Why cans, pizza, and manhole covers are round.
Why one and two weren’t considered numbers by the ancient Greeks.
Why squares show up so often in goddess art and board games.
What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies.
How the human body shares the design of a bean plant and the solar system.
How a snowflake is like Stonehenge, and a beehive like a calendar.
How our ten fingers hold the secrets of both a lobster and a cathedral.
And much more.
Mégalithes, mosquées, temples grecs, hindous ou bouddhistes sont décryptés à la lumière de la symbolique des nombres. Cette géométrie sacrée sert de lien entre les divers courants religieux, en soulignant comment la Vie et ses manifestations indiquent une recherche constante de la lumière de l’esprit, selon une grande variété d’expressions symboliques. ?Dans son premier ouvrage “La Symbolique des Nombres et de la Géométrie”, Léonard Ribordy avait remarquablement démontré comment une antique philosophie, malgré les progrès fulgurants des connaissances scientifiques, avait gardé toute la lumière de sa jeunesse.
Ce message symbolique étant resté gravé dans les traces archéologiques des civilisations passées, l’auteur nous propose dans ce nouvel ouvrage un voyage dans le temps et dans l’espace, en analysant la structure sacrée des temples anciens et contemporains des différentes civilisations du monde entier. Ainsi est né ce nouvel essai centré sur l’Architecture et la Géométrie sacrées à la lumière du Nombre d’Or.
?Léonard Ribordy est ingénieur en Génie-Civil EPFL, d’origine suisse, né en 1939, à Saint Maurice (Valais). Son intérêt pour les choses de l’esprit et sa passion pour les sciences, l’architecture, l’histoire et les mathématiques l’ont incité à construire des ponts entre les sciences et la spiritualité dans l’espoir d’apporter un peu de lumière dans un monde tourné vers un matérialisme stérile, peu compatible avec l’évolution humaine.
The priests of ancient Egypt preserved a geometrical canon, a numerical code of harmonies and proportions, that they applied to music, art, statecraft, and all the institutions of their civilization. Plato, an initiate in the Egyptian mysteries, said it was the instrument by which the ancients maintained high, principled standards of civilization and culture over thousands of years.
In The Dimensions of Paradise, John Michell describes the results of a lifetime’s research, demonstrating how the same numerical code underlies sacred structures from ancient times to the Christian era. In the measurements of Stonehenge, the foundation plan of Glastonbury, Plato’s ideal city, and the Heavenly City of the New Jerusalem described in the vision of Saint John lie the science and cosmology on which the ancient world order was founded. The central revelation of this book is a structure of geometry and number representing the essential order of the heavens and functioning as a map of paradise.
About the Author(s) of The Dimensions of Paradise
John Michell, educated at Eton and Cambridge, is the pioneer researcher and specialist in the field of ancient, traditional science. He is the author of more than twenty-five books that have profoundly influenced modern thinking, including The New View Over Atlantis, Secrets of the Stones, and The Temple of Jerusalem: A Revelation.
Praise for The Dimensions of Paradise
“John Michell’s The Dimensions of Paradise is inarguably among the most important Gnostic transmissions of recent generations. With his candid, uncomplicated style, John has made widely available the visions, the laws, and the numbers held within pure geometry and which integrate earth and sky, movement and form, cosmos and mankind.”
Robert Lawlor, author of Sacred Geometry: Its Philosophy and Practice and Voices of the First Day
“John Michell has produced one of the primary texts for understanding the number system that encoded the prehistoric world view. He reveals how sacred geometry, myth, gematria, and the structure of numbers created a big picture lost soon after Plato, a knowledge replaced by derivative religious and materialistic ideas. The Dimensions of Paradise is an essential key to comprehending monuments such as the Great Pyramid and Stonehenge, but it also provides an initiatory journey into the ancient mind itself.”
Richard Heath, author of Sacred Number and the Origins of Civilization
“As usual, this is a dense, yet inspiring, read and one that has some practical nuggets in it for those who are looking for a kind of three-dimensional sacred geometry they can apply to daily life.”
Institute of Hermetic Studies, Mar 2008
” . . . a top pick for New Age libraries interested in sacred geometry.”
The Midwest Book Review, April 08
“A must for anyone looking for the science hidden within the matrix of life.”
Rahasya Poe, Lotus Guide magazine, July 2009
Beginning with these legends, the author uncovers fascinating interconnections between the Celtic and Mediterranean cultures and philosophies. Taking the biblical image of “wisdom as master craftsman,” Strachan explores the deep layers of Mystery knowledge shared by the world of Jews and Greeks and that of the northern Druids-using the secret geometry of masons and builders, which Jesus would have encountered in his work as a craftsman in Palestine, as well as the biblical Gematria, or numeric encryption.
* Introduction by Christopher Bamford
* “Ancient Temple Architecture” by Robert Lawlor
* “The Platonic Tradition on the Nature of Proportion” by Keith Critchlow
* “What is Sacred Architecture? by Keith Critchlow
* “Twelve Criteria for Sacred Architecture” by Keith Critchlow
* “Pythagorean Number as Form, Color, and Light” by Robert Lawlor
* “The Two Lights” by Arthur Zajonc
* “Apollo: The Pythagorean Definition of God” by Anne Macaulay
* “Blake, Yeats, and Pythagoras” by Kathleen Raine
About the Authors
ROBERT LAWLOR is the author of Sacred Geometry; Earth Honoring; and Voices of the First Day. After training as a painter and a sculptor, he became a yoga student of Sri Aurobindo and lived for many years in Pondicherry, India, where he was a founding member of Auroville. In India, he discovered the works of the French Egyptologist and esotericist, R. A. Schwaller de Lubicz, which led him to explore the principles and practices of ancient sacred science.
KEITH CRITCHLOW is the author of Order in Space; and Time Stands Still. A painter, Critchlow discovered geometry intuitively. A period of intensive geometric practice and work with Buckminster Fuller led him to recognize that the universal principles of geometry are revealed and confirmed both by the area of design where art and mathematics meet and in the study of nature and ancient and medieval sacred cosmological architecture of temples, cathedrals, and mosques. He has been a senior lecturer at the Architectural Association in London and taught Islamic Art at the Royal College of Art. He has also participated as geometer in various sacred architectural projects, and is a cofounder of Temenos, a journal devoted to the arts and imagination, and Kairos, a society that investigates, studies, and promotes traditional values of art and science.
ARTHUR ZAJONC is Professor of Physics at Amherst College, where his research has concerned the nature of light and the experimental foundations of quantum mechanics. He has also taught and written extensively on interdisciplinary aspects of science, the history of science, culture, and spirituality, especially the works of Goethe and Rudolf Steiner. He is the author Catching the Light and The New Physics and Cosmology, featuring dialogues with the Dalai Lama. He has been a visiting scientist at many laboratories and was a Fulbright professor.
ANNE MACAULAY lives in Scotland where she has, for many years, studied the origins of the alphabet, the history of the guitar, the figure of Apollo, and other mysteries surrounding Pythagorean thought. She has lectured at Research into Lost Knowledge Organization (RILKO) and was a trustee of the Salisbury Center in Edinburgh.
KATHLEEN RAINE was a British poet with an international reputation as a scholar of the imagination. A renowned student of William Blake, a penetrating critic, and a profound autobiographer, she wrote numerous books and articles. Kathleen Raine was a cofounder and the editor of Temenos.
Christopher Bamford is Editor in Chief for SteinerBooks and its imprints. A Fellow of the Lindisfarne Association, he has lectured, taught, and written widely on Western spiritual and esoteric traditions. He is the author of The Voice of the Eagle: The Heart of Celtic Christianity (1990) and An Endless Trace: The Passionate Pursuit of Wisdom in the West (2003). He has also translated and edited numerous books, including Celtic Christianity: Ecology and Holiness (1982); Homage to Pythagoras: Rediscovering Sacred Science; and The Noble Traveller: The Life and Writings of O. V. de L. Milosz (all published by Lindisfarne Books). HarperSanFrancisco included an essay by Mr. Bamford in its anthology Best Spiritual Writing 2000.
It is one of the most elegant and beautiful ratios of the mathematical universe because of its combination of elegance and simplicity–hence the divine nature of its name. Drawing on art, architecture, philosophy, nature, mathematics, geometry, and music–and beautifully illustrated in the Wooden Books fashion with all manner of images–The Golden Section will tell the story of this remarkable construct and its wide ranging impact on civilization and the natural world.
This valuable reference book introduces the origins and principles of geometry using these basic tools, and shows some of the geometric constructions used by artists, architects, and mathematicians of old.
From the observations of Ptolemy and Kepler to the Harmony of the Spheres and the hidden structure of the solar system, John Martineau reveals the exquisite orbital patterns of the planets and the mathematical relationships that govern them. A table shows the relative measurements of each planet in eighteen categories, and three pages show the beautiful dance patterns of thirty six pairs of planets and moons.
These images are awesome not just for their beauty alone, but because they suggest an order underlying their growth, a harmony existing in nature. What does it mean that such an order exists; how far does it extend?
The Power of Limits was inspired by those simple discoveries of harmony. The author went on to investigate and measure hundreds of patterns—ancient and modern, minute and vast. His discovery, vividly illustrated here, is that certain proportions occur over and over again in all these forms. Patterns are also repeated in how things grow and are made—by the dynamic union of opposites—as demonstrated by the spirals that move in opposite directions in the growth of a plant.
The joining of unity and diversity in the discipline of proportional limitations creates forms that are beautiful to us because they embody the principles of the cosmic order of which we are a part; conversely, the limitlessness of that order is revealed by the strictness of its forms. The author shows how we, as humans, are included in the universal harmony of form, and suggests that the union of complementary opposites may be a way to extend that harmony to the psychological and social realms as well.
Schwaller de Lubicz’s stone-by-stone survey of the temple of Amun-Mut-Khonsu at Luxor allows us to step into the mentality of Ancient Egypt and experience the Egyptian way of thinking within the context of their own worldview.
His study finds the temple to be an eloquent expression and summary–an architectural encyclopedia–of what the Egyptians knew of humanity and the universe. Through a reading of the temple’s measures and proportions, its axes and orientations, and the symbolism and placement of its bas-reliefs, along with the accompanying studies of related medical and mathematical papyri, Schwaller de Lubicz demonstrates how advanced the civilization of Ancient Egypt was, a civilization that possessed exalted knowledge and achievements both materially and spiritually. In so doing, Schwaller de Lubicz effectively demonstrates that Ancient Egypt, not Greece, is at the base of Western science, civilization, and culture.
To understand the temple of Luxor, twelve years of field work were undertaken with the utmost exactitude by Schwaller de Lubicz in collaboration with French archaeologist Clement Robichon and the respected Egyptologist Alexandre Varille. From this work were produced over 1000 pages of text and proofs of the sacred geometry of the temple and 400 illustrations and photographs that make up The Temple of Man.
The Temple of Man is a monument to inspired insight, conscientious scholarship, and exacting archaeological groundwork that represents a major contribution to humanity’s perennial search for self-knowledge and the prehistoric origins of its culture and science.
Clearly explained excercises talk the reader through construction of the basic geometric forms and act as invaluble aid to conception. Constant reminders of the interpretations of other world religions and spiritual practices, as well as references to those of modern science, give the reader an undeniable sense of the universality of the symbols studied.
With many illustrations and an awe inspiring amount of information, this book is literally bursting to give new life to the noble study of geometry.
Is there a secret language all around us? What’s so special about the shape of the Great Pyramid? How can there be something sixy about circles?
Lavishly illustrated by the author, this small introduction to one of the oldest and most widespread subjects on Earth will forever change the way you look at a triangle, arch, church window, fabric design, graphic or spiral.
[A három megszokott dimenziót felépítő geometriai szemlélet] folytatását a valóságos életben találják meg. Az idő merőleges a három dimenzióra, ez a negyedik és növekszik. Ha az időt megelevenítik magukban, érzelem jön létre. Ha az időt önmagukban gyarapítják, mozgatják, az érző állati lényt kapják meg, amelynek valójában öt dimenziója van. Az emberi lénynek valójában hat dimenziója van.
Drunvalo also founded the Flower of Life Workshops with over 300 trained and certified facilitators teaching in over sixty countries.
He is consultant for the international Internet magazine, Spirit of Ma’at, http://www.spiritofmaat.com with over 1 million viewers each year.
Drunvalo is a world traveler and has given workshops, seminars and lectures on sacred geometry, human energy fields, spirituality, meditation and living in the heart in 45 countries.
His meditation with the angels and his work with prana and energy healing has helped tens of thousands of people. Drunvalo has expressed that healing in these areas are of extreme importance for the difficulties with one’s own body often stops us from continuing on our spiritual path. His research on the 3rd dimension with natural products and methods to help heal Mother Earth and all life forms is also a major focus in his life.
Over 40 years’ research has been carried out on the positive effects that rhythms and specific water flow has on water’s capacity to support life. Energizing Water presents this cutting-edge research to the general and professional reader at a time when interest in finding solutions to water’s huge worldwide problems is growing rapidly.
Three aspects determine water quality: its chemical constituents (including its oxygen levels); its organic aspects (with the danger of contamination by effluent, pathogens and algae); and its ‘energetic’ nature. The latter facet has been recognized from time immemorial by traditional societies, who have developed their own sciences in relation to water quality, using terms such as prana and chi for energy. Now, through the introduction of quantum physics into the life sciences, modern science is beginning to accept this concept, measuring energy as light emission.Research into energetic water quality – and particularly into the creation of moulded surfaces that support biological purification of the chemical and organic elements, as well as enlivening the energetic attributes – goes back to George Adams’ and John Wilkes’ pioneering work in the 1960s. The invention of Flowform technology in 1970 carried this research further, providing the world with one of the first modern-day, biomimicry eco-technologies. This creative technology applies nature’s best methods to produce extraordinary results, and this book outlines the background story on research and application of the Flowform method today.
JOHN WILKES originated the Flowform Method in 1970 following periods of work with George Adams and Theodor Schwenk. After further research, project work led to installations in many countries. In 2002 an Institute was built at Emerson College providing more adequate space for research into the qualitative effects of rhythmic movement on water.
JOCHEN SCHWUCHOW is a freelance research and teaching consultant at Emerson College in England.
IAIN TROUSDELL is director of the Healing Water Institute in NZ.
Gordon Strachan was a lecturer, church minister, and independent thinker. He was the author of six books, including Jesus the Master Builder (2000); Chartres: Sacred Geometry, Sacred Space (2003); The Return of Merlin; and Prophets of Nature (2006).
Having been originally trained as a classical painter, he has authored many books on geometry, including Order in Space, Islamic Pattern as a Cosmological Art, and Time Stands Still.
Critchlow was formerly a professor of Islamic Art at the Royal College of Art in London and teaches at the The Prince’s Foundation for the Built Environment in London. He founded Visual Islamic and Traditional Arts (VITA), which moved from the Royal College of Art to The Prince’s Institute of Architecture in 1992-3, where he was Director of Research. The Institute later evolved into The Prince’s Foundation, within which Prince’s School of Traditional Arts was housed. He is a Professor Emeritus at VITA and serves as Director for Research.
He is a leading expert in Sacred architecture and Sacred geometry and founded Kairos, a society which investigates, studies, and promotes traditional values of art and science. He served there as Director of Studies.
His architectural work includes the Krishnamurti Study Centre in England, the Lindisfarne Chapel in Crestone, Colorado in the United States with a special design for the vaulting of the dome, and The Sri Sathya Sai Institute of Higher Medical Sciences in Puttaparthi, India. Isaac Tigrett, who had founded the Hard Rock Cafe enterprise, secured Critchlow’s aid to design a hospital in the Prasanthi Nilayam ashram in Puttuparthi.Critchlow’s use of sacred geometry played a major role in these architectural designs and projects.
Dr. Critchlow is president of the Temenos Academy.
After leaving The School he continued publishing, inviting other alumni and friends, such as Daud Sutton (MA 1998) and Professor Scott Olsen, to help him create a small series of books specialising in the age-old themes he studied at The School. Now, nearly twelve years and 50 books later, Wooden Books may be found in bookshops throughout Britain and America.
During the 1970s he was the driving force behind Askin Publishers, producing lovely editions of classic magical works such as Agrippa’s Fourth Book of Occult Philosophy and the Archidoxes of Magic by Paracelsus, several titles by Austin Osman Spare, Aleister Crowley, Dr Donald Laycock (The Enochian Dictionary) and others, all of which are now collector’s items. The first of these was a huge quarter leather edition of the primary source book of Enochian magic, the True & Faithful Relation of what passed between Dr John Dee…and some Spirits. During the 1970s he co-wrote books with Francis King, including the still popular Techniques of High Magic, which has gone through many editions since it was first released. Also with Francis King he wrote Nostradamus. Then he followed this with the best selling Millennium Prophecies.
His interest in Western geomancy spurred him on to create the most complete and classic work in that field Terrestrial Astrology which is soon being reprinted as Geomancy in Theory and Practice.
In 2004 he began publishing Source Works of Ceremonial Magic. The first title was The Practical Angel Magic of Dr. John Dee’s Enochian Tables with co-author David Rankine, opening the doors on real 17th century angel magic in a way never done before. This was followed by The Keys to The Gateway of Magic and then The Goetia of Dr Rudd, a complete 17th century version of the Lemegeton as used by a practising magician. He and David Rankine produced a new edition of three versions of the most famous grimoire, the Key of Solomon as The Veritable Key of Solomon. Most recently they deciphered and translated the Grimoire of St Cyprian, the Clavis Inferni.
In 2006 he published The Complete Magician’s Tables with complete tables of Magic, Kabbalistic, Angelic, Astrologic, Alchemic, Demonic, Geomantic, Grimoire, Gematria, I Ching, Tarot, Pagan Pantheon, Plant, Perfume and Character Correspondences in more than 800 Tables, four times as many tables as Aleister, Crowley’s Liber 777, or any other imitator.
He was responsible for launching and publishing the first full colour magazine on feng shui, Feng Shui For Modern Living, which was distributed in 41 countries with translated editions in German and even in Chinese. At its peak the English edition sold over 121,000 audited copies per month, and Stephen was nominated at the PPA awards as UK ‘Publisher of the Year’ (the UK print media equivalent of the Oscars).
He was educated at Sydney University graduating in English Literature, Geography and Ancient Greek Philosophy. His interests include feng shui, ancient civilisations, geometry, travel, computers, magic and the Middle Ages. He is the author of more than 30 books published worldwide in 20 different languages. His books have had introductions by such diverse people as Colin Wilson, HRH Charles Prince of Wales, and Jimmy Choo shoe designer to the stars.
Architecte de formation, Stéphane Cardinaux cherche à concilier la science physique et la science éthérique à travers l’expérimentation des énergies subtiles. Son activité se répartit entre l’enseignement de la géobiologie et de la bioénergie, la recherche, les bilans bioénergétiques et les analyses de lieux d’habitation.
Le site de Stéphane Cardinaux : http://www.geniedulieu.ch/.
In India, he discovered the works of the French Egyptologist and esotericist, R. A. Schwaller de Lubicz, which led him to explore the principles and practices of ancient sacred science. Between 1965-8, Robert met his wife, Deborah Lawlor. In 1972, they left Auroville for a year so Robert could study sacred geometry and read Sri Aurobindo. They came back to Auroville in 1973 until 1975. In 1979, Lawlor (then living in Tasmania) participated in the Lindisfarne Fellows Conference, held at Zen Center’s Green Gulch Farm, with Keith Critchlow from London. In 1980, Lawlor met together with William Irwin Thompson and Rachel Fletcher to teach in the Lindisfarne Institute’s Summer Program in Sacred Architecture, which provided the context for the design and building of the Lindisfarne Chapel. Critchlow’s Twelve Criteria for Sacred Architecture derives from a lecture given at this time. In 1981, a gathering of about 50 members of the Lindisfarne Association met in Crestone, Colorado under the name, Homage to Pythagoras, which included Lawlor, Thompson, Fletcher, Chritchlow, Christopher Bamford, Arthur Zajonc, Anne Macaulay, Kathleen Raine, Robert Bly, Joscelyn Godwin, John Michell, and Ernest McClain.
This Franco-Germanic blend lends a curious characteristic to his work. The writer, Christopher Bamford, suggests that Schwaller thought in German, but wrote in French. He was given the title “de Lubicz” by the Lithuanian poet and diplomat O. V. de Lubicz Milosz, for his efforts on behalf of Lithuania in the aftermath of World War I.
René Adolphe Schwaller de Lubicz is known to English readers primarily for his work in uncovering the spiritual and cosmological insights of ancient Egypt. From 1938-1952, he and his family resided in Luxor, Egypt conducting research concerning many of the great monuments and temples, particularly the Temple of Luxor. In books like Esotericism and Symbol, The Temple in Man, Symbol and the Symbolic, The Egyptian Miracle, and the monumental The Temple of Man, Schwaller de Lubicz argued that Egyptian civilization is much older than orthodox Egyptologists suggest. He also argued that the core of ancient Egyptian culture provided a fundamental insight into “the laws of creation.”
Nothing in Egypt is accidental or purely ornamental – every element from the type of building material used, the size of the blocks, the dimensions of the walls, number symbolism, the placement of hieroglyphs and symbols, the orientation of the site – all were consciously chosen to have a predetermined effect. Even apparently mundane scenes of daily life can have profound symbolic importance. For example, scenes of the Pharaoh single-handedly overcoming an enemy army are not merely vainglorious boasting; they represent the forces of light overcoming those of darkness – the same battle that each evolving human being must fight every day.
In The Temple of Man, Schwaller demonstrates how the Egyptians were aware of, and consciously used, advanced mathematical concepts normally attributed to the Greeks. One of these was the Golden Section, a mathematical function which occurs throughout nature, for example in the ratios of a spiral galaxy or the orbits of the planets. When used in architecture, it allows the building to become an embodiment of these same universal principles, which were later used in Greek temples and Gothic cathedrals, and which account for some of their power. These elements work synergistically together to express the particular nature of the cosmic principles built into the temple.
Schwaller de Lubicz’s Egyptian studies were only a part of his overall work as a 20th Century alchemist and philosopher. One book by Schwaller de Lubicz, Symbol and the Symbolic (Du symbole et de la symbolique), expresses much of the philosophy of Time elaborated by the Zen masters. To read Lubicz is to understand how an Adept alchemist thinks, how the Elixir affects or clears his perception of reality. Lubicz only understood Egyptian esotericism after completing his alchemical studies. He makes clear that comprehension of ancient Egyptian thought will only be feasible if we change our Western mental paradigm.
His 1969 volume The View Over Atlantis has been described as probably the most influential book in the history of the hippy/underground movement and one that had far-reaching effects on the study of strange phenomena: it “put ley lines on the map, re-enchanted the British landscape and made Glastonbury the capital of the New Age.” In some 40-odd titles over five decades he examined, often in pioneering style, such topics as sacred geometry, earth mysteries, geomancy, gematria, archaeoastronomy, metrology, euphonics, simulacra and sacred sites, as well as Fortean phenomena. An abiding preoccupation was the Shakespeare authorship question. His Who Wrote Shakespeare? (1996) was reckoned by The Washington Post “the best overview yet of the authorship question.”
His formal art education began at the age of 11 (1951). He was the youngest student ever taken by Genevieve Ingram Frickle, a well known portrait and landscape painter, living, working and teaching in Wichita. She developed his natural drawing talent and taught him to see as an artist. Illinois – In 1954, the family moved to the Chicago area (Park Forest, Illinois) and Charles graduated from Rich Township High School in 1958.
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.
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.
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.
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.
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.
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.
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!
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.
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.
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.
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.
Movements of the planets are found to correspond accurately with simple geometric figures and musical intervals, pointing to an exciting new perspective on the ancient idea of the “harmony of the spheres.”
Hartmut Warm’s detailed presentation incorporates the distances, velocities, and periods of conjunction of the planets, as well as the rotations of the Sun, Moon, and Venus. Numerous graphics?including color plates?illustrate the extraordinary beauty of geometrical forms that result when the movements of several planets are viewed in relation to one another. Moreover, the author describes and analyzes concepts of the “music of the spheres,” with special emphasis on Kepler’s revolutionary ideas. The book also discusses current scientific beliefs about the origin of the universe and the solar system, enabling the reader to understand fully how this remarkable research supplements contemporary materialistic views of the cosmos. The appendix includes his mathematical and astronomical methods of calculation, as well as a detailed discussion of their accuracy and validity based on modern astronomical algorithms.
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.
His more than 300 colour illustrations reveal the secret code within these geometrical figures and how they express the spiritual meanings in the key numbers of 1 through 12. He identifies the various regular shapes and shows their constructions; their natural symbolism; their meetings, matings and ways of breeding; and their functions within the universal order. In the process, Michell helps us see the world in a new light. Disparate shapes and their corresponding numbers are woven together, resolving themselves into an all-inclusive world image that pattern in the heavens, as Socrates called it, which anyone can find and establish within themselves.
An understanding of the Platonic Solids, and their close cousins, the Archimedean Solids, has long been required of students seeking entry into ancient wizdom schools. This book, illustrated by the author, is a beautiful introduction to three-dimensional mathemagical space.
In this charming little book, Anthony Ashton uses a Victorian device called a Harmonograph to tell the story of Harmony and the intervals in the scale. With useful appendices and exquisite line drawings, this is a unique and original introduction to this magical subject.
Charles H. Hapgood – Maps of the Ancient Sea Kings: Evidence of Advanced Civilization in the Ice Age
Hapgood concluded that these ancient mapmakers were in some ways much more advanced in mapmaking than any people prior to the 18th century. It appears they mapped all the continents. The Americas were mapped thousands of years before Columbus. Antarctica was mapped when its coasts were free of ice. There is evidence that these people must have lived when the Ice Age had not yet ended in the Northern Hemisphere and when Alaska was still connected with Siberia by the Pleistocene, Ice Age ‘land bridge’.
Hemenway, Priya: A titkos kód – A művészetet, a természetet és a tudományt szabályzó rejtélyes formula
Ez a könyv nem csupán az aranymetszésnek a természetben, a művészetben, az építészetben, a zenében és a tudományban megjelenő sokrétű formáját mutatja be, hanem olyan változatait is, mint például az emberi belső fül aranyspirálja. A több mint 300 illusztráció és ábra segítségével megmutatja a világegyetem törvényeinek ezt az izgalmas szeletét és az ebben feltáruló rejtett „isteni tervet”.
A szerző, Priya Hemenway a montreali McGill Egyetem hallgatójaként matematikát és klasszika-filológiát tanult. Ezután több évig élt Indiában, tanulmányozta a keleti gondolkodást és filozófiát, a meditációt és a szent iratokat. Jelenleg a Bay Area régiójában él, s íróként és fotósként dolgozik.
that the way to cognizing the spiritual world is based on the natural scientific attitude, and that certainty of such knowledge is comparable to the certainty found in mathematics and natural science.
Drawn from Schiller’s notebooks, this important volume describes natural scientific research by scientists working at the Goetheanum and following suggestions from Rudolf Steiner, leading, for example, to research on gases at low temperatures and high vacuum. The Schiller File is an important resource for those who wish to better understand how to approach and practice natural science from the perspective of spiritual science
“…Theodor Schwenk is a seminal exponent of an alternative reading of nature… To study this book is a transforming experience in which meaning and beauty are restored to our world…” – Kathleen Raine
Why does water always take a winding course in streams and rivers? Do common principles and rhythms underlie its movement – whether it be in the sea, in a plant, or even in the blood of a human being?
In this seminal and thought-provoking work, the laws apparent in the subtle patterns of water in movement are shown to be the same as those perceptible in the shaping of bones, muscles and a myriad of other forms in nature. Fully illustrated, Sensitive Chaos reveals the unifying forces that underlie all living things. The author observes and explains such phenomena as the flight of birds, the formation of internal organs such as the heart, eye and ear, as well as mountain ranges and river deltas, weather and space patterns, and even the formation of the human embryo.
A perennial bestseller since publication, Sensitive Chaos is an essential book for anyone interested in the mysteries of life on earth.
THEODOR SCHWENK (1910-1986) was a pioneer in water research. He founded the Institute for Flow Sciences for the scientific study of water’s movement and its life-promoting forces. A prolific writer and lecturer, he contributed original insights to the production of homeopathic and anthroposophic medicines, developed ‘drop-pictures’ for analysing water quality and methods for healing polluted and ‘dead’ water.
It is the living movement of water that makes life on Earth possible. Based on spiritual science and on their own numerous experiments, Theodor and Wolfram Schwenk show that our Earth is a living organism, with water as a sensory organ that perceives vital cosmic influences and transmits them into earthly life. This pioneering classic on water is more relevant now than ever before.
An Introduction to Modern Geometry
This classic examination of Projective Geometry will be a great aid to Waldorf teachers and others seeking to penetrate the thinking behind this important topic.
Steiner suggested that it was important to understand counterspace as a necessary supplement to the conventional approach. His colleague George Adams found a way of describing counterspace through mathematics.
This book seeks to relate the phenomena of our world to both space and counterspace, in order to lead to a new scientific understanding. If counterspace is real, then the resulting interplay between it and ‘ordinary’ space must be significant. This concept is applied to gravity, liquids, gases, heat, light, chemistry and life. Each aspect is a separate investigation, but the various threads begin to weave into a unified whole. A new concept of time, and indications for a new approach to relativity and quantum physics begin to emerge.
The results presented in this book are part of a ‘work-in-progress’, shared by others around the world, involving a new scientific consciousness. It attempts to approach a spiritual understanding without surrendering scientific and mathematical rigour.
NOTE: This book contains advanced mathematical and scientific proofs which are likely to be too difficult for the general reader.
NICK THOMAS trained as an electrical engineer in the Royal Air Force, serving as an engineering officer for sixteen years and, subsequently, worked in data communications for Nortel. He then became General Secretary of the Anthroposophical Society in Great Britain for 21 years. With Lawrence Edwards and John Wilkes he researched the practical application of projective geometry. His major research interest is the development and application of Steiner’s discovery of negative space to building a bridge between natural and spiritual science. He lectures widely on this and other subjects. His new book Space and Counterspace is just published.
Many people feel alienated by modern science and its impersonal view of our world, based on the concept of the ‘detached observer’. Our human intuitions suggest that we need a broader-based science which can encompass phenomena currently excluded, such as human consciousness, qualities and values. In this groundbreaking book, Nick Thomas presents a wider view of science using the theory of ‘counterspace’. Counterspace exists alongside space as we know it, and was first proposed by Rudolf Steiner, and developed by the Cambridge mathematician George Adams. Through its startling lens, key aspects of our world – such as gravity, time, light and colour, as well as the stars, the solar system, and the classical elements – can be viewed and understood in dynamically new ways.Thomas’ work and ideas are on the cusp of a true revolution in the way modern scientific method can penetrate even deeper into the mysteries of our natural world.
George Adams,Olive Whicher – The Plant between Sun and Earth, and the Science of Physical and Ethereal Spaces
Although science has explained in great detail the complex chemical and physiological nature of plants, it has neglected the study and recognition of how matter is arranged into the shape and pattern of living things. Goethe’s organic concept and Rudolph Steiner’s imaginative idea of formative forces have inspired the authors in this work….
“In order to describe these principles of form, it was necessary to folow new ideas contained in modern Projective Geometry — developing a new geometry of living things.”
She shows the broad and profound nature of “counterspace”—etheric sunspace—and sheds light on unsolved questions of science and life. Liberally quoting Rudolf Steiner, she places the development of mathematics and spiritual science within the context of the evolution of consciousness.
Anyone interested in projective geometry, the science of the etheric realm, and the future of thinking will find this a fruitful text.
After extensive research, however, he found that it has extraordinary mathematical properties, suggesting that it may be no less than the source of the number system used when ancient humanity first built cities. He shows that the starcut diagram underlies many significant patterns and proportions across the world: in China, the shaman’s dance; in Egypt, the Great Pyramid; in Europe, a Raphael fresco; in Asia, the Vedic Fire Altar, and many others. This book is an intellectual adventure, written for a general reader without specialist knowledge. Illustrated with around 180 photographs, drawings and diagrams, it tells the story of many fresh discoveries, bringing sacred geometry to life in an original and inspiring way.
The book is written from a rather scientific standpoint so don’t expect a discussion on higher consciousness. However if you’ve ever considered the importance of a visualization in the use of sacred geometry such as ancient mandalas for meditation or energy projection you will find that nature manfiests through these scientic explorations and to some extent may validate some people’s belief that simply because we cannot see things doesn’t mean they are not there.
In the book, Edward’s gave a fuller account of his research, widening it to include the forms of plants, embryos and organs such as the heart. His work suggests that there are universal laws, not yet fully understood, which guide an organism’s growth into predetermined patterns. His work has profound implications for those working in genetics and stem-cell research. Edwards died in 2004 at the age of 91 and Graham Calderwood has edited and revised this classic work.
Lawrence Edwards researched and taught projective geometry for more than 40 years. Here, he presents a clear and artistic understanding of the intriguing qualities of this geometry. Illustrated with over 200 instructive diagrams and exercises, this book will reveal the secrets of space to those who work through them. It is also a valuable resource for Steiner-Waldorf teachers.