Interpret, he who can – cryptology as a method for the unread runic inscriptions

In ninth-century Baghdad the philosopher al-Kindi described how to break a cipher: count how often each sign occurs, and compare it with how often letters usually occur in the language. At the same time the first stones with the younger futhark were being carved in Scandinavia. Twelve hundred years later the same idea can help with the runic inscriptions nobody has been able to read.

The Scandinavian Runic-text Data Base holds 112 Viking-age inscriptions with at least ten runes in which the editors have not been able to interpret more than a single word. Are they broken texts, futhark rows – or something else entirely?

Runic writing is already a cipher

The younger futhark has sixteen signs for about thirty sounds. ᚢ can be u, o, y or w, and ᚴ can be k, g or ng. Reading a runestone is thus breaking a cipher in which one sign stands for several letters. Here we use the same kind of probabilities in a new way: not to read the texts, but to measure how much they resemble language. The yardstick is the 2,757 inscriptions the editors have interpreted.

The first tool: count the runes

In 1922 the cryptologist William Friedman introduced a measure called the index of coincidence: the chance that two signs drawn at random from a text are the same sign. In language some signs are very common, and the chance is then greater than if all signs were equally common.

The futhark rows stand out at once. In a futhark each rune occurs once, so the chance of drawing two alike is almost nil. But between language and non-language counting makes no difference: both groups have roughly the same distribution of runes as real text. Whoever carved an incomprehensible line used the runes about as often as in ordinary texts. Counting is not enough. It is order that gives the game away.

The second tool: which rune follows which

In English q is almost always followed by u. Runic text has similar rules: after ᛋ comes ᛏ one time in three, and after ᚦ usually ᚢ or ᛁ. We let a language model learn which rune usually follows the two before it, from all the interpreted inscriptions. Then we measured how hard the next rune is to predict in each text, in bits per rune. One bit is one yes-or-no question: in a real runic text about 3.0 questions are needed on average to guess the next rune. Shuffle the runes of the same texts and 5.1 are needed.

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We set the limits before we saw the results. An inscription counts as language-like if it is as predictable as at least one in ten real texts cut the same way. It counts as not language if it is harder to predict than 99 of 100 such texts, or lies closer to the shuffled texts than to the real ones. A futhark row has at least six runes in the order of the futhark.

What we found

The language test concerns the rune sequence itself, and that can be tested whatever it stands on. All objects are therefore included. But runestones, other stones and loose objects belong to different contexts, and we report them separately. When we say something about carvers, signatures or style groups, it applies to the runestones only.

The futhark rows are easy to recognise, such as G 311 on Gotland: fuþork · hnias tbmlR. Some deviate, such as DR EM85;470C: fuþrkhainsl. U 466 and U 522 in Uppland also contain futhark rows within longer sequences. 12 of the 18 futhark rows stand on loose objects such as rune bones and sticks.

The language-like ones are mostly fragments in which single words can be recognised: staina on U 549, karfastr on Sö 378, faþur on U 9. They lack an interpretation because they are broken, not because they are meaningless. These are the ones worth trying to read.

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In between stand four inscriptions, among them Öl Fv1976;96B on Öland: §A þursikfahinþrihufþahinmiramultikafran.

Those that do not resemble language form the largest group. This does not mean that the inscriptions lack language, but that the order of the runes does not resemble Old Norse as it is usually written on runestones. 27 of them stand on runestones, 21 on loose objects and 7 on other stones. Gs 3 in Gästrikland has ...a + nisauit × osis × ioiklku × ihbtmsr × l, and Vg 19 in Västergötland tua : rRbur · fuen : þua : isR · R...r :. No Old Norse words look like that. Among the runestones, Rundata's own notes call 9 of the 27 that do not resemble language nonsense inscriptions, but none of the 27 language-like ones. The test and the runologists thus often agree.

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What could they be? Research mentions several possibilities:

• Carvers who had not mastered writing. Rune sequences that look like writing but are not words. Marco Bianchi discusses such inscriptions in Runor som resurs (2010). Against this speaks the great pride the carvers took in their craft, as we show below.
• Abbreviations, codes or formulas. Things that meant something to the one who carved them, but are not ordinary text.
• The objects' own contexts. Coins, amulets and rune bones were used differently from runestones. Of the amulet U NOR1994;26A Rundata writes: "Nonsense inscription, magical?".
• Hard-to-read or misread runes. The test judges the editors' reading, not the object itself. Some of the inscriptions are known only from older drawings. If the reading is uncertain, so is the verdict.
• A mixture. A few inscriptions have both. On an earth-fast boulder in Södermanland (Sö 324) raiste stain þans at, "raised this stone in memory of", stands amid sequences that resemble no word, and Rundata itself notes "Nonsense?". So there is language there, just not throughout the text. But it is rare: most of the runestones that do not resemble language contain no known words at all.

Could the carvers write?

The carvers took pride in their craft, and some challenged the reader. On the Ågersta stone in Uppland (U 729) it says: Raði drængR þaR rynn se runum þæim, sum Balli risti, "May the man who is rune-skilled interpret those runes which Balli carved". At Nybble (Sö 213) and Skillsta (U 887) it is enough with Raði saR kunni, "Interpret, he who can". In Hávamál too the runes are knowledge to be interpreted: "Do you know how to carve? Do you know how to interpret?" (stanza 144).

In his dissertation Runor som resurs (2010) the runologist Marco Bianchi described runic inscriptions without linguistic content in Uppland and Södermanland, and suggested that they were more often carved in areas with few runestones, by less practised carvers. We can test that on the runestones. In Uppland and Södermanland the runestones that do not resemble language have a median of 45 other runestones within ten kilometres, the language-like ones 43. No difference in the direction Bianchi suggested is seen (p = 0.35). The groups are small, 19 against 16 runestones, so this does not rule out his idea, but it finds no support here.

At the same time, some of the incomprehensible sequences come from named carvers. U 811 at Hjälsta church, þuliak × oaRtþiol × atiurai × fasatiR, is attributed to Torgöt Fotsarve, who has 22 stones in the Scandinavian Runic-text Data Base. If the attribution is right, a practised carver cut a sequence that does not resemble language.

The figures cannot settle which explanation holds. Here we count runestones only, since coins, amulets and rune bones are hardly ever signed. Only one of the 27 runestones that do not resemble language is signed, against about one in nine interpreted runestones. But signatures belong to the later runestones. Runestones are dated by the style of their ornament (Gräslund 2006), and in the late style groups Pr3–Pr5, roughly 1045–1130, about one runestone in four is signed. In the early RAK, roughly 980–1015, only three in a hundred are. 14 of the 27 runestones have no style group, and among such runestones only four in a hundred are signed. With the same spread over the style groups as among the interpreted runestones, about three would be signed. One is. So small a difference arises by chance about one time in four. There is thus no evidence that the carvers behind these runestones were less practised or more anonymous than others. That is why we want to go further and test whether some of the sequences are codes.

What the style groups do not see

The style groups are one of runic research's most important tools. Anne-Sofie Gräslund divided the runestones by the shape of the rune band and the animal ornament, from RAK, where the rune band has straight ends without animal heads, to Pr5 with slender, elongated animals in profile. With them a runestone can be dated to within a few decades. The system applies to runestones, so it is natural that coins, rune bones and sticks have no style group. But among the runestones too the system sees only a part, and the part it does not see is not chosen at random.

Over a third of the runestones, 35 per cent, have no style group, and the loss is uneven. In Västergötland, Östergötland, Uppland and Södermanland about two thirds or more have a style group, on Öland, Gotland and in Småland fewer than half. The damaged runestones drop out most often: a Swedish runestone with lost runes has a style group in 54 per cent of cases, a whole one in 83 per cent. And of the uninterpreted runestones only 46 per cent have a style group, against 73 per cent of the interpreted ones.

This means that every conclusion built on the style groups, such as when the carvers began to sign or when a formula came and went, applies only to the runestones that have one. That includes our own analyses. And the runestones that are hardest to understand, the damaged, the uninterpreted and those outside the Mälaren valley and Västergötland, are exactly the ones least seen.

There is a further weakness. RAK describes something that is missing: a rune band without animal heads. In Uppland such stones count as the earliest, but there only 50 of 1,178 runestones are RAK. In Denmark 182 of 239 runestones are RAK, and in Västergötland 81 of 131. Whether RAK means the same time there as in Uppland we do not know. Read as a date, it makes most runestones in Denmark and Västergötland early by definition.

What we have learned

The article contains many figures. Here are the most important points, in the order they came.

1. There are three kinds of uninterpreted inscription. Of the 112, 18 are futhark rows, 35 are broken texts in which single words can be recognised, and 55 are sequences that do not resemble language. Four cannot be decided.
2. It is the order that tells, not the runes. The sequences that do not resemble language use the runes about as often as ordinary texts. The difference only shows when we ask how easy the next rune is to guess.
3. The objects differ. The futhark rows mostly stand on loose objects such as rune bones and sticks, 12 of 18. Among the runestones the language-like ones and those that do not resemble language are equally many, 27 of each.
4. The test and the runologists often agree. Among the runestones, Rundata's editors have themselves called 9 of the 27 that do not resemble language nonsense inscriptions, but none of the 27 language-like ones.
5. The language-like ones are worth reading. They are not meaningless but broken, and there the probability model can help with the gaps.
6. What the others are, we do not know. Nothing in the figures shows that the carvers were unpractised. The runestones that do not resemble language are not unusually seldom signed once the style groups are taken into account, and Bianchi's pattern of fewer stones in the district does not show in our data. The stones themselves speak of rune lore as something to be proud of. That is why we want to test whether some of the sequences are codes.
7. The style groups see only part of the stones. Over a third of the runestones have no style group, most often exactly the damaged, the uninterpreted and those outside the Mälaren valley and Västergötland. Conclusions built on the style groups apply only to the rest.

What the measure cannot do

• One yardstick for all objects. Four in five interpreted texts stand on runestones. Short texts on rune bones and amulets may differ from the language of the runestones without being incomprehensible.
• Unusual language looks like non-language. The model has learnt from the interpreted texts. A text in an unusual dialect, in verse or with its own spelling can look incomprehensible to it without being so.
• Danish and Norwegian inscriptions. The model has learnt mostly from Swedish texts. Among the Danish ones 12 of 24 are judged not language, among the Swedish 39 of 76. We compare each inscription with texts from the same country, but some bias may remain.

How we did it

• The material: all Viking-age inscriptions in the Scandinavian Runic-text Data Base (3.1, 2018). Inscriptions with at least two interpreted words are the yardstick for language; the others with at least ten runes in Rundata's reading are tested. Runes known only from older drawings and uncertain runes are counted. Dividers are not counted; lost runes split the text into pieces.
• The objects: from Rundata's information on object and material. Runestones are what Rundata calls runestone or fragment of runestone, including those that have been destroyed or lost and are known only from older drawings. Other stones are for example grave slabs, rock faces and whetstones. Loose objects are of metal, bone, horn or wood. Everything about carvers, signatures and style groups applies to the runestones only.
• The rune sequences: a Kneser–Ney model over three runes in a row (NLTK), trained in five rounds so that no text is judged by a model that has seen it. Each uninterpreted inscription is compared with 200 pieces of real texts from the same country, cut to the same lengths, and with the same pieces shuffled.
• Tests: Mann–Whitney for the number of other runestones within ten kilometres, runestones only. Signatures are compared within the style groups, with an exact probability for each stone (utdata/sprakprov/signaturer.py). The coverage of the style groups is counted in utdata/sprakprov/stilgrupper.py.
• The script: scripts/runlm_sprakprov.py.
• Correction 17 October 2026: the first version counted Rundata's alternative readings as text. 16 inscriptions then got their runes doubled, and 11 passed the ten-rune limit only because of that. Now only the main reading counts, and the test covers 112 inscriptions instead of 123. The groups and the Bianchi test have been recomputed. The weak tendency in Bianchi's direction that the first version showed disappeared.

Read on in Part II: [Interpret, he who can II – what stood in the gap?](/en/artiklar/tre-punkter-i-texten/) puts the language test to work on the gaps in the inscriptions that can be read, where our probability model proposes what stood there.

Sources

• Scandinavian Runic-text Data Base (Rundata), Department of Scandinavian Languages, Uppsala University. Open Database License.
• Al-Kadi, I. A. 1992. Origins of cryptology: The Arab contributions. Cryptologia 16(2), pp. 97–126.
• Bianchi, M. 2010. Runor som resurs. Vikingatida skriftkultur i Uppland och Södermanland (Runrön 20). Uppsala University.
• Bird, S., Klein, E. & Loper, E. 2009. Natural Language Processing with Python. O'Reilly (NLTK).
• Friedman, W. F. 1922. The Index of Coincidence and Its Applications in Cryptography. Riverbank Laboratories.
• Gräslund, A.-S. 2006. Dating the Swedish Viking-Age rune stones on stylistic grounds. In: M. Stoklund et al. (eds), Runes and their Secrets: Studies in Runology. Copenhagen: Museum Tusculanum Press, pp. 117–139.
• Hávamál, stanza 144, in Guðni Jónsson's edition of the Edda (heimskringla.no). The translation is ours.
• Kneser, R. & Ney, H. 1995. Improved backing-off for m-gram language modeling. Proceedings of ICASSP 1995, pp. 181–184.