Notes from Mathilde Scholl 1904–1906

GA 91 — 27 August 1906

8. The Fourth Dimension IV

Infinite is only that which finds its conclusion in no second, but runs back into itself, which finds a conclusion only in itself. Therefore also only the line is an infinite straight line, which finds its conclusion in itself, namely that, which forms a circle. Straight is the line, which always keeps the same direction. The circle line is the only line which always keeps the same direction. Because it has the direction after its starting point back. Any line that maintains this direction back to its starting point, returning to that starting point, forms a circle.

So, if we transfer the finite relations of bodies into the infinite, we find there a transformation of all things. The human being stands in the infinity. What we can see of man is like a moment cut out of his infinite cycle, the moment in which past and future meet. If we go further in the mental image, man must return to the past in the future. But this return is an enriched one. He has grown, bringing with him all the experiences he has gained along the way. The circle, the snake biting its tail, is not only a representation of the infinite straight line, but of all infinity.

The following can be learned from the example of the strip of paper glued together. First, if the strip is placed with its ends on top of each other and then cut lengthwise - following the direction of the line - two circular strips of equal size are formed. Think of this in terms of space. By dividing an object located in three-dimensional space, two parts of a body previously forming a whole are created.

Second, if the strip is rotated around itself one and a half times (180 degrees) and then cut through, the result is a strip twice as large when cut through in the direction of the line. So any circular line in space that is rotated one and a half times around itself, when it splits, creates one twice as big. This is the secret of growth.

To do this, a body must live in the fourth dimension, in time. In space, through division, division takes place; in time, in the fourth dimension, through division, growth takes place.

Thirdly, by further rotation of the strip of paper, division always produces new entities. These represent the manifold growth phenomena in nature: In the single rotation (360 degrees): the two intertwined circles; in the one-and-a-half rotation (540 degrees), the loop; in the double rotation (720 degrees), a circle and a second one that wraps all the way around once, forming a loop through which the other circle can be pushed.

All these operations illustrate the possibilities of the fourth dimension, the dimension of time, of growth, of change from within, of life, of movement, of the fluid, of the stream of time returning into itself and emerging from itself, emerging into something new.