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As I was going through the Times…

Stephen Chrisomalis, Wayne State University

Recently, there has been a “Puzzle Moment” in the science section of the New York Times, with an eclectic mix of articles combining scientific pursuits with cognitive and linguistic play of various sorts. One that caught my eye is ‘Math Puzzles’ Oldest Ancestors Took Form on Egyptian Papyrus’ by Pam Belluck [1], which is an account of the well-known Rhind Mathematical Papyrus. The RMP is an Egyptian mathematical text dating to around 1650 BCE, and is one of the most complete and systematic known accounts of ancient Egyptian mathematics. It’s a fascinating text, written in the Egyptian hieratic script rather than the more famous hieroglyphs, and it gives us considerable insight into the economy, social organization, and technical practices of the Second Intermediate Period.

The central conceit of the Times article is that the well-known “As I was going to St. Ives” poem-puzzle has its earliest ancestor in the RMP. This is vaguely true in that the RMP has a section involving repeated multiplication by seven, resulting in an addition problem. But Ahmes the scribe, despite his insistence that his text would reveal “obscurities and all secrets”, was not writing a mystery, but an exercise that formed part of scribal training, in an era where the literacy rate was at most 1-2%. While one can argue fairly that this is not a ‘real’ problem, and that the structure of it is meant to hold the learner’s attention through its repetitions, to call it a puzzle is only true in the broadest possible sense.

I’m a professional numbers guy, not an Egyptologist, but the article we are presented with not only tells us nothing new about the Rhind. I was very pleased, on the one hand, to see Marcel Danesi, whose work may be familiar to many readers of this blog, commenting on the widespread cross-cultural and cross-historical interest in puzzles (not only numerical puzzles, but including them). It’s not often enough that linguistic anthropologists get quoted in the Times. And like Danesi, I have broadly universalist sympathies. But I disagree with Danesi, who has made this claim about the RMP elsewhere, in his The Puzzle Instinct (Indiana, 2004, pp. 6-7) that it was “shrouded in mystery” or that “mystery, wisdom, and puzzle-solving were intrinsically entwined in the ancient world.”

The better example of numerical play in Egyptian scribal traditions mentioned in the Times article is the Horus eye, or wedjat, a combination of six symbols whose constituent parts signify the fractional series {1/2, 1/4, 1/8, 1/16, 1/32, 1/64} which when summed totals 63/64, or nearly one (see below). As the Egyptologist Sir Alan Gardiner reckoned it, the remaining 1/64 would be provided by Thoth who would heal the Eye and thus produce unity. It’s a nice story, and at least at some periods or for some writers, this narrative may have been relevant.


But the Horus-eye illustrates one of the central problems in the transliteration of Egyptian texts, namely that while the vast majority of Egyptian mathematically-relevant texts are written in the cursive hieratic script, they are transcribed, and all-too-frequently theorized, as if they were hieroglyphs. This transcriptional practice leads us to think of the Rhind as a hieroglyphic text that just happens to be in hieratic in the original, but in the case of the Horus eye it couldn’t be more misleading. The Horus symbols in the Rhind don’t look like the above image, and more generally, the hieratic numerals look nothing like, and behave nothing like, the hieroglyphic numerals. We now call of these six Horus eye components by the less evocative name of ‘capacity system submultiples’ in recognition of the fact that these components were originally nonpictographic, part of a metrological system of grain measurement, and only at a much later date were they composed into the wedjat-eye. This isn’t to say that the Egyptians weren’t numerically playful, but they weren’t especially playful in the Rhind.

In short, the RMP is not an especially good example of numerical play in Egypt, and certainly not an especially relevant example from a cross-cultural perspective. It illustrates, to be sure, that mathematical texts are not purely functional or economic documents, but include semiotic and linguistic elements far beyond their pragmatic use. But this is not new knowledge about the Rhind or about mathematics. And it runs a grave risk of othering a document whose function was largely pedagogical, and is thus not so different than, for instance, the ‘ready-reckoners’ of early-capitalist sixteenth-century England.

I am thrilled to see numerical texts treated as objects of inquiry beyond the facile ‘Did they get the answer right?’ I am sympathetic to Danesi’s claim that puzzles and riddles have universal salience. Yet I worry that, at least in the case of the Rhind, the link to puzzle-like behavior is so far-fetched that it turns our best glimpse into Egyptian sociomathematical practice into an inappropriately arcane and obscurantist account. This ‘mysteries of lost Egypt’ nonsense should have been set aside decades ago.

If you wanted to pull out some cross-cultural examples of numerical play, you could easily find lots of better examples, from well-covered territory such as Hebrew gematria practices, to the richly evocative varnasankhya systems of number-word associations in premodern South Asian texts, to the complex cluster of quasi-cryptographic numerical systems used by Ottoman administrators and military officers. Or if you were really stuck on Egypt, you could investigate the cryptic numerals used on late Egyptian votive rods and Ptolemaic inscriptions, richly infused with homophony. (For a more extensive discussion of these and others, see my Numerical Notation: A Comparative History (Cambridge, 2010). There is a rich, although disciplinarily diverse, comparative body of material on numerical practices including puzzles, but the Rhind just isn’t part of it.

(Crossposted to Glossographia)