Rudolf Steiner (Murakirály, 1861. február 27. – Dornach, 1925. március 30.), osztrák filozófus, író, dramaturg, tanár, az antropozófia megalkotója, emellett a művészet területén is intenzív tevékenységet fejtett ki, nagy számú festmény, szobor, építészeti munka, terv és vázlat maradt fenn tőle.
He was active as a pacifist in the First World War and did social work with the Quakers, in particular with the Friends’ War Relief organisation in Poland. He worked for the rest of his life for Anthroposophy with a special interest in the scientific side as well as developing the social aspects. He interpreted Steiner’s lectures in England and later translated many of them into English. He discovered how to describe Steiner’s findings about negative space in geometric terms. He worked particularly with projective geometry and the application of path curves.
He was inspired to carry out scientific research after studying projective geometry with George Adams, following a “moonlighting” second career testing whether the path curves he had learnt about applied to real forms in Nature. This he confirmed for the forms of many flower and leaf buds as well as for the human heart. He found important rhythmic processes active in leaf bud forms over the winter months which correlate with planetary rhythms. He was a friend, inspirer and helper to many others.
In particular he seeks to reconcile Steiner’s spiritual research with the findings of science, and has found projective geometry to be a beautiful and appropriate approach. Lawrence Edwards befriended him early on and helped him greatly. Some of his interests and work are outlined in these pages.
Schwenk talks about the need for “water consciousness”, maintaining that the movement of water, by its very essence, signifies change. Cosmic consciousness is symbolized by water, where all particles merge into a single, transcendental entity. Man, according to Schwenk, will come closer to the secret of life by studying the cyclicality of movement opened from above. Schwenk further notes myths and tales pertaining to the treasure hidden under water, introducing the quandary-assumption that the treasure is, in fact, the water itself!
Olive Mary Whicher joined George Adams in London in 1935, and worked with him in research in mathematics and physics. She has published a number of books, including a few in collaboration with Adams. She has taught at Emerson College and traveled widely as a lecturer in Europe and the United States. She died January 2006.
Paul Schatz was a German-born sculptor, inventor and mathematician who patented the oloid, discovered the inversions of the platonic solids including the “invertible cube” which is often sold as an eponymous puzzle, the Schatz cube. From 1927 to his death he lived in Switzerland.
En 1923, a los 18 anos, escucha por primera vez a Rudolf Steiner durante el Congreso de Navidad en el que se estaba refundando la Sociedad Antroposófica. En 1924 vuelve a la escuela. En 1926 empieza estudiar matemáticas y astronomía, a la vez que se convierte en director de la Rama antroposófica Pestalozzi en Zurich. Paralelamente, sigue con sus estudios de epistemología y música. En 1930 se gradúa con matrícula de honor.
Ese mismo ano se casa con Anna Katherina Ernst, de cuyo matrimonio nacerán dos hijas.
En abril de 1932 empieza a ejercer como profesor en el Instituto Técnico de Winterthur, donde es nombrado vicerrector en 1937. Después de la guerra, desde 1946, ensena matemáticas en la Universidad. En 1951 es nombrado director del Instituto Técnico de Winterthur.
Locher acoge las indicaciones de Steiner sobre la importancia de la geometría proyectiva y crea libros de texto sobre el tema. Luego descubre una aproximación matemática a la idea del contraespacio que Rudolf Steiner había desarrollado para entender el cosmos con fundamento espiritual. En sus exposiciones, Locher desarrolla el aspecto matemático en forma de geometría polar-euclidiana y deja para otros investigadores el encontrar la correcta relación con los fenómenos de la ciencia natural. Profundiza en los principios de polaridad y metamorfosis generando para ellos una base matemática. Estos ensayos se reúnen en su libro “Metamorfosis geométricas”. En el movimiento antroposófico Locher es conocido por sus ensayos en el semanario Das Goetheanum que posteriormente serán reunidos en el libro “La matemáticas como preparación previa para el conocimiento espiritual”.
De 1953 a 1962 es director de la Sección matemático-astronómica del Goetheanum, y en 1962 entra a formar parte de la Junta Directiva de la Sociedad Antroposófica, pero fallece el 15 de Agosto del mismo ano.
Helmut Warm, born 1956, is a civil engineer and independent researcher in astronomy, geometry, the history of harmonics, and musical aesthetics. He has taught, lectured, and published widely on these and other subjects and, in particular, on his discoveries relating to the solar system and its inherent order. He lives in Hamburg, Germany.
This has led him to take up research concerning the number seven, and in 2000 he discovered a new geometric form never seen before. Putting this form through the alchemical transformative process of Earth, Water, Air, and Fire, many previously unknown geometric structures have emerged. Also this geometric form demonstrates a remarkable correlation to the form and functioning of the human heart. On the basis of experimentation with various related geometric forms and the movement of water in a vortex, Frank is uncovering indications concerning the relationship between etheric formative forces and the geometry, structure, and physiology of the human heart. Thus the form is called the Chestahedron, both after its discoverer and because the form relates to the geometry of the heart, which sits in the chest.