the simplest representations, the starting point must be zero or

one, with corresponding consequences. The numbers, then, are in no way funda­

mental but simply part of the symbolization.

9. The work of the American philosopher Charles Sanders Peirce is particularly important for the study of relations, work which was taken up later by Bertrand Russell; see The Principles of Mathematics.

10. See Alexander Marshack, The Roots of Civilization. This was a very original book in drawing attention to the amount of detailed, shared, and structured knowl­

edge required for any advance. It is far removed from mystical cant about ancient wisdom, insisting that the real ancients found things out through hard work just as we do today.

11. Described in the chapter “Doing Movements” in J. G. Bennett, The Way to be Free.

12. Reported in J. G. Bennett’s autobiography Witness.

13. The most intriguing is that seven is the largest number of objects that can be formed into subsets of three, each having one and only one member in common with every other subset of three (pointed out by Oswald Veblen to Arthur Young;

see Young, The Reflexive Universe). If we have seen objects labeled a, b, c, d, e, f g—then the subsets are abc, ade, afg, bdf beg, cdg, cef There can be no more than seven such subsets. This property vividly suggests the fundamental interconnec­

tivity of the law of three and the law of seven. However, it is important not to lose sight of the fact that these are just properties of numbers like countless others. For example, three is the largest number of objects from which we can take subsets of two, such that only one member is common to each pair, and there are three such subsets. Thirteen is the largest number of objects within

tivity of the law of three and the law of seven. However, it is important not to lose sight of the fact that these are just properties of numbers like countless others. For example, three is the largest number of objects from which we can take subsets of two, such that only one member is common to each pair, and there are three such subsets. Thirteen is the largest number of objects within