Imaginary symmetry?
The seductive idea that the ancient Romans, Greeks or Egyptians planned monuments like the Parthenon according to the so-called "golden ratio" - allegedly the distance from the navel to the head compared to the body length - has been discredited in recent years. Now a mathematician has also set out to refute the thesis that decorations in ancient Egyptian burial chambers correspond to concepts based on knowledge and application of mathematical symmetry. According to a new analysis presented at last week's annual meeting of the American Mathematical Society, at least some of the tomb patterns represent merely household objects, rather than sophisticated abstract patterns. A repeating pattern of spirals framed by zigzag lines is found on the ceilings of many tombs. From this, some scholars concluded that the early Egyptians used modern notions of symmetry in their designs. An endlessly repeating pattern allows one to plan an intricate pattern for an entire quilt rather than going through trial and error. This assumption also plays a role in the classification of repeating patterns into 'frieze groups' and 'wallpaper groups'.
But "our obsession with symmetry may be blinding us to asymmetry," says Smith College mathematician Marjorie Senechal in Northampton, Massachusetts, who is reinterpreting the findings of Occidental College-based anthropologist Elizabeth Barber Angeles introduced. In 1991, Barber discovered that a 3,500-year-old tomb was decorated with designs hitherto unknown in Egyptian art, but which appeared on Minoan textiles. Several of these patterns were awkwardly lined up, as in many tombs. Barber thought that the ceiling patterns were probably representations of imported Minoan mats, which the Egyptians hung from their rafters to catch falling lumps of clay. This explanation was consistent with the fact that burial ceilings were sometimes decorated with other non-abstract images of objects seen in the sky, such as birds or stars.
Barber only intended to show a link between Egyptian and Minoan civilizations. Senechal drew conclusions in a different direction: if the Egyptians hadn't designed a pattern to fill an infinite plane, they didn't need to know anything about modern symmetry theory either.
