Mysteries of the Hopewell: Astronomers, Geometers, and Magicians of the Eastern Woodlands

2. Sacred Geometry

Chapter 2 S A C R E D G E O M E T R Y Geometry existed before the Creation. It is co-eternal with the mind of God .l.l. Geometry provided God with a model for the Creation .l.l. Geometry is God Himself. —Johannes Kepler .l.l. our brains lack the capacity to take in the universe as a whole; we have to structure it in order to put little bits of it into our heads. —Ian Stewart and Martin Golubitsky Fearful Symmetry: Is God a Geometer? It was a god-awful climb as I struggled up the last few hundred feet to the small temple. At 14,170 feet above sea level, my lungs burned as they grabbed at every stray molecule of oxygen. I was in Nepal, along the Tibetan border, on my way to Base Camp I, Mount Everest. Chomolungma—“Goddess Mother of the World”—that is what the Sherpas call the mountain. And scattered along its way, in the shadow of the mountain, are a number of small Buddhist temples, safe havens for a tired traveler. After several years of working as a business executive in New York City, I needed this change of scenery to restore my connectedness to 32 the real world. As a matter of fact, after this little trip, I would leave New York and pursue an advanced degree in anthropology. Such matters were far away, however, as I climbed the last few dozen feet of trail and came into the open. Like others of its kind, this temple boasted a rectangular courtyard and several small square buildings —welcome order after days of travel through a jumble of rock, ice, and sky. Years later, in journeys to other sacred places, I would again find these same geometric patterns. In fact, the predilection, desire, or even compulsion to build sacred or religious structures in symmetrical geometric patterns seems universal. From the shrines of Tibet to the temples of India and cathedrals of Europe, humankind has for thousands of years defined its sacred spaces and built its sacred structures in geometric shapes. The logic of this behavior perhaps can be explained by the magical premise attributed to the mythical father of alchemy, Hermes Trismegistus, the Thrice Great Hermes: “That which is in the lesser world (the microcosm ) reflects that of the greater world (the macrocosm).” In other words, sacred structures are designed to replicate, on a smaller scale, our vision of the universe, which is geometric in nature. Through our interactions with these microcosmic shrines, temples, and churches, we then strive to bring our consciousness into harmony with the macrocosmic universe through prayer, meditation, contemplation, and other mind-altering techniques. Echoing the thoughts of philosophers throughout the ages, Nigel Pennick (1980:7) has pointed out that “Geometry exists everywhere in nature: its order underlies the structure of all things from molecules to galaxies, from the smallest virus to the largest whale.” While this statement is undoubtedly true in a very deep sense, the interesting paradox is that this underlying geometry is not especially self-evident. Nor is this underlying geometry the simple Euclidean geometry that we learned in high school. As explained by mathematician Benoit Mandelbrot: Clouds are not spheres, mountains are not cones, coastlines are not circles , and bark is not smooth, nor does lightning travel in a straight line. More generally .l.l. many patterns of Nature are so irregular and frags a c r e d g e o m e t ry 33 mented, that, compared with .l.l. standard geometry, Nature exhibits not simply a higher degree but an altogether different level of complexity. (Mandelbrot 1977:1) More than a century ago, the same sort of realization led artist Eugène Delacroix to note that, “It would be worthy to investigate whether straight lines exist only in our brains” (quoted in Shlain 1991:33). Indeed, where we find straight lines or absolutely regular curvature in the world around us, we usually interpret these findings as evidence of human activity. Irregularity and variation of shape characterize natural forms, whereas perfect geometric shapes are usually more representative of the human mind and the human hand. Except for snowflakes, beehives, rock crystals, and a few other such things, strict Euclidean geometric patterns are mostly something that we superimpose on the universe. The real world is much more fuzzy. In fact, it took...