It is clear that the existence of a house and that of an idea are

quite different existences.

Of such different existences we know very many. A book exists, and also the contents of a book. Notes exist, and so does the music that the notes combine to make. A coin exists, and so does the purchasing value of a coin. A word exists, and the energy which it

contains.

We discern on the one hand, a whole series of physical facts, and on the other hand, a series of metaphysical facts.

As facts of the first kind exist, so also do facts of the second kind exist, but differently.

From the usual positivist point of view it will seem naive in the highest degree to speak of the purchasing value of a coin separately from the coin; of the energy of a word separately from the word; of the contents of a book separately from the book, and so on. We all know that these are only "what people say," that in reality purchasing value, energy of a word, and contents of a book do not exist, that by these conceptions we only denote a series of phenomena in some way linked with coin, word, book, but in substance quite separate from them.

But is it so?

We decided to accept nothing as given, consequently we shall not negate anything as given.

We see in things, in addition to what is external, something internal. We know that this internal element in things constitutes a continuous part of things, usually their principal substance. And quite naturally we ask ourselves, where is this internal element, and what does it represent in and by itself. We see that it is not embraced within our space. We begin to conceive of the idea of a "higher space" possessing more dimensions than ours. Our space then appears to be somehow a part of higher space, i. e., we begin to believe that we know, feel, and measure only part of space, that part which is measurable in terms of length, width and height.

As was said before, we usually regard space as a form of the universe, or as a form of the matter of the universe. To make this

"MATTER" ONLY A LOGICAL CONCEPT 31 clear it is possible to say that a "cube" is the form of the matter in a cube; a "sphere" is the form of the matter in a sphere; "space"—an infinite sphere is the form of the entire matter of the universe.

H. P. Blavatsky, in The Secret Doctrine, has this to say about space:

The superficial absurdity of assuming that Space itself is measurable in any direction is of little consequence. The familiar phrase (the fourth dimension of space) can only be an abbreviation of the fuller form the "Fourth dimension of Matter in Space.". . . The progress of evolution may be destined to introduce us to new characteristics of

But the formula defining "space" as "the form of matter in the universe" suffers from this deficiency, that there is introduced in it the concept of "matter," i. e., the unknown.

I have already spoken of that "dead-end siding," x=y, y=x, to which all attempts at the physical definition of matter inevitably lead.

Psychological definitions lead to the same thing.

In a well-known book, The Psychology of the Soul, A. I. Herzen

says:

We call matter everything which directly or indirectly offers resistance to motion, directly or indirectly produced by us, manifesting a remarkable analogy with our passive states.

And we call force (motion) that which directly or indirectly communicates movement to us or to other bodies, thus manifesting the greatest similitude to our active states.

Consequently, "matter" and "motion" are something like projections of our active and passive states. It is clear that it is possible to define the passive state only in terms of the active, and the active in terms of the passive—again two unknowns, defining one another.

E. Douglas Fawcett, in an article entitled Idealism and the Problem of Nature in The Quest (April, 1910), discusses matter from this point of view.

* "The Secret Doctrine," The Theosophical Publishing Society. Third Edition, p. 271, vol. 1.

Matter (like force) does not give us any trouble. We know all about it, for the very good reason that we invented it. By "matter" we think of sensuous objects. It is mental change of concrete but too complicated facts, which are difficult to deal with.

Strictly speaking, matter exists only as a concept. Truth to tell, the character of matter, even when treated only as a conception, is so unobvious that the majority of persons are unable to tell us exactly what they mean by it.

An important fact is here brought to light: matter and force are just logical concepts, i. e., only words accepted for the designation of a lengthy series of complicated facts. It is difficult for us, educated almost exclusively along physical lines, to understand this clearly, but in substance it may be stated as follows: Who has seen matter and force, and when? We see things, see phenomena. Matter, independently of the substance from which a given thing is made, or of which it consists, we have never seen and never shall see; but the given substance is not quite matter, this is wood, or iron or stone. Similarly, we shall never see force separately from motion. What does this mean? It means that "matter" and "force" are just such abstract conceptions as "value" or "labor," as "the purchasing value of a coin" or the "contents" of a book; it means that matter is "such stuff as dreams are made of." And because we can never touch this "stuff" and can see it only in dreams, so we can never touch physical matter, nor see, nor hear, nor photograph it, separately from the object. We cognize things and phenomena which are bad or good, but we never cognize "matter" and "force" separately from things and phe

nomena.

Matter is as much an abstract conception as are truth, good and evil.

It is as impossible to put matter or any part of matter into a chemical retort or crucible as it is impossible to sell "Egyptian darkness" in vials. However as it is said that "Egyptian darkness" is sold as a black powder in Athos, or elsewhere, therefore perhaps somewhere, by some one, even matter has been seen.*

*This is irony which the English speaking may easily fail to understand. Some unscrupulous monks of the monastery of Athos, famous throughout Greece and Russia, made a practice, it is said, of selling "Egyptian darkness" in little vials, thus making capital out of the credulity and piety of the illiterate Russian pilgrims who were wont to visit this monastry in great numbers. Transl.

THE STUDY OF SPACE

33

In order to discuss questions of this order a certain preparation is necessary, or a high degree of intuition; but unfortunately it is customary to consider fundamental questions of cosmogony very lightly.

A man easily admits his incompetency in music, dancing, or higher mathematics, but he always maintains the privilege of having an opinion and being a judge of questions relating to "first principles."

It is difficult to discuss with such men.

For how will you answer a man who looks at you in perplexity, knocks on the table with his fingers and says, "This is matter. I know it; feel! How can it be an abstract conception?" To answer this is as difficult as to answer the man who says: "I see that the sun rises and sets!"

Returning to the consideration of space, we shall under no circumstances introduce unknown quantities in the definition of it. We shall define it only in terms of those two data which we decided to accept at the very beginning.

The world and consciousness are the facts which we decided to recognize as existing.

By the world we mean the combination of all the causes of our sensations in general.

By the material world we mean the combination of causes of a definite series of sensations: those of sight, hearing, touch, smell, taste, sensations of weight, and so on.

Space is either a property of the world or a property of our knowledge of the world.

Three-dimensional space is either a property of the material world or a property of our receptivity of the material world.

Our inquiry is confined to the problem: how shall we approach the study of space?

CHAPTER III

What may we learn about the fourth dimension by a study of the geometrical relations within our space? What should be the relation between a three-dimensional body and one of four dimensions? The four-dimensional body as the tracing of the movement of a threedimensional body in the direction which is not confined within it. A four-dimensional body as containing an infinite number of threedimensional bodies. A three-dimensional body as a section of a four-dimensional one. Parts of bodies and entire bodies in three and in four dimensions. The incommensurability of

I'

dimensional and a four-dimensional body. A material atom as a section of a four-dimensional line.

F we consider the very great difference between the point and the line, between the line and the surface surface and solid,

i. e., the difference between the laws to which line and plane, plane and surface, etc., are subjected, and the difference of phenomena possible in point, in line, in surface, we shall indeed come to understand how much of the new and inconceivable the fourth dimension holds for us.

As in the point it is impossible to imagine the line and the laws of the line; as in the line it is impossible to imagine the surface and the laws of the surface; as in the surface it is impossible to imagine the solid and the laws of the solid; so in our space it is impossible to imagine the body having more than three dimensions, and impossible to understand the laws of the existence of such a body.

But studying the mutual relations between the point, the line, the surface, the solid, we begin to learn something about the fourth dimension, i. e., of four-dimensional space. We begin to learn what it can be in comparison with our three-dimensional space, and what it cannot be.

This last we learn first of all. And it is especially important, because it saves us from many deeply inculcated illusions, which are very detrimental to right knowledge.