Sacred Geometry

by Karen Speerstra

What’s under and behind some places of power?  Could it be “sacred geometry”? And what is sacred geometry, anyway? We recognize Geo-metrics…measurements of the earth. But how can we measure the sacred? And we certainly can’t “form” it or “contain” it—with numbers and shapes, squares and cubes and triangles, circles and dodecahedrons. Or can we? And if, as Walt Whitman believed, spirit and soul are sacred, might the “spirit and soul of the earth” also be sacred? And can it somehow be measured?  Can we rationalize the irrational?

Why are people drawn to certain rock alignments, to places like Chaco Canyon where it said heaven and earth meet? To cathedrals, pyramids, wells and hot springs? Isn’t it to connect with a “sacred something”?

Certain places catapult us into out-of-the-ordinary space and time. Venerated places are saturated with holiness; they drip energy that speaks directly to our hearts, bypassing the logic of our brains which might ask,  “Why this rock and not that rock?” “What makes this place any different from that place, over there?”

David N. Elkins, a psychology professor, says he believes in the sacred “because I simply no longer have the strength to sustain disbelief.” He wrote about eight alternative paths to the sacred in Beyond Religion: the feminine, the arts, the body, psychology, mythology, nature, relationships and dark nights.  Of course no one, not even Elkins, can know the true nature of the sacred. It’s like trying to define a kiss. A kiss more than lips meeting. It’s more than faces brushing and skin touching. It’s a mysterious union that can't be measured. Still, our minds search for ways to understand.

Some call sacred geometry a very murky field; others are convinced human constructions such as the great pyramid and alignment of early stone works as well as later buildings that have lasted and continue to call to us, were governed by ancient mathematical and astronomical principles. For instance, the claim is made by Peter Tompkins and others that the base of the Great Pyramid of Cheops equals the circumference of a circle with radius equal to the height of the pyramid. 

Perhaps we feel something “different” in buildings or when we observe various artworks because they are constructed from careful geometric proportions. Ratios. Sequences. Progressions.

Measuring with Compass and Squares

Back in 1921 Sir Thomas Heath wrote a serious history of Greek mathematicians. In it, he said, “”There is presumably no problem which has exercised such a fascination throughout the ages as that of rectifying or squaring the circle; and it is a curious fact that its attraction has been no less (perhaps even greater) for the non-mathematician than for the mathematician.”

Vitruvius, the Italian architect who lived from 70-25 B.C. wrote the manual many early Christian architects called their bible. He said, “Geometry…teaches us the use of the rule and compasses…and rightly apply the square, the level, and the plummet.” That's all early masons used to build cathedrals, and some calling themselves Masons today, still find these principles to be symbolically important. Our own capital city, thanks to Thomas Jefferson,is built on a Pythagorean square based on the number 10, ironically enough given our recent Iraq history, one that Babylon was also built on. A 10x10 square contains 36 squares around a perimeter of 360˚. In other words, Washington D.C. squares the circle!

In 1521, Cesare Cesariano translated Vitruvius into Italian and added this familiar illustration.

It’s Vitruvius’ “perfect human body” [male body--female bodies at that time weren't considered so perfect] with the central point being the navel and his arms and legs, like a pair of compasses. 

“And just as the human body yields a circular outline,
     so too a square figure may be found from it.
For if we measure the distance form the soles of the feet to the top of the head,
    And then apply that measure to the outstretched arms,
    The breadth will be found to be the same as the height.”
(Vitruvius, The Ten Books on Architecture)

Earlier geometric principles inspired Bernard of Clairvaux, who founded the Cistercian order and sought to build “perfectly” proportioned Christian architecture, to ask “What is God? He is length, width, height and depth.” In order to discover these building secrets, he sent nine men, who eventually grew into the mighty Templars, down to Jerusalem to scope out what was left of Solomon’s Temple and to discover the secrets of sacred geometry. And perhaps uncover the “Ark” as well.  Numbers, he believed, as Pythagoras taught, are the sources of form and energy in the world.

The Father of Geometry

Pythagoras, who lived in the late 500’s B.C. bequeathed us geometry, calling it the measurement of earth and the heavens. He spent 20 years learning  ancient arts from the Egyptians.  And then he studied with the Persians. But who taught the  Egyptians and Persians? I prefer to think the Atlanteans. And before them…? 

What we know of Pythagoras comes only from his disciples and later people such as Aristotle, because, unlike the Platonists, Pythagoras saw no need to write things down. He established ways of living that some monks and ascetics still emulate.  For instance, he taught people to value silence, to be vegetarians, to wear linen. He practiced self-denial, used incense, music, and rigid cleanliness. In his Timaeus, Plato built on what he had learned from the Pythagorians and brought us the term world soul.  Lovelock later picked it up and reinterpreted Gaia. And now Obama brings us green czars and czarinas to help save our planet. That’s how our world evolves. We are all dwarves stepping up onto the shoulders of prior giants.

We, too, can learn meanings hidden in music and signs, as the early Druids and Pythagoras taught. We are more than just earth, air, fire and water, Pythagoras said. We are justice, soul, reason, opportunity. He said whole numbers are the numbers to pay attention to. Zeroes and irrational numbers didn’t hold much meaning for these early mathematicians. After all, odd numbers were feminine, irrational, and even numbers, rational and masculine.  Except for One. The monad was the source of all numbers. The possibility that “One” could be feminine didn’t get much traction from the Pythagoreans. Or from most later aesthetics and male writers, for that matter. But perhaps "Her" time has now come.

The Golden Ratio

We sense unity and wholeness when we look at art formed by what is now called the “golden ratio.” Euclid, in Elements, first put it to us this way, “A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.” O.K. So what does that mean for us mathematically challenged?

The golden ratio, expressed in Greek by their 21st letter, ø, divides something that is whole, like a wall, a room, sculpture or a picture into two parts.  One larger, one smaller. But the division is not random. It is carefully planned, thank you Euclid, so that the ratio of the larger to the smaller is perfectly proportioned roughly one to 1/3 to 2/3. Actually, it’s 1.618 033 988 749 894 848 etc. In most pleasing paintings, the sky will come down about 1/3 of the way into the composition. It’s called the golden mean, the golden section, the golden number, the divine proportion.

This gridded image shows us how to visualize the 2/3, 1/3 ration--and gives us an illustration of the Fibonacci sequence…add the two prior numbers together for the next number:  1, 2, 3, 5, 8, 13, 21, 34—you get the idea.

These are the proportions that please most of us—they make us feel whole and at ease when we enter a space or view a work of art. When they’re not there, we feel more fragmented and sometimes, even nervous.

Sacred Sites and Sighting the Sacred

Old sites call to me. I prefer visiting temples of Isis and Artemis before they became temples of Apollo. Or later Christian sites. I want to stand next to Her holy wells before they were surrounded by monastery walls. I look for Her signs on stones—spirals, meanders, eyes—before they were marked by crosses and crescents.  One such valued symbol is the visica pisces—the almond formed by two overlapping  same-sized circles with two intersecting points.

Visica pisces literally means “fish bladder” and was a sign of feminine genitalia long before Christians scratched it in the dust to secretly write the code word for “Jesus.”  Interestingly enough, Delphi—dolphin—means womb. Delphi was "Her" place long before it became Apollo's.

We're great usurpers of sacred geometry. I think of Her sign every time I follow a car marked by the Christian fish.  Whether interpreting calendars or creating buildings, it’s always easier to build over something than to start something entirely new. For instance, astronomers have now tracked back the night sky to the time Jesus was born and some people are upset because “the Bethlehem star,” a brilliant convergence of planets at the time, happened in June, not December. But Mithra's birth, announced by shepherds, was on December 25, according to ancient teachings, so early Christians thought they’d just use that special day instead. And August 15 was, for many centuries,  a day to celebrate the Goddess—so Mary’s holy day was easily folded in. And as we know, most cathedrals, such as Chartres, were built over earlier worship spots—many with standing stones and holy wells.

For the record, I’m a devout Christian, but one who likes to think she can hold several ideas at the same time.  My God can be feminine as well as masculine. Or neither, which is more likely.  I look for Her “almond” symbols, Her meanders and spirals in art and architecture as well as her sacred geometry in nature.  And I spot them everywhere, because I believe “She” is everywhere. A Divine Wisdom underlies our sacred geometry.

The Chinese teach that we can create wholeness in towns and single homes as well as other buildings by observing how energy or chi flows and placing them properly.  We can manipulate and direct that flow of wind/water (feng shui) to increase our wealth, health and longevity.

The Muslims, masters at that riddle of squaring the circle, place the crescent (a form of the vesica) or the Mother’s moon, at the fore. Vedic mandalas are still used to plan and design buildings.

 

And the dome is, after all, simply a circle and a square.

Thomas Jefferson based his design for Monticello on several buildings he saw while in France, but the columns and dome were inspired by the ancient Roman temple of Vesta, goddess of the hearth—Her sacred space!

India picked up the dome motif and set it into Taj Mahal.  Russians in their Onion Domed churches. Then Buckminster Fuller put self-bracing triangles together and the geodesic dome was born.

The Romans poured a concrete dome and called it their Pantheon, the “dome of heaven.” The sky set into the earth.

Another of “Her” spaces, the Hagia Sophia (Her Holy Wisdom) in Istanbul, is a classic domed structure.

Umayyad Khalif in 685 A.D began building the octagonal Dome of the Rock—Mosque of Omar—in Jerusalem. It features a dome, originally perfected in Persia (Iran.)  The famous Jerusalem rock covered by this golden dome was connected to Abraham—father of three major religions. Muslims believe it to be the rock from which the prophet Muhammad ascended into heaven.

 

[Photo by John Spier]

The Ka’ba was built in the courtyard of the al-Haram Mosque in Mecca, over another sacred rock. Many believe both original rocks were very early goddess sites, perhaps meteor stones, venerated by people who loved the Earth Mother.

Today, the Ka’ba (Arabic word for “cube”) is the holiest site in Islam and pilgrims travel there yearly for the rite of  the Hajj. Much earlier, it was a worship site of Al-Lat, who it is said, preceded Al-Lah. She was called the Old Moon Mother of Mecca and women danced around the famous black stone before Muhammed threw out all her symbols. Funny thing about symbols. You can throw them out, but they keep coming back. Take “The Mother’s” morning star and crescent moon, for example. You still see them fluttering on flags. Her priestesses used to circle her holy cube seven times, counterclockwise. It is still done, but now only by men, and it’s enacted in Allah’s name. Feet remember what heads forget. Once a Sufi saint walked around the sacred Ka’aba and was suddenly blinded by my light.  Later, he wrote he learned that day that “women represent God’s powerful embodiment.”  Love can come at sacred places, like a sledge-hammer to pulverize hearts.

Two other of Al-lat’s triple names were Manat, (fate and time) Al-Uzza (morning star) and Al-Lat.  When oaths were sworn, people said, “By the salt;  by the fire; and by Al-Lat who is the greatest of all.” Early priests called themselves “Sons of the Old Woman.”

And that black stone inside the cube?  It is a polished black stone legend says fell to earth as a meteor long ago—a feminine fecundity stone named for “the girl with the well-developed breasts” or “the nubile one, ready to be made pregnant.” The famous stone, as are many holy men, is covered by Al-Lat’s black skirt. Today the kiswa or black cloth covering is made from eight curtains, a pair hung on each side of the cube. They are embroidered in gold calligraphy: “There is no God but Allah and Muhammed is the Prophet of Allah.”

According to Islamic belief, God ordered worship places on earth to reflect the house of heaven and Adam, it is said, built the first one. The Ka’ba was built by Abraham and Hagar’s son Ishmael.  Some say the black cube fell right where Hagar, Abraham’s second wife, conceived Ishmael. It is a fecund place where heaven meets earth. And a place where much blood has been shed. Fatimah’s son, Husayn, was slaughtered in a battle of 70 of his men against 4000, only fifty years after his grandfather, Muhammad’s death. Sunni. Shi'a. Arrows still fly. Once, an arrow tipped with naphtha set the Ka’aba afire and the sacred stone split into three pieces from the blaze. “Like the torn bosoms of mourning women,” they said. The three pieces are now held together by a triangular necklace of silver pointing downwards, like a vulva. A yoni. The downward pointing triangle has been "Her" feminine symbol since the days of cave-paintings.

 

[This photo of the Black Stone enshrined in the Ka’ba is courtesy of Creative Commons License, Tour SaudiArabia]

The Arabic alphabet comes from Her 28 phases of the moon. Legend has it Al-lat even inspired the invention the camel-saddle. Practical? Yes! She inspired ideas and inventions.  She IS Necessity, Mother of invention. Her name attests to the belief she was the goddess of milk…lat. Latte. Think of her next time you’re at Starbucks.

Squares, circles, spirals. No wonder our kids, and our “inner children” love spirographs and computer programs that builds fractals and wonderful complex figures from lines and circles.  Nature shows us how. Take the chambered nautilus growing in a logarithmic spiral.

Hexagonal honeybee cells. Fractals of broccoli. And sunflower seeds brilliantly display their “sacred geometry.”

Like Leonardo da Vinci, Lincoln was so obsessed with squaring the circle, that at one point in his life he spent many sleepless nights trying to get it right. From 1504 on, Leonardo filled notebooks with his attempts. Early Greeks certainly knew the meanings behind the circle, the square, the cube, the ellipse, the parabola, the hyperbola. And over the past twenty years or so, crop circles show us even more of these beautiful shapes, teasing and begging us to figure out what they mean. Most of the ones  belowappeared in Britain's August grainfields.

Sacred Geometry is literally a world-wide, huge topic—and one not all of us need to or even could completely understand. But if you're seeking more, I’ll point you to two books I have found very helpful. Like the golden mean itself, one is bigger, and one smaller. The big one is actually a textbook my friend Paul Calter wrote, available from Wiley: Squaring the Circle: Geometry in Art and Architecture. The other slimmer book is by Robert Lawlor called simply Sacred Geometry. In Calter’s book, you’ll find a fascinating appendix: “The Art-Math Tourist” with a list of 52 places he illustrates in his book—not an exhaustive list, but certainly an intriguing one, from Agra, India and the Taj Mahal to Wimbourne St. Giles, England with a polyhedron atop a parish church. And at the Collective Wisdom site you’ll discover Carol Frenier’s indexed list of places for your further contemplation of sacred geometry. (add hyperlink here)

What’s behind and under the places that tug at us—old or more recent ones—where you sense beauty, peace and wholeness?  Have you had any experiences of geometry becoming music? Or music becoming geometric symbols?  Of space opening up to something much larger and wholly beyond us? It could be "holy math"?  Sacred geometry?

 

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