Sunday, May 29, 2011

Wilson Bentley: The Snowflake Man (No Two Snowflakes are Alike)

ON the ninth day of February 1865, Lee's army was evacuating Richmond while Grant's army was moving southward to block the retreat. And on that same day, in the small village of Jericho in northern Vermont, Wilson Alwyn Bentley was born. By the time of his death, 66 years later, he was known to thousands around the world as the Snowflake Man. His researches into the mysteries of rain and snow were discussed in over 100 newspaper and magazine articles, in 10 technical articles in the Monthly Weather Review, and in his book 'Snow Crystals." His painstaking work, carried out entirely by himself on his small Jericho farm, was so thorough and gave such new insights into the formation of precipitation that he deserves the title of America's First Cloud Physicist.
The Bentley homestead was in a valley on the east end of Jericho snuggled up at the base of Bolton Mountain. The country winters were long and hard, and in those days attendance at the one-room schoolhouse was very infrequent. Perhaps it was because of this that Bentley obtained his lifelong passion to study and understand water in all of its forms-dew, frost, clouds, rain, and especially snow in the form of ice crystals. At the age of 60 he recalled those early days:
I never went to school until I was fourteen years old. My mother taught me at home. She had been a school-teacher before she married my father, and she instilled in me her love of knowledge and of the finer things of life. She had books, including a set of encyclopedia. I read them all.
And it was my mother that made it possible for me, at fifteen, to begin the work to which I have devoted my life. She had a small microscope which she had used in her school teaching. When the other boys of my age were playing with popguns and sling-shots, I was absorbed in studying things under this microscope: drops of water, tiny fragments of stone, a feather dropped from a bird's wing, a delicately veined petal from some flower.
But always, from the very beginning, it was snowflakes that fascinated me most. The farm folks, up in this north country, dread the winter; but I was supremely happy, from the day of the first snowfall-which usually came in November-until the last one, which sometimes came as late as May.
During the next two years young Bentley spent many a winter's day in a cold room at the rear of the farmhouse, peering through the microscope at ice crystals collected from the passing storms. He was fascinated by the beauty and intricacy of the crystals, and attempted to capture this by making drawings of them. He made hundreds of sketches but was painfully aware that what he drew was a poor substitute for what he saw. One day he chanced to read, probably in his mother's encyclopedia, about cameras that could take photographs through a microscope. Bentley and his mother somehow persuaded his father that they must buy a bellows camera and a microscope objective. His father, however, to the end of his days thought the whole thing a lot of nonsense, and that the proper thing for a farmer to do was farming.
For over a year Bentley experimented with the microscope, the camera, and the dry plates of that day that were used to record the photographic image. He knew nothing about photography and failure followed upon failure. But through persistence and learning by trial and error he slowly approached his goal. He learned how to work rapidly before the ice crystal changed shape, how to use transmitted light by pointing the camera to the sky, and how to get sharpness of detail on the crystal by using a large f-stop. And then, during a snowstorm on 15 January 1885, he obtained the first photomicrographs ever taken of an ice crystal:
The day that I developed the first negative made by this method, and found it good, I felt almost like falling on my knees beside that apparatus and worshipping it! It was the greatest moment of my life.
(A snowflake is usually composed of many ice crystals that collide and stick together as they fall. But almost always individual ice crystals can he found in any snowfall. Sometimes, when it is snowing lightly, the air contains a multitude of twinkling ice crystals which drift slowly earthward to produce a blanket of snow.)
For 13 years Bentley worked quietly and obtained over 400 photomicrographs of ice crystals. He kept detailed meteorological records, and pondered over the meaning of the shapes and sizes of the crystals and why they often varied from one storm to the next. The outside world had yet to hear from him. He was shy and soft-spoken, and felt that his meager education prevented him from discovering anything which had not been found by research workers in the universities. Interestingly enough it was a university professor, George Perkins of the University of Vermont, who heard of Bentley's work and convinced him that he did indeed have something worthwhile to tell the outside world. His first article was published in 1898 in Appleton's Popular Scientific Monthly. In that article we see the style that was to characterize all of his writing; Bentley observed nature with both the eye of the poet and the eye of the scientist. Listen to what he has to say concerning the structure of an ice crystal:
A careful study of this internal structure not only reveals new and far greater elegance of form than the simple outlines exhibit, but by means of these wonderfully delicate and exquisite figures much may be learned of the history of each crystal, and the changes through which it has passed in its journey through cloudland. Was ever life history written in more dainty hieroglyphics!
This publication opened the floodgates of Bentley's creativity and over the next ten years he observed, photographed, and experimented with ice crystals, raindrops, and dew. He wrote many popular and technical articles, most of them on his studies of ice crystals. His main ideas were set forth in detail in a number of scientific papers in the Monthly Weather Review. A 1902 paper, one of the most extraordinary and detailed of his writings, exploded with ideas and hypotheses. The previous winter had been a frenzy of activity for Bentley and he obtained over 200 photomicrographs! His analysis of his data convinced him, among other things, that different segments of a storm (east, north, etc.) produced their own predominant type of ice crystal, that the form of the crystal (stellar, hexagonal plates, etc.) was a function of the air temperature, that the circulation within the storm could be deduced from the crystal structure, and that the change in form often noted in a single crystal reflected the changes in the temperature of the air through which the crystal fell on its journey to the ground. In this latter suggestion, which Bentley discussed in detail, he was years ahead of the meteorological thinking of his time. Thirty years were to pass before Nakaya in Japan was to consider it again.
During the summer months Bentley's curiosity was directed to the problem of the origin of rain. In his day hundreds of routine measurements were being made across the country of the amount of rain that fell per day or per Weak, but no one thought to ask the important question concerning the sizes of the raindrops. No one, that is, except Wilson Bentley. He reasoned, quite correctly, that if you wish to find out how rain is formed there was no better place to start than by measuring the sizes of the raindrops. In the year 1898 he began his studies on rain, for he had "the desire to add, if possible, a little to our knowledge regarding rainfall phenomena. . . ." And add he did. For seven years, from 1898 through 1904, he made 344 measurements of the sizes of raindrops from seventy different storms. In 1904 he published, again in the Monthly Weather Review, an incredible paper which on the basis of ingenuity and number of new ideas is perhaps unmatched in the world's scientific writings on raindrops and raindrop phenomena.
What did Bentley discover about rain? What didn't he! He found that the largest raindrops are about one-quarter of an inch in diameter (about 6 mm). He suggested that in some cases the size was determined by the size of snowflakes high within the cloud-the flakes had melted before they got to the ground. Bentley went on to tell how he had found different sizes of raindrops in different types of storms. He believed that there was a connection betWean lightning and raindrop size. And from an examination of his hundreds of raindrop samples he deduced that rain could have its origin either from melting snow or from a process that involved no ice or snow at all. But sometimes, he concluded, the sizes of the raindrops indicate that both processes may have operated at the same time. We know today that most of what Bentley suggested is indeed true, although some of his ideas are still being debated. Most astonishing of all is that he recognized a dual origin of rain, an idea that has been firmly established only in the past 20 or 30 years.
Are you curious about how Bentley measured the sizes of raindrops? The first measurements ever made of drop size were done in England only three years before Bentley began his work. Did Bentley know about it? Apparently not, for he never mentioned it nor did he copy the technique of measuring the size of the splash when raindrops hit a piece of slate or dyed paper. He developed an ingenious method of measuring raindrop size that utilized materials found in his own farmhouse. He took some flour from the kitchen, sifted it into a pan until he had a layer about an inch deep. He exposed the pan of flour to the falling rain for several seconds. Each raindrop soaked up some flour and formed a tiny dough pellet. When the pellets were dry he measured them and so found the size of the original raindrop. By dropping drops of known size from the end of broom splints into the flour he found that the diameter of the dough pellet was about equal to that of the drop. This simple yet effective technique is still being used today.
These years of excitement and discovery occurred shortly after Bentley's father had died. He had the problem of taking care of his mother, who by this time was an invalid, and of running the farm. He shared the operation of the farm with his brother who, with his wife and eight children, lived in one half of the old farmhouse. The farm did well and they built it up from a ten to a twenty-cow dairy farm. And Bentley did his share of the work. Though small in size, probably not more than 120 pounds in weight and little over 5 feet in height, he was agile, muscular, and extremely well coordinated. He could dig a row of potatoes and pitch hay as fast as any other farmer in the valley. Although introverted and sensitive, his sense of humor and gentle nature made him liked by all. Nevertheless, many of the people in the village, like his father and brother, thought him just a bit odd and he was the butt of many a village joke.
One long time Jericho resident told this writer that one night he went to a kitchen tunk (square dance) at a local farmhouse. Bentley was there, too. Shortly before the dance was over a number of the boys sneaked outside to where Bentley's horse and buggy were waiting, and reversed the large rear wheels with the smaller front wheels. Then they hid and waited to see Bentley's reaction when he came out. But there was no reaction! "He went home like that and drove the buggy several days before he noticed it. I don't know what you'd call that." One might call it absentmindedness or one just might call it an example of Willie Bentley's puckish humor. Maybe he knew that the wheels had been reversed from the start and simply decided to play along with the game.
Bentley never married though it appears he came close to it once or twice. After the death of his mother he lived alone in his side of the house. His bachelor's quarters were a sort of organized confusion. A kitchen stove, a huge wood box, a couple tables, a piano covered with piles of sheet music, movie magazines, books, manuscripts, odds and ends of experiments, photographic equipment, correspondence, and photographs of ice crystals all blurred together in one large room. But somehow, by methods known only to him, Bentley was able to find things when he wanted them.
He was polite and never aggressive in his speech, but his excitement showed when he began talking about nature. He had delicate, rounded facial features and was described as being handsome in his youth. A well-groomed shock of dark hair receded with the years until at age 60 his hairline ran vertically over his head from ear to ear. As if to counteract this, he grew a large, bushy mustache. He had no real use for clothes, and his only dress-up suit served his purposes for many a year. It was shiny and green with age, and desperately in need of pressing. In the winter he kept warm in a large, dark overcoat and a soft felt hat that was clamped tightly to his head with a long scarf that came down over his ears and was tied beneath his chin.
He had musical talents and had been taught to play the piano, probably by his mother. He also could play the clarinet, cornet, and violin. But the piano was his favorite. He would entertain himself and the neighborhood children by playing and singing the popular songs of the day. With his clarinet he played in a small brass band that he had organized. And with his violin and his humor he entertained the villagers by imitating birdcalls, frogs, barnyard animals, and certain people in the village!
Willie Bentley seldom complained about anything, and he seldom got angry. He loved people, and he loved the world of nature, that grand, mysterious world that produced the ice crystals, the rain, the fog, and the dew. He had a very special view of this world and was often saddened because he could not communicate what he saw to others. In this was both the triumph and the tragedy of the life of Wilson Bentley. At this point in his life, about 1910, he was 45 years old, and though he would live another 21 years the majority of his creative contributions had been made. Although they would be little recognized during his lifetime, they were permanently recorded in the pages of the Monthly Weather Review. They could not be erased or lost. That was his triumph.
His tragedy was the wall of silence that greeted his work during these years. When asked toward the end of his life what his neighbors thought of him, Bentley replied,
Oh, I guess they've always believed I was crazy, or a fool, or both. Years ago, I thought they might feel different if they understood what I was doing. I thought they might be glad to understand. So I announced that I would give a talk in the village and show lantern slides of my pictures. They are beautiful, you know, marvelously beautiful on the screen. But when the night came for my lecture just six people were there to hear me. It was free, mind you! And it was a fine, pleasant evening, too. But they weren't interested.
Could we really expect them to be interested? How many people, even today when science is a prime mover in our society, are really interested in science? Very few. They may respect it but do not understand it, and thus have little interest in it. In 1910 the villagers of Jericho did not understand what Bentley was doing, and quite naturally they showed little interest in his work. They were practical Vermont farmers who understood that they had to plant so many acres of corn or potatoes, and that a herd of cows had to be milked twice a day. They well understood this and thus they were interested in it. They found it difficult to understand why one of their kind would waste his time looking at snow, raindrops, or dew. This would never bring in more money or make the crops grow faster. The price that Bentley had to pay in loneliness is the price that all must pay whose inner vision allows them to see what others can never see.
We can understand the reaction of Bentley's friends and neighbors to his work, but it is not so easy to understand the reaction of the world of science. This was silence, utter and complete. During the ten years that Bentley's creative efforts were at their maximum not one article by others about his work appeared in the Monthly Weather Review. None of the many brilliant ideas suggested by Bentley in his articles was ever followed up by other meteorologists. His work wasn't even mentioned! Even criticism of his efforts would have been better than no comment at all. One can only conjecture as to the reasons for this silence from the world of meteorology. Was it because of an intellectual arrogance that blinded the PhD's of the world of science from realizing that a "simple farmer" could also discover the truths of nature? Or was it because Bentley revealed his emotions in his writings, a heresy in the objective world of science writing. No doubt both contain an element of truth, but probably the main reason was that Bentley and his ideas were far ahead of his time. No scientists in America in the first 10 years of this century understood anything about the sizes of raindrops, or how ice crystals formed in storms, or whether lightning had anything to do with it. Bentley travelled alone into a new research frontier.
Although Bentley's inner drive to know and understand was exceedingly strong, and he was capable of spending many long and lonely years in this pursuit, he needed someone in the world of science with whom he could share the excitement of crossing the frontiers of knowledge. The creative person cannot work forever in a vacuum; he must communicate and interact with his peers. Bentley did not have this interaction, and this may have been the reason why he did little creative work after about 1910.
But he never stopped thinking. He was just as excited as ever about the world around him. But he began to write more and more for the general public. The poet and the artist in Bentley took over. He had to tell of the beauty and the elegance he saw in the world of the ice crystals, the frost and the dew. He wrote many articles for such magazines as Country Life, National Geographic, Popular Mechanics, and The New York Times Magazine. He began to lecture more and more, not only to local groups in surrounding communities but to scientific organizations like the Buffalo Museum of Science and the Franklin Institute in Philadelphia. He prepared boxes of lantern slides of dew, frost, ice crystals, and clouds. He sold these at little or no profit to himself, and in the 1920's dozens of colleges and universities in America had the Bentley slides to show to students in the sciences. No doubt these slides still exist, buried in the back of instrument rooms beneath years of accumulated dust.
By 1920 Bentley was known to thousands, not by name but as the Snowflake Man. The best of his photomicrographs were in demand by jewelers, engravers, and by the textile industry. He kept busy supplying the outside world with his latest pictures while continuing his work in his own world, the world of his farm and the surrounding valley. His mind was always active and his interests seemed to know no bounds. He studied the aurora and kept detailed records of its appearance in the northern sky. He made weather observations three times a day, recording the type and amount of low, middle, and high clouds, temperature, and precipitation. He was an amateur geologist, and roamed the countryside collecting rock specimens for his collection. He wanted others to see the beauty of nature and contributed to the Fresh Air Fund to help bring city children to the countryside. His admiration for the delicate beauty of the ice crystal extended itself to the delicate beauty of girls faces, especially their smiles. He made a catalog of smiles such as he made a catalog of ice crystals. He often would question a strange girl on the street who was smiling in a certain way. "I found many possessing charming smiles. When complimented and questioned if they knew why they smiled prettily, the lucky possessors answer was invariably 'no.' " One wonders what unspoken questions the girls had after such encounters!
In 1924 the first research grant ever awarded by the American Meteorological Society was given to Bentley for ". . .40 years of extremely patient work." The grant was no doubt small but it was the recognition by the scientific community that meant most to Bentley. He had never been overly concerned with money, and certainly made no attempt to make his studies into a profit-making venture. It is likely that he could have, had he wanted to. In the balance sheet of life he gave the acquisition of money a very low priority. In 1926 he made this clear when he said, "From a practical standpoint I suppose I would be considered a failure. It has cost me $15,000 in time and materials to do the work and I have received less than $4,000 from it."
A few years later Dr. William J. Humphreys, chief physicist for the United States Weather Bureau, responding to requests from all over the country to preserve in one collection the best of the Bentley photomicrographs, organized a drive to obtain the necessary financial support. He was successful, and Bentley turned to the enormous task of sorting through some 4,500 photomicro graphs. For one reason or another the work went slowly but, finally, in the summer of 1931 the material was handed in to the publisher. In November the book, "Snow Crystals," was published. It had a short introduction by Humphreys, but by far the major part of the book was a magnificent collection of nearly 2,500 photomicrographs. Most of the pictures were of various forms of the ice crystal; about 100 were of frost and dew. In Jericho Bentley received a copy of the book but, unfortunately, we have no record of how he felt when he held in his hands the work of a lifetime, a work now preserved for all the world to see.
But winter was fast approaching and he had little time to admire the book. He was 66 years old, and though in good health did not get around or do things quite as rapidly as he had before. The camera had to be ready for the first snow. This was the same camera with which he had taken his first photomicrograph 46 years before. It was old, it was battered, but it still worked. With it he had taken his 5,381st photomicrograph on the first of March of the preceding spring. He looked forward to the winter ahead with as much zest as he had approached that first winter with the camera.
He made routine entries in his log book of weather conditions, entries that marched over the pages and through the years to give a unique record of weather in that part of Vermont. On Monday, the 7th of December, 1931, he finished his entry, "Cold north wind afternoon. Snow Flying." That was the last entry Wilson Bentley was ever to make.
The following week both his nephew and wife knew that something was wrong. Bentley stayed in bed for several days, but he refused any help. Nothing was wrong, he said, he had taken care of himself for over 40 years and he didn't need any help now. But by the end of the next week it was clear that something was very much wrong. A doctor was called but it was too late. Wilson Bentley died of pneumonia on the afternoon of the 23rd of December, 1931.
The following day the obituary columns of many a newspaper across the country reported his death. But perhaps the most poignant and understanding comments came from his own hometown paper.
Longfellow said that genius is infinite painstaking. John Ruskin declared that genius is only a superior power of seeing. Wilson Bentley was a living example of this type of genius. He saw something in the snowflakes which other men failed to see, not because they could not see, but because they had not the patience and the understanding to look.
Truly, greatness blooms in quiet corners and flourishes under strange circumstances. For Wilson Bentley was a greater man than many a millionaire who lives in luxury of which the 'Snowflake Man' never dreamed.
His friends and neighbors had understood him after all.
In writing this brief account of the life of Wilson Bentley I have not been completely objective. I didn't intend to be; in fact, I couldn't be. Any biographical account must be partly subjective, for all the facts that detail a person's life are never known, even by the person himself. In Bentley's case the facts are few and far between. I have talked to many people about Bentley and written to many more. I believe I know most of the published material by and about Bentley, but still the gaps exist. I need help in filling these gaps, for I would like to attempt the much more detailed biography that Bentley deserves. I would appreciate it if you would share with me any information you may have on Bentley. If you knew him, if you heard him lecture, if you have any pictures of him or any of his letters I would be most happy to hear from you. His letters especially would be very welcome. The voluminous correspondence that was in the farmhouse at the time of his death appears to have been lost. But much must still exist; the few letters that have been sent to me have been very informative.
I cannot list here all those with whom I have corresponded or talked with. But there are three I must mention. Mrs. Harold Hunt of Jericho, the former Amy Bentley who as a child lived in the other side of the Bentley farmhouse, has been very helpful with her childhood memories of Wilson Bentley. Miss Blair Williams of the University of Vermont is to be complimented for her efforts to tell what she knows of the Bentley story not only to me, but through television to the citizens of Vermont. And to Miss Ruth Nash of Pollack Pines, California, and her indomitable spirit, my thanks for her lively and detailed accounts of Jericho and Wilson Bentley of some 70 years ago. 

Saturday, May 28, 2011

Sacred Geometry: The Pi - Phi - Fibonacci Sequence and The Square


Interview With The Artist #4 - The Square
By Leslie Page

Writers note: when Charles and I began our Sacred Geometry interviews, He allowed me, in a very unconditional way, to ask the questions that spontaneously came to my mind. These exchanges were consequently very scattered, covering a wide range of subject matter. This interview is actually a composite of clips from several of our tapes (Numbers 2, 3, and 6) and is supplemented with an additional conversation we had about the sacred geometric archetype, known as The Square.

L.P. "Charles, I know the Sanskrit word 'Mandala,' means 'Circle,' but the square is obviously a very important aspect in the creation of Mandalas. In fact, the vast majority of the classical Eastern Mandalas I have studied are based on the square. And then, a few days ago I was reading a Hindu author who suggested the circle was literally the same thing as a square, which really confused me. Do you understand his point of view?"

C.G. "Yes I do, but that is a fairly abstract and esoteric concept. Lets start at the beginning and build from there. At some point I believe your question will be answered — automatically."

L.P. "All right. That makes sense. I know you are convinced Sacred Geometry begins with the single point (Bindu) which naturally evolves into The Circle. How does The Square fit into this evolution?"

C.G. "The Square naturally evolves within the Vesica Piscis
(Fig. 1). Actually, all form and phenomena evolves from the Vesica Piscis but let's just concentrate on The Square. The Square naturally evolves from the center point of the Vesica Piscis. The center point of the Vesica Piscis (X) is created by the intersection of our original radius (the line between points A. & B.) and a new line connecting points C. and D. (Fig. 2)."

(Fig. 1) - Vesica Piscis: Origin
(Fig. 2) - New Center - X

L.P. "All right, I've got it. Keep going."

C.G. "That new center point (X) is extremely important because it establishes numerous transcendental possibilities. One of those possibilities is the creation of a new and smaller circle, its radius between points A and X. I call this form 'The First Transcendental Circle'
(Fig 3.). This circle is half the diameter of our original circle and The Square naturally evolves within that smaller circle (Fig. 4). When you see where The Square comes from it automatically reveals its intimate connection to the circle "

Fig. 3: First Transcendental Circle
Fig. 4: Origin Of The Square

L.P. "I see it, Charles. Very simple — logical."

C.G. "Yes, Leslie. Sacred Geometry is beautifully simple. The perfect logic of Sacred Geometry is one of the reasons I am so enthralled with it.

L.P. "So let's talk about The Square as it relates to our world. You have told me, on numerous occasions, that the geometric archetypes form God's first and most esoteric language. What does The Square have to say to you Charles? What does it say to us?"

C.G. "That's true Leslie, Sacred Geometry is THE root language, and I am an interpreter of that language. For instance, notice the relative orientation of the square as it is originally created within the Vesica Piscis. This is what we call the Dynamic or Projective Position
(Fig. 5). When a square rests on one of its sides we call that the Static or Receptive Position (Fig. 6). The same holds true for all the geometric shapes such as The Triangle, The Square, The Pentagon, The Hexagon, The Octagon, etc. They all have both a static and dynamic orientation which colors their relative messages. Even the Two Circles Of Common Radius, has a receptive and projective orientation. The contemplation of a square in its static and dynamic positions reveals markedly different psychological effects. Each has a different voice and a different energy.

Fig. 5: The Dynamic Square
Fig. 6: The Static Square
L.P. "That is a very interesting observation, Charles. They definitely feel very different. The Dynamic Square is just that, and looks like something is happening or about to happen. On the other hand, The square in its static position feels completely at rest and stable, the basic shape of building blocks. Blocks can be easily stacked, like bricks, but you can't balance a brick on one of its corners."

C.G. "Yes, that is the obvious example as it relates to the construction of walls and buildings (the three dimensional world) but it goes much deeper than that. I am convinced that the two dimensional archetypes have a direct relationship to our archetypal psychology, holding intrinsic messages about the nature of the cosmos. That dynamic square we find within the Vesica Piscis, is firmly rooted within our subconscious minds and constantly effects the nature of our physical and emotional orientation to the universe. Even if we rotate the Two Circles Of Common Radius from its dynamic orientation
(Fig. 4) to its static orientation (Fig. 7), That first square remains in its dynamic position.

Fig. 4: Two Circles
Of Common Radius
Origin Of The Dynamic Square
Fig. 7: Two Circles
Of Common Radius
Origin Of The Dynamic Square

L.P. "All right. How does this dynamic square, you suggest is so firmly held within our subconscious minds, actually effect our relationship to the cosmos?"

C.G. "One of the most obvious examples is seen in the natural human creation of maps and their consistent orientation to the four directions. Virtually all maps, no matter where or when they were made, make reference to the four directions, North, South, East, and West. This world wide and timeless phenomena proves our human concept of the four directions is coming from within, as we keep reinventing it again and again and again. The four corners is a root psychological archetype naturally developing through the deeper sacred geometric archetypes of The Vesica Pieces and The Dynamic Square."

L.P. "So Charles, you are saying the ancient concept of the four directions evolved directly from the cross and the square which is to be found in the Vesica Piscis, and somehow bubbles up from the deepest aspects of our consciousness.?"

C.G. "Yes, exactly. The repeating revelation of the four directions comes from the deepest archetypes of our consciousness which are effecting our view of the material world. Sacred Geometry is at the heart of literally everything and is continually shaping our understanding whether we realize it or not."

L.P. "That is an interesting point of view, Charles, and is, for an old Jungian like myself, pretty hard to resist. Tell me more about your open-eyed meditational work and its relationship to the square?"

C.G. "Yes, Mandalas. As you stated earlier, most classical Mandalas make reference to the four directions, with doorways in the form of geometric shapes set at each side of the square and one or more circles placed within
(Figs. 8 & 9).

Fig. 8: "Shri Yantra"from the book "Tools For Tantra"
by Harish Johari
published by Destiny Books
Fig. 9:
Journey To The Sacred Mountain

A Mandala by Charles Gilchrist

And Leslie, here's the answer to your first question: a squared circle is created by duplicating its diameter four times, enclosing that circle (Fig. 10). In that sense, a square which perfectly encloses a circle is equivalent to that circle. That circle and square are like the left and right hands of the same energy. In that sense, The Square equals The Circle. That is what your Hindu author was writing about. Compare the squared circle enclosing a dynamic square and you have the graphic roots of classical Mandala (Fig. 11)"

Fig. 10: The Squared Circle

Fig. 11: The Squared Circle
Enclosing Dynamic Square

L.P. "Now I understand what that Hindu writer meant when he said the circle is equivalent to the square; its obvious now. I have already come to realize the squared circle and the four directions are a major aspects of classical Mandalas, but now I see how the classical Mandala relates to and grew from that root geometric archetype: the Vesica Piscis. Keep going."

C.G. "Consider the ancient astrological symbol for the Earth. It is that same circle and dynamic cross we find within the Vesica Piscis (Fig. 12). And, Leslie, we are living on the fourth planet from our sun, and that ancient astrological symbol of our Earth is a circle divided into four parts. And here's another connection: In esoteric numerology, the Earth is assigned the vibration of four. The ancients recognized our Earth has a certain correspondence to Fourness. These realities are far from coincidence."

(Fig. 12) - The Astrological Symbol For Our Planet Earth

L.P. "Wait a minute, Charles. Are you saying the Square has something to do with the number four? I mean in the metaphysical sense?"

C.G. "Absolutely! It's totally obvious. The circle is a perfect symbol of unity and oneness. Divide a circle into four equal parts and you have a square. The Square is the sacred geometric equivalent of Fourness. You could say the squareness IS Fourness, North, South, East and West; and from the astrological point of view, Fire, Earth, Air, and Water. There's more, Leslie."

L.P. "I'm with you, Charles. Keep going."

C.G. "Consider this, Leslie. A major symbol of the Christian tradition is the elevated cross, which also obviously comes from the Vesica Piscis. Christ, who was crucified on that elevated cross, was a great spiritual master of life. He was at one with the creator, a great prophet of unconditional love who advised us to center our consciousness in the heart, and further suggested that all our actions should spring directly from the heart. And the heart, Leslie, is the fourth energy center of the human body which has forever occupied that same relative position of Fourness. The Hindus and Buddhists call this energy center the fourth Chakra.

It is very obvious: Fourness, The Cross, and The Square, are interrelated at the deepest possible levels. We humans, even though we may not be conscious of these esoteric truths, intuitively realize these energies and develop our symbolism in perfect correspondence. It happens over and over again. The principles of Sacred Geometry shape our thinking and feeling."

L.P. Wow, Charles. That is a very compelling knot of information. My mind is spinning. How about the Native Americans? They where also very connected to the cross and the four directions. They somehow must have been plugged in to this collective metaphysical energy."

C.G. Yes, obviously. And that proves the point that a functioning culture does not have to have some highly developed scientific technology to discover the deepest truths of the universe. It comes from within. For multiple thousands of years, Native Americans have been deeply centered in the perfections of Sacred Geometry. Their philosophies and rituals are saturated with a kind of intuitive geometrical thinking. Black Elk, the wonderful and tormented Lakota Shaman, is perhaps the most eloquent spokesman for that kind of mystical realization of the geometric archetypes.

Not only did Black Elk find potent spiritual truth associated with the circle and the four directions, but he also perceived the six, three dimensional directions; North, South, East, West, Up and Down. In the end, he also found the seventh direction which is a very abstract concept: our internal metaphysical center; the universal omnipresent center of us all; the true Sacred Mountain. This brilliant spiritual leader was a so called primitive pagan. But in fact he was a significant member of a highly developed and naturally functional culture; a culture which had lived in harmony with nature for thousands of years; a culture which most white men perceived to be sub human, Godless, and barbaric — the fools. This brilliant shaman (Black Elk) had developed a highly intimate relationship with the creator; a psychological relationship which functioned within a perfectly attuned geometric architecture. He called the circle, the 'Sacred Hoop' of his nation."

L.P. That's beautiful — really. Let's get back to The Square Charles, seen as a deep psychological archetype. I find this point of view to be extremely interesting, even compelling.

C.G. Yes, so do I Leslie. I can clearly see that the world wide and timeless tradition of creating Mandalas is springing from the roots of consciousness: The Single Point and its natural evolution called Sacred Geometry. Because Sacred Geometry is the root architecture of the universe, it is also is the root architecture of our minds. This realization leads us to the Collective Human Mind, a mind which transcends all individual human differences and unifies us all.

L.P. "That kind of holistic thinking would suggest that we humans did not invent the Mandala but rather only discovered a possibility already existing within the depths of our unity."

C.G. "Yes, exactly. When we contemplate a classical Mandala, we may not consciously perceive the effects that square is having on us but non the less, that static square is moving us toward the eternal stillness forever held within that geometric form. The Static Square, The Dynamic Square, and The Circle (all parts of the classical Mandala) are transcendental doorways leading into the pure aspects of God Mind to be discovered at the heart of our human minds. God Mind is omnipresent and omnipotent, and the creation and/or contemplation of Mandalas can bring us to the most intimate grocking of The One."

L.P. "I am reminded of a group of small classical Mandalas you created: The Four Corners Suite. I love those pieces, very beautiful
(Figures 13, 14, and 15)."

(Fig. 13)
Deasert Wheel
(Fig. 14)
(Fig. 15)
Sky Power
Three Mandalas from the suite of thirteen - see Gallery #2

C.G. "Thank you Leslie. Yes, the thirteen Mandalas of 'The Four Corners Suite' are definitely classical. I felt a great healing in the production of that project which reinforced my appreciation of the immense powers held within in the classical form. "

L.P. "Charles, we mostly talk about two dimensional archetypes, very conceptual and abstract. I'm interested about the relationship this two dimensional world of yours has to our three dimensional world. Lets talk about The Square as it relates to it's three dimensional version: The Cube.

C.G. "That is a very interesting and important area. You could write a book about that one , Leslie. You are right of course. The two dimensional realm is completely conceptual, the mental blueprint of the three dimensional universe. As an iconographer and an interpreter of the archetypal language called Sacred Geometry, I have discovered at least three different dialects. Each of the first three dimensions is speaking a variation of the language and the interplay between those dialects is fascinating.

L.P. "For instance?"

C.G. "Consider the two dimensional Square: it has four sides and four corners, and naturally evolves from The Circle. And, as we have seen, that Square has a natural correspondence to Fourness. But when The Square evolves into the next dimension and becomes a Cube, it also expands vibrationally. The Square which becomes The Cube, now has six sides which are all exact duplicates of the original square
(Fig. 16). That Cube also has eight corners, and twelve edges, and both perfectly encloses the sphere, and in turn is enclosed by The Sphere. Compared to The Square, The Cube is sending us infinitely more subtle and complex messages. That is why I suggest beginning students should concentrate on the two dimensional archetypes first, or should at least be aware that the messages of a basic two dimensional form are not exactly the same as the messages of its three dimensional counter point."

(Fig. 16) - Cube In Cube
Acrylic Mandala by Charles Gilchrist - see Gallery #6

L.P. "I can immediately see this multi dimensional area we've just touched on (dialects of the language of Sacred Geometry) is going to need a lot more time. We should probably plan another interview for that, but how about one last word on The Square."

C.G. All right, good. As we have seen, Leslie, The Square is a tremendously important Icon of Sacred Geometry, an archetype of prime significance, and much more than just a symbol for this and that or even the basic shape of building blocks. The Square forms a major visual sound in the two dimensional language of Sacred Geometry, and that visual sound holds harmonious correspondence to the sounds of The Circle. The Square is a unique visual mantra which, because of its root purity, acts as a natural doorway to the universal truth of God Mind. In that mind, The Square vibrates as a visual sound like a mantra, forever teaching us about the nature of the universe in a most pristine and uncluttered voice. Listen carefully, The Square is full of balance and healing (Fig. 17).

(Fig. 17) The Square

Friday, May 27, 2011

Flatland: A Romance of Many Dimensions

With Illustrations by the Author, A SQUARE
(Edwin A. Abbott 1838-1926)

To The Inhabitants of SPACE IN GENERAL
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE Dimensions
Having been previously conversant
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE OR EVEN SIX Dimensions
Thereby contributing
To the Enlargement of THE IMAGINATION
And the possible Development
Of that most rare and excellent Gift of MODESTY
Among the Superior Races

If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to represent him in this preface, in which he desires, firstly, to return his thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a second edition of his work; secondly, to apologize forcertain errors and misprints (for which, however, he is not entirely responsible); and, thirdly, to explain one or two misconceptions. But he is not the Square he once was. Years of imprisonment, and the still heavier burden of general incredulity and mockery, have combined with the natural decay of old age to erase from his mind many of the thoughts and notions, and much also of the terminology, which he acquired during his short stay in Spaceland. He has, therefore, requested me to reply in his behalf to two special objections, one of an intellectual, the other of a moral nature.
The first objection is, that a Flatlander, seeing a Line, sees something that must be thick to the eye as well as long to the eye (otherwise it would not be visible, if it had not some thickness); and consequently he ought (it is argued) to acknowledge that his countrymen are not only long and broad, but also (though doubtless in a very slight degree) thick or high. His objection is plausible, and, to Spacelanders, almost irresistible, so that, I confess, when I first heard it, I knew not what to reply. But my poor old friend's answer appears to me completely to meet it.
"I admit," said he - when I mentioned to him this objection - "I admit the truth of your critic's facts, but I deny his conclusions. It is true that we have really in Flatland a Third unrecognized Dimension called `height,' just as it is also true that you have really in Spaceland a Fourth unrecognized Dimension, called by no name at present, but which I will call `extra-height'. But we can no more take cognizance of our `height' then you can of your `extra-height'. Even I - who have been in Spaceland, and have had the privilege of understanding for twenty-four hours the meaning of `height' - even I cannot now comprehend it, nor realize it by the sense of sight or by any process of reason; I can but apprehend it by faith.
"The reason is obvious. Dimension implies direction, implies measurement, implies the more and the less. Now, all our lines are equally and infinitesimally thick (or high, whichever you like); consequently, there is nothing in them to lead our minds to the conception of that Dimension. No `delicate micrometer' - as has been suggested by one too hasty Spaceland critic - would in the least avail us; for we should not know what to measure, nor in what direction. When we see a Line, we see something that is long and bright; brightness, as well as length, is necessary to the existence of a Line; if the brightness vanishes, the Line is extinguished. Hence, all my Flatland friends - when I talk to them about the unrecognized Dimension which is somehow visible in a Line - say, `Ah, you mean brightness': and when I reply, `No, I mean a real Dimension,' they at once retort `Then measure it, or tell us in what direction it extends'; and this silences me, for I can do neither. Only yesterday, when the Chief Circle (in other words our High Priest) came to inspect the State Prison and paid me his seventh annual visit, and when for the seventh time he put me the question, `Was I any better?' I tried to prove to him that he was `high,' as well as long and broad, although he did not know it. But what was his reply? `You say I am "high"; measure my "highness" and I will believe you.' What could I do? How could I meet his challenge? I was crushed; and he left the room triumphant.
"Does this still seem strange to you? Then put yourself in a similar position. Suppose a person of the Fourth Dimension, condescending to visit you, were to say, `Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you infer a Solid (which is of Three); but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.' What would you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra- Cubes - we are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said -
`One touch of Nature makes all worlds akin'."1
On this, point the defence of the Square seems to me to be impregnable. I wish I could say that his answer to the second (or moral) objection was equally clear and cogent. lt has been objected that he is a woman-hater; and as this objection has been vehemently urged by those whom Nature's decree has constituted the somewhat larger half of the Spaceland race, I should like to remove it, so far as I can honestly do so. But the Square is so unaccustomed to the use of the moral terminology of Spaceland that I should be doing him an injustice if I were literally to transcribe his defence against this charge. Acting, therefore, as his interpreter and summarizer, I gather that in the course of an imprisonment of seven years he has himself modified his own personal views, both as regards Women and as regards the Isosceles or Lower Classes. Personally, he now inclines to the opinion of the Sphere that the Straight Lines are in many important respects superior to the Circles. But, writing as a Historian, he has identified himself (perhaps too closely) with the views generally adopted by Flatland, and (as he has been informed) even Spaceland, Historians; in whose pages (until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration.
In a still more obscure passage he now desires to disavow the Circular or aristocratic tendencies with which some critics have naturally credited him. While doing justice to the intellectual power with which a few Circles for many generations maintained their supremacy over immense multitudes of their countrymen, he believes that the facts of Flatland, speaking for themselves without comment On his part, declare that Revolutions cannot always be suppressed by slaughter; and that Nature, in sentencing the Circles to infecundity, has condemned them to ultimate failure - "and herein," he says, "I see a fulfillment of the great Law of all worlds, that while the wisdom of Man thinks it is working one thing, the wisdom of Nature constrains it to work another, and quite a different and far better thing." For the rest, he begs his readers not to suppose that every minute detail in the daily life of Flatland must needs correspond to some other detail in Spaceland; and yet he hopes that, taken as a whole, his work may prove suggestive as well as amusing, to those Spacelanders of moderate and modest minds who - speaking of that which is of the highest importance, but lies beyond experience - decline to say on the one hand, "This can never be," and on the other hand, "It must needs be precisely thus, and we know all about it."