Novelist. Author of APSARAS and tales from the beautiful Saigh Valley. First person to quantify spiritual values.

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Monday, 16 June 2014

The other Golden Ratio

The Golden Ratio,ɸ, is recognised as the product of a numeric sequence found throughout the naturally world. From the formation of sunflower and other seeds, the branching of boughs and roots of plants to the genetic breakdown of bees the eye-pleasing effects of the ratio has been adopted by artists and architects alike. Painters use canvases whose length to width dimensions mimic the ratio and builders from antiquity have constructed edifices according to the rule. Indeed the pyramids of Giza are built according to the Golden Ratio of 1: 1.618.... The number, a number like pi which is described as irrational, meaning that it cannot be expressed as a fraction, is derived from the fibonacci series of numbers, 1, 1, 2, 3, 5, 8, 13, 21 where a term is  calculated by adding the previous two terms.
The relationship between successive terms is described mathematically by the equation:  

ɸ² = ɸ + 1

One of the solutions to this quation gives  ɸ ~ 1.618.... Try dividing 13 by 8 or 21 by 13 to see the point.
However there is another solution; one almost never considered.  ɸ ~  - 0.618...
What is the significance of this value? Has it any significance?
 If one wanted to construct a pyramid using this negative ratio, it is my assertion that you would need to take into account the value 'i' the square root of minus one. We are again in the realm of negative dimensions.
(For more insights see my book: 'SPIRITUAL MAN: AN INTRODUCTION TO NEGATIVE DIMENSIONS'. Available for download from Amazon for the price of a pint.)

One of the characteristics of the positive Golden Ratio is that it promotes what humans think of as 'beauty'. I also maintain that it also suggests, lightness and  'good'. Could it be therefore, that the negative value will lead to what we might consider to be 'ugly' results which also represent darkness and evil?

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