In search of the miraculous

dimensions. Beyond this period there is either nothing or the same period may repeat itself on another scale.

'As I have already said, the system of cosmoses, the exposition of which we have just heard, strikes me above all by the fact that it fully corresponds to the 'period of dimension' which is the basis of my New Model of the Universe, only this system of cosmoses goes still further and explains many things which were not clear in my model of the universe.

'Thus, if we take the Microcosmos, that is, the 'atom' or 'microbe,' as G. has defined it, then the Tritocosmos for it will be four-dimensional space, the Mesocosmos will be five-dimensional space, and the Deuterocosmos six- dimensional space.

'This means that all the possibilities of the 'atom' or 'microbe' are realized within the limits of the solar system.

'If we take man as the Tritocosmos, then, for him, the Mesocosmos will be four- dimensional space, the Deuterocosmos five-dimensional space, and the Macrocosmos six-dimensional space. This means that all the possibilities of the Tritocosmos are realized in the Macrocosmos.

'Therefore parallel with this, all the possibilities of the Mesocosmos are realized in the Ayocosmos and all the possibilities of the Deuterocosmos, or the sun, are realized in the Protocosmos or the Absolute.

'As every cosmos has a real physical existence, every cosmos therefore is three- dimensional for itself or in itself. In relation to a lower cosmos it is four-dimensional, in relation to a higher cosmos it is a point. To put it differently, it is, itself, three-dimensional, but the fourth dimension lies for it in the cosmos above and the cosmos below. This last point is perhaps the most paradoxical, but nevertheless it is exactly as it should be. For a three- dimensional body, such as is a cosmos, the fourth dimension lies as much in the realm of very large magnitudes as in the realm of very small magnitudes; as much in the realm of what is actually infinity as in the realm of what is actually zero.

'Further we must understand that the three-dimensionality of even one and the same body can be different. Only a six-dimensional body can be completely real. A five- dimensional body is only an incomplete view of a six- dimensional body, a four- dimensional body is an incomplete view of a five-dimensional body, a three- dimensional body is an incomplete view of a four-dimensional body. And of course, a plane is an incomplete view of a three- dimensional body, that is to say, a view of one side of it. In the same way a line is an incomplete view of a plane and a point is an incomplete view of a line.

'Moreover, though we do not know how, a six-dimensional body can see itself as three-dimensional. Somebody looking at it from outside may possibly also see it as a three-dimensional body, but in a completely different kind of three-dimensionality. For instance, we represent the earth to ourselves as three-dimensional. This three- dimensionality is only imaginary. As a three-dimensional body the earth is something quite different for itself from what it is for us. Our view of it is incomplete, we see it as a section of a section of a section of its complete being. The 'earthly globe' is an imaginary body. It is the section of a section of a section of the six-dimensional earth. But this six-dimensional earth can also be three-dimensional for itself, only we do not know and we can have no conception of the form in which the earth sees itself.

'The possibilities of the earth are actualized in the Ayocosmos; this means that in the Ayocosmos the earth is a six-dimensional body. And actually we can to a certain extent see in what way the form of the earth must change. In the Deuterocosmos, that is, in relation to the sun, the earth is no longer a point (taking a point as a scale reduction of a three-dimensional body), but a line which we trace as the path of the earth around the sun. If we take the sun in the Macrocosmos, that is, if we visualize the line of the sun's motion, then the line of the motion of the earth will become a spiral encircling the line of the sun's motion. If we conceive a lateral motion of this spiral, then this motion will construct a figure which we cannot imagine because we do not know the nature of its motion, but which, nevertheless, will be the six- dimensional figure of the earth, which the earth itself can see as a three- dimensional figure. It is necessary to establish and to understand this because otherwise the idea of the three- dimensionality of the cosmoses will become linked with

our idea of three-dimensional bodies. The three-dimensionality even of one and the same body can be different.

'And this last point seems to me to be connected with what G. calls the 'principle of relativity.' His principle of relativity has nothing in common with the principle of relativity in mechanics or with Einstein's principle of relativity. It is the same again as in the New Model of the Universe; it is the principle of the relativity of existence.'

At this point I ended my survey of the system of cosmoses from the point of view of the theory of many dimensions.

'There is a great deal of material in what you have just said,' said G., 'but this material must be elaborated. If you can find out how to elaborate the material that you have now, you will understand a great deal that has not occurred to you till now. For example, take note that time is different in different cosmoses. And it can be calculated exactly, that is, it is possible to establish exactly how time in one cosmos is related to the time of another cosmos.

'I will add only one thing more:

'Time is breath—try to understand this.'

He said nothing further.

Later on one of G.'s Moscow pupils added to this that, speaking with them once of cosmoses and of different time in different cosmoses, G. had said that the sleep and waking of living beings and plants, that is, twenty-four hours or a day and night, constitute the 'breath of organic life.'

G.'s lecture on cosmoses and the talk following it greatly aroused my curiosity. This was a direct transition from the 'three-dimensional universe' with which we had begun, to the problems which I had elaborated in the New Model of the Universe, that is, to the problems of space and time and higher dimensions, on which I had been working for several years.

For over a year G. added nothing to what he had said about cosmoses.

Several of us tried to approach these problems from many different sides and, although all of us felt a great deal of potential energy in the idea of cosmoses, for a long time we got no results. We were especially confused by the 'Microcosmos.'

'If it were possible to take man as the Microcosmos and the Tritocosmos as the human race, or rather as organic life, it would be much easier to establish the relation of man to other cosmoses,' one of us, Z., said in this connection, who with me had attempted to understand and to develop further the idea of the cosmoses.

But on the one or two occasions that we began to speak to G. about it he persisted in his definitions.

I remember once when he was leaving Petersburg, it was possibly even his final departure in 1917, one of us asked him at the station something relating to cosmoses.

'Try to understand what the Microcosmos means,' answered G. 'If you succeed in understanding this, then all the rest about which you ask now will become clear to you.'

I remember that when we talked about it later the question was quite easy to solve when we took the 'Microcosmos' as man.

It was certainly conditional, but nevertheless it was in complete accord with the whole system which studied the world and man. Every individual living being—a dog, a cat, a tree—could be taken as a Microcosmos; the combination of all living beings constituted the Tritocosmos or organic life on earth. These definitions seemed to me the only ones that were logically possible. And I could not understand why G. objected to them.

At any rate, some time later when I returned again to the problem of cosmoses I decided to take man as the Microcosmos, and to take the Tritocosmos as organic life on earth.

With such a construction a great number of things began to be much more connected. And once, looking through a manuscript of 'Glimpses of Truth' given me by G., that is, the beginning of the story that was read at the Moscow group the first time I went there, I found in it the expressions 'Macrocosmos' and 'Microcosmos'; moreover 'Microcosmos' meant man.

Now you have some idea of the laws governing the life of the Macrocosmos and have returned to the Earth. Recall to yourself: 'As above, so below.' I think that already, without any further explanation, you will not dispute the statement that the life of individual man—the Microcosmos—is governed by the same laws.

—'Glimpses of Truth'

This still further strengthened us in our decision to understand 'Microcosmos' as applying to man. Later it became clear to us why G. wished to make us apply the concept 'Microcosmos' to small magnitudes as compared