UNIVERSAL GEOMETRY
is there still anything sacred? In this issue of the Pentagram, a contribution about universal geometry is presented that, in ancient times, was often even referred to as ‘sacred geometry’. In the past, if someone was not particularly gifted, he usually found mathematics and geometry difficult subjects in school, because they were often quite abstract. How would we then be able to fathom a concept like universal geometry? May we even speak of divine-spiritual mysteries in numbers? And what is universal in them? What would be sacred in them? When we observe the events in the world, we may certainly say that nothing is sacred in our world, and the question is justified as to whether our approach is, therefore, not based on fantasy. Yet… when a flower radiates in the light, with a deep blue colour and a perfect form, or if a cloud formation passes by on the horizon in the morning sun, with many hues of colour, light and shadow, we may automatically become enchanted. What is it that touches us? Is it something sacred? Once we think about it, ‘it’ withdraws. The moment has passed. Let us try to briefly hold on to this lofty moment. In the short hymn to Aton, the Egyptian sun god, we read: ‘Your dawning is beautiful, O living Aton, Lord of Eternity! You are radiant, light and strong. Your love is great and mighty. Your rays will create the eyes of all your creatures… You are mother and father to those, whose eyes you have formed. If you rise, they see through you.’ We have ‘seen’ something, with our eyes, but also with a deeper organ of perception. How did the magnificent structure, the eye’s geometry, develop that enabled us to see? The ancients said: ‘The eye was created by the light,’ at least according to Plotinus, a fascinating thinker in the way of Plato. Our modern sciences discovered that fishes are unable to develop eyes without the influence of light. Does the light contain something 14 pentagram 2/2011
that expresses the geometry of the eye? Or in other words: does the light transmit an idea for manifesting itself in matter? For millions of years, the light of the sun has radiated over our planet. And the planet ‘answers’. The flowers of the vegetable kingdom reflect the light in the most beautiful way. It is often said that they contain light. The perception of the light by the flowers resembles that by the eye. LUX AND LUMEN Plato explained in his dia-
logue, Timaeus, that God caused the world to be created by his demiurges in such a way that number, ratio and geometry underlie the world. He assumed that number, ratio and geometry flow into our world from the spiritual world. In Genesis, on the first day of creation, God says: ‘Fiat Lux – Let there be light.’ The early church fathers recognised in this first Light a spiritual reality that they called lux and that, to them, was the soul of the universe. They considered our familiar light an emanation of the spiritual light, called lumen. For a long time, these two kinds of light were distinguished. One kind contained the ideas of the creator while the other led to bodily manifestations (because without light, nothing grows). On this basis, a vision developed during the thirteenth century that linked the first germs ‘The ancient of days’; an image of the Creator, who builds as the Great Architect of the World. William Blake, The ancient of days, 1794. Oil painting on cloth, British Museum, London.
