Udja Eye and Egyptian fractions

It was one of those friend meetups. No, my engineer friend did not approach me with a twinkle in his eye to top his last math problem. However, my sociologist friend had something…

“Eh Vince, I got something to show you. You know about the Udja Eye?”
“The what?”

So he showed me this book “The Secret History of the World” by Jonathan Black (or Mark Booth as the author explained).

“It’s got fractions and stuff. Wait, lemme find it for you…”

Then he flipped through the book, and “Here! Udja Eye.” It looks interesting. “I was thinking you could do something with it for one of your Math Wizard powers.” (bless the man) I noted the term down for further research because another friend wanted to read through the book first.

Fast forward maybe a week later, that friend with the book (my engineer friend, coincidentally) practically shoved the book at me. “Vince, you have got to read it.” As of this writing, I haven’t started reading it yet. I wanted to find out more about this Eye first. It looks like this:

Eye of Horus
[source image]

According to my research, apparently “Udja Eye” was not a popular term. It was frequently referred to as “Wedjat (Eye)”, “Wadjet (Eye?)”, “Udjat Eye”, “Oudjat” or the easier to pronounce version “Eye of Horus“. It had been Eye of the Moon, and then Eye of Ra. Which is confusing (to me at least), because Ra (or Horus) is the Egyptian god of Sun.

“I see it’s an Egyptian thing…” you say.
“Are you trying to be funny?”

Oh wait,

Since Horus was said to be the sky, he was considered to also contain the sun and moon. It became said that the sun was his right eye and the moon his left, and that they traversed the sky when he, a falcon, flew across it.

That kind of explained the eyes of moon and sun thing. Wait, what falcon? Oh nevermind…

So what about the fractions? It turns out that the Eye of Horus is composed of 6 fractions.

[source image]

Don’t ask me why it’s reversed…

In the Ancient Egyptian measurement system, the Eye Of Horus defined Old Kingdom number one (1) = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64, by throwing away 1/64 for any rational number. Eye of Horus numbers created six-term rounded-off numbers. The Old Kingdom definition had dropped a seventh term, a remainder 1/64, that was needed to report exact series.

The confusion sets in…

I did some more research. And Wikipedia failed me. I don’t want to look at any other search results because “Udja Eye” (and its variants) is an esoteric topic, and appears to have connections with the occult. Basically I don’t trust search results on this. I’m looking specifically for the math background, but some historic information is also appreciated. And possibly needed (to explain the math stuff). This feels like a “Da Vinci Code” moment…

I read up on Egyptian mathematics and fractions. Still no clue.

So I’m undergoing psychic damage because of:

  • What is “Old Kingdom” math? How does it work?
  • Why is the 7th term (1/64) dropped? Is it because the Egyptians valued the 5 senses and thought (so total 6)? Or the ancient Egyptians couldn’t work with the higher precision?
  • Did the hieroglyphics for the fractions appear first? Or was the Eye of Horus formed, and then individual parts were used to denote the fractions?
  • Horus‘ mother, Isis did what to her murdered husband Osiris’ uh, manhood? It was thrown in the Nile and eaten by a catfish?!?
  • In a battle, Horus ripped off his uncle Seth’s (who’s the murderer of Osiris) testicles (?!? must they be so graphic)?
  • Seth tried to seduce Horus and inseminate him with his, oh I can’t even go on…
  • What is wrong with these people?!?

*take deep breath* Ok. So. Maybe the book my sociologist friend lent me will shed some light…