When walking around the Dolomites, you may stumble upon these spontaneous examples of natural symmetries and, under certain aspects, cosmic symmetry. At this point memories start surfacing, long-buried memories of your time as a student, lost to the eddies of time. The teacher’s voice echoes among the valleys: it no longer sparks any fear just a vague sweet nostalgia.
In Ancient Greece, symmetry was not only perceived as a geometric property of figures and bodies, but it was a concept applied to numerous disciplines, among which architecture, music, organisms, cosmology, and the first scientific observations.
If only we had listened better! We could have avoided one or two bad grades, no doubt about that.
The Pythagoreans studied symmetries in relation to harmonies in maps and musical instruments and even in the axis of the planets. Among the written classics, the Timaeus underlines how symmetry, understood first and foremost as a proportion of parts, had to be at the heart of any growth correlated to natural elements, living beings, and the astronomical system.
Who knows what you are doing now, dear teacher. But there is nothing sweeter than thinking about your lessons and see what you did under a new light, and think about symmetry perceived as a proportionate, compassionate, dramatic property of figures and bodies projected across a spatial dimension. Ah, blessed Dolomites, this is what your moving beauty can make me think of sometimes.