The “Golden Mean”: Elusive Perfection

Leaf displays Golden Ratio.

Perfection is frazzled at the edges.

I am fascinated by the “Golden Ratio,” or “Golden Number,” or “Golden Mean.” That is the number Phi (Φ). What fascinates me is not so much the mathematical intricacies of the number Phi–though I relish in such explanations by those of my friends who spend their weekends solving math problems. (Here is an explanation, for instance:

The golden ratio is made up of two numbers such that the ratio between the sum of those two numbers and the larger quantity is identical to the ration between the larger number and the smaller one. That ratio is the irrational constant approximating 1.6180339887.

Rather, what fascinates me about Phi is its varied application in the natural and artistic world. Here are a few examples:

• Playing cards

American flag

• The petals of a flower

• Da Vinci’s Last Supper

• The Great Pyramids of Egypt

• The Parthenon

• Taj Mahal

The examples go on and on–in nature, art, and architecture.

Bee on a flower.

Bee contemplates Fibonacci Sequence

From a philosophical perspective, the “Golden Ratio” poses the following dilemma: Whereas nature pursues perfection, it never quite reaches it. Here’s why: The “Golden Ratio,” which is the ideal of perfection, is approximated but never reached. Try it out:

⁃ Look at a Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

⁃ Take any two contiguous numbers.

⁃ The ratio of the larger number to the smaller approaches the Golden Ratio.

⁃ But since the Golden Ratio is an irrational number, that approximation becomes smaller and small but can never be reached completely.

Therefore, perfection in nature, art, architecture, etc. can be approximated but never completely reached.

That is why the first law of spirituality is forgiveness. We forgive because no one is perfect.

Also, the second law of spirituality is love of enemy. Your enemy is the only one who will actively seek your imperfection and relentlessly pursue it. Thefore, your enemy is an accurate image of your imperfection. Though your enemy you can grow and develop. Without your enemy, you stagnate.

All of these insights can be gleaned from the Golden Mean.

Thank you.
Paulo-Juarez Pereira
Ypsilanti, Michigan
December 2012


Photo Credits:
Leaf: Author: Jer Kunz; Source:; Creative Commons License: Attribution-NonCommercial-ShareAlike 2.0 Generic (CC BY-NC-SA 2.0)

Bee: Author: ‘Ajnagraphy’; Source:; Creative Commons License: Attribution-NonCommercial-ShareAlike 2.0 Generic (CC BY-NC-SA 2.0)

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