The Valenzetti Equation seems to be central to finding the Island, its electromagnetic pulses, and the overall nature of the space-time continuum on and off the Island. I think all but a foregone conclusion at this point that the Numbers are a part of this equation. DHARMA was aware of Valenzetti's research and likely used it in locating the Island. But as we saw in Season 2, when we met Desmond in the Hatch and learned more about the Swan, we saw the Numbers being input into a computer to stop the electromagnetic pulses from getting out of control.

I think there's a direct relationship between the Numbers and the Hieroglyphs, beyond just seeing them appear together in the Swan. My hunch is the ancient civilization or group of people who lived on the Island long ago were aware of what we call the Valenzetti Equation, albeit by a different name. The hieroglyphics may very well be the ancients' own interpretation of the same phenomena Valenzetti was trying to decipher with his research and his equation.

As to why we see Egyptian hieroglyphics in the show: Take a look at a globe. Not a paper or digital flat map, but a globe. Locate Cairo, Egypt. Notice its proximity to Tunisia. Let's assume there was a civilization in Tunisia in ancient times that came into contact with or under the influence of the Egyptian empires of the day. They would certainly have knowledge of their writing and culture.

Now, looking at that globe, find the approximate opposite of Tunisia (where Ben landed after turning the wheel). Tunisia is literally on the direct opposite side of the world from the South Pacific, the alleged location of the Island. If, as Eloise Hawking has told us, there are many pockets of energy over the world that open a door to the Island, Tunisia's location would be interesting if not significant.

The ancients who built the Temple, the Ruins, and the Four-Toed Statue may have come from Egypt via Tunisia, where there is a doorway to the Island. They came to understand the properties of the Island, built the frozen wheel to manipulate the electromagnetism, space and time, and perhaps even the healing properties of the Island. They described these phenomena with their language and writing in hieroglyphics. Millenia later and independent of this civilization on the Island, Valenzetti researched similar properties and ended up describing the same thing the ancients had already known.

So the hieroglyphics we see around the Island, but particularly in the Swan, are simply an ancient Valenzetti Equation.

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