The Fourth Dimension
GA 324a
Introduction by David Booth
The centerpiece of Rudolf Steiner's view of history is the idea that human consciousness has evolved through time. Steiner's world-view combines this thought with the inspiring idea that our spirits are part of the whole of this evolution, even when it preceded our particular life span. Many of Steiner's lectures treat the differences between tribal, classical, and modern cultures from the perspective of evolving consciousness.
When you are familiar with this perspective on history, the question will arise: Could evolutionary changes in consciousness be detected over the course of mere decades? Or does it require the passage of centuries for them to come about?
The subject of these lectures, the fourth dimension, is interesting not only for its own sake and for its scientific applications, but also because of the illumination that it casts on the recent, observable evolution in human thought. Steiner asserted that the middle of the nineteenth-century was a singular point in the development of human consciousness,- at that time man's thoughts were more closely connected to the brain than they had ever been previously, or would ever be again. The brain was, because of its close connection with the mind, spiritualized to the greatest degree. Conversely the mind was brought most strongly into the material world. Ingenious materialistic theories were the cultural symptom of this unique historical condition. He went on to claim that this nineteenth-century descent of mind into matter was not his own original discovery but was well known within secret societies. Steiner had discovered the facts independently, however, and was not bound by oaths of secrecy. He believed that the time had come to bring such spiritual knowledge into public view.
If you assume, hypothetically, that this theory of historical evolution is correct, you would expect the nineteenth century to feel a tension between the inherently non-materialistic concept of a fourth dimension and the secular tendency to materialize all concepts. Part of the charm of the fourth dimension is that it is a geometrical concept that interests popular culture as much as it does mathematicians. In both its popular and scientific applications, the fourth dimension has had both gnostic and agnostic exponents.
The first mathematician to explore the fourth dimension, William Rowan Hamilton, was born in 1805; he was reading the Bible at the age of three when he also began learning Hebrew characters. By the age of 10 he could read Hebrew, Persian, Arabic, Sanskrit, Bengali, Latin, and Greek, as well as several modem European languages. He was skilled in mental arithmetic and was placed in competition with a boy from Vermont who toured as a calculating prodigy. Hamilton was disappointed, however, when he found that his opponent, young Mr. Colburn, seemed to have no knowledge apart from his unusual arithmetical talents and did not seem to be interesting as a friend.
While he was studying at university, Hamiliton fell under the influence of the Tractarian movement that sought to revitalize religion from its spiritual content. He was influenced in this by the more radical, subjective branch of the movement that was inspired by the philosophy of Samual Taylor Coleridge. Driven, perhaps, by Coleridge's notion of algebra as the science of time, Hamilton discovered a four-dimensional manifold of numbers, the "quaternions"—usually called hypercomplex numbers today. You may be surprised, if you read Hamilton's writings, to see how he shrinks back from embracing a fourth dimension as such. Hamilton did explore the fourth dimension, but still refused to actually accept the notion of a four-dimensional space. He carried out his research at a time in which—according to our hypothetically accepted view of cultural revolution—man's consciousness had descended to the greatest degree into matter. Hamilton used three dimensions (the vectors), along with a fourth (the tensor), that were kept separate so that they did not combine into a single four-dimensional manifold.
If you were to take up Hamilton's other mathematical work—his name is still honored for his ingenious methods of mathematical physics—you would likely be struck by the profound materialism that can be read between the lines of his skillful calculations. The active, creative logic of the nineteenth century was reaching for the fourth dimension, but the spirit of materialism held it back.
In the next phase of development, the concept of fourth dimensional space as such was accepted. Ludwig Schlaefli, a Swiss schoolteacher, treated four dimensions as the compelling conceptual continuation of the first three spatial dimensions. It may be that the isolation from adult scholarship that is a natural part of a schoolteacher's life allowed Schlaefli to develop this new geometry during his early career, before he joined the mathematics department of the University at Bern. It is interesting that Grassmann, who also explored an ingenious algebra of higher dimensions, was, like Schlaefli, a schoolteacher whose writings were ignored for many years. In fact, these intrepid pioneers, true heroes of the free human spirit, ran the social risk of being thought mad. Actually they deepened and renewed cultural traditions from the past as they relied on pure thought to take them beyond what could be confirmed in the sensory world.
Each new pioneer into the world of free ideas found the journey easier, particularly if the new ideas illuminated other branches of knowledge. In geometry, for example, it was noticed that the lines in ordinary three-dimensional space could be regarded as elements of a manifold of four dimensions. Connections of this kind soon made the fourth dimension acceptable to mathematicians. It did not take long, however, for the fourth dimension to be taken up by spiritualists, an association that runs parallel to its frequent appearance in late twentieth-century UFO literature. This entry into popular occultism was the third distinct phase of development. Nineteenth-century seances attracted spirit beings who produced physical effects, were associated with peculiar psychological states, and disappeared again—like the UFOs of our time. It was as convenient then (as it is now) to assign them a home in the inaccessible dimensions of space.
The nineteenth-century astronomer Zollner set out to demonstrate scientifically that the immaterial beings attracted to spiritualistic seances were from the fourth dimension. Even though his demonstrations were never successful, he became so absorbed in the effort that his colleagues considered him to have been deluded by the medium Slade, who was certainly fraudulent some of the time. In this phase, the fourth dimension became a means of conceiving of mysterious phenomena in a quasi-materialistic way.
In the final phase of nineteenth-century thought, the fourth-dimension became a subject for meditation. It seems to have been taken up specifically within the Theosophical Society only after Helena Blavatsky's death in 1891. The Theosophical Society had made public a great deal of what had previously circulated only within secret societies, but these revelations had depended on Madame Blavatsky, who had begun her intercontinental career as a private medium while still a teenager. After her death, the movement experienced some fragmentation, but was basically under the guidance of Annie Besant, a relatively recent convert from materialistic socialism. The post-Blavatskian Theosophical Society therefore needed a new way to offer training for higher knowledge in order to retain members. The writings of Howard Hinton on the fourth dimension suited the purpose beautifully.
The career of Howard Hinton was connected in a peculiar way to the ideas of his father. James Hinton was a naval doctor who lost his faith as a result of reading the Bible and became a vigorous opponent of Christianity. He displaced the mystery of the Trinity to make room for "the mystery of pain" and preached the virtue of such mortifications of the flesh as, for example, going about in winter without an overcoat. As James Hinton became increasing philosophical he acquired faith in a Kantian noumenal world that lies behind phenomenal experience. This higher world was feminine, nurturing, free of social and legal restraint. Virtue consisted in harmonizing one's intentions with the noumenal world, and could not be captured by merely regulating behavior. The person who acts selflessly for the greater good of humanity was as likely to break the law as the brutish criminal.
In the course of propounding these ideas, James Hinton needed mathematical help on the subject of quadratic equations, which in his mind were associated with some ethical issues. He engaged the widow of the mathematician George Boole for help; she became his secretary. This association between Mrs. Boole and James Hinton brought about the acquaintance of James Hinton's son Howard and Mrs. Boole's daughters.
Howard Hinton, rather like his father, had been inspired by Hamilton's writings to adopt a materialistic form of Kantianism. When he began work as a schoolteacher, however, he came to doubt that knowledge could ever come from an external authority. In an effort to find some knowledge about which he could feel certainty, he made himself a set of colored blocks, which he rearranged in various ways to make larger cubes. Using these blocks, he felt he could acquire knowledge of spatial position that was beyond all doubt. As he looked for patterns in the rearrangement of these blocks, he began to investigate the fourth dimension, which he saw as governing sequences of transformation in three dimensions.
He taught his system to the young Alicia Boole, whom he knew because of his fathers work with Mrs. Boole. Alicia later became famous among mathematicians for her capacity to visualize four-dimensional objects. She acquired this ability from following Howard Hinton's exercises with the blocks. Hinton eventually married Alicia's older sister Ellen.
Howard Hinton's personal life fell into tragic chaos. A brief imprisonment for bigamy led to his leaving England and taking the position of a schoolteacher in an English language school in Japan for several years. Later he came to America. The psychologist William James was one of his American supporters. There seems to have been significant behind-the-scenes interest in America in Hinton's notion of using higher dimensions as a way of acquiring clairvoyance. Hinton himself turned away from his previous investigations, however, and concentrated on the production of a novelty for that time—a pitching machine for baseball practice. This may have excited the coaching staff at the colleges where he worked but it did nothing to enhance his philosophical reputation. He took a job as a patent examiner in 1902. The new position eventually took his mind off baseball and back to what his supporters really wanted to know about, the connection between the fourth dimension and clairvoyance.
By the time of Hinton's death in 1907, his writings had inspired theosophists in India and England to investigate the fourth dimension for themselves. Naturally these topics would have been of interest to the German theosophists as well. That interest forms the background of these lectures of Rudolf Steiner. In them, we see Steiner very much at home in the visualization of multiple dimensionality spaces. He operates from concepts that bridge the more mathematical and more "spiritual'' views of the fourth dimension. Readers may find him difficult at times, but also deeply rewarding, as he guides them out of the familiar world of three dimensions and into ever deeper regions of inner space.