So, having followed Deagol's link, I've discovered that it makes a whole lot more sense than he did.

I've pulled a few things, and then I'll explain what I think. I'm sorry if I'm repeating anything other people have already said, but there are 500 pages of research out there on the forums, and it might have slipped past me.
Rational numbers could also be expressed, but only as sums of unit fractions, i.e. sums of reciprocals of positive integers, except for 2/3 and 3/4. The hieroglyph indicating a fraction looked like a mouth, which meant "part":

So, we have a basic shape, and it means "part." As in, a part of something? A part of something like, say, a super-secret worldwide organization?
To back this up, Wikipedia's other page on this says that the shape (symbol D22) is also a mouth and can mean "[one] among."
http://en.wikipedia.org/wiki/Egyptian_fraction
Wikipedia continues on to say that fractions were created by taking the reciprocal of a number and assigning integer values to it. In layman's terms, this means that you took the mouth part and added a certain symbol to indicate what kind of fraction it was. There are two special symbols, as mentioned above, to indicate 2/3 and 3/4 -- these are the Watcher symbols...almost.
The Watcher symbol is distinguished from the basic fraction symbol (remember that it can mean "[one] among") by the addition of a dot in the center. In the past, it has been hypothesized that it is representative of the sun, or an eye. Egyptian fractions have something to say about this too:
Wikipedia wrote:In the Ancient Egyptian measurement system, the Eye Of Horus defined an Old Kingdom rounded off notation that continued in use in the Middle Kingdom, with each part of the eye representing a different fraction. The definition of one(1) was 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 , written as a 6-term rounded off number. It dropped the remainder 1/64. The metaphorical side of this information linked all six fractions, 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64 to separate parts of the eye, as noted by:
* 1/2 was represented by smell, symbolized by the right side of the eye in a form of the nose. The pyramid text says: "Behold [the fire] rises in Abydos and it comes; I cause it to come, the Eye of Horus. It is set in order upon thy brow, O Osiris Khenti-Amenti; it is set in the shrine and rises on thy brow."
* 1/4 was represented by sight or the sensation of light, symbolized by the pupil. The pyramid text says: "Perfect is the Eye of Horus. I have delivered the Eye of Horus, the shining one, the ornament of the Eye of Ra, the Father of the Gods."
* 1/8 was represented by thought, symbolized by the eyebrow. The pyramid text says: "...the Eye of Horus hath made me holy...I will hide myself among you, O ye stars which are imperishable. My brow is the brow of Ra."
* 1/16 was represented by hearing, symbolized by the left side of the eye in the form of an arrow pointing towards the ear. The pyramid text says: "That which has been shut fast/dead hath been opened by the command of the Eye of Horus, which hath delivered me. Established are the beauties on the forehead of Ra."
* 1/32 was represented by taste, by the sprouting of wheat or grain from the planted stalk, symbolized by a curved tail. The pyramid text says: "Come, the Eye of Horus hath delivered for me my soul, my ornaments are established on the brow of Ra. Light is on the faces of those who are in the members of Osiris."
* 1/64 was represented by touch, symbolized by a leg touching the ground, or what can also be thought of as a strong plant growing into the surface of the earth. The pyramid text says: "I shall see the Gods and the Eye of Horus burning with fire before my eyes!"
The 'Eye of Horus' fractions were further discussed in the Egyptian Mathematical Leather Roll following elementary definitions that built the Egyptian fraction system.
Soooo....here we have a symbol which means "part of" or "one among," and we have six divisions, each of which represents an essential function of the whole.
I'm not saying that this is what we've been looking for, but it certainly makes me stop and think.