In search of the miraculous

with various laboratories at its service.

Passing further to the cosmos of small cells, which stand on the border or beyond the border of microscopic vision, I again saw an explanation of the inexplicable. For example, cases of almost instantaneous infection by epidemic and infectious diseases in general, particularly those where the causes responsible for the infection have not yet been found. If three seconds is the limit of life for a small cell of this kind, and is equal to the long life of man, then what would be the speed at which these cells mul­tiply when for them fifteen seconds would be equal to four centuries!

Further, passing to the world of molecules, I first of all came face to face with the fact that the brevity of the existence of a molecule is an almost unexpected idea. It is usually supposed that a molecule, although structurally very complicated, taken as the basic, so to speak, living interior of the bricks from which matter is built up, exists as long as the matter exists. We are obliged to part from this pleasant and soothing thought. The molecule, which is alive inside cannot be dead outside and in remaining alive it must, like everything living, be born, live, and die- The term of its life, equal to an electric spark or to one ten-thousandth part of a second, is too small for it to act directly on our imagination. Some comparison, some analogy, is necessary in order to understand what this means. The dying cells of our organism and their replacement by others bring us near to this idea. Dead matter, iron, copper, granite, must be renewed from. within more quickly than our organism. In reality it changes under our eyes. If you look at a stone, shut your eyes, and immediately open them again, it will now not be the stone which you saw; in it not a single one of the molecules which you saw the first time now remain. But even then you did not see the molecules themselves, but only their traces.

I came again to the New Model of the Universe. This explained also 'why we cannot see molecules,' about which I have written in Chapter

II of the New Model of the Universe.

Further in the last cosmos, that is, in the world of the electron, I felt myself from the very beginning in the world of six dimensions. The question arose for me as to whether the relation of dimensions could not be worked out. The electron as a three- dimensional body is too unsatisfactory. To begin with it exists for one three-hundred- millionth part of a second. This is a quantity far beyond the limits of our possible imagination. It is considered that an electron within an atom moves in its orbit with the speed of one divided by a fifteen-figure number. And since the whole life of an electron in seconds is equal to one divided by a nine-figure number, it follows that during its lifetime an electron makes a number of revolu­tions round its 'sun,' equal to a six-figure, or taking into account the coefficient, a seven-figure number.

If we take the earth in its revolution round the sun, then according to my table it makes in the course of its lifetime a number of revolutions round the sun equal to an eleven-figure number. It looks as though there was an enormous difference between a seven-figure and an eleven-figure number but if we compare with the electron not the earth, but Neptune, then the difference will be considerably less, namely the difference between a seven-figure and a nine-figure number, that is, two figures in all instead of four. And besides the speed of revolution of an electron within the atom is a very approximate quantity. It should be remembered that the difference in the periods of revolution of the planets round the sun in our system represents a three-figure number because Mercury revolves 460 times faster than Neptune.

The relation of the life of an electron to our perception appears thus. Our quickest visual perception is equal to 1/10, 000 second. The existence of an electron is equal to 1/30, 000 of 1/10, 000 second, that is, one three- hundred-millionth part of a second, and in that time it makes seven million revolutions round the proton. Consequently, if we were to see an electron as a flash in 1/10, 000 second, we should not see the electron in the strict sense of the word, but the trace of the electron, consisting of seven million revolutions multiplied by thirty thousand, that is, a spiral with a thirteen-figure number of rings, or, expressed in the language of the New Model of the Universe, thirty thousand recurrences of the electron in eternity.

Time, according to the table which I had obtained, undoubtedly went beyond four dimensions. And I was interested by the thought whether it was not possible to apply to this table the Minkovski formula V-1 ct, denoting time as the fourth 'world' co­ordinate. The 'world' of Minkovski in my opinion corresponded precisely to each of the cosmoses separately. I decided to begin with the 'world of electrons' and to take as t the duration of the life of an electron. This coincided with one of the propositions in the New Model of the Universe, that time is life. The result should show the distance (in kilometers) that light travels during the life of an electron.

In the next cosmos this should be the distance that light travels during the life of a molecule; in the next— during the life of a small cell; then during the life of a large cell; then during the life of a man; and so on. The results for all cosmoses should be obtained in lineal measurements, that is, they should be expressed in fractions of a kilometer or in kilometers. The multiplication of a number of kilometers by V-1, that is, by the square root of minus one, ought to show that here we are not dealing with lineal measurements and that the figure obtained is a measure

of time. The introduction of the square root of minus one into the formula, while it does not change the formula quantitatively, shows that the whole formula relates to another dimension.

In this way, in relation to the cosmos of electrons, the Minkovski formula takes the following form:

V-1. 300,000. 3.10^-1 that is, the square root of minus one, which has to be multiplied by the product of 300, 000, that is c, or the speed of light, 300, 000 kilometers per second, and 1/300, 000, 000 second, that is, the duration of the life of an electron. Multiplying 300, 000 by 1/300, 000, 000 will give 1/1000 kilometer, which is one meter. 'One meter' shows the distance which light traverses during the life of an electron, traveling at the speed of 300, 000 kilometers a second. The square root of minus one, which makes 'one meter' an imaginary quantity, shows that the lineal measurement of a meter in the case in question is a 'measure of time,' that is, of the fourth co-ordinate.

Passing to the 'world of the molecule,' we obtain the Minkovski formula in the following form:

V-1. 300,000. 1/10,000 One ten-thousandth part of a second, according to the table, is the duration of the life of a molecule. Multiplying 300, 000 kilometers by 1/10, 000 will give 30 kilometers. 'Time' in the world of molecules is obtained in the form of the formula V-1. 30. Thirty kilometers represents the distance which light travels during the life of a molecule, or in 1/10, 000 second.

Further, in the 'world of small cells' the Minkovski formula takes the following form:,

V-1/. 300, 000. 3 or V-1. 900, 000

that is, 900, 000 kilometers multiplied by the square root of minus one. 900, 000 kilometers represents the distance which light travels during the life of a small cell, that is in 3 seconds.

Continuing similar calculations for the further cosmoses, I obtained for 'large cells' an eleven- figure number, showing the distance which light travels in 24 hours; for the 'Microcosmos' a sixteen- figure number, showing the distance in kilometers which light travels in 80 years; for the 'Tritocosmos' a twenty- figure number; for the 'Mesocosmos' a twenty-five-figure number; for the 'Deuterocosmos' a twenty-nine- figure number;

for the 'Macrocosmos' a thirty-four-figure number; for the 'Ayocosmos' a thirty- eight-figure number; for the 'Protocosmos' a forty-two-figure number or V-1. 9. 10⁴¹; in other words it means that during the life of

the 'Protocosmos' a ray of light travels 900, 000, 000, 000, 000, 000, 000,-000, 000, 000, 000, 000, 000, 000 kilometers.[2]

The application of the Minkovski formula to the table of time, as I had obtained it, in my opinion showed very clearly that the 'fourth coordinate' can be established only for one cosmos at a time, which then appears as the 'four-dimensional world' of Minkovski. Two, three, or more cosmoses cannot be considered as a 'four-dimensional' world and they require for their description five or six co-ordinates. At the same time Minkovski's consistent formula shows, for all cosmoses, the relation of the fourth co­ordinate of one cosmos to the fourth co-ordinate of another. And this relation is equal to thirty thousand, that is, the relation between the four chief periods of each cosmos and between one period of one cosmos and the corresponding, that is, the similarly named, period of another cosmos.