Square Wave

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Math and the Night Sea

Photo by Pamela Palma

The Wave has many origins, but somehow I always associate its soul with a wheat field in Andulsia. I spent the summer of 2002 in southern Spain, being half resident artist and half maintenance man, at an archeology dig run by Luis and Josep Gibert. There were thirty of us living communally in three large caves, and we quickly fell into a late night then sleepy siesta sort of lifestyle. Outside the caves the landscape opened up to panoramic views of wheat fields. There was lettuce and alfalfa near the stream, and olive and almond trees far away on the flanks of purple mountains. And the chiming of bells from tended flocks of sheep. At night the land became dark and the huge sky filled with stars. During the day I looked at plants, their pods and thistles, and studied the silhouette of surrounding mountains for clues about shapes that seemed at home in the expanse. I also studied what large –scale human made things looked good. The second most beautiful thing I found were tall stacks of hay bales. The most beautiful thing I found were the wheat fields. I began spending hours in the middle of the wheat fields, mesmerized by their expanse of orange gold, the way they tickled the under belly of the wind, the rattle of wheat heads, and their complete nourishing goodness. What joy to be in the middle of their whispering expanses in a warm sunset!

Then one day a photographer showed up with a huge fan strapped to his back and a swath of blue material for a sail and flew around taking aerial pictures. Damn! I thought, that cloth looks good! So I began thinking more about the wind and making kites. I made eight kites that wouldn’t fly before I made an orange one out of an old table cloth and scraps of wood that flew if I tied my shirt to the end of its tail. Back I went to the wheat field and flew the kite and looked at the large view and colors and felt the warm breeze and listened to Arabic music that came from a Moroccan radio station.

It is possible to walk through an entire day without seeing anything. I am now looking at a sweetgum tree outside my window. What I see is flickering green over a brown mass, surrounded and penetrated by blue. But from this visual cue comes a mountain of memories and knowledge. Its growth, passiveness (the fact it won’t come hopping toward me on the one big trunk!), the significance of a leaf turning red, memory of how it looked in different lights, the sound it makes in the wind, the strength of the limbs grasped, the twittering of roosting birds. When I see the tree all the knowledge is bundled together and it is this mental image of the tree that is practical and expedient, and for the most part the only thing I am capable of seeing. Whether light or dark I still see the same tree, because my mature mind substitutes a conception of the tree for the actual tree.

When we see a painting our minds also rush to imagine the image. Great works of art feel gut wrenching because the force a beautiful world to gather itself from our sinews and rush out to meet the painting in front of our eyes. And sometimes the world that we are driven to imagine feels more real than the ensemble of props and cues that the actual world has become.

The contact of our senses with the world is superficial. Our eyes see a landscape of reflected surfaces. Our ears are thin little walls held up to an ocean of sound. Our hands caress contours. Our imaginations are incredibly proficient at stitching whole and meaningful entities out of an experience of surfaces. But despite our imaginations, it is not all that competent, and there are those magical times when the world reveals itself directly. Times when you find yourself joyfully running among warm boulders, or while talking to someone, suddenly becoming aware of the magnitude of the wonder that you are both alive at the exact same time, and peering into each other’s eyes. For me these times are often accompanied by a sense that behind the surface of things there is a huge billowing presence of life and energy. What is visible is the effervescence of a bubble pushing into the present moment. The surface is the bird we see. On one side, sweeping the bird into existence is a ferocious energy, expanding, life giving and hungry. On the other side is our imagination of the bird, conceptual and also convex. There are times when the expanse of our imagination meets the expanse of existence, and we are awe struck.

These were the thoughts from the wheat field. I left Spain thinking about soaring, wind swept surfaces that mark the boundary between what I can and cannot imagine. I hope part of our minds see the wooden wave as an abstract undulating surface, a floating expanse independent of substance. And I hope its contemplation will prepare the eyes to see beyond their normal resting places. Maybe, upon leaving the high-ceilinged room, we will see not only the soaring of birds, but also the mighty space that hungers for the soaring of birds.

Besides the wheat field The Wave has many other origins. One is simply the inspiration of moving into a big new studio with lots of vertical space. Another comes from living on a sailboat and being surrounded by water. Certainly an ongoing obsession with caterpillars plays a no small part, nor does an unaccountable fear of making anything remotely useful or profitable. I keep thinking too about a sailing trip seven years ago, alone at the night watch, surrounded by a terrifying and beautiful jumble of moonlit swells.

The Wave took seven months to build and is made of five components: two camshafts orientated at right angle to each other on ten-foot tall platforms, two matrixes, one long and narrow, the other big and square, fixed fourteen feet above the ground, and the wave itself, suspended by 81 cables. One camshaft pushes levers that manipulate north/south waves, while the other drives east/west waves. On each camshaft are nine plywood circles sequentially offset 45 degrees. The first and last circle are in the same position ensuring that the rotation of the camshaft generates a segment of a wave exactly one wave length long. The motors rotating the camshafts can be varied in speed giving the generated wave a period between 100 and 10 seconds in either direction. Each camshaft can be controlled independently, and furthermore each can change amplitude on the fly. Amplitude changes are caused by forcing all nine circles to be more or less centered on the shaft. When they are completely centered the amplitude is zero, and at the other extreme they create an amplitude of over two feet.

All 81 cables are fixed (nine per lever) to the camshaft parallel to the long narrow matrix. This matrix lowers and raises the wave by pulling on a chain of pulleys that take up length on all cables equally. The nine bundles of nine cables then pass into the large square where they separate and drop down to the 81 intersections of the wave. The square matrix weighs 135 lbs, is made of oak, contains 243 pulleys and is hoisted and held up by three trailer winches. Its purpose is to add the two sets of perpendicular waves together.

The wave itself, made of 144 fifteen inch long lengths of tapered fir dowels, hangs from a total of a third a mile of steel cable. Its motion can be described as Asina+Bsinb+C where C is the over height of the wave, A and B are the variable amplitudes, and a and b are functions of the speed of rotation and position of each cam. I had an embarrassingly fun time figuring it all out and am thoroughly enchanted with the outcome, which is far more sensuous and organic than I could have anticipated. I hope you enjoy The Wave as much as I do.

Thanks to Mom, Dad, my brother and sister for unceasing support, love, and help moving heavy things around; Gary Scott for being friend, mentor, teaching me carpentry, providing employment and letting me “store” the company tools; Frank Bletsch, Bruce Douglas, Peter St. John, George Dawnay, Dan Torop, Cullen Gerst, Lorca Rossman, Rick Millikan, Jason Kral, and Jeff St. John for countless hours of indispensable technical and artistic help; Richard and Nancy Funk for letting me climb all over the warehouse and being a daily source of encouragement; Antje for being so positive and so flexible about sharing the studio; Dory for expert forklift driving; Jody Cox, Pamela Palma, and Amber Menzies for saving my life every other week when I found myself penniless and starving right around dinner time; Perrin Meyer for his joy in the math of waves; Rebecca LeGates for design help; and thanks to Alan at Berkeley Architectural Salvage for giving me oak and fir on credit right as the wave was nearing completion.

Reuben Margolin
Emeryville, CA