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The Enneagram

A Lecture by G.I. Gurdjieff

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(Note: A similar version of this lecture is presented in Chapter 14 of In Search of the Miraculous by P.D. Ouspensky.)

In every man there has been implanted a need of (desire for) knowledge, differing only in its intensity. But the passive human mind, while utilizing every means possible to it of taking in (and working over) impressions, often gets into an impasse in trying to find an answer to the question "Why".

Man's eyes are dazzled by the bright play of the colors of multiformity, and under the glittering surface he does not see the hidden kernel of the one-ness of all that exists. This multiformity is so real that its single modes approach him from all sides - some by way of logical deduction and philosophy, others by way or faith and feeling. From the most ancient times down to our own epoch, throughout the ages of its life, humanity as a whole has been yearning for a knowledge of this one-ness and seeking for it, pouring itself out into various philosophies and religions which remain, as it were, monuments on the path of these searches for the Path, leading to the knowledge of unity. These searches radiate to the Path just as the radii of a circle join at the center, getting closer into contact with each other the nearer they get to the center. The goal itself determines the direction of the paths and brings the wanderers on the paths to a knowledge of the one-ness which reaches the depths where that knowledge becomes a reality to the knower and cannot be communicated to another who has not reached the same stage of development. The words and notions of conversational language become dead and empty, conveying nothing to him who does not carry such knowledge within himself. In the same way as the sensation off tooth-ache cannot be imparted to one who has not experienced it, and just as the difference of colors cannot be conveyed to one blind from birth, and the wealth of auditory sensation cannot be communicated to the deaf, similarly you cannot tell or relate in words the depth of knowledge which has become part of a man's being. The words and notions of different epochs change according to conditions of place and time; unity is eternal and immutable. The laws, acting in us, and producing the plurality assumed by us, are everywhere the same. From the most, ancient times humanity has understood this, and by utilizing the language of symbols and formulas, more perfect than our contemporary language, has gone on handing its knowledge down to the succeeding generations. And everybody approaching the symbol and possessing a complete understanding of it, possesses a perfect synthesis of it. Speaking figuratively, he has this symbol within himself. A symbol, by expressing the knowledge of the laws of unity, has at the same time expressed the path to it. Side by aide with the basic symbols, as if they absorbed into themselves wider spheres, there started up and sprang into existence in subjection to them other symbols and formulae. Everything in the world is one and is governed by uniform laws, and for that reason the "Emerald Tables" of Hermes Trismegistus put it; "As above, so below". All the laws of the cosmos we shall find in the atom. And in any phenomenon existing as something complete according to laws. (That is, in any whole.) The knowledge of the laws of the plurality of the One was always based on the similitude of the microcosm to the macrocosm - of man to the universe, and vice versa. The fundamental laws of the 3 and of the 7, of the active, passive, and neutral principles, the laws of activity, are to be found and confirmed in everything, and therefore in arriving at a knowledge of the world's structure, man was unable to avoid the path of self-knowledge. Man's nearest and always readily accessible object of knowledge was always himself, he being the expression of the action of all the laws of the cosmos. The formula "Know Thyself" is, in this respect, full off the profoundest meaning: it is one of the symbols of the knowledge of truth. By becoming acquainted with the symbols expressing the laws of creation, man will learn the laws themselves, and by learning these in himself he treads the path of self-knowledge, and in this sense every symbol teaches us about ourselves. By learning to distinguish the laws of evolution and involution, synthesis and analysis, yes and no, good and evil, energy and matter, forward and retrograde movements, man will also discern the reciprocal action of these laws.

He will learn the great laws known to the ancient wisdom, the laws of the binary and ternary as applied to the cosmos and to oneself. By binding them together, and enclosing them within the circle of eternity, and their manifestations within the circles of recurrences and cycles that happen according to law, within (the circle) of the spring of eternity on the plane of our own time, within the circle of eternal vibration and of the struggle with oneself on the path to self-knowledge, he with his whole being, step by step traverses the path of construction in himself of the great symbol which has come down to us under the name of "Solomon's Seal".

Figure 1. Solomon's Seal

What I have just said shows how difficult it is to convert the language of symbols into our own language, how little purpose there is in interpreting the symbol to a man who has not attained to an understanding of it. And however strange it may be, the fact remains that the sense of the symbol, the discovery of its nature, can only be given to, and received by, him who previously knew already, and for him the symbol will be the synthesis of his knowledge, the same formula for the expression of knowledge as it was to him who constructed it. Will a man unacquainted with this system of symbols understand a great deal if he is told that the knowledge of unity by the means of self-knowledge and self-perfection for man is the neutralization of the binary by the ternary and its transmutation into the quaternary in order to close the pentagram and realize the "Seal of Solomon", or if I draw thus:

Figure 2. Symbolic Path

But let us suppose that we are talking of the harmonic development of man's body, and as the law is everywhere one we apply the stated formula to this development. How can we translate the quoted formula in that relation? What must we substitute in order to decipher it? All sensations, impressions, feelings and thoughts of man are divided into correct and incorrect, necessary ones and useless ones, pleasant and unpleasant, pleasure and pain. This is the binary along which all impressions, all life of man, travel.

This binary is every person who looks into himself. We may live by these transitory dimensions, giving ourselves up to their current and allowing them to carry us away. But to the whole of this process going on within us apart from our will, to all these "it wishes" we may oppose our "I wish", bind together yes and no, provoke a dispute between two opposites, a struggle of two principles, and neutralize them by the tertiary. A great dispute, if it is not purposeless, must give a result, a conclusion and an effect, and then four elements will be available: yes, no, dispute, result; that is, the transmutation of the binary into the quaternary. That is the first half of the formula. The second part of it speaks for itself and thereby points out the direction of the solution. Every result representing the completion of a circle gives something new, which in its turn can act reciprocally with something else. This "something", expressing itself conditionally, may be right or wrong, that is, it either provokes the formation of that for which it was produced, or obstructs it. Take any circle you like: let us suppose that I urgently need for my purpose some information or other which I can only get from one of my acquaintances. But I am not on good terms with him, he having once insulted me, and in order to apply to him for the required information I have had to sustain a tough fight with my self-pride. There might be many other considerations entering into the matter, such as the fear of a refusal, or of unpleasantness on his part, etc., which we will not go into now. In the upshot I resolved to go to him with my request and at all costs to get an answer. If my conclusion is firm enough not to allow any contingencies to shake it, my decision will assist my undertaking. But if under the influence of different considerations I come to the opposite decision, it will obstruct my errand, but it may be that it will conduce to the preservation of my composure and a saving of my nervous energy. In any case as regards my errand it will be a hindrance. Consequently, every result must be considered in relation to what a given effect was produced for.

But as we are speaking about the harmonic development of the physical body, of man's machine, every "dispute" in us must lead to development, that is, to the acquisition of a new, non-habitual functioning of that machine. We know that in it are five main centers: thinking center, formulatory apparatus, emotional center, moving and sex centers. The one-sided development of any one of them leads to hypertrophy, the type of a one-centered man. There will be five such main types. But if all five centers are developed in one man, he "locks up" within himself the pentagram by the fact that he brings his life and the work of all five centers into harmonic correspondence. By manifesting according to law and living harmoniously he represents the finished physical type of man. He is the type of the synthesis of 5 in 1. He is one, and at the same time five, for he can live just as one of the five and like all together. He is a six pointed star, and by becoming the possessor of this harmony and isolating himself in it from all outside influences, locking himself up in an independent circle, in a life enclosed in himself, he is the personal realization of "Solomon's Seal".

Figure 3. Man as Pentagram

You see how the series of symbols quoted is expounded when applied to the process we are considering. Nor is this a full interpretation. It can be visualized and understood by those who in this respect already possess certain knowledge and understanding. But a symbol that expresses an all comprehensive law, is ipso facto itself all comprehensive and for that reason it cannot be interpreted in a way that is not exhaustive, it can only be lived through (experienced).

I once more return for a while to the process of the harmonic development of the physical body already considered by us, and will remind that according to the fundamental law of the octave every finished process is a transition of the note "Do" through a series of successive notes to the "Do" of the next octave. The seven basic tones of the octave express the law of the septenary and the "Do" of the next octave added to complete the process, gives the 8 steps of a complete octave, being the symbolical expression of the binary of the quaternaries: "Do, re, mi, fa" - "sol, la, si, do". In each of these quaternaries: "Do, re, mi, fa" - "sol, la, si, do", there is one interval: "mi-fa", and "si-do", requiring the participation of an outside force, and only from the outside. If we consider the process at the point of completion, we shall get with these two intervals 9 steps - the ternary of the ternaries, three trinities. By adding the top "Do", we complete the process of the ninth step.

Figure 4. The Octave

Those of you who are acquainted with the Kabbalah may now apply its symbol of the nine in interpreting the laws of active operation in the processes of the harmonization of the nourishing of man's physical body. Look into these two series of symbols. By the nature of the thing they speak of one and the same thing and in them are given all whole numbers from one to ten. The last figure is the very same unit, or, to put it differently, is the "Do" of the next octave, that is, the end of the previous, the beginning of the next cycle. Consequently, the process of development and work contains in itself all the figures of the cycle from 1 to 9. Here we step right up to what may be called the symbolism of figures.

People acquainted with the system, which with us in the west bears the name of occultism, during their study of it, run up against the method of operating with figures known under the appellation of theosophical addition. I will not here stop to go into it, but will merely state that for many people this method of the synthesization of numbers appears so arbitrary that they regard it merely as a curious process, but one that is quite devoid of content. But all the while it has a deep significance for the man who has come to know the unity of existing things and who has the key thereto, reducing all multiform cycles to the basic facts which govern them. The number connects up with the geometrical form of the symbol; the number in the symbol pours out into the form. They mutually complete and outline each other. To those acquainted with the Kabbalah I may give a passing reminder also of the symbolics of letters and of the combined symbolics of words.

Word, number, and form, when combined, give a still more perfected symbol. It is not possible for me to dwell in detail on every aspect of symbolism. For the sake of those acquainted with occultism in its different parts, I can only mention the system of the great symbols called "Tarot", and the symbols of magic, astrology and alchemy, each of which represents a symbolical system, that is, the path leading to a knowledge of the truth of unity. But in order to tread this path, its symbolism must not be approached with a "literal" understanding and interpretation. As I pointed out, it is necessary to experience them, discover them, and by delving deep down into yourself to make them your own property.

The symbol expressing the laws of the unity of the infinitely multiform has an infinite multitude of sides or points of view from which to consider it, just as an algebraical formula of the roots of quadratic equations may be applied to the solution in numbers of an infinite multitude of problems of the section ruled by the formula. In the case of one man who already possesses all the data for knowledge, the symbol synthesizes him (these data?). In another, it awakens even the processes hidden deep down within him, uncovers them and gives significance and life to them.

Symbols, transposed into the words of our language, and handed down in those words, harden into a filament, they tarnish and may give rise to fatal errors in people who do not understand the symbols or understand them literally. Truth gets encased in a shall of error, and to enable the approacher to get near to it a great effort is required on his part. What monstrous errors have arisen from the symbols of alchemy, particularly of magic, in those people who, literally and one-sidedly, without possessing the all comprehensive knowledge of unity, adopted its symbols! The symbol is a barricade against words, it delves into the thing, taken by itself, and taken in its own reality. A knowledge of the symbol leaves no room for dispute, it deepens the understanding which does not remain merely theoretical, but presses on to the real result of being able to do, to the result of knowing and being, to the realization of great doing. Pure knowledge is not transferable, and by being expressed in words, is veiled by them, but whoever wishes and is able to see this veil, will find it transparent. And in this sense it is possible to speak of the symbolism of speech, but it is not everyone who can understand even merely this symbolism. To understand the spoken inner meaning of the thought and its spirit is possible only at a certain stage of development and with an effort on the part of the hearer. In those cases where a person is simply disputing in the ordinary sense of the words, by merely contending for his own opinion, he wastes his time in vain without acquiring anything new. In order to be able to understand speech when it is used symbolically, it is first of all necessary to learn and to be able to listen. In cases of profound knowledge, any attempt at understanding literally is foredoomed to failure, and, at best, will yield nothing, and, less favorably, may lead to error and absurdity. Truth is taken by force and it is possible to him who uses force to get it. Necessity compels me to dwell on this so long because in our conditions of modern culture and education it is in our nature to aspire to scholastical definitions, and, without noticing it ourselves, we unconsciously fetter ourselves with our soi-disant desire for accuracy in that sphere, right from the moment we set foot upon its territory until we reach the center. For this reason every concrete particular, communicated before the notion of the nature of the phenomenon or law was formed in man, by virtue of this psychological singularity of our modern reception, makes it difficult for us to be able to understand this nature. I do not mean by that, that accurate and concrete definitions do not exist; on the contrary, they do exist, and possess in the full sense of the word, the diversity of these qualities, but not just in what and in the manner we anticipate. And if anyone presupposes that he can wander along the path of self-knowledge, guided only by concrete facts, and waiting for them without taking any trouble to assimilate the indications received, he needs first of all to understand the meaning of symbolism, and always to remember that he alone, and only by his own effort and wish will be able to encompass his aim. Nobody will ever be able to give him what he has never yet possessed, nobody will be able to perform for him the work which he, and only he himself can and must perform. All that another can do for him is to jog him on to work, but the work itself he himself must do. And from this point of view symbolism, rightly received, plays the part of this jog to our knowledge. I have in mind presently to acquaint you briefly with one of these symbols, and would therefore wish that all that I have said should assist you to come to an understanding of it in such a way that the explanations I shall broadly outline might serve as a jog to those who are desirous of penetrating more deeply into a knowledge of the nature of the laws, and at the same time help them to synthesize the material I have on different occasions given them here.

I now speak of the basic law of the unity of the many, the law of the octaves. It has repeatedly been stated that this law is all comprehensive, that every process in its gradual development, independently of its scale, is fully determined by the law or the construction of the seven toned gamut. In other words, the seven toned gamut in its structure shows forth all the properties of this law. It has also been said that every completed process is formed from an elementary phenomenon, considered as "Do", and from a derivative phenomenon "Do" of the succeeding octave higher or lower, according as the process is evolutive or involutive. Every note, every tone of the gamut on another scale, is again in the same way a whole octave, as it were a closed round cycle. Every interval between two contiguous tones is again a whole octave. Those intervals between mi and fa, and between "si" and "do", which cannot be bridged in the process we are considering on their own energy and require in order to pass on outside assistance - assistance from the outside only - thereby connecting their own processes up with other processes. In other words, the law of the octave connects all processes of world creation, and offers to the initiated the scale by which he can pass on, and the law of the structure of the octave, and makes it possible for him to know everything and every phenomenon just as they are and in all their reciprocal relations, together with the things and phenomena connected with them. And so for the synthesization of all knowledge relating to the law of the structure of the octave, there exists a symbol, with the form of a geometrical figure. But before passing on to the description itself of the symbol, I shall say a few words about the teaching that utilizes this symbol, and its relation to other systems that have recourse to symbolic methods for handing down knowledge.

At the beginning of the lecture I stated that the paths leading to a knowledge of unity are to it as the radii of a circle are to its center. And the closer they get to it, the more they get into contact. Therefore theoretical facts serving as fundamentals and theses in one direction may be explained from the point of view of theses in another direction, and vice versa. That is why the symbol I have touched on today can be applied in explaining the theory of the teaching we have under consideration. Owing to this property it is possible to form an intermediate direction serving as it were as the middle way between two adjacent directions. And in the absence of a full knowledge of the main directions, such a middle course can lead only to a constant change of the directions and to their confusion, can only lead to complication and errors. And instead of approaching the center, a man going the intermediate road, gets hopelessly entangled, loiters about, and finds no issue. Of the principal directions more or less known to us we may name four: the Hebrew, the Egyptian, the Persian, and the Hindu; of the last named we only know the philosophy, of the three first, we partially know their theory. Two of the directions resulting from the mixing up of the others, and which are hopelessly involved in consequence of this mixing, although they contain particles of the truth they have received, but railed to comprehend, are at the present time theosophy and occultism. For this same reason, the practice of both of them without complete knowledge leads to disastrous results. It is impossible for me to dwell in greater detail on this extraordinarily interesting question of the different directions and their origins. This question will in due course be made the theme of a separate lecture. I wish to emphasize the fact that the teaching whose theory is now being expounded here by us, is completely alone in its direction, is independent of other directions and unknown by them. We will not go into its theory and origin now. As in the case of other directions, it makes use of the symbolic method, and I now intend to acquaint you with one of its symbols. Of course the superscription surrounding the outside of the symbol have been translated into expressions that are comprehensible to us. Its general structure, which links it up, in the geometrical figure, with the full expression of the law of the octaves, is somewhat more complicated than this structure I am going to set before you, but it fully synthesizes the internal laws of one octave and of the knowledge of the nature of the thing considered in itself, that is to say, existing in isolation, as it were, only as regards its processes and life. This symbol is formed as follows:

Figure 5. The Enneagram

The circle is divided into five different parts, six points connected by a figure which is symmetrical in relation to the diameter, passing through the top point of division and the center of the circle, and which is drawn as they say, with one stroke of the pen. Furthermore, the top point of division is the apex of a regular triangle connecting up the points of division on the complicated figure. This symbol will not be met with in the study of occultism, either in books or in the oral tradition. Such tremendous significance is attached to it by those who know that it has never at any time or at any place been published or communicated in entirety. But allusions to it are found even in occult literature. For certain reasons I shall not say where, but you may come across such a translation of this very symbol; "double binary of the ternaries, taken in pairs, giving the quaternary is neutralized into an elongated pentagram by the big free ternary". And this is formed as follows:

Figure 6. A Partial Enneagram

Meanwhile, you will never find any explanations on this figure, or on this formula. Nearly all the elements are really available here geometrically; four small triangles connected in pairs, the quaternary in the form of the double binary of the ternaries, and the big triangle, the free, (no hatching) ternary. Only one point of division is here lacking. There are eight apices or if we count on the outside of the sketch of our figure we get five, which are united by the elongated pentagram. Evidently this symbol is sometimes delineated by the septenary which is peculiarly formed, that is to say, by a heptagon with a point inside; this is interpreted quite arbitrarily and therefore I will not quote this interpretation, but will only reproduce the figure itself. It is drawn thus:

Figure 7. Another Partial Enneagram

Leaving aside all these fragments of a distorted and incomprehensible symbol, we will now proceed to examine it in the form in which I quoted it. I have already said that this is the symbol of the octave. The octave comprises 7 tones and the 8th serves as a repetition of the first. Together with two external shocks to fill up what we will call the "gaps" in the octave, we have before us 9 elements. Having stopped up the second gap in the spiral ascent of the octave, that is, "si-do", we get in reality what is an already closed cycle, and ipso facto, the ninth element being there to close the cycle, this completes the symbol as a whole. The isolated existence of the thing or phenomenon which is under consideration is a closed circle of the process of the changes of the life of the thing considered, which process is forever renewing itself and flows on without interruption. It is symbolized by the circle of the figure. The separate points of division of the circle of uninterrupted change symbolizes the successive fundamental steps of the process. The whole symbol in its entirety is "Do", is something according to law and which exists whole. It is a circle, a complete cycle, it is the "nought" of our decimal system of numbers, representing by its own outline a closed cycle. It has everything within itself for its own existence. It is isolated from what surrounds it. The sequence of the stages of the process must be bound by the sequence of the cycle of the remaining numbers from 1 to 9. Where are the places of these figures to be? I have already mentioned that the 9th step being forthcoming to fill up the gap "si-do", it thus completes the circle, that is, it closes the circle which begins anew at that point. The top of the ternary closes the binary, its basis, receiving from itself, as a principle, the possibility of manifestation and incarnation in a multitude of forms; in the same way as the apex of the triangle multiplies eternally in the line of its base, and therefore every beginning and completion of the cycle is formed at the apex of the triangle, is synthesized at one point in which beginning and end meet, the circle closes, sounding in the uninterrupted flow of the cycle like the two "do's" in the octave. But the ninth step closes and again starts the cycle. Therefore in the top point of the triangle corresponding to "Do" will be the figure 9. All the remaining points will be numbered in sequence from 1 to 8. We will get:

Figure 8. The Enneagram Numbers

Let us now proceed to examine the complex figure enclosed in the circle and try to find the law of its structure. To that end I will remind you that the laws of unity are reflected in all phenomena. The so-called decimal system of calculation in vogue with us, is in its profoundest principles only very very imperfectly known to us in the theory of numbers that is built upon the basis of these eternal laws. Taking the unit, just as we have done here, as the symbol of the existence of the whole octave in one note, we must, in order to secure a passage from one tone of this octave to another, split up the unit into 7 parts. I make the reserve that what we understand by the unit shall here in its symbolical meaning correspond to the "nought" of the symbol under consideration. Now, in order to get say the distance of any one of the tones from the primary tone, we must take the corresponding number of seventh parts of the unit, that is, 2/7, 3/7, and so forth. Let us work all these parts out as decimal fractions which are based on the same laws as the whole of our decimal system of reckoning. There is this series:

0 equals 1.

1 / 7 = 0.142857

2 / 7 = 0.285714

3 / 7 = 0.428571

4 / 7 = 0.571428

5 / 7 = 0.714285

6 / 7 = 0.857142

7 / 7 = 0.999999

In contemplating this series you will at once notice that the period of these functions, except in the case of the last one, is made up of the same numbers running in a definite sequence, and by knowing the initial number of the period you can immediately re-establish the whole period in full. But if we dispose them in a circle in their natural sequence, after linking them up by a closed broken line, we shall get a certain figure. If all 9 numbers are arranged in a circle in their natural sequence as we did in the symbol under consideration, the closed line of the period of the denominator 7 gives us the interior figure or the symbol. According to this figure, by merely taking the direction of its structure as a guide, we shall establish the period in full in every separate instance. The unit "Do", or seven-sevenths, is symbolized by the point 9. The numbers 3 and 6 also enter into the period, which in conjunction with 9 will give the independent triangle - the free ternary of the symbol. I may remark briefly that if we use the theosophical addition, that is, by taking the sum of the ciphers of the period, we shall get 9 (1+4+2+8+5+7=27 and 2+7=9), that is, a whole unit in correspondence with our symbol, that is, in each note we shall again find a whole octave, subject within itself to the same laws as the primary octave, of which the tone under consideration is a part. If you will now recall what was said by me about the sequence of the stages of the process of the formation of the octave and will connect it up with the manner in which we constructed the figure of the symbol with the aid of the numbers of the period, you will mark the places of the tones on the symbol and get a sketch of the octave in this form:

Figure 9. The Enneagram Tones

That is how the matter stands as regards the outside geometrical structure of the symbol. Its form is pre-determined by the fact that it serves to express the law of the 7 whereon the octave is built. It is septimal relative to the tone "Do", that is, in a certain sense the tone "Do" may be considered neutralizing. When it was a question here of applying the laws of the octaves to the structure of the chemical elements, every substance derived on the basis of laws was symbolically termed a "hydrogen" of various gradations of density and other qualities which went to define it as a substance. By the law of the 3, it was built up from active, passive, and neutral substances correspondingly termed "oxygen", "carbon", and "azote" (or "nitrogen"), that is, the following structure was obtained:

C+O+ N > H

In the same sense as the tone "Do", though being a resultant, is at the same time a neutralizer of the octave, so, too, the "hydrogen" was at the time mentioned as simultaneously being a resultant and a neutralizer, that is, it was related to "nitrogen". The substance of "hydrogen" is the synthesis, the result of the reciprocal action of three substances: of the active "oxygen", the passive "carbon", combined with the neutral "nitrogen", that is to say, it is built up according to the law of the trinity. In the same way, too, the tone "Do", the apex, marked by the number 9, is in its completion constructed on the same law and, constituting the triangle 9, 3, 6, binding into one the three dots which do not enter into the period (as we will name the complex geometrical figure within the symbol) ties into one the law of the 7 and of the 3. The period does not include two of the numbers just mentioned. Two of them correspond to the gaps in the gamut, the third is, as it were, superfluous and at the same time takes the place of the fundamental tone not comprised in the period. But if you will remember that each thing or phenomenon which according to the law of relativity is able to cooperate with a phenomenon homogeneous and "having equal rights" with it, sounds like "Do" in its own corresponding octave, therein you will perceive this fact symbolized, that "Do" can go out of its own circle and, according to law enter into relations with another circle, that is to say in another cycle play the role, which in the cycle under notice is played by the shocks filling up the gaps in the octave. That is why here, too, having in itself this possibility, it is bound up by the symbol of triunity with those places where there are shocks of outside principles, where the octave is for joining purposes permeated with what is only outside it. The "law of the 3" steps, as it were, outside the law of the 7, the triangle glistens through the period and these two figures by their combination give the internal structure of the octave and its tones, of its atomistic structure, as it were. You will be within your right in asking the question why one of the gaps - 3 - is not in its own place between mi and fa, and the other - 6 - has got between "sol" and "la", whereas its place is between "si" and "Do". I shall endeavor to give you what explanation is for the nonce possible of this phenomenon. If the condition were observed that the second gap should be in its own place, we should get this circle:

Figure 10. The Enneagram Gaps

If we now group the 9 elements of the closed circle that we have before us in the following way

Figure 11. The Three Ternaries

we shall get a symmetrical structure of the three ternaries, that is, ternary of the ternaries, 3 equals triunity. The laws of symmetry are little studied with us in the west, but even so you probably know what is called symmetrical asymmetry, that is, symmetry, based on laws, appearing as asymmetry. And the symbol that we are now examining, representing as it does the figure of a perfect synthesis of the laws of the octaves, while being symmetrical in form, also includes that asymmetry of which we are now speaking (see drawing). But that is not all: by carrying the gap to what seems to be not its own place, it thereby shows to him who knows how to read it, what shock is needed, and when and wherein, to carry from "si" to "Do", which in its turn explains the circumstance already mentioned in the lecture on the mechanics of the world structure, namely, that the transition from "la" to "si" is, from the point, of view of the difference in the number of vibrations of the tones, of greater length than all the other transitions in the octave. Almost as definite too are the indications in the symbol of the shock needed at the gap "mi"-"fa", which I am not able to talk about in detail at present. All I can do is to remind you once more of the role of these shocks in the processes going on in man and the universe.

When we were examining the application of the law of the octaves to the cosmos, it took the following form as far as it concerns the step "Sun - Earth":

Figure 12. The Cosmic Octave

It was also mentioned that the transition "Do" to "si", the filling up of the gap, proceeds inside the Sun's organism: when it was a question of the Absolute, it was pointed out plainly that this transition is an internal act of will. Transition from "fa" to "mi" is performed mechanically by the aid, as it were, of a special machine enabling the "fa" which enters it, by a series of processes and without altering its tonality, to acquire the properties of the "sol" standing above it, and together with it the ability to pass on by itself (in the shape as it were of a store of internal energy) for conversion into the following tone - in this instance "mi". The thing is absolutely the same throughout all the processes. If we will proceed to examine the processes off the nourishing and working of the human organism, we shall find in them - as we have more than once mentioned here, these same gaps and shocks. Let us reconstruct the scheme of the working of the physical body of man in the way that we have already done here. Three kinds of food are taken in by man. Each of them is the beginning of its own octave (1st, 2nd, and 3rd "Do").

The first octave, that of the food of the bottom storey we have examined fully enough to explain the nature of the gap. When in its process of changes it reaches the stage corresponding to the note "mi" (3rd "mi") it approaches the gap which by itself it is unable to cross. The 2nd "Do", air, which comes to its aid, and which we take in by breathing, passing over into the 2nd "re" and blending with the 3rd "mi", is transferred by us into the 3rd "fa". The food we take in by eating and drinking is introduced into our body in the overwhelming majority of cases in greater quantities than are needed. It cannot be fully assimilated, that is, the chemical process by which the substance necessary for the maintenance of life is produced in our body, requires the component parts to be in strict correspondence. To elucidate this let us take any example from chemistry. Kitchen salt is the union, in certain circumstances, of the mineral natron with chloral gas (NaCl). If we take 23 lbs of natron and 35.5 lbs of chlorine, we shall get exactly 58.5 lbs of household salt. If with the same quantity of chlorine we took 3O lbs of natron, instead of 23, in that case 7 lbs of natron would not amalgamate. In exactly the same way, if we took 4O lbs of chlorine to 23 lbs of natron, 4.5 lbs of the former would remain free. In both cases there would be 58.5 lbs common salt. In other words natron and chlorine combine in constant conditions as to weight in the proportions of 23:35.5. All chemical elements possess this property of proportional constancy, and that property of theirs gave the basis on which their atomic weights were deduced. Similarly, for the production in the organism of a substance which is characterized by definite properties, it is necessary to bring the original substance into strictly definite correspondence with another, with which it enters into reciprocal reaction. This bears on the qualitative as well as the quantitative side of the phenomenon. The food which is taken into man's organism is also converted from the substance produced at the stage of the 3rd "mi" into the substance at the stage of the 3rd "fa" with the aid of a chemical admixture from "Do" of the air. This means that the process of breathing enters into reaction with the process of assimilation and digestion of food. The final substance of this process will be the substance at the stage of the 3rd "si", which in order to pass into the completed "Do" requires a fresh shock. As the scheme we have submitted shows that 3 octaves participate in this process, their influence affects the final result by defining its quality, that is, in the graduated transition from one stage to another, there are everywhere exact determinants. The substance of stage 3 must set out to receive a result known beforehand which defines the requisite quantity and quality of the substance we are considering. This is the reason why any breathing exercises without an accurate knowledge of all the laws will not give the result that is required. But let us even suppose that a man can regulate two of the component parts of the process, two of its determinants - food and breathing. Here again this will not be sufficient. It is in such cases necessary to know and to be able to regulate the 3rd determinant - the food of the top storey - the first octave, that which we have here agreed to call "impressions". Only with a full and harmonious correspondence of all three kinds of food, by strengthening or weakening the different parts of the process, do we get the requisite result. That is why all sorts of breathing and other exercises that are not in strict correspondence with other processes connected with them may inflict irremediable injury on the one doing them. The shock which comes from outside, by the substantial nature of the air in the mechanical process of breathing, and which fills up the gap "mi"-"fa" is similar to the shock that bridges this gap in any other octave. And the very process of the development of the octave within the human body, the transmutation of the 3rd "Do" of food over a series of stages into the "Do" of the next octave, is similar to the same processes in other places.

Figure 13. The Enneagram of Foods

When we constructed the first cosmic octave of our already existing world ray (passing through the sun and earth), its separate tones were disposed as follows:

Figure 14. The Cosmic Octave

Then this original octave according to the law of the triunity was split up into three subordinate octaves, and this same ray was constructed somewhat differently, namely:

Figure 15. Three-Storied Cosmic Octave

In this way the cosmos resembled by the three-storied nature of its structure the same three-storied structure of man. Where, in the cosmic octaves of the second order, the gap "fa"-"mi" is placed, under the action of all influences that here cone together, a process occurs similar to the process of the passage of food in the human organism - by the conversion of the "Do" of one octave into the "Do" of the next octave. That is why at these places are outlined the "machines", in a manner of speaking, that are there, similar to the human body. Very roughly the process of transition "fa"-"mi" may be represented thus: the cosmic "fa" goes into that "machine" similar to the food of the bottom storey and begins the cycle of changes. Consequently, at its beginning it sounds in the machine as "Do", the 3rd "Do". The substance of the note "sol" of the cosmic octave, which assists the tone "mi" (3rd) within the machine to pass into the tone "fa" (3rd), filling up the interval between them and sounding as "Do" (2nd), serves as the substance entering into the middle storey similarly to the air when breathing, At its own place the cycle of the tone of cosmic "la", which enters the top storey of the machine as first "Do", joins up with the, so to say doubled cycle which we have now got. In the final sum total of the process "fa", which has come into the machine as 3rd "Do" is converted into the 3rd "Do" an Octave higher, and leaves the machine as a tone which is able to pass into the adjacent tone. Before this I said that "fa", without changing its tonality, acquires the property of "sol", and also its ability to pass into the next tone, that is, into "mi" in the case now considered, What I meant is this: as we see, the machine's food are the cosmic tones "la, sol, fa". In the order of their sequence, by the law of the triunity "la" will be the active, "sol" the neutralizing, and "fa" the passive principle, The active, reacting (linking up with the aid of the neutralizing) with the passive gives some result. It has been pointed out at another time that if the number defining the qualities of the active is "1N", then the same figure for the passive "4N" ,and for the result "2N", that is, it may be outlined symbolically thus:

Figure 16. Magnitudes Triangle

If, in the places of these magnitudes we substitute the tones that feed the machine we shall get this symbol:

Figure 17. Tones Triangle

which at the same time shows that the substance "fa" by blending with the substance "la" gives in the result substance "sol". But as this process occurs within the octave, which as it were unfolds itself inside the tone "fa" in the manner indicated for "do", when examining the symbol, it may be stated that "fa" without changing its tonality, acquires the properties of "sol".

We have in a way been diverted from our original aim of examining the symbol. As a matter of fact, those of us who know how to listen have approached nearer to an understanding of it. As a perfect synthesis it contains in itself all elements of knowledge of the law expressed by it, and out of it may be deduced and developed in detail in the most accurate fashion all that we have just been saying. By all I have said today, I have not exhausted even the smallest part of what can be said on the subject. In the future we shall once more return to it and dwell on it in greater detail. I by no means think that I have been able to explain anything, as I did not pursue that aim. My task was to give my listeners a sensation of the taste of the understanding with which one must approach the search after the laws of truth. Once more I repeat: in order to understand in these matters, constant efforts are necessary.

Before closing the lecture, I wish to say a few words on what is termed "Initiation". Initiation is customarily regarded as some act whereby one man "The Knower" transfers to another man "The non-knower" knowledge and powers hitherto not peculiar to him and without any trouble on his part; assigning it as thing which becomes his inalienable possession. But from all that has been said by me today, you will already be able to understand, that there is no such transfer and cannot be. There is only self-initiation, which is got by constant and stubborn work, by constant efforts. No one conceals the knowledge of truth. It simply cannot be transferred, just as the finest mathematical ideas cannot be transferred to a man unacquainted with mathematics. And in questions relating to the transfer of a knowledge of the Truth, matters are more complicated than in the example quoted. You have been able to convince yourself of this today. It is possible to teach a man mathematics, but an understanding of the truth he conquers for himself. And woe to man, if under the influence of the poison of what seems Truth, and striving after "practical" results without possessing a perfect understanding and knowledge of what must be done and how to do it, he starts experimenting on himself, often doing himself irreparable harm. Harmony is destroyed and it is incomparably better to do nothing at all than to do without possessing the knowledge.

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