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Ancient Mathematics

We have in Our possession a science of which, should We convey but one word to the beings, every one would be made to believe in the Manifestation of God, and His Knowledge, and be acquainted with the secrets of all sciences, and attain a position whereby they would find themselves able to dispense with the sciences of both the ancients and moderns.

- From "The Tablet of Wisdom".

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Because symbols are dependent upon interpretation, please take all of this "for checking"...I do not wish to mislead anyone, but merely share what has been useful for me...

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Before the concept of "zero", the ancient Babylonians would merely leave a blank space in their mathematical calculations.

Zero is a "no-thing" (i.e.: not any one particular thing). Since it is potentially anything, it is everything (i.e.: pure potential). This is why the inverse of Zero is Infinity. Further, because there are not yet any distinct individual entities, pure potential could also be considered Oneness.

Therefore,

Zero = Infinity = One

All other digits extend from One as "fractals of Unity". To use an analogy, it is like embryogenesis. Why is it called "cell division" if they are multiplying in number? Because they divide out of a higher potential. The fertilized egg is a giant pluripotent (stem) cell that divides itself into many specialized cells. Creation is the same on all levels of scale.

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The ancient Africans (or Egyptians) had a symbol for Zero called Nfr (pronounced "Nefer"), which is usually translated as "beauty". The hieroglyph for Nfr looks like a circle with a cross on top of it and is said to be a "stylized depiction of a heart and windpipe" [most likely as a reference to the concept of The Hall of Two Truths - "It is the heart that brings forth every issue, and the tongue that repeats the thought of the heart."]

The "Parthenon of gods" of later Egyptian dynasties (called The Ennead) found their origin in Aton (or Aten), the ONE God, which was symbolized by the "winged disk" hieroglyph, an image of the Sun. The Sun was thought of as the Giver of Life because its radiant rays provided warmth that helped animate all life upon the planet Earth. It was considered the embodiment of Love that permeated all of Nature. Many things were said to be "Nefer" in homage to it. Their concept of law was founded upon emulating it. What could one do to be Loved other than give Love?

Later, this concept of ONE God fractionated into the concept of two gods (a Male and Female pair), Isis and Osiris, with its own set of mythology. For example: Osiris became the Sun, and his evil brother Set symbolized nightfall (and is supposedly where we get the term "sunset"). When Osiris wasn't fighting with his brother, he and Isis had a baby named Horus (supposedly where we get the term "hour" from)...So this Mother-Father Union birthed a solar calendar.

The Egyptians had two distinct ways of writing. Hieroglyphs were usually used for sacred teachings (such as the spiritual concepts and mythology presented above), and another calligraphy-like script called Hieratic for mathematics and science. The hieroglphys were usually etched in stone in the walls of temples that embodied their teachings (to be preserved for posterity), while hieratic was used in papyrus scrolls (many of which did not last). [It is somewhat similar to the distinction between "ecclesiastical" and "vulgar" Latin.] But there was a lot of overlap between the two as well. Their mathematics was a reflection of their cosmogony.

Egyptian numerals are a lot like tally marks. There is a specific hieroglyph for each power of ten (1, 10, 100, 1000, etc.). There was no concept of decimals, so anything less than 1 was written as a fraction of a specific type (called "Egyptian Fractions"). These fractions are always written with 1 as the numerator, shown as a dot above the hieroglyphs that act as the denominator. Any number other than 1 can be written as a series of Egyptian Fractions (usually beginning with the largest portion first and then moving to the smallest, the denominator of each fraction being a unique number).

The symbol for Horus (a sort of "All-Seeing Eye" called the Oudjat), is said to be made up of a collection of fractions like this:

Notice that if we list them from greatest-to-least we get halving:

1/2 = 0.5

1/4 = 0.25 (2 + 5 = 7)

1/8 = 0.125 (1 + 2 + 5 = 8)

1/16 = 0.0625 (6 + 2 + 5 = 13 & 1 + 3 = 4)

1/32 = 0.03125 (3 + 1 + 2 + 5 = 11 & 1 + 1 = 2)

1/64 = 0.015625 (1 + 5 + 6 + 2 + 5 = 19 & 1 + 9 = 10 & 1 + 0 = 1)

If this symbol is the "right eye", what would happen if we add the "left eye"? Would we make our full Doubling Circuit (in both directions)?

Ironically enough, all of the Egyptian's arithmetic calculations are accomplished through doubling and halving.

If they wanted to perform geometry...say, to find the the angle of inclination for building a pyramid (which they called a Seked)...then they would leave that "trigonometric function" as a ratio. You can give whole number values to any decimal by treating it as a ratio. All of the Egyptian Fractions are referenced against 1. In VBM however, all other numbers are referenced against 9 (which is like the number 1 one octave up), and we usually make decimals into whole numbers by adding them together. [If the number is a repeating decimal perhaps we could use the numbers in the division that forms it to assign it a single digit?]

These VBM math patterns seem to show up in some form consistently throughout all ancient cultures (e.g.: Native American, Mesoamerican, Chinese, Arabic, Indian, etc.). All of our modern mathematics is a continuation of them.

For example, in the 1600's, there was a man by the name of John Napier who helped develop quicker and easier ways to do arithmetic. Probably most well known for his "Napier's Bones" (a set of rods that help one to do lattice multiplication) and "Logarithms" (a way of adding and subtracting powers to multiply and divide), he also came up with a thing called "Positional Arithmetic" (which is essentially an abacus made out of counters and a chessboard - Note that a chessboard is a grid of 64 squares). [You can play with an online version of it here. Scroll down the page.]

...We will continue in the next posts to cover more of these types of patterns throughout history. Everyone please feel free to share your own observations as well. Thanks for reading!

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Permalink Reply by Barbitone on January 18, 2012 at 5:01am

"The symbol for Horus (a sort of "All-Seeing Eye" called the Oudjat), is said to be made up of a collection of fractions like this:"

I've often heard of these fractions being associated with the eye of horus but I dont know why? Why is that part 1/8 etc......??

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Permalink Reply by Sage on January 18, 2012 at 12:47pm

This is a very good question. I would like to know more about it too.

After a quick browse, it seems there are layers of meaning to the symbol:

*One is mythological-spiritual and has to do with a story about how Seth killed Osiris (turning him from the God of The Sun into The God of The After-Life). In order to avenge his father's death, Horus fought Seth for 80 days, a battle in which he lost his left eye. Seth tore up the eye into 6 pieces. Thoth found these pieces and magically put them back together. When he returned the eye to him, Horus gave it as a gift to his father. This became a symbol of healing (Rx) and respect for one's parents. But also an amulet to protect the "dead" by helping them to see themselves Reborn in the Light.

*We can add a literal component to this story as well by keeping in Mind the mathematics. Adding up all the fractions only gives 63/64. It takes a spiritual aspect (Thoth's Magic) to complete the fraction and make it equal Unity.

*There is a very intriguing interpretation about how the individual fractions are symbolic of each of the bodily senses.