Drawing a Line in the Sand: Where Art, Math, and Spirit Intersect

Perhaps the most interesting and universal art form is also the most ephemeral: drawings made on smoothed dirt.  Many are based on common geometric forms: the circle, concentric circles or overlapping circles, and the circle bisected by perpendicular lines.

It can be argued that people have a universal fascination with geometric forms, especially the circle.  The very oldest form of  rock art all over the world is the cupule, a circular indentation engraved in a rock surface.  While these cupules probably had many different meanings and functions in the society, the presence of these earliest forms of “making my mark” in the Americas, Africa, Australia,India, Europe, and the Pacific Islands is very interesting.  They are also by far the most common form of
rock art, appearing in groups of hundreds, sometimes thousands in a single location.  A Neanderthal burial site in Europe dated between 40,000 and 70,000 years ago includes a stone slab marked with sixteen cupules, most of them grouped in pairs.
The stone was placed over the body of the deceased teenage girl so that the sixteen marks faced toward her.  Cupules in Australia have been found to be at least 60,000 years old; some experts put the date closer to 116,000 years ago. The record is a series of cupules found in a cave in India that experts claim are over 200,000 years old.

On the Big Island of Hawaii, a large grouping of cupules and concentric circles
fills an old lava field right next to one of the big tourist hotels.  Perhaps it served the same function as the hotel’s register book.  Unfortunately, it’s impossible to know how these forms functioned in the societies that left them behind. There are records of relatively modern practices that involved these cupules, but there is no guarantee that these practices were similar to those used long ago.

What we can see is the continuation of this desire to draw certain geometric patterns, but not purely as a mathematical exercise.  These forms are tightly connected with cultural heritage, spiritual value, and personal commitment. What’s more, in many
examples they are purposely temporary, designed to be drawn, seen, and obliterated
within a short period.

In Guatemala, some villages have the custom of decorating the street before an important Catholic feast day.  People use colored sand, leaves, nuts, and flower petals to create beautiful patterns that cover a wide pathway down the middle of the street.   When the priest leaves the church after mass on the feast day, he leads the procession of believers down this decorated path that in some cases goes all the way around the block and back to the church.  Why make these beautiful designs?  They’re a way to give praise and glory to God.  They’re also a source of local pride.

The Sona drawings in West Africa are famous as feats of both mathematical design and story-telling, two items seldom combined in western culture.  The story-teller marks out a grid of dots in the sand then begins the story and the diagram at the same moment.  If the diagram has only one line, it must be continuously drawn so that the diagram and the story finish at exactly the same time.  Try this one, a very simple example, on a piece of graph paper.  If it works, try it on plain paper.  Then try to tell a story while you draw it, without stopping, of course.

You can get a larger version of the drawing by clicking on the image.

Some of the sona diagrams are very complicated, like these from “SONA: Sand drawings from Africa”; the person who can complete one of these perfectly while telling a story deserves to be the center of attention!

These are finished drawings, but you can find grids and explanations including steps  involved in drawing many of these if you put “sona” or “West African sand drawings” in your search engine.

The same grid idea is at work in the Rangoli design from India (chalk drawing in photo).  However, instead of drawing lines between the dots and following an algorithm, the artist has used the dots as guides to create a hexagon.  Six 6-sided flowers form the ends of the bisected X while a seventh lies at the center of the diagram.  Filling out the space are three 3-sided flowers, three 1-leaf forms, and three concentric circles.  It’s a geometric delight, but its purpose is to be walked on.  The designs are created, usually by women, for entryways.

Very large versions of rangoli designs have been created to cover entire streets.  Curiously, the logo for one rangoli website is a sona drawing.

The most famous sand drawings in North America are those done by the Navajo hataali (native healer) as part of a chant, a ceremony that usually takes several days.  The hataali must be skilled in the complicated art of the sand paintings required for each ceremony as well as the songs that go with them.  The person who is being healed will eventually sit on the sand painting, and it will be destroyed at the end of the ceremony.

Tibetan Buddhist mandalaIn Tibet, perhaps the most complicated sand paintings of all are created by the monks as part of the initiation ceremony of new monks.  The mandalas can take weeks to create and are thought to be infused with spiritual power.  After three days, the sand is swept up into a pile and cast into a river so the spiritual energy collected in it may be dispersed into the world.  (For information about the meaning of the symbols in the mandalas the Buddhist monks make, read the Dalai Lama’s explanation for non-Buddhists.)

It’s curious, in all of these examples, that the simple geometric forms of circle, concentric circles, circle bisected by perpendicular lines, and circle-square
combinations are so common.  This is part of what people call sacred geometry, but it’s important to realize that the geometry is not an end in itself.  It is part of an expression of spiritual connection and awe.

I included several examples of Sona drawings as well as a maze story in Misfits and Heroes: West from Africa because they seemed a logical fit for an ancient storyteller.  Since storytellers were the teachers as well as the entertainers in the society, they would probably have used the sand drawings to remind people of important moral
lessons or historical events.  While I created the stories they told, I used forms I found in Paulus Gerdes’s book Geometry from Africa: Mathematical and Educational Explorations as well as his article “SONA: Sand Drawings from Africa,” and Claudia Zaslavsky’s book Africa Counts: Number and Pattern in African Cultures, all of which are fascinating reading.

In the photo to the left, the children are making sandroings (sand drawings)  in a competition.  It’s a celebration of line and pattern, echoing a practice that is thousands of years old.

 

 

Here is a photo of an elaborate rangoli design that takes up a whole street in Singapore:

 

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