Friday, September 09, 2011

The Royal Road to Harmony, Post 7

At left is an alternate cover for a marvelous book by His Royal Highness, the Prince of Wales. The 2010 book by the man known worldwide as Prince Charles is called Harmony: A New Way of Looking at Our World. I have been attempting to relate its wisdom in this, my The Royal Road to Harmony series of posts.

Our despoliation of the planet in the name of material progress has brought us to the verge of environmental and ecological ruin, says Charles, and so he urges us to recover the wisdom of the ancients to fuel a rebirth of feeling connected to nature — and, via nature, to the divine source of the natural world. If we feel intimately connected to nature and in that manner to God, we will naturally begin once again to treat the Earth sacramentally.

The book begins:
This is a call to revolution. The Earth is under threat. It cannot cope with all that we demand of it. It is losing its balance and we humans are causing this to happen.
In this series I am hoping to show my fellow Catholics in particular, and more broadly the rest of us, how we might respond to Charles's call.

For Catholics and others, there are many ports of entry into ecological awareness. Here's one that I'll adapt from Charles's discussion of the Fibonacci sequence.

If you start with the two numbers 0 and 1 and add them together, then keep adding each result back to the immediately previous one, you get:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …

This is the Fibonacci sequence. The uncanny thing is how often it shows up in nature. For example:


These are the bones of a human hand, which nature has produced by means of Darwinian evolution. The lengths of the bones leading from the tip of the middle finger to the bones of the wrist are in the ratio of 2:3:5:8. The numbers in the 4-way ratio are Fibonacci numbers, being the fourth through the seventh of the Fibonacci sequence above.

The ancients, starting with the Greek philosopher Pythagoras — or perhaps earlier, with the Egyptians — held there was a 'sacred geometry' which governed otherwise chaotic nature. The five-pointed pentagram was one of the geometric figures they adored:



It can be derived from a spiral that represents the Fibonacci sequence:


Here, the numbers in the boxes represent the length of each square's sides. They are consecutive Fibonacci numbers. By using higher and higher numbers from the Fibonacci sequence, the spiral can be extended indefinitely.


The Fibonacci Sequence in Nature

Some say that, in the natural world, the Fibonacci spiral matches up with the curvature of a nautilus shell:


As for the Fibonacci-derived pentagram, it's found frequently in nature:


(Starfish)



(Seedless papaya)
(Remember, the human body was created by Mother Nature
as a product of Darwinian evolution.)

The Fibonacci sequence, from which the pentagram can be derived (see above), also shows up in natural processes such as the family tree of a bee:

(From an extended discussion called
'Deciphering Nature's Code' that is well worth reading.)

A male honeybee comes from an unfertilized egg and has only one parent, a female. A female honeybee comes from an egg laid by a female and fertilized by a male, so she has two parents. So the family tree of a male honeybee, with earlier generations shown as you go down the diagram, looks like this ... with the numbers of bees in the various generations forming a Fibonacci sequence.

Of course, not everything in nature is a Fibonacci stand-in. The point is really that nature is inhabited by often unseen number patterns and geometric forms, not that it is all number pattrens and forms. We humans are no different, in this respect, than animals, plants, and ... everything else that exists. There are, for example, demonstrable ways in which our intuitive notions of physical beauty in buildings, faces, and even music manifest an innate preference for Fibonacci-derived ratios.

If we know no more than that, we know there is no harmony to be found that does not respect and include all of physical nature. That is so because all of nature, including human nature, is grounded in the very same templates of reality, the hidden patterns which 'sacred geometry' is merely an effort to uncover.

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