In search of the miraculous

by Ouspensky

  "In order to understand the mechanics of the universe it is necessary to resolve complex phenomena into these elementary forces.

  "The first fundamental law of the universe is the law of three forces, or three principles, or, as it is often called, the law of three. According to this law every action, every phenomenon in all worlds without exception, is the result of a simultaneous action of three forces—the positive, the negative, and the neutralizing. Of this we have already spoken, and in future we will return to this law with every new line of study.

  "The next fundamental law of the universe is the law of seven or the law of octaves.

  "In order to understand the meaning of this law it is necessary to regard the universe as consisting of vibrations. These vibrations proceed in all kinds, aspects, and densities of the matter which constitutes the universe, from the finest to the coarsest; they issue from various sources and proceed in various directions, crossing one another, colliding, strengthening, weakening, arresting one another, and so on.

  "In this connection according to the usual views accepted in the West, vibrations are continuous. This means that vibrations are usually regarded as proceeding uninterruptedly, ascending or descending so long as there continues to act the force of the original impulse which caused the vibration and which overcomes the resistance of the medium in which the vibrations proceed. When the force of the impulse becomes exhausted and the resistance of the medium gains the upper hand the vibrations naturally die down and stop. But until this moment is reached, that is, until the beginning of the natural weakening, the vibrations develop uniformly and gradually, and, in the absence of resistance, can even be endless. So that one of the fundamental propositions of our physics is the continuity of vibrations, although this has never been precisely formulated because it has never been opposed. In certain of the newest theories this proposition is beginning to be shaken. Nevertheless physics is still very far from a correct view on the nature of vibrations, or what corresponds to our conception of vibrations, in the real world.

  "In this instance the view of ancient knowledge is opposed to that of contemporary science because at the base of the understanding of vibrations ancient knowledge places the principle of the discontinuity of vibrations.

  "The principle of the discontinuity of vibration means the definite and necessary characteristic of all vibrations in nature, whether ascending or descending, to develop not uniformly but with periodical accelerations and retardations. This principle can be formulated still more precisely if we say that the force of the original impulse in vibrations does not act uniformly but, as it were, becomes alternately stronger and weaker. The force of the impulse acts without changing its nature and vibrations develop in a regular way only for a certain time which is determined by the nature of the impulse, the medium, the conditions, and so forth. But at a certain moment a kind of change takes place in it and the vibrations, so to speak, cease to obey it and for a short time they slow down and to a certain extent change their nature or direction; for example, ascending vibrations at a certain moment begin to ascend more slowly, and descending vibrations begin to descend more slowly. After this temporary retardation, both in ascending and descending, the vibrations again enter the former channel and for a certain time ascend or descend uniformly up to a certain moment when a check in their development again takes place. In this connection it is significant that the periods of uniform action of the momentum are not equal and that the moments of retardation of the vibrations are not symmetrical. One period is shorter, the other is longer.

  "In order to determine these moments of retardation, or rather, the checks in the ascent and descent of vibrations, the lines of development of vibrations are divided into periods corresponding to the doubling or the halving of the number of vibrations in a given space of time.

  "Let us imagine a line of increasing vibrations. Let us take them at the moment when they are vibrating at the rate of one thousand a second. After a certain time the number of vibrations is doubled, that is, reaches two thousand.

  1000 2000

  fig. 7

  "It has been found and established that in this interval of vibrations, between the given number of vibrations and a number twice as large, there are two places where a retardation in the increase of vibrations takes place. One is near the beginning but not at the beginning itself. The other occurs almost at the end.

  "Approximately:

  1000 2000 fig. 8

  "The laws which govern the retardation or the deflection of vibrations from their primary direction were known to ancient science. These laws were duly incorporated into a particular formula or diagram which has been preserved up to our times. In this formula the period in which vibrations are doubled was divided into eight unequal steps corresponding to the rate of increase in the vibrations. The eighth step repeats the first step with double the number of vibrations. This period of the doubling of the vibrations, or the line of the development of vibrations, between a given number of vibrations and double that number, is called an octave, that is to say, composed of eight.

  "The principle of dividing into eight unequal parts the period, in which the vibrations are doubled, is based upon the observation of the non-uniform increase of vibrations in the entire octave, and separate 'steps' of the octave show acceleration and retardation at different moments of its development.

  "In the guise of this formula ideas of the octave have been handed down from teacher to pupil, from one school to another. In very remote times one of these schools found that it was possible to apply this formula to music. In this way was obtained the seven-tone musical scale which was known in the most distant antiquity, then forgotten, and then discovered or 'found' again.

  "The seven-tone scale is the formula of a cosmic law which was worked out by ancient schools and applied to music. At the same time, how-

  ever, if we study the manifestations of the law of octaves in vibrations of other kinds we shall see that the laws are everywhere the same, and that light, heat, chemical, magnetic, and other vibrations are subject to the same laws as sound vibrations. For instance, the light scale is known to physics; in chemistry the periodic system of the elements is without doubt closely connected with the principle of octaves although this connection is still not fully clear to science.

  "A study of the structure of the seven-tone musical scale gives a very good foundation for understanding the cosmic law of octaves.

  "Let us again take the ascending octave, that is, the octave in which the frequency of vibrations increases. Let us suppose that this octave begins with one thousand vibrations a second. Let us designate these thousand vibrations by the note do. Vibrations are growing, that is, their frequency is increasing. At the point where they reach two thousand vibrations a second there will be a second do, that is, the do of the next octave.

  do do

  fig. 9

  "The period between one do and the next, that is, an octave, is divided into seven unequal parts because the frequency of vibrations does not increase uniformly.

  , do, re, mi, fa, sol, la, si , do, fig. 10

  "The ratio of the pitch of the notes, or of the frequency of vibrations will be as follows:

  "If we take do as 1 then re will be 9/8, mi 5/4, fa 4/3, sol 3/2, la 3/2, si 15/8, and do 2.

  1 9/8 5/4 4/3 3/2 5/3 15/8 2

  do re mi fa sol la si do fig. 11

  "The differences in the acceleration or increase in the notes or the difference in tone will be as follows:

  between do and re 9/8 : 1 = 9/8

  between re and mi 5/4 : 9/8 = 10/9

  between mi and fa 4/3 : 5/4 = 16/15 increase retarded

  between fa and sol 3/2 : 4/3 = 9/8

  between sol and la 5/3 : 3/2 = 10/9

  between la and si 15/8 : 5/3 == 9/8

  between si and do 2 : 15/8 = 16/15 increase again retarded

  "The differences in the notes or the differences in the pitch of the notes are called intervals. We see that there
are three kinds of intervals in the octave: 9/8, 10/9, and 16/15, which in whole numbers correspond to 405, 400, and 384. The smallest interval 16/15 occurs between mi and fa and between si and do. These are precisely the places of retardation in the octave.

  "In relation to the musical (seven-tone) scale it is generally considered (theoretically) that there are two semitones between each two notes, with the exception of the intervals mi-fa and si-do, which have only one semitone and in which one semitone is regarded as being left out.

  "In this manner twenty notes are obtained, eight of which are funda­mental: do, re, mi, fa, sol, la, si, do and twelve intermediate: two between each of the following two notes:

  do-re re-mi fa-sol sol-la la-si

  and one between each of the following two notes:

  mi-fa si-do

  "But in practice, that is, in music, instead of twelve intermediate semitones only five are taken, that is one semitone between:

  do-re re-mi fa-sol sol-la la-si

  "Between mi and fa and between si and do the semitone is not taken at all.

  "In this way the structure of the musical seven-tone scale gives a scheme of the cosmic law of 'intervals,' or absent semitones. In this respect when octaves are spoken of in a 'cosmic' or a 'mechanical' sense, only those intervals between mi-fa and si-do are called 'intervals'

  "If we grasp its full meaning the law of octaves gives us an entirely new explanation of the whole of life, of the progress and development of phe-

  nomena on all planes of the universe observed by us. This law explains why there are no straight lines in nature and also why we can neither think nor do, why everything with us is thought, why everything happens with us and happens usually in a way opposed to what we want or expect. All this is the clear and direct effect of the 'intervals,' or retardations in the development of vibrations.

  "What precisely does happen at the moment of the retardation of vibrations? A deviation from the original direction takes place. The octave begins in the direction shown by the arrow:

  "But a deviation takes place between mi and fa; the line begun at do changes its direction

  and through fa, sol, la, and si it descends at an angle to its original direction, shown by the first three notes. Between si and do the second 'interval' occurs—a fresh deviation, a further change of direction.

  Fig. 14

  "The next octave gives an even more marked deviation, the one following that a deviation that is more marked still, so that the line of octaves may at last turn completely round and proceed in a direction opposite to the original direction.

  Fig. i

  "In developing further, the line of octaves or the line of development of vibrations may return to the original direction, in other words, make a complete circle.

  Fig. 16

  "This law shows why straight lines never occur in our activities, why, having begun to do one thing, we in fact constantly do something entirely different, often the opposite of the first, although we do not notice this and continue to think that we are doing the same thing that we began to do.

  "All this and many other things can only be explained with the help of the law of octaves together with an understanding of the role and significance of 'intervals' which cause the line of the development of force constantly to change, to go in a broken line, to turn round, to become its 'own opposite' and so on.

  "Such a course of things, that is, a change of direction, we can observe in everything. After a certain period of energetic activity or strong emotion or a right understanding a reaction comes, work becomes tedious and tiring; moments of fatigue and indifference enter into feeling; instead of right thinking a search for compromises begins; suppression, evasion of difficult problems. But the line continues to develop though now not in the same direction as at the beginning. Work becomes mechanical, feeling becomes weaker and weaker, descends to the level of the common events of the day; thought becomes dogmatic, literal. Everything proceeds in this way for a certain time, then again there is reaction, again a stop, again a deviation. The development of the force may continue but the work which was begun with great zeal and enthusiasm has become an obligatory and useless formality; a number of entirely foreign elements have entered into feeling—considering, vexation, irritation, hostility;

  thought goes round in a circle, repeating what was known before, and the way out which had been found becomes more and more lost.

  "The same thing happens in all spheres of human activity. In literature, science, art, philosophy, religion, in individual and above all in social and political life, we can observe how the line of the development of forces deviates from its original direction and goes, after a certain time, in a diametrically opposite direction, still preserving its former name. A study of history from this point of view shows the most astonishing facts which mechanical humanity is far from desiring to notice. Perhaps the most interesting examples of such change of direction in the line of the development of forces can be found in the history of religion, particularly in the history of Christianity if it is studied dispassionately. Think how many turns the line of development of forces must have taken to come from the Gospel preaching of love to the Inquisition; or to go from the ascetics of the early centuries studying esoteric Christianity to the scholastics who calculated how many angels could be placed on the point of a needle.

  "The law of octaves explains many phenomena in our lives which are incomprehensible.

  "First is the principle of the deviation of forces.

  "Second is the fact that nothing in the world stays in the same place, or remains what it was, everything moves, everything is going somewhere,

  is changing, and inevitably either develops or goes down, weakens or degenerates, that is to say, it moves along either an ascending or a descending line of octaves.

  "And third, that in the actual development itself of both ascending and descending octaves, fluctuations, rises and falls are constantly taking place.

  "We have spoken so far chiefly about the discontinuity of vibrations and about the deviation of forces. We must now clearly grasp two other principles: the inevitability of either ascent or descent in every line of development of forces, and also the periodic fluctuations, that is, rises and falls, in every line whether ascending or descending.

  "Nothing can develop by staying on one level. Ascent or descent is the inevitable cosmic condition of any action. We neither understand nor see what is going on around and within us, either because we do not allow for the inevitability of descent when there is no ascent, or because we take descent to be ascent. These are two of the fundamental causes of our self-deception. We do not see the first one because we continually think that things can remain for a long time at the same level; and we do not see the second because ascents where we see them are in fact impossible, as impossible as it is to increase consciousness by mechanical means.

  "Having learned to distinguish ascending and descending octaves in life we must learn to distinguish ascent and descent within the octaves themselves. Whatever sphere of our life we take we can see that nothing can ever remain level and constant; everywhere and in everything proceeds the swinging of the pendulum, everywhere and in everything the waves rise and fall. Our energy in one or another direction which suddenly increases and afterwards just as suddenly weakens; our moods which 'become better' or 'become worse' without any visible reason; our feelings, our desires, our intentions, our decisions—all from time to time pass through periods of ascent or descent, become stronger or weaker.

  "And there are perhaps a hundred pendulums moving here and there in man. These ascents and descents, these wave-like fluctuations of moods, thought, feelings, energy, determination, are periods of the development of forces between 'intervals' in the octaves as well as the 'intervals' themselves.

  "Upon the law of octaves in its three principal manifestations depend many phenomena both of a psychic nature as well as those immediately connected with our life. Upon the law of octaves depends
the imperfection and the incompleteness of our knowledge in all spheres without exception, chiefly because we always begin in one direction and afterwards without noticing it proceed in another.

  "As has been said already, .the law of octaves in all its manifestations was known to ancient knowledge.

  "Even our division of time, that is, the days of the week into work days and Sundays, is connected with the same properties and inner conditions of our activity which depend upon the general law. The Biblical myth of the creation of the world in six days and of the seventh day in which God rested from his labors is also an expression of the law of octaves or an indication of it, though an incomplete one.

  "Observations based on an understanding of the law of octaves show that 'vibrations' may develop in different ways. In interrupted octaves they merely begin and fall, are drowned or swallowed up by other, stronger, vibrations which intersect them or which go in an opposite direction. In octaves which deviate from the original direction the vibrations change their nature and give results opposite to those which might have been expected at the beginning.

  "And it is only in octaves of a cosmic order, both descending and ascending, that vibrations develop in a consecutive and orderly way, following the same direction in which they started.

  "Further observations show that a right and consistent development of octaves, although rare, can be observed in all the occasions of life and in the activity of nature and even in human activity.

  "The right development of these octaves is based on what looks an accident. It sometimes happens that octaves going parallel to the given octave, intersecting or meeting it, in some way or another fill up its 'intervals' and make it possible for the vibrations of the given octave to develop in freedom and without checks. Observation of such rightly developing octaves establishes the fact that if at the necessary moment, that is, at the moment when the given octave passes through an 'interval,' there enters into it an 'additional shock' which corresponds in force and character, it will develop further without hindrance along the original direction, neither losing anything nor changing its nature.