The Secret Geometry of The Dollar

I. Where did the Golden Ratio come from?

(I.) The golden ratio in modern times goes by several names in many languages. It is probably now known by more people in the present generation than the total of all others in recorded history. But at this time it is still a more or less unknown even to the majority of the well educated. As a graphic ratio, it seems to have always been with us, but we don't really know where it originally comes from.

It is a subtle, glittering thing from the darkness and distance of remote antiquity, an astonishing element of proportion that appears here and there amidst much that is dull and uninspired. And, this comes from times much earlier than people were supposed to be thinking about such things. It mysteriously appears on occasion in the layout of sacred sites, ancient artwork, and even in pottery styles with no explanation, ordinarily unnoticed by archaeologists. Here lies a world almost unexplored, even to this day: the vast field of sacred proportions in archeology and ancient architecture.

The golden ratio first surfaced from obscurity in the writings of western civilization by way of the ancient Greeks. Even then there are only a few exact references about the ratio in their writings. The Greeks must have gotten it from the Egyptians. To the Greeks and all other ancients, these were holy secrets, mathematics and geometry were religion. Any teacher in ancient Greece would actually risk death from zealots were they to reveal anything about geometry to those not initiated within the temples. This, unfortunately went for writing these ideas down--since they might then be read by the unwashed and profane.

Wondrous mathematical ideas were conveyed to temple students by word of mouth only, much in the way Masonic Mysteries are still taught today. Perhaps taught by diagrams sketched in the dust, such as Socrates is said to have done. More solid evidence of the Greeks' knowledge of this ratio can be learned from measuring remaining stone ruins than from reading their literature. For the most part their books will refer to it only through veiled comments and praise for the beauty of this proportion. As we will see later, this ratio is easily generated on paper by means of simple geometry. But its vastly unusual character would have required a great amount of time for thinkers to become acquainted with it in a primitive time, and much investigation for any culture to develop an awareness of it.

The first use of the term "Golden Section" was found in the literature of relatively recent times. At the end of the Middle Ages it appears in book De Divina Proportione, a translation of the Roman work of Campanus by an Italian, Luca Paccioli, in 1509. This work, oddly enough, was illustrated by Leonardo da Vinci, a personal friend of Paccioli. It contains many examples of the use of the golden ratio in two and three dimensions. Paccioli and others of his time attributed various mystical or supernatural properties to this proportion, in addition to believing that it contained the very essence of beauty. It is now variously called the "golden section," the "divine proportion," "golden ratio," "golden cut" or "golden mean," all of which are inter-changeable terms for the general idea in present day usage.

The term "golden mean" might be said to tie the geometric idea to Greek moral philosophy, such as Aristotle's concept of ideal human virtues, which he said lay as an ideal balance between two extremes in one avenue of moral behavior. For the ideal of "courage" to be at the mean, for instance, it must lie at some special point of balance somewhere between being recklessly bold and it’s complete absence--which would be not being bold enough. But not just half-way in between. This idea is said to be similar by analogy to the golden ratio, by this ratio's being a sort of elegant, dynamic balance point on a line between two ultimate extremes, or in a similar way within a geometric rectangle. Ancient Greek culture, especially the Athenian, prized a kind of personal balance and a refinement of virtue. A variety of dissimilar talents and abilities were to be hoped for all in one person, balanced and "polished to a hair." The ability to speak logically, compose poetry, perform well on the battlefield, compete in sports, perform music and oration, for example, were all required of a well rounded individual. Physical beauty and efficient, exact function were thought to go together. This concept was a place that geometry, man, and Divine Essence come together in ancient thought. This was a sort of an over-all aesthetic ideal under one general heading.

Their whole idea of personal virtue was based upon a concept that is fundamental to ideas like geometry, mathematics and logic. It was called "arete", meaning more or less what we mean today by "virtue." But to be technically correct, it was a term that conveyed excellence, exactness, precision and nobility all together as one idea. The ancient Greek, Egyptian and Hebrew cultures shared this idea in common; the Egyptian word was "maat", meaning very much the same thing, and in Hebrew, "sidek", or "righteousness." These cultures were concerned with exact measurement as well as careful speech. For these peoples, mathematics and exactness was a sacred idea, which allowed them to be ceremonially pure in matters relating to divinity. This sort of exactitude was present in almost all important writings of antiquity, especially those of the Biblical writers, whose attention to precise detail is quite elaborate. This was also true of the sacred architecture of ancient times, almost everywhere in the world.

This concept of arete may allow us to look back to a distant time, to many peoples of the bygone ages, who, as a rule, spoke more carefully, wrote more exactly, and gave the works of others a much closer reading than is true of us, even today. It is fascinating somehow, to think of a whole world of religious and intellectual thought requiring excellence and spoken exactitude. This was generally true in their preservation of oral traditions, logical argument and works of art. Our current idea of "classical form" was present even then, with an equal or even greater reverence among the ancients.

Although the term "golden mean" from philosophy may actually be quite ancient, there is little evidence that the geometric golden proportion was actually called by that title in ancient times. Whatever name it had, it would have likely been a secret name, with religious connotations among those of the inner court of the temple. Most likely it was not spoken aloud, but by mouth to ear like the deep secrets of many old traditions. Until Euclid, we have no record of this proportion being called anything at all. He called it "the extreme and mean ratio."

One of the names this proportion has been given is a Greek letter, φ or, “phi,” (the Greek letter “f” pronounced “fee”.) This seems to have appeared in literature in Victorian times, (1860’s) as a symbol to denote the function in mathematics. The Letter “phi” is thought to be taken from the name of Phidias, the classical Greek artist and architect who, tradition has it, used the golden ratio a