In Search of the Miraculous

"It is difficult to explain at present," said G.; "you will understand this later."

"But do you really mean that the concept Microcosmos cannot be used in relation to

man?" asked one of the audience. "This creates a strange difference in terminology."

"Yes, yes," said G. "Man is the Tritocosmos. The Microcosmos is the atom or rather"—he paused as though looking for a word—"the microbe.

"But do not stop over this question. All that will be explained later."1

Then he again turned to me.

"See what you can say from your point of view, taking everything just as I said it."

"First of all we must examine what the ratio of zero to infinity means," I said. "If we understand this, we shall understand the relation of one

11 mention this here because later G. changed this.

cosmos to another. In the world accessible to our study we have a perfectly clear

example of the relation of zero to infinity. In geometry this is the relation of one unit of a certain number of dimensions to another unit of a greater number of dimensions.

The relation of a point to a line, of a line to a plane, of a plane to a solid, of a solid, that is, of a three-dimensional body to a four-dimensional body, and so on.

"If we adopt this point of view, we shall have to admit that the relation of one

cosmos to another is the relation of two bodies of different dimensions. If one cosmos

is three-dimensional then the next cosmos, that is, the one above it, must be fourdimensional, the next—five-dimensional, and so on. If we take the 'atom' or 'microbe,'

as you say, that is, the Microcosmos as a point, then relative to this point man will be

a line, that is, a figure of one dimension. The next cosmos, the earth, will be a plane

relative to man, that is, it will have two dimensions, as is actually the case for direct perception. The sun, the solar system, will be three-dimensional for the earth. The

starry world will be four-dimensional for the sun. 'All worlds' are five-dimensional,

and the Absolute or Protocosmos is six-dimensional.

"What personally interests me most in this system of cosmoses is that I see in them

the full 'period of dimensions,' of my New Model of the Universe. It is not merely a coincidence of details—it is absolutely identical. I do not know how it has come

about; I have never heard of seven cosmoses related to one another in the ratio of zero

to infinity. Nevertheless my 'period of dimensions' coincides with this absolutely

exactly.

"The 'period of dimensions' contains within itself seven dimensions:

The zero-dimension, the first, the second, and so on up to the sixth dimension. The

zero-dimension or the point is a limit. This means that we see something as a point, but we do not know what is concealed behind this point. It may actually be a point,

that is, a body having no dimensions and it may also be a whole world, but a world so

far removed from us or so small that it appears to us as a point. The movement of this

point in space will appear to us as a line. In the same way the point itself will see the space along which it moves as a line. The movement of the line in a direction

perpendicular to itself will be a plane and the line itself will see the space along which it moves in the shape of a plane.

"Up to now I have examined the line from the point of view of the point, and the

plane from the point of view of the line, but the point, the line, and the plane can also be taken from the point of view of a three-dimensional body. In this case the plane

will be the boundary of the body, or its side, or its section. The line will be the

boundary limiting the plane, or the section of the plane. The point will be the limit or

the section of the line.

"A three-dimensional body differs from the point, the line, and the plane by the fact that it has a real physical existence for our perception.

"The plane is in fact only a projection of a body, the line is a projection of a plane, and the point is a projection of a line.

"A 'body' has an independent physical existence, that is, it possesses a number of

different physical properties.

"But when we say a thing 'exists,' we mean by this existence in time. But there is

no time in three-dimensional space. Time lies outside the three-dimensional space.

Time, as we feel it, is the fourth dimension. Existence is for us existence in time.

Existence in time is movement or extension along the fourth dimension. If we take

existence as an extension along the fourth dimension, if we think of life as a fourdimensional body, then a three-dimensional body will be its section, its projection, or its limit.

"But existence in time does not embrace all the aspects of existence. Apart from

existing in time, everything that exists, exists also in eternity.

"Eternity is the infinite existence of every moment of time. If we conceive time as

a line, then this line will be crossed at every point by the lines of eternity. Every point of the line of time will be a line in eternity. The line of time will be a plane of eternity.