Reginald Thomas Maitland Scott (1920)
The dimensions are degrees of consciousness. The degree of consciousness in which we now live is usually termed the third dimension. People who talk of the dimensions mention three and hint ponderously of a fourth. The mystery of the unknown fourth dimension gives to the subject vast interest and some terror. Let us then consider, as simply as possible, the three “known” dimensions and note their relationships. Having noted the relationship which lies between the dimensions of which we are commonly aware let us attempt to vision another dimension or other dimensions by means of this relationship.
What is termed the first dimension may be represented by a straight line. It is consciousness in one direction only. It is the possibility of motion in one direction only. A creature that could move forward or backward in one straight line and that had no consciousness outside that line could be considered as existing in the first dimension. However if a creature in such a dimension moved the slightest distance from the straight line, to the right or the left, above or below, it would utterly disappear to the consciousness of all other first dimensional creatures. If it came back again and touched the straight line it would instantly appear to its former brothers as if by magic.
What is termed the second dimension may be represented by a plane surface. It is consciousness and the possibility of motion in two directions only or in any combination of these two directions. A creature that could move about at will upon a flat surface and that had no consciousness outside that flat surface might be considered as existing in the second dimension. Such a creature might be conscious of other creatures upon the same flat surface. However if a resident in such a dimension moved the slightest distance up or down from the flat surface it would magically vanish to the consciousness of all other second dimensional creatures. If it returned and again touched the plane surface it would appear again to its former brothers with strange and incomprehensible suddenness. Such a situation may be dimly realized by the consideration of an insect crawling upon a flat leaf.
What is termed the third dimension may be represented by a cube. It is consciousness and the possibility of motion in three directions or in any combination of these three directions. A bird or man with his flying machines will illustrate life in the third dimension. Consciousness and motion are possible up or down, to the right or to the left, forwards or backwards.
To ascertain the relation of the first dimension to the second dimension let us compare a straight line to a plane. It will be seen that, if an infinite number of straight lines be placed side by side, a plane will result. Therefore the second dimension may be obtained from the first dimension by multiplying the first dimension by infinity. Conversely, the first dimension may be obtained from the second dimension by dividing the’ second dimension of infinity.
To ascertain the relationship of the second dimension to the third dimension let us compare a plane to a cube or solid. It will be seen that, if an infinite number of planes be placed one on top of the other, a cube or solid will result. Therefore the third dimension may be obtained from the second dimension by multiplying the second dimension by infinity. Conversely the second dimension may be obtained from the third dimension by dividing the third dimension by infinity.
By thus examining the three dimensions which are known to us it is apparent that a rule may be obtained for arriving at succeeding dimensions. This rule may be stated in a rough mathematics as follows. To obtain from the dimension under consideration the next higher dimension it is necessary to multi ply the dimension under consideration by infinity. Conversely to obtain from the dimension under consideration the next lower dimension it is necessary to divide the dimension under consideration by infinity.
What is termed the fourth dimension has been dealt with by several books which even attempt a diagram of this dimension. So intricate and complicated are these explanations that it is doubtful if there are twelve people in the world who profess to understand them and these twelve people are unable to make the rest of us see the truth that they see. Avoiding utterly the in tricacies of their higher mathematics let us attempt to glimpse
Something beyond the third dimension by means of our simple rule. The fourth dimension, if it bears the same relationship to the third dimension that the third dimension bears to the second dimension, must have the value of the third dimension multi plied in some way by infinity. Man, in the third dimension, has the power of motion in all conceivable directions and his consciousness may be thrown in any direction. How then may the scope of man be multiplied by infinity so that he may leave the third dimension and enter the fourth dimension? Clearly it is impossible for our present brain to grasp a new direction and yet it is necessary to increase by infinity the scope of a creature in the third dimension in order to reach the fourth dimension. In the third dimension we may move in any direction. We may move here, there or anywhere. However, we have to move. Suppose that we did not have to move. Suppose that we could occupy all positions in all directions without moving. Would not this be multiplying our scope by infinity? It would mean omnipresence. We credit Divinity with the power of omnipresence. May not the Great Architect be as familiar with the fourth dimension as are we with the third dimension?
The entrance to such a state of consciousness that would permit of omnipresence seems manifestly impossible in this physical world. If we believe in any existence after death, how ever, we must believe in the superphysical. It is only in such a superphysical existence that the probability of omnipresence can seem reasonable to our present physical minds. That which causes us to speak and act in our earth life vanishes just as magically at death as does the insect which rises from the flat leaf and leaves its comrades in ignorance of where it has gone. Evolution is slow, however, and it is improbable that full omnipresence bursts suddenly upon the individual at death. It would be more reasonable to expect a gradual growth of such an increased power. In dreams we often feel, act and endure long experiences in many different situations and awake to find that the clock has ticked away but a few minutes or even seconds. Here, then, is a faint realization of omnipresence. Probably our powers immediately after death have only the partial qualifications of omnipresence which we experience in dreams.
Obviously it would be unreasonable in this article to at tempt anything higher than the fourth dimension. Many people have striven to throw light on something higher than the third dimension. Fewer people have attempted to reach a dimension lower than the first dimension. Let us follow the path downward and see where it leads.
A dimension lower than the first dimension might be termed the zero dimension. According to our rule it would be arrived at by dividing the first dimension by infinity. A creature in the zero dimension would have a scope equal to the scope of the first dimension divided by infinity. The first dimension is represented by a straight line. A straight line is composed of an infinite number of points placed side by side. An infinitely small portion of a straight line is equal to a point. The zero dimension, therefore, may be represented by a point. Mathematically a point has no size. It has position and position only. A rock upon the hillside has position. It has no motion or consciousness outside itself.
A dimension lower than the zero dimension might be termed the minus one dimension. According to our rule it would be arrived at by dividing the zero dimension by infinity. A creature in the minus one dimension would have a scope equal to the scope of the zero dimension divided by infinity. The zero dimension, being represented by a point, it will be necessary to divide a point by infinity in order to gain an understanding of the minus one dimension. It will be noted that the division of anything by infinity leaves no quality whatever of the thing divided. In the case of the straight line a point was obtained which has no quality of the line since it has no length. Since a point is position and nothing but position it is really an infinitely small portion of position which we seek when we divide a point by infinity. An infinitely small portion of position is no position at all. Therefore existence in the minus one dimension must be without all quality of position. How is this possible? Let us consider position. The quality of position is a relation ship to something else. The position of the door-mat is in front of the door. The position of the hat is on top of the head. How then can existence in the minus one dimension have no position? Necessarily it must have no defining relationship toward any thing else. If it is in any one place it must have such a relation ship and consequently it must have position. Therefore it must be in more than one place. In other words it must be omnipresent,—the quality that we found in the fourth dimension. We have examined six dimensions,—the minus one, the zero, the first, the second, the third and the fourth. This examination has shown us that the minus one dimension and the fourth dimension appear to have the quality of omnipresence. Therefore the minus one dimension and the fourth dimension are either identical or merely have a similarity. If they are identical it would indicate that humanity is travelling a closed circle. By means of an army analogy let us grasp at the possibility that these two dimensions have a similarity but are not identical.
In an army the evolution of a good soldier is upward toward the rank of general. Good soldiers are instructed and promoted by the orders of the general. These orders are continuously promulgated and are posted on all sides. They are omnipresent. A good general is continually inspecting his command. He is, in a sense, omnipresent. The orders are the minus one dimension and the general is the fourth dimension. And since the general has authority over him it may well be that our evolution is ever upward through unending vistas of experience.