The Serpentine Cipher, deciphered

All right, if you follow me over on Twitter, you’ll have seen, over the past few weeks, a puzzle I presented there (with hints and historical digressions) that ended with the successful decipherment of what I can now tell you is called the Serpentine Cipher – this particular word is just the word SERPENTINE. And you will certainly see that each sign certainly is serpentine-looking:

This text is super short and decipherment is certainly a challenge without hints and without some additional information. It starts with the numerical notation used by Johann Joachim Becher in his 1661 Character pro notitia linguarum universali. This was, as the Latin name suggests, one of many 17th century ‘universal language’ schemes, meant to encode concepts rather than words tied to any specific language. Becher’s system used a different number for each of 10,000 concepts, distinguished with lines and dots around a frame:

Becher’s notation wasn’t completely original to him, though. It’s a variant of the Cistercian numerals described in David King’s magisterial 2001 book, Ciphers of the Monks. The system became better known in 2020 via the Numberphile Youtube channel:

King’s book shows how this local development, in parallel to Indo-Arabic / Western ciphered-positional numerals (the digits 0-9), spread throughout European intellectual life into strange places, from volume markings on Belgian wine barrels to modern German nationalist runology. But among the more notable places you find this kind of numeration is in various ciphers, universal language schemes, and other sorts of semi-cryptic efforts to encode language in the 16th and 17th centuries. Although we now know, very firmly, that the Cistercian numerals were a medieval European invention, they were often described as ‘Chaldean’ and/or assigned considerable antiquity / mysticism.

My own contribution to this reception literature was in a post here a few years ago, Cistercian number magic of the Boy Scouts, showing how it ended up in 20th century Scouting literature:

Anyway, the Serpentine Cipher isn’t based on any of that, but is taken directly from Becher. But you can’t just use Becher’s universal cipher at this point, because a ‘universal language’ of 10,000 individual concepts is pretty damn useless. Instead, to solve it, you needed to convert the five glyphs to numbers, and then those to specific pairs of letters – so that five glyphs produces a plaintext of ten letters.

So if you got that far, you found that the five glyphs were five numerals written quasi-positionally, without a zero, in a mixture of base 5 and 10: 737, 3233, 473, 1633, and 473. The fact that the third and fifth glyphs are identical is important, but also potentially misleading. By the way, the reason you don’t need a zero is that the ‘place values’ aren’t linear, but oriented on the same frame, so you can simply leave one blank to indicate an empty space. It’s a kind of ‘orientational’ or ‘rotational’ zero-less place-value. The downside is that unlike a linear phrase it isn’t infinitely extendable.

Next, you needed to notice that each number is the product of exactly two prime factors. By the Fundamental Theorem of Arithmetic, every number is the product of some unique set of prime factors. So there’s no ambiguity: 737 is *only* 11 x 67. And by chance, there are 25 primes below 100, so, borrowing Z = 101, we can associate each prime with a letter:

  • A = 2
  • B= 3
  • C = 5
  • D = 7
  • E = 11
  • F = 13
  • G = 17
  • H = 19
  • I = 23
  • J = 29
  • K = 31
  • L = 37
  • M = 41
  • N = 43
  • O = 47
  • P = 53
  • Q = 59
  • R = 61
  • S = 67
  • T = 71
  • U = 73
  • V = 79
  • W = 83
  • X = 89
  • Y = 97
  • Z = 101

Thus, each glyph can be treated as a product, and thus as a two letter sequence. 737 = 11 (E) x 67 (S), the 5th and 19th primes. (For words like PIZZA that would use the ZZ glyph (101 x 101 = 10201) you have some different options for that fifth place-value, but these are rare enough to ignore for now). Then all you have to do is ‘serpentine’ between the two letter-pair combinations for each number to figure out which pairs lead to the solution. Voila!:

An added bonus of using the word SERPENTINE is that it illustrates one of the key (mildly) confounding properties of the cipher, namely that an identical glyph (473) always has two readings, both of which occur in this one word.

Now, note that the only glyphs that will have even values are ones that use A=2, because the product of odd numbers is always odd. This would have provided a hint – if I’d given you a word with any As in it. (You can also use A=3 … Z=103 if you like, but there will be more products >10000 then.)

Really, once you see all those 11s, it’s not a bad guess that those 11s are Es – but of course, without knowing exactly what their position is, it makes deciphering such a short text tricky. But I don’t pretend that this would stand up to serious cryptanalysis as-is.

Finally, if you have a ‘straggler’ odd letter left out at the end of a word or phrase you can either multiply three letters into a product (though that gets unwieldy, e.g., WRY = 83 X 61 X 97 = 491,111) or just have a single number (a prime) at the end. Either one of these might tip you off as to a word boundary. Of course, you don’t have to stop at word boundaries, so you can SP LI TU PT HE WO RD SI NT OP AI RS LI KE TH IS.

Anyway, thanks to all who played along. I think this is a bunch of fun, doesn’t need much more than basic arithmetic, and provides a neat digression into the history of number systems and early modern cryptography. Paul Leyland was the first correct decipherer and is thus a winner of a copy of my book, Reckonings: Numerals, Cognition, and History, which, while it is not really about ciphers at all, does have a lot of stuff relevant to number systems and early modern history.

Finally, this cipher is presented in memory of my dear friend Victor Henri Napoleon, who was one of the original decipherers of an early/experimental version of the Serpentine in 2017, and who passed away suddenly last week at the age of N (43). You will be missed, Vic!

Language, Culture, and History: a reading list

Having appropriately propitiated the curricular deities, it appears that this coming fall, I’m going to be teaching a graduate seminar in linguistic anthropology on the topic of Language, Culture, and History.   The readings will be drawn from linguistically-oriented historical anthropology and ethnohistory, anthropologically-oriented historical sociolinguistics, and linguistically-oriented archaeology, if that makes any sense.  Maybe not?

Anyway, last night I put together my ‘long list’ of 40-odd books that we might potentially read. Some of these will come off the list due to price or availability.  Others I haven’t looked at thoroughly yet, and when I do will come off because they aren’t suitable.  That might get me down to 25, but then I’ll need to get it down to 13 or 14, one a week. The rest can go on a list from which individual students can pick to do individual book reviews and presentations.

Here’s the list, below.  Additional ideas of books that fit these general themes would be welcome. Any thoughts?

Continue reading “Language, Culture, and History: a reading list”

Neolithic Chinese sign-systems: writing or not writing?

The Guardian just reported today on a find from Zhungqiao (near Shanghai) of artifacts bearing writing-like symbols that date back over 5,000 years.  If this were substantiated, this would take the history of Chinese writing back an additional millennium or more from the earliest attested ‘oracle-bones’ and other inscriptions of the Shang dynasty.

The article reports that the artifacts in question were excavated between 2003 and 2006, and the information is both slight and non-specific, and doesn’t link to any specific publication as of yet, so it’s difficult to know how, if at all, this relates to the host of other reports of writing or writing-like material from Chinese Neolithic sites (the Wikipedia page on Neolithic Chinese signs is quite extensive).    The signs from Jiahu are much older than those of the newly reported find, for instance.

I think that the difference that’s at question, and discussed in the Guardian piece, is the presence on some of these artifacts of series of several signs in a row, thus suggesting sentence-like structure rather than, say, ownership marks or clan emblems or just decoration, which is what most of the other Neolithic signs have been determined to be.    I have to say that, if the stone axe pictured in the article is representative of the new finds, then I’m dubious of the entire enterprise – those do not look, to me, to have a writing-like nature, and some of them may not be ‘signs’ at all.   I hate to be so negative, but the tendency to announce finds in the media that never come to anything in publication is so great that we should indeed be highly skeptical when such announcements are made in the absence of a published site report or article.

The mystical Eye of Horus / capacity system submultiples

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.

Coexistence and variation in numerals and writing systems

Well, it only took about 20 minutes for Dan Milton to solve the mystery of the Egyptian stamp: it has four distinct numerical notation systems on it: Western (Hindu-Arabic) numerals, Arabic numerals, Roman numerals, and most prominently but obscurely, the ‘Eye of Horus’ which served, in some instances, as fractional values in the Egyptian hieroglyphs:

egypt-stampAt the time I posted it this morning, it was the only postage stamp I knew of to contain four numerical notation systems.   (As Frédéric Grosshans quickly noted, however, a few of the stamps of the Indian state of Hyderabad from the late 19th century contain Western, Arabic, Devanagari, and Telugu numerals, and also meet that criterion, although all four of those systems are closely related to one another, whereas the Roman numerals and the Egyptian fractional numerals are not closely related to the Western or Arabic systems.    So that’s kind of neat.  I have a little collection of stamps with weird numerical systems (like Ethiopic or Brahmi), multiple numeral systems (like the above), unorthodox Roman numerals (Pot 1999), etc., and am looking to expand it, since it is a fairly delimited set and, as a pretty odd basis for a collection, isn’t going to break the bank.  In case I have any fans who are looking for a cheap present for me.  Just sayin’ …

We in the West tend to take for granted, today, that really there is only one numerical system worthy of attention, the Western or Hindu-Arabic system, which is normatively universal and standardized throughout the world.  We also tend to feel the same way about, for instance, the Gregorian calendar.   That’s a little sad but not that surprising.   But we also take it for granted that, in general, throughout history, each speech community has only one set of number words, one script, and one associated numerical notation system.    Of course, a moment’s reflection shows us this isn’t true: virtually any academic book still has its prefatory material paginated in Roman numerals, not to mention that we use Roman numerals for enumerating things we consider important or prestigious, like kings, popes, Super Bowls, and ophthalmological congresses.   And this is not to mention other systems like binary, hexadecimal, or the fascinating colour-based system for indicating the resistance value of resistors.    I’ve complained elsewhere that we put too much emphasis on comparing one system’s structure negatively against another, but to turn it around, we should ask what positive social, cognitive, or technical values are served by having multiple systems available for use.

We need to be more aware that the simultaneous use of multiple scripts, and multiple numeral systems, simultaneously in a given society is not particularly anomalous.       In Numerical Notation (Chrisomalis 2010), I structured the book system by system, rather than society by society, which helps outline the structure and history of each individual representational tradition, and to organize them into phylogenies or families.  But one of the potential pitfalls of this approach is that it de-emphasizes the coexistence of systems and their use by the same individuals at the same time by under-stressing how these are actually used, and how often they overlap.    Just as sociolinguists have increasingly recognized the value of register choice within speech communities, we ought to think about script choice (Sebba 2009) in the same way.   With numerals, we also have the choice to not use number symbols at all but instead to write them out lexically, which then raises further questions (is it two thousand thirteen or twenty thirteen?) – many languages have parallel numeral systems (Ahlers 2012; Bender and Beller 2007).   We need to get over the idea that it is natural or good or even typical for a society to have a single language with a single script and a single numerical system, because in fact that’s the exception rather than the norm.

The stamp above is a quadrilingual text (French, Arabic, Latin, Egyptian) in three scripts (Roman, Arabic, hieroglyphic) and four numerical notations (Western, Arabic, Roman, Egyptian).    We should think about the difficulty of composing and designing such a linguistically complex text – it really is impressive in its own right.  We should also reflect on the social context in which the language of a colonizer (French), the language of the populace (Arabic), and two consciously archaic languages (Latin and Egyptian), and their corresponding notations, evoke a complex history in a single text.  Once we start to become aware of the frequency of multiple languages, scripts, and numeral systems within a single social context, we have taken an important step towards analyzing social and linguistic variation in these traditions.


Ahlers, Jocelyn C. 2012. “Two Eights Make Sixteen Beads: Historical and Contemporary Ethnography in Language Revitalization.” International Journal of American Linguistics no. 78 (4):533-555.

Bender, Andrea, and Sieghard Beller. 2007. “Counting in Tongan: The traditional number systems and their cognitive implications.” Journal of Cognition and Culture no. 7 (3-4):3-4.

Chrisomalis, Stephen. 2010. Numerical Notation: A Comparative History.  New York: Cambridge University Press.

Pot, Hessel. 1999. “Roman numerals.” The Mathematical Intelligencer no. 21 (3):80.

Sebba, Mark. 2009. “Sociolinguistic approaches to writing systems research.” Writing Systems Research no. 1 (1):35-49.

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