I did not want to argue with Volinsky. I had read Wundt. And of course what Wundt had written was not at all what I had said to Volinsky. Wundt had come close to this idea, but others had come just as close and had afterwards gone off in a different direction. He had not seen the magnitude of the idea which was hidden behind his thoughts about different forms of perception. And not having seen the magnitude of the idea he of course could not see the central position which the idea of the absence of consciousness and the idea of the possibility of the voluntary creation of this consciousness ought to occupy in our thinking. Only it seemed strange to me that Volinsky could not see this even when I pointed it out to him.
I subsequently became convinced that this idea was hidden by an impenetrable veil for many otherwise very intelligent people—and still later on I saw why this was so.
The next time G. came from Moscow he found us immersed in experiments in self- remembering and in discussions about these experiments. But at his first lecture he spoke of something else.
"In right knowledge the study of man must proceed on parallel lines with the study of the world, and the study of the world must run parallel with the study of man. Laws are everywhere the same, in the world as well as in man. Having mastered the principles of any one law we must look for its manifestation in the world and in man simultaneously. Moreover, some laws are more easily observed in the world, others are more easily observed in man. Therefore in certain cases it is better to begin with the world and then to pass on to man, and in other cases it is better to begin with man and then to pass on to the world.
"This parallel study of the world and of man shows the student the fundamental unity of everything and helps him to find analogies in phenomena of different orders.
"The number of fundamental laws which govern all processes both in the world and in man is very small. Different numerical combinations of a few elementary forces create all the seeming variety of phenomena.
"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.