The Eye of Horus, one of the most famous symbols from ancient Egypt, was actually a math problem

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The Eye of Horus, one of the most famous symbols from ancient Egypt, was actually a math problem

Pretty everyone has seen the Eye of Horus somewhere at some point. It’s been in every single movie, TV show, book and video game even remotely touching on anything to do with ancient Egypt, and it’s been turned into millions of cheap head shop pendants, but it’s more than meets the eye— it’s not just a cool symbol, but it’s a math problem.

The Eye of Horus is, from a design standpoint, both beautiful and iconic. And whoever created it might have been thinking of exactly that while dreaming it up. But it’s not just a stylish symbol. It has a deeper meaning: The Egyptians used it to express fractions of volume. Each stroke counts for a subdivided piece of the whole.

The inner corner of the eye indicates one half, the iris is one fourth, the eyebrow is one eighth, the outer corner of the eye is one sixteenth, and the decorations below the eye are one thirty-second and one sixty-fourth respectively. They were combined, in various ways, to measure the unit capacity for grains.

This eye may seem like a straightforward notation system, but it’s not just that. It’s also a pictogram. A good analog for this is a simple tally system kept by a child. Four slashes indicate units, and one diagonal slash across the four indicates a group of five. Look over a list, and it’s easier to get a sense of the different amounts that have been tallied than to read the numerals for all of them. (Similarly, some people in East Asia still use the character for “correct” as a kind of tally system.)

By using different marks to make a complete Eye of Horus, people in charge of many different quantities of something can skim a list quickly. And they can get a sense of how many storage units are at what capacity, just by looking for how many completed eyes there are, and whether the incomplete eyes are built from the inside out or the outside in.

And other tallying systems use basic pictograms as well. We have an easy-to-see tallying unit for five, the four lines with a slash, but we have a base ten numbering system. Other societies had an simple way to represent ten objects; a simple box with two diagonal lines crossed inside it. Each element in its construction represented a stage of counting to ten. First there are four dots representing the four corners of the box. Then there are four lines, each one side of the box. That adds up to eight, with the two diagonal slashes through the center bringing it up to ten. To tally and count by tens, all anyone had to do was look at the number of completed boxes.

We might do well to bring a working pictogram system back into common usage, here in the West. Although it would only be helpful in certain situations, like when most of the things being tallied fall between one and a hundred, or when all of the objects being tallied are fractions, it’s very useful in practice. Anyone who has had to scan down a list of numbers knows that they’re nearly impossible to remember as a whole.

A system that allowed people to look down a list and see the entire list as a whole, zeroing in immediately on differing amounts without having to read the whole thing, would be useful anywhere people have to keep handwritten and quickly-changing records. All we’d need to do is come up with simple symbols that can be broken down into tens, hundreds, or parts of a whole, and we can create a new-old system of notation.

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