APPENDIX 3

CREATION REPRESENTED IN NUMBER SYSTEMS

The meaning of number has evolved over the millennia. What did they mean to the Ancient Egyptians? Certainly we have evidence that by the time of Pythagoras, circa 500 BCE, Greeks traveled considerably throughout Egypt and the Near East. Certain wise men of Greece gave credit for what they learned to the various active temple centers of Egypt. What has been passed down to us from the Egyptians through the Greeks is known today as the Pythagorean numerology system, and it relates directly to creation and awakening higher consciousness. We draw heavily on the interpretation of the original Egyptian material by R.A. Schwaller de Lubicz and by John Anthony West.1 In this appendix we address the difference between the quantity represented by a number and the quality that might be represented.

It is remarkable today that these early points of view respecting creation have become so foreign to us in our preoccupation with the theories and concepts promoted in science. Science searches for origins in a purely material context, making it necessary for us to differentiate explicitly between the exoteric and esoteric views before the breadth of what is conveyed in the myths can be fully appreciated. In terms of original creation, the Egyptian god Atum can be seen as the initial differentiation of a “sense of being” out of the void. This is the initiation of “life” in the universe. This is the first “One.” Exoterically, it could be equated to the elusive search for the big bang. Esoterically this is the initial awakening of higher consciousness. Such a difference in modes of thinking is made even clearer if we shift our attention from the creation of the “One” out of the void, to the creation of the next number, two. Again, our attention is customarily taken by our habit of counting objects. Our usual mode of thinking says that one must divide into two, resulting simply in the arising of two ones. But this is not the intention in these creation myths, and, indeed, is not allowed in the Pythagorean numerology system; in it, it is patently ridiculous to suppose that there can be two ones. Surely, even for us, there can be only one unity!

According to the Pythagorean system, while we may believe that we can conceive of oneness, or wholeness, this is really only a superficial, intellectual conceit based on our learned behavior in counting. In fact, we experience our world only by perceiving differences between objects and by quantifying their number, rather than by recognizing wholes or absolutes. Thus it is difficult for us to appreciate that we do not divide a one to make a two. In the Pythagorean system, two represents the creation of an essentially new quality, the very essence of which is the quality of division.

Rather than viewing this contradiction—between just counting two items versus recognizing the number two as a step in the creative process—as inconsequential, we should be alert to the fact that in our usual rather inattentive or “automatic” counting mode, we neglect important and significant properties of what numbers can represent. When we look at the process of creation, we cannot simply count things. In the creation myths we are being led to inquire more deeply about the idea that the creation of “one” leads simultaneously to the creation of “two.” A reconciliation between the two numbers enables the one and the two together to result in three. The creation of threeness in the Pythagorean numerology system is seen as a new unity. What are the possibilities that this opens to us?

R. A. Schwaller de Lubicz provides us with a remarkable example that illustrates how number concepts can play into ideas about germination and creation.2 While we shall not repeat his derivation in detail here, we wish to show how he introduces the power of generation by relating it to the mysterious mathematical ratios called φ (phi) and π (pi).

The basic idea is that φ expresses the division of unity, or the number one, into two parts. This division is, however, not a simple division into two equal parts. Instead, we are led to consider a natural ratio by which division is endlessly repeated in biological systems as either a divisor or multiplier at all scales of space and time, without losing sight of the singular relationship that is invoked by the constant proportion. We can use this ratio to express our perception of the endless power of germination by relating it to the remarkable capacity of the ratio φ to divide any linear quantity into two parts in a proportionate division that remains constant despite any changes—divisions or multiplications—in the initial length. That is, there is one unique and simple ratio of two numbers that is not dependent on scale, which when it is expressed in symbols, becomes evident through the act of solving the algebraic equation:

a : b :: b : (a+b) for particular values of “a” and “b”

The precise derivation and solution is given in readily accessible fashion by Lawlor, in explanation of the definition developed in relation to the Egyptian knowledge of this ratio by R. A. Schwaller de Lubicz.3 The derivation has been known for many years by those interested in sacred geometry and has also been taught to students of art in various universities. As shown by R. A. Schwaller de Lubicz, the value of φ is also a simple π such that π = 1.2 φ². However, it is not generally known that knowledge of these ratios originated in Egypt or that they are utilized in the proportions of the Great Pyramid. The derivation is, nevertheless, of primary importance to us for better understanding the remarkable insights of this ancient culture, enabling our greater appreciation of its unobtrusive sophistication.

We also observe here that knowledge of the special ratio φ underlies our continued use today of the five-pointed star to signify the starry objects of the sky. Similar illustrations were made over many dynasties on the ceilings of Egyptian tombs. This same ratio establishes the proportions that the Egyptians assigned generally to such “square” spaces as doors, the floor proportions of many of the massive ancient Egyptian temples, and the walls of rooms constructed in those temples. This ratio φ seems to touch some instinctive sense in us that, while widely known to be pleasing, is not often explicitly recognized. Remarkably, it was lost to knowledge after the Egyptian civilization disappeared, until it was apparently “rediscovered” and taught in Pythagorean times in southern Italy. It seems highly probable that knowledge of it was actually transmitted to the early Greek scholars such as Pythagoras during their prolonged visits to the still-remaining Egyptian centers of teaching.

It cannot be emphasized too strongly that if we view myth as leading toward a wisdom that can express a renewed sense of meaning in the modern world, we must be prepared to allow those myths to be interpreted according to different modes of thought. We have already recognized that stories may be viewed as “external,” in the sense that they tell of events in a manner that captures our imagination or puts new interpretations on well-known worldly events. But they must also enable us to be led into a world of internal inquiry where perceptions of the “quality” of what is observed enables us to probe them in new ways. While we are less accustomed to the various forms of analogical interpretation, what we do know can at least enable us to see that there is a necessity to open our minds and hearts to unexpected means of perception. The study of the Pythagorean numerology system from this point of view can enable us to appreciate that among modern people there has been an oddity of neglect or partiality, at least in our modes of ordinary thought.

Such limitation, if seen in its true nature as abstraction, has sometimes been loudly decried by philosophers, who maintain that we need to consider how thought must be complemented by “experience,” as was insisted on by Goethe.4 Translation of experience into internal perceptions of both body and emotions leads to new possibilities of comprehension that have been elaborated by Hadot.5 There is irony in the fact that failure to appreciate the gulf in understanding that has arisen between these two approaches may be largely responsible for the dichotomy that has developed between much of academic Egyptology and the view of Egypt interpreted and presented by R. A. Schwaller de Lubicz. The latter emphasizes that the religious and sometimes intimate and poetic perceptions are of primary importance in the awakening of higher consciousness.