(Also Eye of Horus, Eye of Heru, Eye of Ra)
"Prosperous, Sound, Whole"
"The Sound Eye"
The Udjat is one of the most important symbols in the Egyptian mythology. The symbol itself is an eye with a long tail and thick brows which are similar to the markings on a falcon (as Horus had the head of a falcon). The right eye represented the sun while the left eye represented the moon. The Udjat adorned any object requiring divine protection, as well as amulets of protection, and was thought to have to power to ward off sickness, give prosperity and fertility, and to deflect the evil eye.
There are two different myths which give importance to the Udjat. The first tells of Horus seeking vengeance against Seth for the murder of Osiris. During their battle, Seth tore out Horus’s left eye (or, in some accounts, both eyes) and tore it apart. Thoth, the god of wisdom and magic, traveled to the chaos beyond the world and found sixty-three pieces of the shattered eye. Thoth used magic to make up for the missing sixty-fourth piece. When the eye was returned to Horus, he then gave it to Osiris, restoring him to life. The eye being healed by Thoth and bringing Osiris back to life led to the Udjat being associated with healing and protection against illness.
In the second myth, Atum (the creator god) had a son, Shu, god of air, and a daughter, Tefnut, goddess of moisture. After a time, Atum’s offspring were separated from him and lost in the chaos of Nu. He had only one eye with which to search for them (the Udjat) and it was removable, so he sent it off in search of his children. When the Udjat returned with Tefnut and Shu, Atum was so happy he cried tears of joy. When the tears fell from heaven and hit the ground, men grew (the first humans).
The Udjat’s symbolism has lasted into the present. According to some, the pharmacist’s “Rx” is a variation of the Eye of Horus. This is evidenced by the fact that the Rx was originally an eye with an x below it (this can still be seen in the logos of some pharmacies). Another variation of the Udjat is the eye within a pyramid associated with Freemasonry and the eye over the pyramid in the Great Seal of the United States. The significance of these variations seems to be the omnipotence of the Udjat. It is the all seeing eye.
The fractional nature of the Udjat has been cited as evidence that the Egyptians were a super-advanced civilization. The symbol can be divided up into the fractions 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64, which consequently only add up to 63. The fractions were each associated with a portion of the Udjat symbol and those portions were used by the Egyptians to write those fractions. The remaining 1/64 was supposedly Thoth’s magically created piece. This extra 1/64 is thought by some to indicate the Egyptian’s knowledge of infinite sequences and thus calculus. To learn more about this theory, check out: http://www.pyramidtexts.com/article6.htm
Sources:
http://www.kemet.org/glossary/udjat.html
http://www.cybercomm.net/~grandpa/egypt.html