Meditations on the Golden Mean
By Frater Palamedes
The ratio of Mean and Extreme figures. To produce the series, one adds the previous two numbers to achieve the third, like so:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
All life resonates with these numbers. The great 12th century Tuscan mathematician, Fibonacci, saw this. One of the men who first introduced Arabic numerals to Europe, Fibonacci grew up in North Africa, exposed to Muslin as well as Hindu mathematics. It is in this solution that Fibonacci first derives his famous Fibonacci Series. To produce the series, one adds the previous two numbers to achieve the third.
The series is, of course, infinite, but the ratio the two adjacent terms, as they approach infinity, converges to φ or approximately .618. What is more, the ratio of n-1 to n is equal the ratio of (n to n-1)+1. In other words, (1/φ)+1= φ. This is true for no other number in existence. This unique relationship between the ratio and its reciprocal is emblematic of the mirror. Reflecting lower in the higher. That which is below is as that which is above.
0/1: The straight line is the foundation of the world, and from it, all other forms, be they linear or planear are defined. The line and the point together define the plane, as well as parallel and perpendicular lines, according to Euclid. The zero over one. Point over line. From this, all other forms derive. It is the creation out of nothing.
1/1: The All in All. The Undivided Whole. The Universe before differentiation. Of two dimensions, it emanates from the previous state.
1/2: The First Differentiation. It divides the Universe. The “thou art”. The division is equal. Light and Darkness, Heaven and Earth, God and Man, Form and Image.
2/3: The Supernal Triad. Two polarities and their transcendence. The Pillars Machetes, Nomethetes and middle pillar, representing balance. Also, unequal division.
3/5: The Triangle of Spirit crowning the Square of Matter. The formation of the pentagram. Elemental primacy.
5/8: The House of Sacrifice. The 8 through 5 and the 5 through 8.
Eight elements; the four sided rectangular base, two sides of the superstructure, and the two strokes which make up the tau cross which stands over its crossbar. Eight elements for the eight spheres of Creation. Each represented by a word from the Clavis Mystica, the great palindrome which adorns the floor of the Baptistery in the Cathedral of San Giovanni in Florence.
We are the House of Sacrifice. We reaffirm this every time we perform the Kalyx. But whereas the Formula of the House of Sacrifice works from without to bring within, the Formula of the Kalyx works from within to bring forth. We burst forth from our shell when we proceed through the Kalyx. Beginning from the self; the “thou art”. We name ourselves by our naming of the Other. We are within the shell of “thou art”, recalling the famous passage from the Chandogya Upanishads. Next, the Tau position is achieved, symbolizing the bursting forth from the shell of “thou art”. We are the Kingdom, the All in all. The realization of this is the completion of the ritual. The Power and the Glory . In bursting forth from our shell, we become these things Throughout the Ages. But by bursting forth from our shell, we find ourselves enfolded again within it. For the shell is more than just the seed from which we sprout. It is the nautilus shell which leads us back on the Path of Return.