Here is a story about number systems:
The wd3t is the eye of the falcon-god Horus, which was torn into fragments by the wicked god Seth. Its hieroglyphic sign is made up of the fractional powers of 2 from 1/2 to 1/64, which sum to 63/64. Later, the ibis-god Thoth miraculously ‘filled’ or ‘completed’ the eye, joining together the parts, whereby the eye regained its title to be called the wd3t, ‘the sound eye’. Presumably the missing 1/64 was supplied magically by Thoth.
This is my retelling, using many of the same phrases, of Sir Alan Gardiner’s account of the ‘eye of Horus’ symbol used for notating measures of corn and land in his classic Egyptian Grammar (§ 266.1; 1927: 197). It’s a nice story, and it is repeated again and again, not only in wacky Egypto-mystical websites but in a lot of serious scholarly work up to the present day. I talk about it in Numerical Notation. But is it true? Well, that depends what you mean by ‘true’, but mostly the answer is: not really. As I mentioned in a post back in 2010, this is certainly not the origin of the symbols. Jim Ritter (2002) has conclusively shown that these are ‘capacity system submultiples’, which originated in hieratic texts, not hieroglyphic ones, and appear to have had non-religious meanings originally. Even while insisting on the mythico-religious origin of the Horus-eye fractions, Gardiner himself (1927: 198) is crystal clear that all the earliest ‘corn measures’ are hieratic. The hieratic script is very different in appearance and character than the hieroglyphs, being the everyday cursive script of Egyptian scribes, rather than the monumental and more formal hieroglyphs. Ritter shows conclusively that in their origin, and their written form, and their everyday use, the capacity system submultiples have nothing to do with the Eye of Horus.
Ritter distinguishes this “strong” thesis from a “weak” version, in which, many centuries after their invention, the hieratic capacity system submultiples were imported into the hieroglyphic script and that some scribe or scribes wrote about them as if they could be combined into the wedjat hieroglyph. This weak version has more evidence for it, but as Ritter points out (2002: 311), this “does not automatically mean that ‘the Egyptians’ thought like that; for example, those Egyptians whose task it was to engrave hieroglyphic inscriptions on temple walls. Theological or any other constructs of one community do not necessarily propagate to every other; the Egyptians were no more liable than any other people to speak with a single voice.” This is a sociolinguistically-complex, reflective view that I think is essentially correct, and which I adopt in my work (although I would rewrite it today to be even clearer, as I hope I have above). Ritter is not fully convinced by the weak thesis either, but acknowledges that it is tenable.
Ultimately, as Ritter concludes (correctly), our willingness to buy into the ‘Horus-eye fractions’ model tells us a lot about how we view the hieroglyphs, and Egyptian writing in general, as mythically-imbued and pictorial in nature, and ultimately reflects a mythologized view of Egyptians as a ‘mystical’ people, an ideology that goes back to the Renaissance and earlier in Western thought (Iversen 1961). But I would go further, because it is about more than just Egypt. We like stories that give numerological explanations for numerical phenomena, regardless of their veracity, and especially where the numerical system under consideration is from societies we conceptualize as having a more mystical or mysterious relationship with the world than we purportedly do. Very often we are projecting our image of what is going on. This isn’t to say that Gardiner’s description is wrong – he knew the texts better than almost anyone, and correctly identifies how the system worked and the texts in which it was found. But it’s important that when (some) Egyptians transliterated the capacity system submultiples from hieratic to hieroglyphic writing and formed them into the wedjat, they were repurposing and transforming a pre-existing set of signs that had no mystical origin whatsoever. It deserves our attention, both for what it tells us about Egyptian life and also for its importance for the historiography of science, mathematics, and religion in non-Western societies.
(Thanks to Dan Milton, who as the winner of the contest last week asked the question that motivates this post.)
Gardiner, Alan H. 1927. Egyptian grammar: being an introduction to the study of hieroglyphs. Oxford: Clarendon Press.
Iversen, Erik. 1961. The myth of Egypt and its hieroglyphs in European tradition. Copenhagen: Gad.
Ritter, Jim. 2002. “Closing the Eye of Horus: The Rise and Fall of ‘Horus-eye fractions’.” In Under One Sky: Astronomy and Mathematics in the Ancient Near East, edited by John M. Steele and Annette Imhausen, 297-323. Münster: Ugarit-Verlag.