A Beginner's Guide to Constructing the Universe by Michael S. Schneider

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How I Came to Write A Beginner's Guide to Constructing the Universe
By Michael S. Schneider

Michael S. Schneider

As a youngster schooled in the US during the 1950’s Sputnik era I was exposed to the sciences, including NASA rocket launches, facts about the moon and planets, kitchen chemistry, supermarket encyclopedias and Mr. Wizard on television, and became very interested in all kinds of scientific wonders, with a passion for electricity and magnetism, chemistry sets, Erector sets, model rocketry, the microscope and Ripley’s Believe It Or Not books. However, I wasn’t an exceptional math student. Mathematics was mostly presented as the memorization of rules and boring paper drill, but I kept up. Yet in my mid-teens I became earnestly interested in the geometry of nature and began lifelong research into the subject, not suspecting everywhere it would lead. I remember pondering the same hexagonal shape found in the beehive, quartz crystal and metal hex-nuts. I could understand how a crystal grew mechanically in this precise geometry by accumulating atoms, but how did bees know how to produce the pattern which holds more weight of honey than, say, a checkerboard pattern? I wasn’t comfortable with the “trial and error” explanation, and even if it was in their DNA how did that knowledge of superior design get there? And then there were spirals, particularly the logarithmic spiral, appearing in atomic spin-outs, seashells, embryos, tails, claws, my own fists, bathtub whirlpools, dust devils and swirling leaves, tornados, hurricanes, solar systems and galaxies. I found books about each of these subjects but kept looking for one book which would put it all together and explain it in a unified way. I scoured libraries wherever I travelled (this was long before the internet) and kept notebooks of research. Living just outside New York City, the NY Public Library became my primary focus when, before computers, there was only a vast card catalog. At that time (mid 1960’s) the most interesting books which discussed my interests were written in heavy, dusty but well-produced and often gilded volumes of the late 19th and early 20th centuries including The Curves of Life by Cook, On Growth And Form (the unabridged version contained an omitted chapter on Fibonacci numbers!) by Thompson, Nature’s Harmonic Unity by Coleman, The Geometry of Art and Life by Matila Ghyka, and The Elements of Dynamic Symmetry by Jay Hambidge. Immediately I was plunged into the mathematics of various spirals, the Fibonacci numbers, the marvelous Golden Ratio, the Platonic and Archimedean Solids and more. I subscribed to the newly published Fibonacci Quarterly and acquired many of their self-published books on the Fibonacci and Lucas numbers and related subjects. The mathematics was mostly beyond me, but steadily I grew into it. Formulas, proofs and equations became less intimidating as mathematics seemed to be a kind of poetry written in a cosmic, even sacred language.

Since the age of seven I’d been interested in simple electric circuitry and as a teen built some logic circuits described by Claude Shannon, using electromagnetic relays scavenged from old telephone switching banks found in electronics junk shops which were around in those days. In 1964 and ‘65 I visited the New York World’s Fair more than a dozen times, marveling at its techno-vision of the future. At that time I communicated with Edmund C. Berkeley about the primitive but fascinating Brainiac computer kit I had purchased from him (I still have the manual). In 1966 I learned to program an IBM 360 and a Philco 2000 computer in FORTRAN using punch cards. Coincidentally, one of the first assignments, a standard task, was to write a program generating the Fibonacci sequence. In contrast to any techno-vision of the future I attended the Woodstock Festival in 1969.

Absorbed in my research concerning the shapes of nature I decided to major in mathematics at the Polytechnic Institute of Brooklyn to learn this language so that I wouldn’t be intimidated by any mathematics I encountered. Further exposure to the history of mathematics revealed a great world of mathematicians, scientists, philosophers and artists, opening wide the doors of my interests in all directions. I graduated with a B.S. Mathematics in 1972.

I took the saying attributed to Pythagoras that “All is number” and Galileo’s idea of a “Book of Nature” quite literally:

“Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”

I deeply wanted to understand this language and kept looking for one book which would explain it all to me, especially the significance of the shapes of nature’s geometric alphabet: the circles, spheres, triangles, squares, pentagons, hexagons, spirals and the rest which become obvious around us when we simply look. It became clear that shapes represent ideas and principles, and the simpler the number the more pervasive it is throughout nature.

Most people can feel why a circle represents unity, wholeness, completeness, and aren’t too surprised when shown how it holds more inside it than any other shape with the same perimeter. That is, a round pizza can hold more toppings than triangles, squares, rectangles or any other shaped pizza having the same length of crust. Unity is all there really is, but polarity is required for any creation, so One casts its own shadow and pretends to be Two to generate the single digits:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

The number Two is clearly about polarity, division, opinion, contrast, conflict, cooperation and creation. It was reviled in ancient times for breaking unity yet has a crucial role in the cosmic creating process. It takes two to create, from two parents to lighting a match by friction, and the two legs of a geometric compass using one still point to generate the infinitely many points of a circle. The Unity broken by Two is restored in Three as we can see in a tripod or braid of hair, the electron and proton balanced by the neutron, as the conflict between two lawyers is resolved by a judge. And so it goes with the simple numbers and their shapes, each expressing its principles in ways only it can. Each number has a different personality and they each play a variety of roles in this dynamic cosmos just as a small group of actors can change their guises for different situations, with just a few actors playing many roles. The universe appears first as an alphabet of shapes forming patterns of words into the sentences, paragraphs, chapters of a book, a great play with great actors in great parts telling great stories. The full company of actors, the numbers 1 through 12, naturally form four groups:

First Principles: 1 and 2
Numbers of Structure: 3, 4, 6, 8 and 12
Numbers of Life: 5 and 10
Numbers of Mystery: 7, 9 and 11

I’ve written a brief summary of the significance and symbolism of the numbers 1 through 12 here.

The more I learned, the more I felt annoyed that I wasn’t taught this shape-language in elementary school. I certainly would have appreciated math instruction better. So at age 20 I decided to organize my research and write the book I was seeking, to share with others in the simplest manner possible the marvelous knowledge I had found. I drew inspiration from past researchers, and took the approach of Renaissance priest Giordano Bruno who wrote about the numbers one through ten, the single digits and the beginning of their next cycle, as universal principles. The single digits, of which all numbers are composed, seemed to be a complete approach which would leave nothing out. Ten, eleven and twelve continue their principles. I wasn’t much of a writer and gradually had to learn to build ideas in a logical, flowing natural order. I found the process of writing to be challenging but charming, and handwrote my manuscripts and illustrated them in the fashion of a Medieval illuminated manuscript. I soon found that this was not what publishers wanted to see, but I persevered, learning something from each failed attempt at publication, all the while kept enlarging and refining every new version.

Three days after graduating college in 1972 my younger brother and I took a few months to hitchhike across the USA from New York to California and Oregon. Along the way I was fascinated by the leaf and branch arrangements of the wide variety of plants I came across in various ecologies across the continent. I delighted in verifying the existence of Fibonacci phyllotaxis and marveled at all the variations on one theme in this world of living mathematics.

Since 1970 I had also been reading Ouspensky’s Tertium Organum and In Search of the Miraculous, along with Gurdjieff’s All and Everything where I was struck by the idea of legominisms, of a worldwide heritage of art and monuments passing important knowledge through the generations, whose message was understood through their symbolism and proportions. I read Churchward’s The Sacred Symbols of Mu camped in the Colorado Rocky Mountains. In 1970 I had also come across the writings of Vitvan, an American master trained in the early 20th century in the ancient Hindu tradition of meditation. His writings provided deeper insight into this cosmos as a vast energy system and the geometric language of nature which can be understood as consciousness manifesting materially as geometric configurations of units of energy, atoms. I think he’s correct in that each of nature’s forms in this living cosmos, from crystals to flowers to creatures, planets, stars and galaxies, is a geometric expression revealing the state in which it’s conscious. Consciousness itself is evolving, trailed by its form. I was amused to realize that the words “matter” and “pattern” derive from the Latin mater and pater, “mother” and “father” -- the cosmos takes the form of matter in patterns; i.e., the Periodic Table of Elements, etc. Through Vitvan I was also introduced to the longest and most profound poem written in English, Savitri by Sri Aurobindo Ghose, the astrological language of Biblical symbolism in The Restored New Testament by James Morgan Pryse, and Science and Sanity by Alfred Korzybski with his teachings of “General Semantics” and how the words we use and think with influence what we “see”.

In Autumn 1972, back in New York City, I came across The View Over Atlantis and a year later City of Revelation by John Michell, and my understanding of the significance of numbers, and legominisms, changed forever. He inspired me, and a great many people, to see the ancient world’s monuments, mythologies, landscapes and traditions anew. He re-introduced the history and significance of feng-shui and ley lines, and revealed our worldwide heritage of monuments as repositories of mathematical and geodetic knowledge. He revived an appreciation of the writings of both Plato and the writer and researcher into anomalous phenomena Charles Fort, of the idea of cultural enchantment and a living cosmos. And perhaps most importantly he revealed the heart of the mathematical traditions in his New Jerusalem and Cosmological Circle diagrams, keys to understanding the proportions of monuments, temples, cathedrals, layouts of cities, placement of capitals and countries and the proportions of the entire cosmos. It helps to realize that the Greek word kosmos means embroidery. I studied his two books closely.

In 1973 I moved to the warmer clime of northern Florida where I was able to examine closely the geometry of the lush world of semi-tropical plants, appreciate the warmth and dignity of Southern friends, and earned a Master’s Degree in Mathematics Education, with an emphasis on the hands-on math laboratory approach. The next year I found myself teaching science and math in the new idea of a Middle School. If you want to know if you really understand a subject, and to learn how to lay out ideas in a simple, growing sequence, teach 11 to 13 year olds. I did that for a dozen years. Fortunately I had leeway in what I taught and was able to introduce the Fibonacci numbers and Golden Ratio to youngsters, showing them the marvels of this mathematics and how to observe them in everyday plants. It was as interesting and eye-opening to them as it had been to me. Most importantly, I learned by teaching children how people in general learn, and saw the importance of hands-on experiences in real-world situations. I felt even stronger that a wider audience should know about this great geometric language of nature and its connections with human culture. In the late 1970’s the school acquired a number of TRS-80 computers and a dot-matrix printer which improved my ability to organize my writings and communicate ideas.

In 1977 I traveled to India for two months as part of a Fulbright-Hayes grant taking public school teachers there to learn about India and create lessons to teach that it wasn’t all elephants and snake-charmers. My specialty was the ancient Indian sciences and mathematics, particularly the astronomical parks with their variety of giant sundials, stardials and moondials. At the time India had virtually no television and I got to see it as it must have been for millennia. I studied the proportions of temples and monuments, visited schools of traditional art (noting their geometric textbooks) and came across interesting people and books which discussed geometry, proportions and the ancient Hindu Vastu Shastra (“Science of Construction”) including The Hindu Temple by Stella Kramrisch, and later Architecture, Time and Eternity by Snodgrass and the idea of the temple as symbol of the journey within.

After a dozen years teaching in a Florida Middle School, in 1986 I returned to New York City and after a stint in the background helping make TV commercials I was fortunate to find work on educational projects for the New York Academy of Sciences, which was was tremendous fun. My job was to wander around the city and look for examples of science and mathematics the public would be interested in. I delighted in the 250-million year old spiral fossils in the limestone façade of Tiffany’s, the variety of 3-cornered cracks in the sidewalks and the spiraling steam rising from mandala-like manhole covers. I often went with binoculars to the 107th floor observation area of the south World Trade Tower and to its 110th level top outside. (Filling the space between those floors I saw the building’s immense concrete counterweight on its giant springs.) From there I could watch birds rise in spirals over the warm, black tar roofs of buildings, then sink in cooler spirals over parks and trees, all without flapping their wings. I saw countless water tanks atop buildings with their metal bands circling the old, wooden, barrel-like cylinders in a pattern from top to bottom in proportion to the increasing water pressure. Bringing science to the public (with help from Mr. Wizard’s experiment designer) we installed an electronic scale into the floor of the tourist elevator of the south World Trade Center Tower to show by digital display how everyone’s combined weight changes due to inertia when it begins to move and then when it slows down. We also put on an exhibition of the scientific-surreal paintings of Remedios Varo. It was wonderful work but stopped when the department closed.

For the next few years I honed my skills by writing articles and regular columns for youngsters in various Scholastic magazines including DynaMath, Science and Computers, and Science World, including articles and posters about spirals, Fibonacci numbers and design in nature. From 1986-87 I was the creator and writer of the weekly "Mother Nature" segment at WNYC-FM radio on the popular live broadcast "Kids America" program, where Mother Nature had a problem each week which were solved with help from the call-in audience. Unfortunately, the actress who played Mother Nature knew no science but wouldn’t follow the script or take direction and sounded like a barfly but the show ran a dozen episodes. In 1986 I also volunteered to run the office part time at the School of Sacred Arts in Greenwich Village where I was able to attend classes learning to paint Tibetan tankhas, studying Egyptian language and symbolism with artist Mark Hasselriis who became a friend, and Jean and Katherine LeMee who taught the mathematics of the musical octave (numerically and geometrically) and thus we sang the proportions of a cathedral. I electrified a painting I made of Egyptian art (all the deities’ eyes were light-sensitive) to play musical notes determined by the shadows of passers by. Fate stepped in when I attended and taught classes in Sacred Geometry at the New York Open Center which is where I first met John Michell and through him Keith Critchlow and others involved with sacred geometry and its philosophical, architectural and other significances. What I liked about this British group was that they weren’t “new age” but a continuation of the traditions of mathematics deriving from (pre-) Egypt through Pythagoras and others including the cathedral builders. This numerical philosophy is timeless and not composed by anyone but is inherent in the universe and periodically re-discovered, and that’s what they did, standing on the shoulders of Plato, the Neoplatonic philosophers and others who pondered the essential nature of numbers and cosmos.

I was absorbed by The Great Pyramid by Thompkins and its Stecchini appendix was my first real introduction to historical metrology, followed by Berriman. After that I read Serpent In the Sky: The High Wisdom of Ancient Egypt and The Traveler’s Key to Ancient Egypt and soon met the author, the symbolist Egyptologist John Anthony West at the NY Open Center, and appreciated his great realization of water erosion around the Sphinx, and through him the writings of Schwaller de Lubicz and Lucy Lamy. John Michell and John Anthony West became close, lifelong friends and colleagues. Through the “sacred geometry” lectures of Keith Critchlow I found myself gravitating to the Cathedral of St. John the Divine, the world’s largest church (601 feet the length of a football field plus a football) in upper Manhattan and its obscure, unique Library of Sacred Geometry overseen by June Cobb. It was located up a narrow, stone spiral stairway and along the triforium above the main space. I visited so many times that I was given a key to its door and spent many hours alone perusing its contents, which included the papers and geometric models of Matila Ghyka donated by his son, and obscure writings I never came across in any other library. I pored over and absorbed everything I could. I also spent many hours there outside, observing the masons creating the Cathedral, erecting the structure and sculpting the statues. Eventually I engaged in conversations with the master mason, Simon Verity, with whom I enjoyed discussing the cathedral’s geometry. He let me examine the cathedral’s large architectural blueprints that the masons were following, including its exact measurements which allowed me to understand even more deeply the mathematical proportions of a cathedral (this one was designed in the French tradition) and its geometric symbolism. I discerned the geometry of the façade and the octagonal space comprising the front patio and stairs to the street. It turned out that the large rectangular block at the front entrance which he was about to carve into a number of statues had the proportions of the square root of 3 and showed him the ways it could be harmoniously subdivided, as well as its intentionally placed relationships with the façade, the door and the space in front of the cathedral. As a result he organized the individual sculptures harmoniously with each other and with the building and space before it. Hardly anyone knows that Simon made the eyes of the line of sculpted personages each follow the visitor up the stairs in their sequence, each looking at a key point in the geometry then passing us to the next set of eyes, watching us enter each step from the street up to the central front door. I have also since learned to play Rithmomachia, the “Battle of Numbers” or “Philosophers Game,” the only game allowed to be played in the Medieval monastary schools and cathedrals. (It was the model for Hesse’s Glass Bead Game.) I can understand why it was studied and played in cathedral settings and among the educated of the Renaissance. It’s based on the mathematics of the musical scale. Players advance numerically and geometrically, building musical harmonies to convert the opponent. The object of the game is not to destroy the opposite side but to incorporate them into a grand musical harmony. Its players were simultaneously studying simple mathematics and number theory, the proportions of cathedrals and the musical composition underlying Gregorian and other chants based on pure Pythagorean tuning. After six centuries the game disappeared when learning mathematics went from a philosophical pursuit to its present business and commercial orientation.

High on my list of delights found in New York City at that time were weekly dinners at the apartment of Charlie and Evelyn Herzer, who were deeply involved in Egyptian studies and had an exceptional Egyptian library. The conversations with Mark Hasselriis, John Anthony West, Rolling Stone writer Jonathan Cott (when he came out with Isis and Osiris), occasional curators from the Egyptian wing of the Metropolitan Museum of Art (including James P. Allen) and a core of others were great and rollicking feasts of food, wine and discussion, perhaps something like Plato’s symposia. At the time I felt I developed enough insight into ancient Egypt to lead public tours of the Egyptian Wing at the Met, discussing more than the usual tour guide would, instead focusing on the symbolism of deities, colors, shapes, numbers, proportions and more assembled in that great collection. I even led workshops including "Science in the Art Museum", "The Mathematics of Islamic Art" and "Showing Children Harmony" for public school teachers in the Met’s Education Department.

All the while I was working on my book about the principles and appearances in nature and culture symbolized by the numbers one through ten, and began to develop a book proposal suitable for a potential agent to represent. At that time, just before Windows first appeared, I found full-time work as a computer consultant and software trainer. I specialized in “desktop computing” (PageMaker, Quark, Photoshop and CorelDraw) so that I could create my own illustrations and learn to apply a professional look and layout to my writings about numbers in order to attract a publisher. I conducted classes for countless corporations, businesses and organizations ranging from Revlon and MTV to the New York Times and the United Nations where I taught for a year. I also spent a lot of time teaching in both World Trade Towers. At one point I helped a rabbi organize a database for studying the letter combinations of the Torah in what became known as the Bible Code. During free time I alternated my writing with electronics projects, having access to the old electronics junk shops found in those days on Canal Street in Chinatown, now long gone. I mostly built electronic musical instruments that could be played without touching them except by shadow or proximity, including a flute played by clouds moving through the sky, and a stringless guitar played by breaking infrared beams.

I had been calling my tentative book “Reading Nature’s Patterns” or maybe “The Timeless Alphabet.” But on a visit to John Michell in London around 1991 he came up with the delightful name “The Beginner’s Guide To Constructing The Universe” and offered to write its Preface, which gave me greater inspiration to complete it. Over the years my stays at John’s place in Notting Hill were unforgettable high points in my life. It was his custom to stay up all night reading, studying and doing geometric constructions with a compass which often turned into watercolor paintings covering most every surface in his flat as they dried. There were readings aloud from Plato, Fort and others, computing the size of the small gold pyramidion once atop the Great Pyramid, discussing historical metrology and geodetic measures, the proportions of Jerusalem and Solomon’s Temple, the growing surge of crop circles about which he published The Cerealogist, and so much more. I witnessed many rosy London dawns transformed by John’s presence. We visited Keith Critchlow’s school where I met students using traditional geometric constructions to produce timeless designs for art and architecture. At Glastonbury we made measurements of architecture to verify his insights. Through John I met Christine Rhone, co-author of Twelve-Tribe Nations and the Science of Enchanting the Landscape, still a friend, and also John Neal who developed their findings into his seminal book All Done With Mirrors, which solves modern confusion about metrology by showing all ancient systems (with metric as the exception) to be interrelated with each by simple fractions, themselves fractions of the Earth’s dimensions, with its three diameters: polar, mean and equatorial. Who or how someone mapped the dimensions of the entire planet in deep antiquity to such an astonishing degree I don’t know, but traditional measures worldwide demonstrate a knowledge of it and sophisticated mathematical skills and understanding beyond what is accepted in today’s orthodoxy. But some astute archaeologist will soon realize the importance of Michell and Neal’s work in this area and stop measuring sites in obfuscating meters but instead apply the exact measures for cubits used by the ancient designers themselves, now available through Neal’s various writings. Through them I met John Martineau (“Miranda Lundy”) author and editor of the important Wooden Books series. Other important books for understanding the tradition of geometric composition in art include The Painter’s Secret Geometry by Bouleau and The Power of Limits by Doczi whose workshop I attended at the NY Open Center and Sacred Geometry by Robert Lawlor (who also translated Schwaller).

In the early 1990’s I taught a small group of students including artists and others interested in nature’s geometric and symbolic language in the loft of artist Buffie Johnson who was a friend of Carl Jung and a student of Egyptology and esoteric studies with Natasha Rambova (the wife of Rudolph Valentino), as was Mark Hasselriis. Finally, in 1992, through luck and perseverance, and my agent John Brockman, the proposal for A Beginner’s Guide To Constructing The Universe was purchased by HarperCollins and edited by Eamon Dolan. I then spent two years working on it full-time which meant writing from sunrise to noon or 2pm, after which I had lunch, explored the city, met friends, pursued research and attended workshops and events. A few times a week I’d stroll across Central Park to the Metropolitan Museum of Art to study the art of various cultures, noting examples of geometry, proportions and symbolism. The book was published in November 1994, their first book published completely digitally since I was able to deliver it on small diskettes. My intention for the book was to share in a simple fashion this research which excited me, digesting and translating what I found for the non-mathematical reader, especially for those people who don’t think they’re a “math person” because their natural appreciation of the wonderful and inspiring world of mathematics was stifled and smothered at an early age with the paperwork of a standardized education with dry textbook “problems” (even the name -- who needs more problems in their life?), and memorizing without understanding, moving too quickly and mired in pointless examples.

Instead, educators would find teaching mathematics easier and fun (but for the standardized requirements) by bringing out the natural excitement of children which comes about when teaching math through the shapes, patterns and proportions found in nature and in worldwide traditions of art, architecture and technology. Reading nature’s geometric language tells us what nature is doing in any situation. Is it going for strength, stability, maximum area or minimum volume? If we understand it’s language we can cooperate with this vast energy-system in which we’re integrated and actually function. In my opinion, learning mathematics through nature should be a basic part of all elementary education. It should be an important part of all environmental studies. I even expect that the simple language of numbers, shapes and proportions will be handy to know someday to communicate with intelligent alien life. Numbers and the principles they represent are timeless. No one invented them, they came with the universe and are all-pervading. Their symbolism arises naturally from each number’s inherent nature, its simple arithmetic properties and its relations with other numbers. That won’t ever change and so it’s no wonder it’s always been the official language of the cosmos. As I wrote, the universe may be a mystery, but it’s not a secret. We can see its principles through the study of numbers which are always the same and available to anyone at any time in history. It seems to me that the most outstanding characteristic of the cosmos is wisdom. As the most fundamental of Plato’s archetypes, numbers are ambassadors from eternity here to help teach this wisdom, showing us who we are and how best to live in this dynamic, beautiful cosmos of wise design. It seems to me that every citizen of this universe has a responsibility to be familiar if not fluent in the language in which it’s all written.

My book isn’t for everyone. If you’re expecting equations, formulas and such abstractions you’ll be disappointed. Rather, it’s about encouraging ordinary people not trained in mathematics to look at the world for themselves through new eyes provided by simple numbers. It’s an introductory education in reading nature’s language, seeing the ways that simple numbers pervade the designs of technology (have you noticed the geometric variety of wheel rims lately?). Numbers inform every culture through religion, mythology, folk tales, fairy tales, sayings and proverbs.

Over the years I collected quotations relevant to numbers, their principles and studies, some of which line the book’s wide margins. They’ve turned out to be quite popular.

Through a casual suggestion from my friend David Fideler, publisher of The Pythagorean Source Book and Library and other traditional works of sacred geometry and perennial wisdom, I found myself Dean of Mathematics and Dean of Science at the private Ross School in East Hampton, New York, during 1996-97. This fascinating experience confirmed that even when a school has unlimited funds its true value comes down to the teachers, their knowledge of the subject in as wide an interconnected context as possible and most importantly having inspiration and a love of learning to ignite their students. In 1996 David and I held a workshop where he audibly demonstrated the mathematics of the Pythagorean musical octave and I presented a class on the Fibonacci numbers in nature.

In the nineteen years, one Metonic cycle, that the book has been in print I’ve felt satisfaction seeing its positive influence on teachers, students, writers, artists and creative people in general, and in inspiring people who didn’t think they could enjoy anything mathematical. I was amused to hear a woman tell me that every day her ten year old grandson climbed a tree to read the book in its branches.

For the past 16 years I’ve been living in northern California where I’ve found a most receptive audience and so have offered classes and workshops to young and old. For three years I had my own Constructing The Universe Classroom for both adults and youngsters dedicated to these studies of mathematics (especially geometric construction) and its relations to nature, art, philosophy and symbolism. A useful text for adults was John Michell’s posthumously published How the World is Made: The Story of Creation According To Sacred Geometry. In these years I’ve also written a series of six Constructing The Universe Activity Book workbooks offering hands-on activities with a compass and straightedge upon images of nature and art to reveal their openly-hidden proportions. Last year I came out with a DVD titled A Journey From 1 to 12 incorporating the fullest expression of number interactions necessary to understand all the forms and proportions of nature through the cosmos. It’s dedicated to John Michell. For the past dozen years I’ve been teaching a course called “Mathematical Ideas for Artists” at the California College of the Arts in San Francisco, California. When I tell people that I teach math to art students the response is nearly universal: oh, those unfortunate, sensitive art students, required to endure a dulling math class. But when I explain that I teach about the proportions of nature, the natural symbolism of numbers and shapes, and the ways that great artists, architects and designers have used this very knowledge of shapes and proportions to create universally beautiful works, most people easily understand and recognize the rightness of this approach. Rather than being rigid, it offers the artist harmonious suggestions. I’m teaching it as Durer might have. Students in the same class with differing majors from furniture and fashion design to sculpture, ceramics, jewelry, graphic, textile and industrial design, photography, illustration, oil painting and architecture all find something perfectly applicable to enrich and improve their different compositions. My delight over these forty years of teaching has been to research and learn wherever my interests go and then create educational materials to teach what I’ve learned. The study of numbers, which I consider to be a healing activity, allows the soul, as Plato said, to purify and become a worthy vessel for wisdom to enter. I especially enjoy teaching youngsters who, before they’re dulled by headucation, naturally understand all this and are eager to learn about the gentle mathematical language of reality. At the moment I’m working on another DVD, this one showing teachers how to teach mathematics through the plant world. I hope to follow it with a book about my research into the intentional geometry and mythological language of symbolic shapes and proportions apparently used to design Egyptian art, crafts, architecture and monuments in keeping with ma’at, maintaining the ideal natural order of cosmos through the righteous and harmonious proportions of all things. In my spare time I enjoy exploring this energy world with a metal detector.

Michael S. Schneider
San Anselmo, CA
19 October 2013



Michael S. Schneider has been an educator for four decades. He delights in teaching about the intersections of nature, science, mathematics and art.

He has a Bachelor of Science degree in Mathematics from the Polytechnic Institute of Brooklyn, and a Master's Degree in Mathematics Education from the University of Florida.

He’s taught youngsters in public and private schools at the Middle School and Elementary school levels since 1974. In 1977, Michael was a Fulbright-Hayes Scholar in India studying ancient mathematics and sciences. He has been a computer consultant at the United Nations, Nickelodeon, MTV, NY Times and many other corporations.

He has worked for the New York Academy of Sciences, and wrote articles, posters and teachers' editions for various Scholastic magazines. Michael was the creator and writer of the weekly "Mother Nature" segment at WNYC-FM radio on the popular live broadcast "Kids America" program (1986-87). He's also held workshops for educators at The Metropolitan Museum of Art in New York through their Education Department including "Science in the Art Museum", "The Mathematics of Islamic Art" and "Showing Children Harmony".

In 1993 Michael worked with master stonecarver Simon Verity to design the geometry harmonizing the statues on the south side of the "Portal of Paradise" (central entrance) to the Cathedral of St. John the Divine in New York City. During 1996-97 Michael was the Dean of Mathematics and Dean of Science at The Ross School in East Hampton, NY. He presently lives in northern California where he's a Senior Adjunct Professor at the California College Of The Arts (San Francisco) teaching art students "Mathematical Ideas For Artists." He's also taught at the Ex'pression College For Digital Media in Emeryville and the Sophia Center For Graduate Studies in Culture and Spirituality at Holy Names University in Oakland.

Michael is the author of "A Beginner's Guide To Constructing The Universe: The Mathematical Archetypes Of Nature, Art and Science" (HarperPerennial paperback 1995), six "Constructing The Universe Activity Books," a DVD “Journey From 1 to 12” and numerous articles concerning mathematics and teaching mathematics through nature, art science and philosophy. His website is http://www.constructingtheuniverse.com/

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