The Fourth Dimension
GA 324a
Questions and Answers I
2 September 1906, Stuttgart
In the original German publication the first question and answer is front 1904 in Berlin. [Note 1] There is no recorded question, only that it was asked by Mr. Schouten [Note 2] and the answer is simply a reply from Steiner that he would be giving a lecture shortly on the fourth dimension.
A Question about the work of the “I." [Note 3]
The "I" works on the astral body, the ether body, and the physical body. All human beings work on the astral body through moral self-education. But even when a person begins the process of initiation or esoteric schooling, much work remains to be done on the astral body. Initiation marks the beginning of more intensive work on the ether body through the cultivation of aesthetic taste and religion. Initiates work consciously on the ether body.
In a certain respect, astral consciousness is four-dimensional. To give you an approximate idea of it, let me say that anything dead tends to remain within the three ordinary dimensions, while anything living constantly transcends them. Through its movement, any growing thing incorporates the fourth dimension within the three. If we move in a circle that is growing ever larger, we eventually arrive at a straight line (Figure 61). If we continue moving along this line, however, we will no longer be able to return to our starting point, because our space is three-dimensional. In astral space, which is closed off on all sides, we would return. In astral space, it is impossible to continue to infinity. [Note 4] Physical space is open to the fourth dimension. Height and width are two dimensions, and the third dimension is the lifting out and entering into the fourth dimension. [Note 5] A different geometry prevails in astral space.
These comments were made after a lecture on Christianity (not yet published in the complete edition of Rudolf Steiner's works) to the Berlin branch.
Jan Arnoldus Schoutan (1883-1971) See Note 1, Lecture 3 (May 17, 1905). This question suggests that the problem of the fourth dimension was topical even in Rudolf Steiner's immediate circle and that his lectures on the subject were meant above all to address related spiritual scientific questions.
This question-and-answer session took place during the lecture cycle Vor dem Tore der Theosophie (GA 95).
By space, Rudolf Steiner apparently means ordinary, perceived space that is defined by the laws of Euclidean geometry. In this type of space, infinity (or, when this space is embedded in projective space, the distant plane) is an impenetrable boundary. According to Steiner, the same does not apply to astral space, whose structure is related to that of projective space. In this type of space there is no boundary, no unattainable infinity. Projective space is self-contained,—we can set out in any direction from a fixed starting point and ultimately return to the same point.
It has not been possible to reconstruct exactly what this sentence means. On the basis of the drawing that has been preserved (Figure 62), the sentence may be a fragment of an explanation with approximately the following contents: In the second dimension, a two-dimensional object within a circle cannot leave the circle without crossing the circumference. The object can easily be moved outside the circle, however, by enlisting the help of the third dimension. Similarly, an object located within a sphere in three-dimensional space cannot be removed without puncturing the sphere, except by passing through the fourth dimension. (See the explanations in the lecture of March 24, 1905, and the accompanying notes.)