The Royal Road to Harmony, Post 4

In this ongoing series of posts about the book Harmony: A New Way of Looking at Our World, by His Royal Highness Prince Charles, I'm at a critical juncture. I now have to start to explain 'sacred geometry'.

From the days of early Greek philosophers such as Pythagoras, and from the times even before that when the pharaohs ruled Egypt, the ancients knew of a hidden correspondence between purely abstract mathematical ideas and the observable natural world. In Post 3 of this series, I showed how the swirls of a pine cone ...

... and those of the golden florets in the eye of a daisy ...

... sweep in clockwise and counterclockwise curves. The number of swirls in one direction and the number in the other are different. Yet both numbers are, and are bound to be, consecutive numbers in the Fibonacci sequence, which is:

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

In the Fibonacci sequence, each number (once you get past the 0, 1 'starter pair' at the left end) is the sum of the two preceding numbers.

In the pine cone shown above, the counterclockwise swirls shown in red number 13, and the clockwise swirls shown in green number 8. 8 and 13 are consecutive Fibonacci numbers. Moreover, the ratio of 13:8, which is 13 ÷ 8 = 1.625, is close to the quantity mathematicians honor as the Golden Ratio, officially 1.6180339887.

Each pair of adjacent Fibonacci numbers, such as 144 and 89, form a ratio that gets closer to the Golden Ratio as you move to the right in the Fibonacci sequence. For example, the ratio 144:89, which is simply 144 divided by 89, equals 1.61797753. It's already quite close to the official value of the Golden Ratio, 1.6180339887.

I haven't myself counted the clockwise and counterclockwise swirls in the daisy photo, but I guarantee that both numbers constitute consecutive Fibonacci numbers, and that the ratio of the larger number to the smaller is (close to) 1.6180339887.

Conclusion: There is a hidden order in nature. And it can be expressed mathematically.


The Wisdom of Pythagoras

Pythagoras, in his day (c. 570–c. 495 BC), knew that. He taught, as Charles writes,

... that there is a precise relationship between the arithmetic of number and the geometry of the physical space around us. In his view, chaos is ordered by number and Nature is made up of precise numerical patterns. ... He held that the nearest the human mind could get to the Divine Mind was through number and, thereby, the principles of proportion and harmony. ... It may seem an odd thing to say in this day and age, but Pythagoras taught that number expressed a divine quality.

Pythagoras urged his pupils, says Charles, to contemplate the patterns of the natural world, so to be "led into communion with the very source of number itself, which is unity."

Prince Charles writes:

Pythagoras considered that the first number represents the ultimate principle of unity. The universal symbol of unity is not the numerical figure 1. It is the sphere or the circle, which is made of a single, unbroken line that loops on itself eternally – ‘eternity’ in the strictest sense of the word means beginning-less and endless.

With statements like that, Charles is leading us away from our skeptical modern attitudes back toward what most of us today would consider a 'mystical' approach to nature. We need to revive the ancient Pythagorean notions, Charles says, such that we might learn once more to treat the natural world as a lens through which to contemplate divinity.


Sacred Geometry

But first we have to get past some rather difficult lessons in geometry.

It might help motivate us to do our lessons if we recognize that so-called 'sacred geometry' gives us insight into sacred art and architecture. For instance, here is a sculpture that can be seen at the medieval High Gothic cathedral that is at Chartres, in France:

'Christ in Majesty', a sculpture
above the Royal Gate of Chartres cathedral

The figure surrounding Christ that looks like an American football standing on end is called a vesica or vesica piscis. It is an almond shape that is formed when two identical circles are overlapped so that the perimeter of one circle touches the center of the other, and vice versa.

The vesica shape controls many aspects of the design of Chartres cathedral. For more about that, see this Huffington Post article at the New World Order website.

The vesica's distinctive height-to-width ratio even shows up in the dimensions of Chartres cathedral's floor plan, when the width is taken as the distance between the north and south entrances (at the sides below) and the height is taken as the distance from the 'West Front' entrance (at the bottom) up to the top of the semicircular apse:

Vesica piscis superimposed on Chartres floor plan,
with the top of the floor plan facing east

What's so special about the vesica's height-to-width ratio? As Charles notes, the height-to-width ratio of the 'Christ in Majesty' vesica is the square root of 3 or 265/153. 153 is 'the number of fish caught miraculously when the risen Christ appears before the Disciples', according to the Gospel of John. (In the name vesica piscis, vesica means 'bladder', the organ within a fish that fills with air and keeps the fish from sinking, and piscis means 'fish'.)

By the 'magic' of geometry, the 'root 3' ratio (i.e., the square root of 3, which is equal to 1.73205081) between the height of the 'Christ in Majesty' vesica and its width is maintained for the vesica superimposed on the Chartres floor plan in the illustration above, and indeed for every vesica that can ever be drawn.

If you want to represent the square root of 3 as the quotient of two whole numbers, 265/153 is as close as you can come. No quotient of smaller whole numbers is as close as 265/153 is to 1.73205081. That's why eyebrows go up at seeing 153 as the specific number of fish caught in John's gospel.

And it is in part why a slightly modified vesica was used to form the fish symbol that has represented Christ and His church since earliest times:

It is said that during the persecution of the early church, a Christian who encountered a stranger would draw a single arc in the sand. If the other person was a Christian, he or she would complete the drawing of a fish with a second arc.


Number and the Kinship of All Living Things

Prince Charles writes that sacred geometry à la Pythagoras (and carried forward by his philosophical successor Plato):

... was based upon the essential kinship of all living things ... [and] it is the central cosmic importance he gave to number which has always fascinated me – a scheme which is not difficult to understand, but one which states quite clearly that we live in an integrated and harmonious universe.

Charles continues:

Pythagoras taught that there is a precise relationship between the arithmetic of number and the geometry of the physical space around us. In his view, chaos is ordered by number and Nature is made up of precise numerical patterns.

So a geometrical figure as simple as a vesica unites pre-Christian Greek philosophies such as that of Pythagoras with early and medieval symbols of Christianity.

Why is the vesica shape sacred, though? In Pythagoras's numerical scheme, as we have seen, the circle or sphere represents the number 1 or unity. Prince Charles writes:

... the second number is what happens once unity becomes more dynamic, once we get ‘duality’. This defines the difference between one thing and the other. And that instantly brings about the necessity for the third number which, for Pythagoras, was a most important number. In fact he called it the first ‘real’ number.

In Pythagoras's scheme, 1 stands for unity and 2 for duality. Duality is a stand-in for the multiplicity we find in this world. Two circles thus stand for multiplicity.

But when the circles are overlapped so the center of each is touched by the other's perimeter, something special happens: a 'third number' is born. There is then a sacredness to the circles' relationship that teaches us

... how life ‘becomes’ – how it unfolds from an indivisible unity – its Oneness – into a multiplicity of many, all of which can only be connected by there being a third element of relatedness. In other words, for the one thing to be known by another there must be a linking relationship, a ratio or ‘joining together’. The Greek word that means ‘joining together’ is harmonia.

The vesica, a 'joining together' of two circles, stands for harmonia, the antidote of chaos. The vesica has long been deemed sacred for that reason.

Charles puts it this way:

Pythagoras and much of the ancient Greek world that followed him knew very well that without harmonia there is no possibility of relationship between the one and the many and therefore no possibility of unity and wholeness.

It seems to me most appropriate that the sacred symbol that metaphorically restores harmony and wholeness is a pair of circles, each touching the other at its center — at its very 'heart', as it were.


Onward and Upward

I hate to say it, but our geometry lesson is about to get even more elaborate. For that, please see the next post in this series ...