The Royal Road to Harmony, Post 3

This is the third post in my series on Harmony: A New Way of Looking at Our World, the marvelous book by His Royal Highness Prince Charles, son and heir of Queen Elizabeth II.

It's a special challenge to write this post clearly and helpfully. The subject this time is a complex and abstruse one.

Let me introduce the subject in my own fashion. The whole point of Charles's book is to show us a way to put our lives back into what he calls harmony and balance.

But keep in mind that the book's no self-help guide. It's about our culture's getting back in balance and harmony with nature.

It's a plea for the worldview known as environmentalism, and it's accordingly a guide that can help all of us budding environmentalists get in closer step with Mother Nature.


What Is Harmony?

But what, after all, is harmony? What is balance? Is there any way that a mere book can teach us that?

Yes, says Charles. There's a rich tradition of thought in the West, and also in many other cultures, traditional and advanced, which provides us with a truly objective, scientifically verifiable kind of wisdom about nature, harmony, and balance.

But (at least from my own point of view) certain problems immediately crop up. One of them is that this traditional wisdom gives us a "grammar of harmony" that demands a willingness to immerse ourselves in a daunting amount of mathematics, often in the form of numerous geometrical diagrams and their elaborate derivations. That's a great big step up for me, and I'll bet it's a big step up for you, too.

Before I get to the actual geometrical diagrams, I'll now try to give some indication of why they're important to the budding environmentalist. Look at this picture of a pine cone (which I borrow from here):

The red and green lines describe the swirling arrangement of the cone's individual scales. The green swirls swoop "clockwise"; they number 8. The red swirls sweep "counterclockwise," and there are 13 of them. Now, here's the big deal: the ratio of 13:8 is (approximately) equal to a very special number, 1.618. (The actual value of 13 divided by 8 is 1.625.)

Smaller pine cones have 5 "green swirls" and 8 "red swirls." The ratio 8:5 equals 1.6, a number that is likewise close to the very special number 1.618.

That number, 1.618, comes from the following procedure:

• Start with the two numbers 0 and 1
• Add them together, getting 1 as the third number in the sequence
• Add the second 1 to the first, getting 2 as the next number
• Add the 2 to the number before it, 1, getting 3 as the next number
• Keep adding the most recent number to the number immediately preceding it to get the next number ...

...  and you get what mathematicians call the Fibonacci sequence:

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

The further you go in generating the Fibonacci sequence, the closer the ratio of a given number to its immediate predecessor gets to 1.618 (or, more accurately, to 1.6180339887... ). For example, 987:610 equals 1.6180327868852459 ... .

Mathematicians refer to 1.618 as the Golden Ratio, to show how special it is.


The Golden Ratio in Nature

But why is the Golden Ratio important to the budding environmentalist?

The numbers in the Fibonacci sequence, which are quite unsurprisingly called Fibonacci numbers, show up in nature all over the place. The 13:8 pine cone swirl ratio is just one example.

Another example can be seen in an illustration from Prince Charles's book:

Notice the daisy close-up in the center picture. The florets in the center of the daisy arrange themselves in clockwise and counterclockwise swirls, just like the scales of the pine cone.

It turns out that, for the daisy as for the pine cone, the ratio of the numbers of swirls in the two directions is always (approximately) the Golden Ratio.

Mother Nature seeks the Golden Ratio.

This is significant because it tells us of a correspondence between physical nature and a beautiful, abstract mathematical relationship made strictly of numbers. The correspondence shows up in pine cones, in daisies, and in many other things in the natural world.

So the "stuff" of nature has a hidden order to it. The Golden Ratio and the Fibonacci sequence can sometimes govern the wild world around us.

What about the other four parts of the illustration above?

Prince Charles uses them in his discussion of what he calls the "golden thread" that runs through many venerable sources of wisdom about the natural world. The thread is the "grammar of harmony." It consists of yet more correspondences between numerical or geometrical constructions we can write or draw on paper and how Nature herself is organized.

These correspondences are revealed in what has been called "sacred geometry." Prince Charles accordingly talks of such things as the perfect "Platonic solids" and how they can be constructed by first drawing a bunch of circles. I'll have more to say about sacred geometry in the next post in this series ...