Blog #233--Golden Ratio Suggests Universal Simplicity

I provided many examples of similarity between various life forms in the book “It’s a Secret, So Pass It On: a Toolbox For Life.” But I didn’t mention one of the most common connections between all that exists within Nature. That is the relationship called Phi by scientists. It has been given many names over the millennia since it was first discovered in the distant past. Among those names is Golden Ratio, Golden Number, Golden Proportion, Golden Mean, Golden Section, Divine Proportion and Divine Section. It will be called the Golden Ratio for the purposes of this discussion.

I apologize to those with an aversion to mathematics, but the following formula shows how the Golden Ratio is defined mathematically: a/b = (a+b)/a = 1.6180339887498948420..., a number with no ending. Specifically, dividing a line into two parts, with the longer part divided by the smaller part, is equal to the whole length of the line divided by the longer part. It is often rounded off to 1.618, but it is significant that it is an indeterminate number since it represents an infinite or potentially spiritual aspect to our lives.

The Golden Ratio is also supported by a number sequence first described by Leonardo Fibonacci. If one adds any two consecutive Fibonacci numbers, one gets the next Fibonacci number. The sequence is: 0, 1 (0+1=1), 1 (0+1=1), 2 (1+1=2), 3 (1+2=3), 5 (2+3=5), 8 (3+5=8), 13 (5+8=13), 21 ( 8+13=21), 34 (13+21=34), 55 (21+34=55), 89 (34+55=89), 144 (55+89=144), 233 (89+144=233), and so on ad infinitum. The higher the numbers, the closer the ratio of the previous two numbers approaches the Golden Ratio. For instance, 233 divided by 144 is 1.618, the number often used by mathematicians and scientists as representing this ratio.

Of course, it must always be remembered that man created numbers and the math that goes with it. Indeterminate numbers like phi and pi (the ratio of the square of the radius of a circle and its circumference) demonstrate an infinite concept hidden within what we believe is a finite world.

With the math out of the way, what is especially significant is the number of times we can identify the Golden Ratio in Nature, and the pleasure we all derive from it. In fact, humans have an instinctive tendency to find beauty in aspects of Nature that demonstrate the Golden Ratio. People considered most attractive usually have Golden Ratio proportions between the width of their faces and the width of their eyes, nose and eyebrows. The ratio of the length from the human navel to the floor is the Golden Ratio when compared with the length from the top of the head to the navel.

Fingers have also been shown to demonstrate this relationship. At a woman’s reproductive peak, the ratio of the length of her uterus to its width is approximately 1.6. Of course, these conclusions are based on averages of entire populations since there are subtle differences from one person to another. The DNA molecule, the basis of all life, measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. Both 34 and 21 are Fibonacci numbers.

Leonardo Da Vinci considered this ratio so important, he used it repeatedly in his paintings “Mona Lisa,” “Vitruvian Man” and “The Last Supper.” Other artists who specifically used it include Michelangelo, Raphael, Rembrandt, Seurat and Salvador Dali. Even today, people use the Golden Ratio for advertising and sales, among other things, because it represents beauty. Toyota’s symbol is devised from it, as one example. Facial plastic surgery and cosmetic dentistry also take advantage of this important ratio to produce beautiful results.

Humans didn’t create the Golden Ratio. We simply found it repeatedly over time in all sorts of places. We then copied it wherever possible. Some of the many examples found in Nature include the following:

* Sunflowers and a number of other flowers produce seeds that follow a natural spiral out from the center of the flower. This spiral arc can be compared favorably with the Golden Ratio and is often called the logarithmic spiral. Some flowers produce petals in numbers identical to the Fibonacci sequence. For instance, the lily has 3 petals, buttercups have five petals, the chicory has 21, and the daisy has 34. It is said these petals are arranged at angles that maximize exposure to the sun and thus survivability.

* The spiraling seed production in pine cones tends toward replicating the Fibonacci sequence. Pineapples and cauliflowers follow similar spiral patterns. Tree branches and root systems also tend to repeat the Golden Ratio pattern.

* The Nautilus snail shell is spiral-shaped, with numerous rectangular sections within it. The angle of the curvature is consistent with the Golden Ratio. A number of other snail shells follow similar patterns.

* Spiral galaxies such as our Milky Way demonstrate the logarithmic spiral quite well. Some hurricanes show the same arc angle.

* Some other species demonstrate the Golden Ratio. Examples include dolphins (the eye, fins and tail), starfish, sand dollars, sea urchins, ants and honey bees. There are more female honey bees than males in a hive, and the ratio is often near 1.618.

* For those who doubt the Golden Ratio has any religious significance because it isn’t mentioned in holy texts, the dimensions of Noah’s Ark and the Ark of the Covenant in the Bible are based on a 3 to 5 ratio, and 5 divided by 3 is 1.666, which is close to the Golden Ratio. Likewise the Kaaba, Islam’s most sacred site in Mecca, is located very close to the golden ratio of the distance between the Earth’s north and south poles.

One can either view the world from a mathematical perspective (left-brain dominant) or a creative one (right brain dominant). Either way, beauty is the result. While the Golden Ratio is not found everywhere and is more of an estimate than a precise figure in most cases, there is plenty of repetition throughout Nature to demonstrate a simplicity within the complexity. When we find it, we are attracted to it. It appears to represent a universal truth that draws us lovingly.

That is why some have associated the Golden Ratio with spirituality. Maybe it is a glimpse into eternity.

http://dreamtime3.wixsite.com/jacktuttlebook

Comments and questions can be directed to dreamtime@insight-books.com.