The Fourth Dimension
GA 324a
Questions and Answers XX
26 August 1921, Dornach
QUESTION: Are toe meant to understand that the Sun moves through space in a spiral and that the Earth also moves in a spiral as it follows the Sun and therefore does not revolve around the Sun?
In a longer lecture series, [Note 139] it would be relatively easy to discuss these issues in more detail; I have referred to them only briefly here. It is almost impossible to explain their foundations in a few words. Let me begin to respond to your question by simply summarizing the results of spiritual scientific research. [Note 140] First of all, any conclusions we draw about (spatial) relationships in the universe on the basis of observation and from specific perspectives are always one-sided. The Ptolemaic solar system represented a one-sided view, and so do all other models of the solar system, including the Copernican model. Our conclusions about the relationships of moving objects are based on our specific vantage point, and these relationships are invariably supplemented or altered by movements that cannot be measured from that perspective.
Having stated this cautious presupposition, I ask you to consider another spiritual scientific finding that will help us develop a view of the relationship of the Earth's movement to that of the Sun. We must imagine that the Sun moves through space on a curved path. If we trace this curve far enough, it proves to be a complicated spiral form. A simplified version looks like this (Figure 65a):
The Earth moves along the same path, following the Sun. When you consider the Earth's possible locations in relationship to the Sun, you discover that when the Earth is here, an observer would have to look to the right to see the Sun.
Now let me sketch another possible location (Figure 65b). The arrows indicate the direction of view. In the first instance, we saw the Sun by looking in one direction, and now we see it by looking in the opposite direction. As you will easily understand if you visualize this model correctly, the consequence of the Earth following the Sun is that we see the Sun first from one side, and then from the other, and the Earth appears to move around the Sun in a circular or elliptical orbit. The primary component of this movement, the fact that the Earth follows the Sun, is differentiated still further by certain other relationships that would take hours to explain. The truth of the matter, however, is that only our direction of view rotates.
As I said, this summary represents the results of lengthy spiritual scientific investigations and is complicated even more when we take other relationships into account. We must realize that as we gain a better overview of the Sun's movements, the simple lines we use to describe the Copernican system to schoolchildren become increasingly complex, until ultimately they can no longer be drawn at all and fall out of the spatial realm altogether. [Note 141] This is what I wanted to say from the perspective of spiritual science.
From the perspective of the history of the physical sciences, I would like to comment that what we find so striking today about the research results I outlined above is inherent in the Copernican view. Copernicus postulated three laws. The first states that the Earth rotates around its own axis,- the second, that the Earth revolves around the Sun,- and the third, that the Earth's movement around the Sun provides only a provisional explanation on the conceptual level. While in fact the Earth stands in a fixed relationship to the Sun. [Note 142]
This third law proves that Copernicus was truly convinced that the second movement he describes, the Earth's revolution around the Sun, was merely a convention assumed for the convenience of certain calculations and that he did not intend to state it as fact. Today, we consistently disregard this third law and believe that the Copernican model of the solar system encompasses only the first two laws. If we were truly to study the entire Copernican view, however, we would quickly conclude that this [third law] is indeed necessary, simply on the basis of astronomical calculations. [Note 143] You see what often happens in the history of science.
Questions and answers (open discussion) during the Summer Art Course at the Goetheanum, August 21 to 27, 1921. Rudolf Steiner's own summaries of his lectures during this conference were published in the Nachrichten der Rudolf Steiner-Nachlassverwaltung ("News from the Rudolf Steiner Archives"), no. 8, 1962, pp. 4-20. (Beginning with no. 29, 1970, the name of this publication was changed to Beitrage zur Rudolf Steiner Gesamtausgabe ["Articles on Rudolf Steiner's Complete Works''].) A detailed conference program was published in the journals Dreigliederung des sozialen Organismus ('The Threefolding of the Social Organism”), vol. 3, no. 5, and Das Goetheanum, vol. 1, 1921-1922, no. 1. Transcripts of the lectures were first published in the periodical Gegenwart ('The Present"). The introductory lecture of August 21, 1921, appeared in vol. 14, 1952-1953, no. 9/10, pp. 353-363; the lecture of August 23, 1921, in vol. 14, no. 11, pp. 417-428; the lecture of August 24, 1921, in vol. 15, 1953-1954, no. 1, pp. 4-19; and the lecture of August 26, 1921, in vol. 15, no. 2, pp. 44-63. Publication of this lecture series is planned for GA 73a. The question-and- answer session appears here in print for the first time.
Compare this and the following passages to the question-and-answer session of October 15, 1920, and the relevant notes.
See also Rudolf Steiner's lectures of May 2, 1920 (GA 201), and January 16, 1921 (GA 323).
In this lecture, Rudolf Steiner lists these laws in the order given by Copernicus in chapter 11 of the first volume of his main work, De Revolutionibus Orbium Coelestinum. See also Notes 2 and 3 to the question-and-answer session of October 15, 1920.
Presumably, Rudolf Steiner refers here to Bessel's reductions, which he mentions in the question-and-answer session of October 15, 1920.