Eritque Craticula Usque ad Tenebras

Eritque Craticula Usque ad Tenebras

The precipice of Winter. The hollow wind of Autumn. We humans are always on the edge of something. In this case, we are on the edge of seasonal change. As we slip from the warm days of Summer into the chillier nights of Autumn, we sense that change is imminent. We are on the edge, slipping from one day to the next, seasons rushing by in a flowing, ever changing stream. A stream, I must add, upon which we are always standing on the edge.

Nature teaches us a great deal of how to be in the world; most of the time, we just choose not to listen. Cement jungles are no place for the breath of the Green Man or the dance of a water nymph. Yet, Nature finds a way to express herself. In Traditional Chinese Medicine, this is expressed as Yin and Yang. A Taoist concept, everything contains Yin and Yang. Yin and Yang are two opposite yet complementary energies. Although they are opposite in their individual qualities and nature, they are interdependent. They are never separate and cannot exist without one another. The hard Yang of the cement contains in it air and space, Yin, in which it yields to the grass growing in its cracks. The meadow is dotted with hard boulders, unyielding and yet grounding to the lush, loamy soil.

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The traditional translation of Yin-Yang is Dark-Bright, which in turn translate to the traditional Chinese icon we see for it – two tear drops, intertwined, with a dot of the other deep in their bellies. Saying they are opposites is a faint allusion to their true natures. They are complex and rich for as simple as they appear. Both are archetypes and ideals, where simple human words are inadequate modifiers. They may be translated as “the shady side of the mountain (yin)” and “the sunny side of the mountain (yang).” Yin may also indicate the feminine, the moon, softness, passivity, sinister, darkness, overcast, or even treacherous. Yang, the “opposite” indicates masculine, the sun, hardness, assertiveness, open, overt, relief, light, and positivity.” There is always a bit of one in the other, a taste which makes them less opposite and more like polarities. Neither is good or bad, they just exist; intertwined for eternity in a dance of possession.

Chapter 42 of the Tao Te Ching (about 500 B.C.E. by Lao Tzu) is where the duality and Yin-Yang are found:

“The Way gave birth to unity,
Unity gave birth to duality,
Duality gave birth to trinity,
Trinity gave birth to the myriad creatures.
The myriad creatures bear yin on their backs and embrace yang in their bosoms.

They neutralize these vapors
and thereby achieve harmony.”

This may be interpreted that while the Way (Tao) gave birth to all of material life, it is contained within that life in the form of this duality. Thus, all matter, of animal, plant, or mineral contains yin and yang. All of Nature contains within it opposing truths, a constant tug of each end of the living spectrum. Being of Nature, we should be intimately at ease with the duality of our natures, right?

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Relative and absolute. We see absolute as our eternal goal – absolute truth. Is this not what the philosopher strives to attain? Is this not what the Freemason seeks? Absolute is the Truth which we hold as dearest, that which give us “rightness” of whatever we are understanding. Yet, relativity is important to our personal lives. We make judgments and choices about the relative Truths we perceive with our senses every day. How does that green shirt go with those pink pants? Does the omelet need more salt? Are we thirsty? These are truths, however small, in which we are always seeking answers and using our senses, our knowledge of duality, to provide answers. We are always on the edge, wondering if we are being deceived, somehow, by falsehood and ignorance. Curiosity is a sword to slay our own ignorance. Curiosity is not sheathed in ego.

The philosopher sees the duality in the people and situations around him. We recognize that there may be two sides to a situation: yours and mine, his and hers, etc. Without this sharing, we cannot see more Truth. We have to stand on the edge of reality, with another human being, and accept that this truth might fill in our blanks. Once we let judgement of Truth go, there is vast chasm in front of us. It is in recognizing duality that the pieces start to come together. Unity. We realize that we cannot have the whole picture. We may not ever have the absolute truth; yet, we may have relative truth to share. In heaps and bounds.

Thus, we are always on the edge of true understanding. Of knowledge. Of peace. Thus, perhaps we are always at an equinox within our natures. Halfway to Darkness. Halfway to Light. Eritque craticula usque ad lucem ac tenebras. A motto of change? A reminder of being on the edge? Perhaps we need not be so afraid of the darkness and the change, go out into nature, and learn what living really means. We can find Nature in everyone we meet, sharing in a brief bit of harmony by seeking to understand. Enjoy this Equinox, with balance and joy, understanding that the world will keep turning, seeking balance and yet, always on the edge. The Darkness is coming. So is the Light.

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Metaphor: The Language of the Mystics

Metaphor: The Language of the Mystics

In the outskirts of every society, you will find the mystics. Some are holy men in monasteries; some are Buddhists seeking enlightenment; some are public figures; some are Christians serving Jesus; some are Freemasons, like myself. Mystics have an amazing amount in common despite all that. They are not satisfied with what they learn in books, with ceremonies passed on for the sake of tradition, or with faith that comes from an assertion that “You really ought to believe in this.” What they want, instead, is conviction— the kind of conviction that comes only from a direct spiritual experience. Many say they have found it.

How do mystic seers convey their experience in words, or in stories? Our ancestors’ answer was: with tons and tons of different images – with metaphors, that is. Metaphors, after all, are symbols used to creatively describe a deeper reality, to give a sense of the color and taste of it. There are many metaphors in the teachings of Freemasonry.

How significant, then, is the relationship between mysticism and metaphor?

There are hundreds, maybe thousands or millions of metaphors in existence about mystical things. Rumi, the great Sufi poet, once said that God created everything in the outer world to serve as a metaphor for the inner. The outside world contains objects that can awaken and remind us of truths that, when applied, can be of real benefit. For example, if you read mystic literature about the soul, you might find the soul as ladder, the soul as garden, the soul as mountain, the soul as ark, the soul as mansion or castle, the soul as shining, living stone or even precious jewel, and so on. There are equally as many metaphors about the path to enlightenment.

34382722213_6e1d57324f_zA metaphor is a comparison. A metaphor establishes a relationship at once; it leaves more to the imagination. It is a shortcut to the meaning; it sets two unlike things side by side and makes us see the likeness between them. A metaphor is a comparison that doesn’t use the words “like” or “as,” while a simile is one that does use those words.

Why do metaphors in the writings of the mystics even matter? As the great consciousness-researchers Julian Jaynes and Owen Barfield both explained in their writings, it is very difficult to discuss consciousness except through metaphor. Metaphors create new ways of thinking, new realities, and new worlds.

Do metaphors shape the way we think? Let us look at an example.

Juliet is the Sun
From Shakespeare’s Romeo and Juliet is the metaphor, “Juliet is the sun.”

This statement equates two different things: one human, the other sidereal. Juliet is a human; the sun is a star. How do they get to be equal?

For the purpose of illustration, I will show how a metaphor is born, logically. We could say:

There is a human called Juliet.
There is a star called the Sun.
The human called Juliet is radiant.
The star called the Sun is radiant.
Therefore, the human called Juliet is like a star, called the Sun (because of the radiance).

Not very thrilling or poetic, is it? How can we make it more exciting? How is the metaphor created? First, we delete all the unnecessary words and steps, only leaving the simile “Juliet is like the Sun.” The final deletion comes about by eliminating the word, “like.” Voila! “Juliet is the Sun.” 34382660583_c940b54102_z

As we can see, this metaphor comes alive through deletion and transformation. Keep taking away words until something “becomes” something else. Keep stripping away the Maya and the illusion until we arrive at the truth: the direct perception or the mystical experience.

In the words of William Blake, “If the doors of perception were cleansed, everything would appear to a man as it is, infinite.”

If you have ever had an “aha” moment, there is something wonderfully joyous about experiencing the mystical – to remember that we have spiritual faculties in us open to the dimensions beyond. Wonder. Awe. The metaphorical language of the mystics points us to the stars – bridging earth to heaven and to a world beyond itself.

But how do we react when we encounter something that exists outside of our realm of study? Does everything have to fit into what is already known, otherwise it doesn’t exist? The experience of the Transcendent seems to defy expression.

One of the greatest mystical saints of all times, St. Teresa of Avila, says that the intellect cannot go with her to the higher realms. It must stay behind. She writes in her book The Interior Castle: “One should let the intellect go and surrender oneself into the arms of love, for His Majesty will teach the soul what it must do at that point.”

I do believe the central role of metaphor in shaping consciousness can be impactful in someone’s life. I also believe the intellect is not always our ally. 35192178685_29b4993ed4_z

Such was the case with Edgar Mitchell, astronaut on the Apollo 14 mission. On his return trip from the moon, he stared out of the window at our blue planet, Earth. At that moment something profound hit him. All of a sudden he was lifted out of his normal consciousness and felt an intense oneness with planet Earth and the universe. In a flash of higher consciousness a higher truth was revealed to him that dramatically changed his intellectual perspective. (Watch Edgar Mitchell’s “We Are One” video)

How lovely to live in possibility, to think in beautiful metaphors, to cherish the precious jewel in each sacred word,  and to overflow with sweeping amazement. Your turn. What mystical metaphor would you want to leave behind as a jewel to humanity?


Note: Featured images are from the Art Exhibition, Beyond the Stars; The Mystical Landscapes from Monet to Kandinsky.

Stoic about Time

Stoic about Time

“True happiness is to enjoy the present, without anxious dependence upon the future, not to amuse ourselves with either hopes or fears but to rest satisfied with what we have, which is sufficient, for he that is so wants nothing. The greatest blessings of mankind are within us and within our reach. A wise man is content with his lot, whatever it may be, without wishing for what he has not.”  – Seneca

In a recent Masonic Philosophical Society meeting, we discussed the likeness of Stoicism to Freemasonry. Seneca, Zeno, Epictetus, and Marcus Aurelius all took center stage. It was a lively discussion and the argument that Stoicism and Freemasonry are the same was extremely compelling. As I always do, I went on my own journey to rediscover what I had learned in school about the Stoics; with what I knew about Freemasonry, I felt that I was well armed to learn some new ways of looking at the Stoics.

I first went to TED Talks, where I always find a wealth of great ideas and food for further thought. There is an excellent animated video on the Stoics, by Massimo Pigliucci, entitled The Philosophy of Stoicism. It’s a very well done quick course on the Stoics. Another excellent TED talk on Stoicism is by Ted Ferriss, “Why you should define your fears and not your goals.” This is about 13 minutes long and is a very practical look at why Stoicism is beneficial and how you can use it in daily life.

What was very interesting was a single quite that Ferriss said helped him change his life: “We suffer more in imagination than in reality.”

Huh, I thought. Of course we do. But why? Another recent reading foray brought me to brain_opener_free_0another idea: time. We humans understand time only superficially, as it applies to us. Our brains are wired to understand and extrapolate possible futures, opportunities missed in the past, and move our lives to live in synchronicity.

There are factions of large people, including myself at one point, who thought that “living in the moment” was the key to being happy. I now don’t think we’re wired that way.

In a recent article in the New York Times, author and professor of psychology Martin E.P. Seligman agrees. “We Aren’t Built to Live in the Moment” examines how our minds work and why. He and his co-authors have outlined this process in their book, “Homo Prospectus.” The article, and the book, are really discussing the philosophy of Stoicism to make it through life.

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Time. We are subjects of Time. 

What really solidified this for me was listening to a recent Radiolab episode, which was a repeat of their first season, discussing “Time.” In it, the two podcasters discussed the idea of time and living in the moment. Robert Krulwich takes his co-host on a journey of reason.

Our mind does not process data at the time it is created. Smell, sound, and light – these are all generated by something and transmitted over some distance to our surroundings, where we pick it up via our senses, and whereupon it is interpreted by our brains. This distance travel take… time. It is not instantaneous. Our minds process – speed is only a matter of relativity. Ergo, we are never experiencing the moment. We are always processing memories. And memories are always subject to misinterpretation.

It’s no wonder we fear. We cannot live in the moment and must always interpret the past to create possible futures. Truly, like we never really touch anything, due to the molecular distance between surfaces, all that we have is an interpretation of our surroundings, received and processed in past, to guide us in our futures. Spending the time to put emotion into it grounds it even future in “memory.”

aurelius

To pull ourselves out of time is impossible, and thus, living in the moment is impossible. Ergo, we need a tool to bring us around to dealing with these memories in such a way as to not freeze us in our tracks. We are brought back to, again, the wisdom of the Stoics. “A bad feeling is a commotion of the mind repugnant to reason, and against nature,” stated Zeno of Citium.

Our modern psychologists agree:

“Homo prospectus is too pragmatic to obsess on death for the same reason that he doesn’t dwell on the past: There’s nothing he can do about it. He became Homo sapiens by learning to see and shape his future, and he is wise enough to keep looking straight ahead.”

– From Homo Prospectus, by Martin E. P. Seligman, Peter Railton, Roy F. Baumeister, and Chandra Sripada

Astronomy and the Quadrivium

Astronomy and the Quadrivium

Perhaps your first thought, as was mine, is: “How can Astronomy be an ‘art?'” Furthermore, how can Astronomy be called a ‘liberal’ art? From a very interesting (and worth exploring) website called “Arts of Liberty,” we have a snippet for explanation:

“To call astronomy an ‘art’ can come as a shock to a modern reader… Perhaps without thinking much about it, we think of “science” as being a genuine and exact knowledge, whereas ‘art’ is more expressive, or touchy-feely.  But, that is not quite adequate, since medicine is also an ‘art,’ and it is anything but touchy-feely… And while ‘science’ and ‘art’ do not appear to be synonyms, it could very well be that the same discipline can be called both a ‘science’ and an ‘art,’ although for different reasons.

To understand this properly requires us to consider a sense of the word ‘science’ not in common use today.  The word ‘science’ comes from the Latin word scientia, which meant a very exact knowledge, a rigorous and sure knowledge of things deduced from self-evident truths.  The ancient Greeks would have called such knowledge epistémé...  

In the vocabulary of the ancients, an ‘art,’ like a science, meant a carefully reasoned-out knowledge, but more than that, it meant a knowledge of how to produce something.  Where there is no ‘product,’ there is no ‘art.’  So it is possible for a form of knowledge to be a ‘science’ but not an ‘art.’  For example, Aristotle considered the study of god to be a ‘science,’ a body of knowledge rigorously reasoned out from self-evident principles, but not an ‘art,’ because it did not teach us how to make gods, or how to do anything about god.”

Ptolemaicsystem-smallClaudius Ptolemy (100-170 CE) was a Greek mathematician living in Alexandria. His work The Amalgest was one of the most influential astronomical works until Galileo’s discoveries in the 17th C. The Amalgest documents many mathematical and astronomical treatises, including works by other mathematicians – works thought to be lost. The most significant piece of this Amalgest (total of 13 books), is the documentation of the geocentric model of the universe. Ptolemy’s work became the accepted theory of the structure of the planets and stars, with the Earth central to all.

This influenced not only astronomy and mathematics but also theology, philosophy, and fine art. Three centuries after it was written, Hypatia and her father Theon, genius mathematicians, added to the work with their own commentary, throwing in their thoughts of elliptical orbits, the procession of the equinoxes, revising Ptolemy’s Handy Tables, and introducing the sexigesimal calculation systems. It’s believed that this rendering of the Amalgest, with the Hypatia/Theon commentary, is the one that was used for the majority of the Middle Ages although no direct reference to Theon survives and Hypatia is mentioned only in a passing 10th C. reference.


And thus, the Quadrivium ends. I hope you’ve enjoyed my answer to the Bro.’s challenge of finding a significant event, work, or person who influenced each specific liberal art. The question was posed, should Freemason’s really learn the liberal arts? The answer, to me, should be obvious. Not only should we learn the liberal arts individually, but understand their context in the whole of being educated about the natural world. Human beings can be taught easily to survive; we cannot just “pick up” how to thrive, generate ideas, and create a better world.

An example of this “Freemasonic mindset” is James Madison, even though he was not a Freemason. In his early twenties, when the United States was in its infancy, he gave up much of his career and life to studying the histories and government of world cultures. He was relentless in his pursuit of the histories and knowledge of government administration, what worked, what didn’t; he studied philosophy, history, theology, art, classical literature, geography – the liberal arts and more. By the time he finished, and began his work in the new nation’s government, he was arguably the single biggest influencer in shaping the United States Constitution and the framework of our Democracy. By learning the past deeply, he was able to innovate and create a new world. To me, that is a main goal of the Service of Freemasons.

Are Sacred Places Important? The Labyrinth at Chartres

Are Sacred Places Important? The Labyrinth at Chartres

In our present time, there seems to be a huge market for “buying” your way to enlightenment. Everyone is peddling a secret. Chant this mantra. Hold this crystal. Buy some incense. Rub that oil. Say these words. Go to this retreat. Some of these things may have some value. Spiritual longing is a real part of the human experience. Labyrinths hold a special attraction for me. Can a labyrinth really be a tool for enlightenment? Are sacred places important?

The first labyrinth that I ever experienced was a Chartres Labyrinth, although I was not lucky enough to be in at the famous labyrinth in Chartres, France. I liked it so much I began to investigate labyrinths in general and the Chartres Labyrinth in particular.

Chartres Cathedral was built one thousand years ago to be the site of a Mystery School. Not only was the cathedral an architectural feat but was one of the leading learning centers at the time. The edifice combined the visionary teachings of Plato with Christian mysticism. You must walk the entire labyrinth path before gaining entrance to the Temple. It is the “way in,” if you will, a Chamber of Reflection of sorts.

Those who have been to the actual site in France say that the effect of the Cathedral is peaceful and nurturing. You are at rest, left to wander or to meditate in tranquility. The atmosphere suggests that the veil between the human and celestial worlds is thin, and God is very near. It represents the ideal of a sacred space: a blending of the divine and material. The impact of Chartres on people at that time must have been enormous. How can a place be so heavenly?

Sacred Geometry

The Divine mystery of the labyrinth walk might be due in part to the magical pattern. One path leads inwards to the center, and the same path leads back out again. Chartres has an eleven-circuit design, divided into four quadrants. They are encircled by an outer ring of lunations, thought to represent a type of lunar calendar. The quadrants suggest the even armed cross. At the center is a Rosette pattern of 6 petals which is the place of 14761614336_92dabf6bf4_zrest. It reminds us of the sacred lotus, symbol of enlightenment.

In medieval times, the path was considered a substitute for a pilgrimage to the Holy Land. It is symbolic of the pilgrim’s journey into his Soul: the Center. It must be a two-way journey, which ends at the starting point. The pilgrim must not seek to remain inside. He goes and comes back. He visits. He walks from the unreal to the real, from the periphery to the center, from the mundane to the spiritual and back. Is this not life?

Symmetry of the Design

In his book, The Mysteries of Chartres Cathedral, Louis Charpentier recalls his first experience of being inside the cathedral. He was immediately struck with the impression that “everything contained its opposite in itself.” He said that the same balance contained in the secret of the Chinese Tai Chi, is at work in Chartres where the “proportions, orientation, position and symbolism have all been designed to alert the psyche and refresh the spirit.”

This idea is hinted at in Chapter 14 of the Tao Te Ching

LabyrinthWhat we look for beyond seeing 
And call the unseen,
Listen for beyond hearing
And call the unheard.
Grasp for beyond reaching
And call the withheld,
Merge beyond understanding
In a oneness
Which does not merely rise and give light,
Does not merely set and leave darkness,
But forever sends forth a succession of living things as mysterious
As the unbegotten existence to which they return.

Charpentier further states:

“If the pilgrim experienced the entire sensuousness of the cathedral, it would be because the body’s senses had apprehended all the musical and geometrical proportions, and all the numbers and lines expressed in the building’s interior.”

Geometric forms that exist in the labyrinth or even the Masonic Temple such as the cube, triangle, sphere, square, or oblong square could act as a doorway into various states of awareness. “God Geometrizes.” Sacred Temples can be said to stand for an unseen condition of something that can be known.

Beauty as an Expression of Truth

Divine archetypes are said to be not only doorways to the unknown, but as Plato has indicated, they are the very essence of beauty. The nature of beauty cannot always be described in words, and so it is possible, that certain symbols act as a bridge between the visible and the invisible. Satisfying both a physical and metaphysical need, sacred architecture can:

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1. Provide an energetic focusing center on the physical plane wherein the mysteries are learned and enacted;

2. Serve those seekers who enter the building and become intellectually and spiritually stimulated.

The more beautiful the appearance in form – the more closely will it correspond with spiritual truth. Buckminster Fuller stated it like this, “When I am working on a problem, I never think about beauty, but when I have finished, if the solution is not beautiful, I know it is wrong.”

My sense is that if a person does not appreciate beautiful or holy things, he will lose them. Without reverence, the sacred feeling will diminish and then be forgotten. Thereafter, his only concern will be his personal comfort and selfish desires.

On the other hand, as we honor holy places we will be entrusted with holy things. Just the opposite of disbelief and despair, the goal is eternal life and peace. Contemplating art and architecture, the spiritual and the divine, moves us away from the mundane world of the daily round.

Do sacred spaces make us more enlightened? Some have scoffed at labyrinths, masonic temples, mantra, and things like crystals or incense for centuries. In times of need, I have tried all of them.

Music and the Quadrivium

Music and the Quadrivium

Music is delivered to us via our sense of hearing, which when young hears a wider range than when we are older. Our mind processes the complex mathematical formulas of sound waves, and that processing, can affect our mood, thoughts, feelings, and memories. Music is found in all cultures, at all human times – humming, hitting things together, singing, instruments. We have found a way, through music, to sounds and words much more integral to our lives than mere language.

There are so many aspects of music that it is impossible to scratch even the surface here. In a recent conversation, I asked a Brother, proficient in music theory, playing music, and song, what he felt the most important aspect of music was. Without hesitation he said, “The perfect fifth.” I asked him to explain.

M_Octave_Fourth_FifthThe human mind likes consonance, or harmony in its music. We find our minds like notes to be evenly spaced, and those that are not are “out of tune.” The perfect fifth is considered the most consonant of musical intervals. However, the musical scale cannot, mathematically, work with all perfect fifths, up octaves and down. There must be adjustment, otherwise it sounds “off.” This equal  interval spacing, what we’re familiar with today, is called equal temperament. There are several tuning methods, and several types of equal temperaments. These differences come from how the octave is divided mathematically.

This brings us to The Well-Tempered Clavier. The Well-Tempered Clavier is a collection of two series of Preludes and Fugues in all major and minor keys, composed for solo keyboard by Johann Sebastian Bach. It is sometimes assumed that by “well-tempered” Bach intended equal temperament, the standard modern keyboard tuning which became popular after Bach’s death, but modern scholars suggest instead a form of well temperament. There is debate whether Bach meant a range of similar temperaments, perhaps even altered slightly in practice from piece to piece, or a single specific “well-tempered” solution for all purposes. There are 24 pairs of preludes and fugues, in each book (48 total) each representing the entire set of musical keys.

Johann Sebastian Bach

Johann Sebastian Bach (1685 – 1750), German musician and composer playing the organ, circa 1725. From a print in the British Museum. (Photo by Rischgitz/Getty Images)

This set of music is significant for a few reasons. The first is that it is really Bach’s catalogue of the styles and techniques of Bach’s day. It inspired many composers and it can be seen, in some ways, as a type of “color card” for music – not unlike the paint chip cards you find in a hardware store. The music exploits tuning methods, temperaments, and construction that Bach would have used on any keyboard instrument.


Interesting book on humankind and music here: The Singing Neanderthals: the Origins of Music, Language, Mind and Body by Steven Mithen. London: Weidenfeld & Nicholson, 2005. ISBN 0-297-64317-7 374 pp.

Geometry and the Quadrivium

Geometry and the Quadrivium

Whist sitting in school, slaving away with compasses and a ruler, one hardly remembers that geometry is the study of the measurement of the earth. Earth. The thing we sit on, utilize, and finally rest in when this is all over. The geometry in schools today looks nothing like the geometry of 3000 years ago. It is difficult to divorce geometry from the other liberal arts when we take into consideration the scale to while discoveries are interconnected. Geometry arose from the needs of agriculture, civilization, and war. For so much of this, we can thank Archimedes of Syracuse. A student of Euclid in the 3rd c. BCE, his advances in the field of geometry furthered irrigation (Archimedes’ Screw), astronomy (the first planetarium), and weights & measures (Archimedes’ Principle). The most interesting, to me, is The Method of Exhaustion (remember Dialectica) also known as “The Method” or “Archimedes’ Method.”

“…, to estimate the area of a circle, he constructed a larger polygon outside the circle and a smaller one inside it. He first enclosed the circle in a triangle, then in a square, pentagon, hexagon, etc, etc, each time approximating the area of the circle more closely. By this archimedes_circleso-called ‘method of exhaustion’ (or simply ‘Archimedes’ Method’), he effectively homed in on a value for one of the most important numbers in all of mathematics, π.” 1

Linked together with this Method is the “Method of Mechanical Theorems.” Proofs are everything to the mathematician, and in his Method of Mechanical Theorems, Archimedes had none that would be accepted. He set out using Eudoxus’ The Method of Exhaustion to prove what he knew to be true. In a letter to Eratosthenes, in manuscripts discovered in 1906, Archimedes outlines his thought processes. This document is known as the Archimedes Palimpsest.

Certain theorems first became clear to me by means of a mechanical method. Then, however, they had to be proved geometrically since the method provided no real proof. It is obviously easier to find a proof when we have already learned something about the question by means of the method than it is to find one without such advance knowledge.

The importance of these discoveries and the methods by which Archimedes came to them may be obvious – who doesn’t need π? However, it is also fascinating to peer inside the mathematician’s mind and view it with a Freemason’s perspective. Here was a man who could see the Plan, understand the Plan, and only needed to bring it to life: a divine spark of wisdom, the will to discover, and beauty in its presentation.

For an interesting and short expose on The Method and the “Archimedes Palmipsest,” whence this Method is documented, review  “The Illustrated Method of Archimedes” by  Andre Koch Torres Assis and Ceno Pietro Magnaghi. The PDF can be found here.

Additionally, the originally translated letter from Archimedes to Eratosthenes can be downloaded here. (Thank you, JSTOR.)


Just a note (1): The Story of Mathematics, Luke Mastin – http://www.storyofmathematics.com/hellenistic_archimedes.html – I’ve done my best to verify statements here, and so should you.

The History of the All Seeing Eye

The History of the All Seeing Eye

What people in the U.S.A. commonly referred to as the “All Seeing Eye” is more appropriately called the “Eye of Providence.” No, not Rhode Island. This would be the more divine providence – the big guy watching over all of us. Or gal. Or it. Whichever you prefer.

The Eye of Providence is the idea that some divine force is watching over us all, sees our deeds and actions, and judges accordingly. The Eye is associated with the Judgement card of the Tarot: Alchemical texts of the 17th Century and Egypt.

While the Eye of Providence, as noted above, has from the 18th Century C.E. onward been associated with Christianity, the idea of an “all-seeing God” has been around for Millenia. What is called “The Eye of Horus” originally was known as the Wadjet Eye, for the goddess Wadjet.

EyeofHorus

The Eye of Horus

Wadjet, as many can read on the Internet and in several Egyptian Mythology books, was one of the oldest deities in Egypt and dates from the pre-dynastic period. She is associated with Lower Egypt as well as the papyrus. Her name symbolizes the color of blue/green – the color of the papyrus plant. She is nearly always associated with a cobra and is considered the protector of pharaohs and the ruling classes of Egypt.

She’s seen as the Goddess, which represents time, heaven, and hell, and she is an ardent protector, especially of children. Over the millennia, she has been merged with many other goddesses, such as Bast and her sister, Nekhebet, Goddess of Upper Egypt, who is shown as a vulture. Wadjet has also been associated with Buto, the city which first revered her – originally named Per-Wadjet.

According to Herodotus, in his Histories ( Herodotus, The Histories, ii 55, and vii 134), “The Egyptians were also the first to introduce solemn assemblies, processions, and litanies to the gods; of all which the Greeks were taught the use by them. It seems to me a sufficient proof of this that in Egypt these practices have been established from remote antiquity, while in Greece they are only recently known.” There is note of a Temple to Wadjet in Buto (Per-Wadjet) that had an Oracle in it; it was considered that the Greek practice of using Oracles was co-opted from the Egyptians who, as Herodotus states, “taught them in their use.” 

The Eye of Wadget

The Eye of Wadget

Originally, oracles were used to be able to link the individual to the divine. A worshiper would travel to the oracle with a very specific and important question relevant to their lives. Kings would consult oracles to strategize on war or gain insight on divine events which would influence their people, like famine or floods. Using auguries drawn from various animals innards, smoke, visions, the flight of doves, or other “symbols,” the oracle would define the upcoming events based on intuition and divine inspiration. Oracles were eventually replaced by priests and religious figures as a way to connect the individual with their god or goddess, and in a way be a conduit for the divine.

We humans have always been looking for a way to have some kind of communion with the mind of our Divine source, whether it is through other individuals, hallucinogens, runes, tarot, channelling, or simply study. We look for some higher source to tell us what we ought to do, what will help us be successful, happy, healthy, or free. In this case, I find the idea of the Eye of Wadjet to be a symbol that connects us to a dusty, mythic past with some vague idea of what it really meant.

We’ve gone from the protection of a goddess to the protection of a country or our ideals, or maybe even our prosperity. I think this is the most interesting thing in this: the symbols we have in our daily lives are historical treasures that have been modified as our cultures modify them. They come to reflect what, and how we think about the world.

Inspired By Art: Nicholas Roerich’s Symbolic Journey

Inspired By Art: Nicholas Roerich’s Symbolic Journey

The Himalayan paintings of Nicholas Roerich (1874 – 1947), Russian painter and philosopher, mesmerized me when I first laid eyes on the collection. I stared at them for hours. I feel a bit as though these paintings knew me better than anyone. It’s like I understood them, and in turn, they understood me. I became interested in why. 

It could be that as a child my imagination was captured by the breathtaking views of mountains. I was inspired as much by the physical grandeur of their peaks as by the spiritual mysteries harbored within them. Indeed, for me the towering peaks represented the very summit of beauty and spirituality. The tallest mountains I ever climbed were in Zermatt, Switzerland.  I had a truly a remarkable time discovering certain wonders in nature such as glaciers and rich vegetation along with snow-capped points. I would take a rest at several spots which were beautiful and magnificent. There were always more heights to scale, another plateau or peak above, views of the Matterhorn.

Was it this experience that caused me to have a connection with Roerich’s art or something else? Are we drawn to art that mirrors a part of our inner self? What was it specifically about Roerich’s art?

Mount of Five TreasuresIt is virtually impossible to separate the artist’s art from his philosophy. Many contemporaries were skeptical of Roerich’s spiritual mission and tended to dismiss his work as being repetitive and unoriginal. However, those who embraced his philosophy experienced something transformative in those same canvases – never ending spiritual realizations.  A brief survey of his life reveals that Roerich was not an adherent of any one established religion or philosophical movement. His name is universally known not only as Master of the brush but also as a thinker and a builder of life.  His art and writings are an evocation to Beauty, to Knowledge, and to Culture. Art education would pave the way to universal beauty and open the gates to spiritual enlightenment. This vision is nicely captured in his philosophical statement of the Master Institute of United Arts which he formed in New York in 1921:

“Art will unify all humanity.  Art is one – indivisible. Art has its many branches, yet all are one.  Art is the manifestation of the coming synthesis. Art is for all.”

Regardless of whether his lofty ideals will ever be realized, or if you agree with the artist’s art philosophy, his paintings are replete with rich symbolic jewels that are a pure delight for anyone to reflect upon.

19284963678_72350b9c8f_oFor example, Roerich refers often to the great treasures stored deep within the Himalayas. The very name Kanchenjunga, he tells us, means, “the Five Treasures of the Great Snow,” because it contains the five most precious things in the world.  He alludes to them in the painting, Treasure of the Mountain. The setting is deep inside a mountain cave.  Roerich causes us to question what treasures he is referring to? Are they rubies, gold, and diamonds?  Or, upon deeper reflection, is he talking about other more inner treasures?

The gurus hold a lamp. Does it suggest that the Light of Wisdom is the treasure of the mountain?   Roerich reminds us that we must think about what we hold valuable. And – taking this to the deeper level of reflection – we should think very clearly about how we find these symbolic jewels.  What does it take?

Pearl of Searching Flickr mediumIn the Pearl of Searching, another journey is pictured. The teacher-student relationship is a theme in many of Roerich’s paintings. Our eye is drawn to the figures and we identify with them, experiencing the panorama that unfolds behind from their perspective. They have reached a plateau and are celebrating the view and a treasure they have found. What is it? What symbolic meaning do we see?

Perhaps the “Pearl of Great Price” is what gives purpose to life.   The mountains themselves symbolize a spiritual world separate from earth but accessible to those who are attuned to the higher realities. The necklace – a symbol of eternity – signifies that this daily seeking is destined to go on forever, an emblem of immortality. This all causes us to consider, “Why are we here?”

Unquestionably Roerich is one of the most interesting 20th century figures. It seems to me that his life was a symbolic journey documented in his massive body of works, each canvas a masterpiece of daring composition, glowing with color. Himalayan is the word not only for his art, but also a metaphor for his thoughts on the process of transformation.

The path to enlightenment, spiritual ascent, the sacred signs of Satyum, Shivam, Sundaram (Peace, Beauty, Truth) – these are the symbolic themes at the heart of Roerich’s paintings and writings, also at the heart of Freemasonry.  They continually cast a spell on me.  Once we begin on this infinite and exponential journey of discovery, we might stop for a moment to enjoy the view or a treasure found, but there is no turning back. Ultimately, we choose the next plateau we want to rise to.

From Roerich’s “Realm of Light”:

“Let us abandon the past for the future. Let us impel our entire consciousness into the future and let us suffuse it with radiance, for this is within the access of humanity.”

Note: To read further on Nicholas Roerich, check out the Nicholas Roerich Museum.

Mathematics and the Quadrivium

Mathematics and the Quadrivium

Personally, I struggled with Math in school. Faced with a math test, any math test, I froze, cried, banged my head against the desk, and ultimately gave up. I saw mathematics as an isolated “thing” to be conquered. You were either good at math, or you were not.

How little I knew, and how little I was taught, about true mathematics. More than numbers, factorials, and fractions, Mathematics is about relationships – of numbers: how they work with each other, work for us, against us, and can talk about any situation. There are mathematics of money, elections, government, science, music, agriculture, capitalism, socialism, any -ism. Math is language and structure: it is a bridge between all aspects of liberal art. Which leads us to the Bridges of Koenigsberg.

bridgesLeonhard Euler, a Swiss mathematician of the 18th Century solved, sort of, the problem of the Seven Bridges of Koenigsberg (Russia, at the time). Koenigsberg had two islands connected by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point (touching every edge only once). Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The bridges did not meet this condition and therefore, no solution could be found to the problem.

Yet, what this Eulerian circuit eventually did provide is the basis for modern topology , which has expanded into areas of quantum physics, cosmology, biology, computer eulernetworking, and computer programming. For example, the Eulerian cycle or path is used in CMOS circuit design to find an optimal logic gate layouts. For anyone wanting to read the paper outlining these paths in the original Latin, it can be found here.  English translations do exist. A good page on the history of topology is here.

Leonhard Euler was a fascinating individual in that he saw mathematics as something that infused all of life. Though his writings, he made applied mathematics accessible to the layman and his scholastic peers alike. An excellent and thorough biography, written by Walter Gautschi, can be downloaded in PDF form here. With a varied interest in all aspects of mathematics  (arithmetic, geometry, algebra, physics), music, anatomy, physiology, and astronomy, he truly was a man of the “Enlightenment.”  While he was not a Freemason from what I can tell, he seemed to hold much regard for the idea of true science, and creating a better world for his fellow man: a Freemason’s true ideals, to be sure.