The Fourth Dimension

The Fourth Dimension: Sacred Geometry, Alchemy, and Mathematics

6 lectures, Berlin, March 24–June 7, 1905;
2 lectures, Nov. 7, 1905 & Oct. 22, 1908;
Questions & Answers, 1904–1922 (CW 324)

Anything dead tends to remain within the three ordinary dimensions, while anything living constantly transcends them. —Rudolf Steiner

“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.” —From the introduction

The point, line, plane and solid objects represent the first three dimensions, but a kind of reversal of space is involved in the ascent to a fourth dimension. Steiner leads us to the brink of this new perspective – as nearly as it can be done with words, diagrams, analogies, and examples of many kinds. In doing so, he continues his lifelong project of demonstrating that our objective, everyday thinking is the lowest rung of a ladder that reaches up to literally infinite heights.

The talks in this series and the selections from the question-and-answer sessions on many mathematical topics over the years are translated into English for the first time in The Fourth Dimension. They bring us to tantalizing new horizons of awareness where Steiner hoped to lead his listeners:

Topics include:

• The relationship between geometric studies and developing direct perception of spiritual realities
• How to construct a fourth-dimensional hypercube
• The six dimensions of the self-aware human being
• Problems with the theory of relativity
• The Trinity and angelic hierarchies and their relationship to physical space
• The dimensional aspect of the spiritual being encountered by Moses on Mt. Sinai

Cover Image credit: Light refracted through a small sample of water while under vibration. From a series of experiments by Dr. Hans Jenny in Cymatics. The photo is from the book Cymatics: A Study of Wave Phenomena and Vibration by Dr. Hans Jenny, published by in 2001 by MACROmedia (used by permission).

The Fourth Dimension is a translation from German of Die vierte Dimension Mathematik und Wirklichkeit (GA 324a).

About the Author

Rudolf Steiner (1861–1925) was born in the small village of Kraljevec, Austro-Hungarian Empire (now in Croatia), where he grew up (see right). As a young man, he lived in Weimar and Berlin, where he became a well-published scientific, literary, and philosophical scholar, known especially for his work with Goethe’s scientific writings. At the beginning of the twentieth century, he began to develop his early philosophical principles into an approach to systematic research into psychological and spiritual phenomena. Formally beginning his spiritual teaching career under the auspices of the Theosophical Society, Steiner came to use the term Anthroposophy (and spiritual science) for his philosophy, spiritual research, and findings. The influence of Steiner’s multifaceted genius has led to innovative and holistic approaches in medicine, various therapies, philosophy, religious renewal, Waldorf education, education for special needs, threefold economics, biodynamic agriculture, Goethean science, architecture, and the arts of drama, speech, and eurythmy. In 1924, Rudolf Steiner founded the General Anthroposophical Society, which today has branches throughout the world. He died in Dornach, Switzerland.

David Booth, PhD, is a theoretical mathematician and longtime Waldorf high school teacher. He is the editor of the Paul Finsler’s papers on set theory: Finsler Set Theory: Platonism and Circularity.