recoveredscience.com We offer surprises about
by H. Peter Aleff |

| | ||||||||

| |||||||||

Set aside, for a moment, what you learned in school about how primitive ancient Near Eastern mathematicians were, and how crude their approximations to the circle constant pi, the only constant they are said to have known. Then imagine, just for this eye- opening exercise in quasi- equations of constants with symbolic values, that some number investigators of old had computed this and three other constants, despite the stories you heard about how even the Bible allegedly said that pi is three. To set this imagined scenario into a realistic context, our ancient researchers would not have considered these mysterious mathematical entities as mere numbers, the way we moderns do, but they would have assigned symbolic properties to these “super- numbers”, as they did with many integers. The Mesopotamians, for instance, believed that numbers were divine. Each god and spirit and demon had and was a number that expressed his or her nature and was interchangeable with that entity’s name, as discussed on the page about perceptions of numbers. If some ancients were aware of those constants, they would then surely have given these extraordinary entities some special positions in their system of number worship. Their digital divinities presided over an analog world view in which everything was symbolically interconnected with everything it resembled in any aspect or feature. Things or beings that shared a perceived trait could be identified with each other and could take each other’s place. Our hypothetical sages would therefore also have connected those constants with their other inter- related frames of reference, and they would have done so in ways that reflected the mathematical properties of each constant. Since these properties are timeless, it was and is relatively easy to assign symbolic matches to the four relevant constants. The most obvious associations are those with the most prominent example: Pi the circle constant is a natural fit for the most prominent circles in nature, the disk of the sun and the pupil of our eye which sees the light that the sun emits. The sun was the eye of the sky, further connecting these circles to each other and setting them apart from all else. The circle number also evokes the sun's circling across the sky.
The typical sign for the sun was a circle in many ancient symbol systems, as, for instance, in Egyptian hieroglyphic writing and in the artistic as well as religious conventions based on it. The properties of the sun, in turn, as well as the spark in our eyes, make this equivalent of Pi also a synonym for fire and light.
If pi was the sun, then the golden ratio phi would have been the moon which it parallels in behavior, as shown on the page devoted to some properties of this remarkable constant. For instance: When you divide 1 by phi, the resulting reciprocal has the same digit sequence behind the decimal point as the original. This is not an artifact of the decimal system but holds true in any notation. Do the same with successive powers of phi, and the mirroring of the digits disappears for the even powers but returns for all odd ones. This regular alternation between the reflection and then none resembles again the equally regular appearance and disappearance of the reflected light on the moon. Moreover, when you measure angles along the circumference of a circle, in what we call now the radians system, then successive twentieths of pi produce functions of phi that wax and wane with the progress of pi along that circle, just as the moon waxes and wanes with its position relative to the sun.
The mirroring of the digits makes phi also the candidate of choice for representing the element of water next to the sun’s fire. Water could mirror, and it was already connected with the tide- and fluid- controlling moon in many mythologies, so the choice fits the ancient traditions. Moon and water were both also identified with the biblical Woman Wisdom whom the Jewish traditions call the Shekhina. She was the shining- white bride of the Messiah and bringer of holiday joy who appears alternately also all veiled in black, mourning the destruction of the Temple. That dual appearance is typical for a lunar figure, and many Kabbalists also compared her directly with the moon. As to her connection with water, she filled the same role of mediator and connecting link between heaven and earth as the life- sustaining gift of rain, and she was the “living water of the Torah”, the “Word of God” on which the Jewish religion is based. The author of Ecclesiasticus 24, for instance, gushed like a waterfall about how Wisdom pours forth like a river and overflows like a stream in full flood.
If pi and phi were sun and moon as well as fire and water, then the constant **e**of compound growth fits the role of the earth in both groups. It pops up in calculations not only of logarithms and interest payments but also of animal herd increases and expected grain harvest yields, and in many other examples of computing what grows on the land. Its property of reappearing unchanged after most mathematical transformations makes it also an perfect symbol for continued renewal.
The fourth of the constants in this system is today at best an obscure mathematical curiosity. However, its definition would have suggested a strong symbolical role to ancient explorers of the number world.
Continue to the surprising results these constants produce when paired with those symbolic values. | |||||||||

| |||||||||

Contact us at recoveredscience.com |