By Wolfgang Held, extracted from “The Quality of Numbers One to Thirty-one“, published 1/03/12 by Floris Books.
Wolfgang Held was born in Germany in 1964. He worked for many years in the Mathematics and Astronomy section of the Goetheanum, where he now runs the publicity department. His latest book, ‘The Quality of Numbers One to Thirty-one’ explores the fascinating characteristics of numbers in relation to our lives. Throughout March we will be featuring selected edited extracts from this book. Today, the 6th of March, we are looking at the number 6.
If you catch single [snow]flakes on a cold sheet of glass and, keeping conditions cold, observe them under a simple microscope, something of the distinctive nature of six will be revealed. Every crystal, sometimes as compact as honeycomb, sometimes finely branching, will show a six-pointed star in millions of variations. More perfectly than in the growth of mineral crystals, these fleeting water crystals reveal and embody hexagonal symmetry; and one can observe this wealth of snow crystal forms for hours without ever tiring of them.
The idea that, when snow falls in winter, something falls from the cosmos to the earth, is more than a merely poetic image. The number six, as expressed in this most archetypal phenomenon, is cosmic in nature.
Working with compasses, the radius of a circle can be transferred onto the circumference exactly six times. The circle, the simplest and most perfect geometric figure, seen in ancient times as the archetype of the cosmos, divides by six. And it is indeed the case that, from moons through planets to the stars and galaxies, almost everything in the universe is round, rotates and thus bears six within it. It is scarcely surprising therefore that Babylonia, the great culture and epoch during which our spiritual relationship with the cosmos began to rupture, invoked six as the measure of all things. Wherever cyclical measurements come into play, in angular and time measurements (6 × 60 = 360 degrees, and 2 × 6 = 12 hours) the cosmic, Babylonian way of enumerating has been preserved. This mathematically cumbersome mode of counting and measuring has retained something of an inner connection with the cosmos.
Just as the circumference of a circle leads us back to our starting point, so the factors of six lead us back to this same number. It rests in itself, and reproduces itself out of its parts. Or one might also say: the inside and outside of six are identical, and it is in absolute accord and congruence with itself. This is why Pythagoras regarded it as the most perfect number.
Six is the focus of many religions. In the Persian religion of Zarathustra, there are six periods of Creation with six angelic beings. The six-pointed star, as an image of the interlacing of above and below, is present as the Vishnu triangle and Shiva triangle in Hinduism. And in Judaism and Christianity, too, six has a special meaning: for both in the Old and New Testament it stands for perfection: the world was created in six days; and on the sixth day at the sixth hour, the Son on the cross united himself with this world.