Category: Literacy and writing

CatCh ‘eM aLL? DIsCoVerIes In VeXIng seCret sIgns

If you’re one of the folks who follows me over on Bluesky (which, by the way, is a pretty cool place for nerds to gather; come check it out!) I’ve been promising a Sooper Seekrit project for weeks, throughout my European vacation. Turns out those two things are related! I spent the last two weeks on family vacation throughout Germany, the Netherlands, Belgium, and Luxembourg, touring museums and historical sites at a pace that exhausts almost everyone who sees the photos. And while I assuredly did take pictures of the usual tourist things, I figure someone else has taken a better picture of those than I would have. So what, pray tell, was I up to?

One word: chronograms.

A chronogram is a text (usually a line or two at most) that encodes a culturally meaningful date in numeral-signs that also serve as letters. In India and the Middle East, alphasyllabic or alphabetic numerals are used, but in early modern Europe, Roman numeral chronograms were all the rage, using the ordinary Roman numerals MDCLXVI both as numerals and as alphabetic letters, usually marking the numerals specially by making them larger or a different colour. So, for instance (my all-time favourite chronogrammatic composition) I noted that the American electoral year 2016 could be encoded as seXIst Mr. trVMp because X+I+M+V+M = 2016. (U and V both count for 5, and I and J both count for 1, in chronogrammatic practice.) And this is exactly the kind of thing they were used for in Europe: to celebrate, or denigrate, a person’s accomplishments, to memorialize the founding of a place, and so on. Why just stick a date on a cornerstone when you can do it up in semi-cryptic gold letters?:

A chronogram above the door to the baptistery of the cathedral at Aachen, Germany: saCrVM paroChIaLe DIVI IoannIs baptIstae, totalling 1766, also seen as MDCCLXVI at the bottom.

A few years ago I had agreed to contribute to an edited book after a fantastic Making a Mark conference at Brown. However, I was unhappy with the fit between the (fairly generic, not really new) presentation I gave there, and the volume’s focus on hidden, secret or other sorts of unusual writing. That’s when I remembered chronograms, and the idea I had had years ago. See, back in the late 19th century, a monomaniacal antiquarian named James Hilton (1815-1907) spent the better part of two decades collecting chronograms, publishing three giant volumes on the subject (Hilton 1882, 1885, 1895) and collecting thousands more that he never published (still held in the British Library). He seems to have been a delightful weirdo, almost entirely theoretically disinclined, a wonderful collector. But with three volumes of inscriptions, all with dates (almost by definition) and most with provenience, I saw an opportunity for a professional numbers guy to step in and do some analysis. Using a mix of theories ranging from cultural evolution to verbal art, I compared the Roman numeral chronograms to the other (Middle Eastern / South Asian) traditions and then did a deep dive on the Hilton corpus, analysing 10342 chronograms across 2681 individual texts. The European tradition has a centuries-long history of development, a craze between roughly 1650-1750, and then a decline into obsolescence. In the end, the book came out in 2021 as The Hidden Language of Graphic Signs, edited by my friends Steve Houston and John Bodel. My chapter (available in preprint form), “Numerals as Letters: Ludic Language in Chronographic Writing” is something I’m very proud of even though it’s a weird little topic.

When my wife suggested that we do a tour of Germany and the Low Countries a few months ago, I didn’t immediately think of chronograms. But for years it’s bugged me that, as obsessive as Hilton was, he surely wasn’t exhaustive. He relied on correspondents and his travels, inevitably. I knew that it was likely that his corpus overrepresented British chronograms and underrepresented Czech and Slovak ones, for instance. All of my analysis was based on what Hilton reported. But how hard would it be, I wondered, to find chronograms that are not in Hilton’s three big books? So I made a point, not of going to places we weren’t otherwise going, but just keeping an eye out, for the telltale signs of chronograms. It would be like Pokemon Go, only instead of imaginary monsters, it would be inscriptions. The areas we were travelling happened to be areas where chronograms were already numerous, so I thought I might find one or two.

Reader, I am pleased to report that it is not hard at all. Over the span of a couple weeks I found 23 chronograms “in the wild” – on buildings, in museums, wherever, and of those, 12 were not in the Hilton corpus (14 including two inscriptions that have two each):

  • 001: 1612, Aachen: IaCob breCht patrVo qVInta hIC LVX MartIa sIstIt VIXIt CanonICVs spIrItVs astra petIt
  • 002: 1593, Aachen: fataLIs ter qVInta DIes et bIna noVeMbrIs annIs seX natVs septVagInta fVIt
  • 003: 1804, Aachen: qVInto IDVs noVeMbrIs Coronato pIa atqVe obseqVIosa CIVItas aqVIsgranensIs gratVlatVr
  • 004: 1804, Aachen: Inter ContInVos eXVLtantIs popVLI pLaVsVs aqVIsgranVM IngreDIentI
  • 005: 1884, Aachen: MarIa foILane CeterIqVe sanCtI patronI hVIC aeDI sVbVenite restItVtae
  • 006: 1963, Luxembourg: saeCLa DeCeM repLens Legat Vrbs VestIgIa prIsCa
  • 007: 1727, Trier: 1) Deo sIbI sVIs VICInIs et posterIs opVs gratVM perfeCere; 2) VrbI et orbI LapIs hIC pIetateM LoqVatVr fVnDatIonIs
  • 008: 1738, Trier: 1) DefLorVIt X MartII In aetatIs sVae Vere praenobILIs et InsIgnIs aLtI rVrIs fLos; 2) paLLVIt X aprILIs III februarII eIVsDeM annI orta aLtI rVrIs
  • 009: 1720, Brussels: haeC DoMVs Lanea eXaLtatVr
  • 010: 1697, Brussels: haeC statVIt pIstor VICtrICIa trophaeI qVo caroLVs pLena LaVDe seCVnDVs oVAT
  • 011: 1697, Brussels: hiC qVanDo VIXIt Mira In paVperes pIetate eLVXIt
  • 012: 1698, Brussels: aVspICe CaroLo natIonVM ConatIbVs baVaro gVbernante brVXeLLa patesCIt oCeanVs

Now, I don’t think it’s possible to conclude that this ratio of about 50% holds across all periods and regions. Looking at it another way, there are 47 chronograms from Brussels in Hilton’s books; I found another 4. There are 21 from Trier; I found another 2. But frankly I thought that, given how many were already in the books, I wouldn’t find any, just by happenstance.

One of my favourite finds was at what used to be St. Nicholas’s chapel of St. Simeon’s Church in Trier, which now houses the Zur Sim Brasserie overlooking the renowned Porta Nigra. We just happened to stop there for lunch, where surely thousands of people have done so before, and as we were leaving, I found this on the wall (#011 above):

It was one of two places where we happened to eat on our vacation that turned out to have a chronogram (the other being much better-known, on Le Roy d’Espagne in Brussels’ Grand Place). It’s not like no one had ever noticed it before; it’s within sight of a major World Heritage Site. But I could only find one place in print discussing it: here (p. 130-131), in an 1100+ page German book on the archdiocese of Trier. Anyway once I found that one, my family knew they were doomed (in the way that all nerdy families eventually learn). And eventually, I found my favourite new chronogram of all (#012, above), in Brussels, at the Musée de la Ville. You might say, as my wife suggested, that it’s a … groundbreaking discovery. Or even that I’ve been afraid of being … scooped (I’m so sorry):

This is a silver ceremonial spade from 1698 created to commemorate the beginning of work on the canal from Brussels to the Sambre river. Like most such objects, it has clearly never touched dirt, but it is exquisite. My photo (through glass) doesn’t do it justice, but you can see the online museum record here for much better photos (but not mentioning that it has a chronogram). You just have to imagine me hopping about taking about a dozen photos of a freaking shovel. But chronograms, while common on inscriptions on stone, or on medals and coins, or in books, are rare on other sorts of artifacts. So yeah, I liked the shovel; got a problem with that? My wife, who works as an archivist professionally at an institution that has a number of non-chronogrammatic spades from various groundbreaking ceremonies, acknowledged that this one was cooler.

Anyway, if I were to discuss every one of the inscriptions above, this post would be far too long, so let me wrap up with another favourite (#006 above), this one from Luxembourg, on the Bock Casemates, marking 1000 years of the city’s history (963 to 1963):

Twentieth-century chronograms are rare and almost always invoke a much earlier history. But this is undoubtedly a modern chronogram in a modern font. And the message is clear: saecla decem replens legat urbs vestigia prisca; or, roughly “Filling ten centuries, the city leaves us its ancient vestiges.” It does indeed. Hilton, having been dead for 56 years at the time, can be excused for not having this one in his books.

As the title of my post suggests, I did not “catch ’em all”, not even all of the ones in the cities I visited. I didn’t try. But surely the fact that I could find a dozen without even going out of my way suggests that, like Pokemon, there are a lot more out there to be found. So if you live anywhere in Europe (especially Germany, Austria, Benelux, but also Czechia, Hungary, northern Italy, eastern France) in a place that has lots of surviving 17th / 18th century buildings, you can play along too! Feel free to comment with photos of your favourite chronograms and I’ll tell you what I know about them. After all, why should James Hilton and I have all the fun?

References

Chrisomalis, Stephen. 2021. Numerals as letters: ludic language in chronographic writing. In The Hidden Language of Graphic Signs: Cryptic Writing and Meaningful Marks, Stephen Houston and John Bodel, eds, pp. 126-156. New York: Cambridge University Press. https://doi.org/10.1017/9781108886505.009

Hilton, James. 1882. Chronograms, 5000 and more in number excerpted out of various authors and collected at many places. London: E. Stock.

Hilton, James. 1885. Chronograms continued and concluded, more than 5000 in number. London: E. Stock.

Hilton, James. 1895. Chronograms collected since the publication of the two preceding volumes. London: E. Stock.

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.

 

500px-Oudjat.SVG
Source: wikimedia.org

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.