Dear Dr. Starman;
From the dates you kindly posted, I take it that
the book doesn't contain the 1923 quote I last posted, but I was
wondering if the 1922 extract was from the "Astronomy" course and if
so, did it include the stated disinclination to use the concept
fourth dimension, with the preference stated as to think in terms of
a negative third dimension, because... well, if the book doesn't
include this view, I'll post the text (it's at elib forum). Also,
Steiner said some really crucial things about the qualities of the
three dimensions, that in fact there is no 'abstract, equal' three
dimensions except in mathematical fantasy, etc. I'm sure you know the
point, and there's no doubt this has more real importance than
saddling Steiner with a concept that he clearly disagreed with... at
least, I'm waiting for as clear evidence of his support as I have for
******* Forgive me for taking so long to respond, but first, I've been rather busy, and second, the subject is a large one. In the last part of his life, Steiner's creations such as Eurythmy and the first Goetheanum show his practical usage of space in a new way. Besides the astronomy course, his lectures in the 1920s are filled with references to this new way of experiencing space. Eurythmy, of course, gives every individual the possibility of this experience. It's quite true that the three dimensions normal human beings experience in the present are qualitatively different from each other; in fact, even movement to the right is qualitatively different than movement to the left, although that is in the same dimension. Above and below, left and right, and backward and forward can all be experienced in a much more intense way than the abstract thinking of the mathematician, as many dancers know.
But the early lectures Steiner gave were seeking to build upon the work that had been done by mathematicians and theosophists around the turn-of-the-century, for instance, Hinton and Claude Bragdon. There was very important work done about 1900 in non-Euclidean geometry, groundbreaking efforts to go beyond the "box" of three dimensions. The "Flatland" analogy made famous in the late 1800s was extended, for instance by Hinton in his "A New Era of Thought" which was later given a still fuller treatment by P.D. Ouspensky in his "Tertium Organum" (the book the Edgar Cayce readings recommended to understand higher dimensions, written before poor Ouspensky unfortunately came under the deleterious influence of Gurdjieff). A good treatment of the entire genre is "The Fourth Dimension And Non Euclidean Geometry in Modern Art" by Linda Henderson. These ideas generated the movement of Cubism, influenced men as widely diverse as Marcel Duchamp and Kandinsky, and even had much to do with how Einstein came up with his theory of relativity.
What is the real tragedy is that all of this has been forgotten and/or distorted. The insight was not that there was a fourth dimension and that this dimension was time: that is a complete misinterpretation. What was worked out was that there was no reason to suppose that the number of dimensions did not go on infinitely; and, and as beings learned to sense each new dimension, all that had been perceived before would change its character. What a being was unable to sense as a dimension of space was perceived as changes in the dimensions of space it was able to perceive, or in other words as change in time. Ouspensky, the building upon Hinton, gives thinking exercises by which this can be directly experienced.
In reading Steiner's lectures about the fourth dimension, it would be helpful to know this background. I recommend the book mentioned above, along with Ouspensky's Tertium Organum. It's quite true that the fourth dimension as we are usually taught about it is not at all anything Steiner agreed with. Instead he said from his own experience that the fourth dimension was more like the second dimension again, in a sense. But this, as expected since the topic is geometry, is just a part of a very large study, and quoting one line from a lecture would be of little use.