The Malt stone – calculated instead of interpreted

On 3 April 1987 the owner of the farm of Ågård by the Kongeå river in Jutland tried to get rid of a stone that the plough had struck again and again. As it was pushed towards the bank down to the river, it turned over and 153 runes came into view. Since then the Malt stone has been read as a memorial with a riddle about the sun and as an account of a funeral ale and the god Thor. It has been read as a greeting to everyone who sees it, as a curse, as a ritual for driving out a dwarf, and as a text in which hidden runes spell the words 'with Freyja'. Seven scholars, seven meanings. Of 133 pairs of interpretations that say something about the same part of the text, only 25 agree.

It was this stone that made me start working on Vitki. It was not because I had an eighth interpretation. It was because there were so many, and so little to tell a good interpretation from a poor one. We ought to be able to understand our history better than that. Instead of choosing the interpretation that sounds best, we ought to be able to let the runes themselves decide, together with everything we know about how people wrote in the Viking Age.

This article is an attempt to do just that. We let probability theory read the Malt stone. It is a model that has learned the runic language from thousands of other runic inscriptions and has never seen any interpretation of the Malt stone. It gives, for every word, how probable it is, and it has been tested on 808 stones where the answer is known.

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The ground: what everyone agrees on

Before anything can be interpreted, the runes must be read, and there the situation is better than its reputation. Runologists agree on 147 of the 153 runes, 96 per cent. The stone is a reddish, layered gneiss, weighing 2,405 kilos and about 220 centimetres high. The runes stand in eight rows: two vertical ones at the top, here called A1 and A2, and six horizontal ones below them, B1 to B6. The vertical row A2 is the whole runic alphabet. A small man's face is carved next to the top row.

Between the runes the carver cut dividers. They are the most important ground we have, because they show where the carver himself thought something ended. Between two dividers the runes stand without spaces. This is what the stone says, with its dividers as dots. Square brackets mean that the readers disagree about that particular rune:

• A1: suaai · titultitul
• A2: fuþąrkhniastbmlʀ (the rune row)
• B1: huaʀisi · alistiąsa · huaʀis[i]
• B2: uifrþuʀ · karþi · afraftasinifauþr
• B3: kul · finʀ · fal[s] · taitirunąʀ · u
• B4: [a]iuinrunąʀ · suli[·]alta · huaʀ · [a sign that looks like three t-runes bound together]
• B5: utu · tuuutbilik[i]kʀ · tuʀra[ki]
• B6: tuli

The rune ą is the one Rundata writes o, and ʀ is an r-sound that later disappeared. The only thing all seven interpretations read alike is the beginning of row B2: a man, Vífrøðr, 'made' something. Everything else differs. That is not because the runes are illegible. It is because the runes between the dividers have to be divided into words and understood, and there every interpreter has made his own choices. Those choices are what probability theory can test.

The model that reads – without having seen the stone

The reading is made by Vitki's probability model for runic text – the same model that today reads damaged inscriptions in the app. How it is built, how it is tested in six different ways and how well its percentages hold, we tell at length in an article of its own, Runorna som fattas. Here the short version will do. The model has learnt spelling and word order from tens of thousands of carved words in the Scandinavian Runic Text Database: for every piece of text it asks two questions – how probable is it that a carver wrote this word with these runes, and how probable is the word after the word before? The vocabulary also holds the words of the Eddic poems, at a small weight, since they are Icelandic and far younger than the stone.

What matters for the Malt stone is two things. First, the model divides the rune sequences into words by itself: a group between two separators is often one word, but sometimes two or three, and the model weighs every way of dividing it – precisely the choices that set the seven interpreters apart. Second, the Malt stone has been removed from everything the model has learnt. It has never seen Rundata's reading of the stone, or anyone else's.

Before the model saw the stone it was tested on 10,669 words with known answers: it read the right word in 81 per cent of cases, and its percentages are calibrated so that it is right about as often as it claims. One caveat follows into what comes next: for rare words – and the Malt stone is full of them – the model is still somewhat overconfident. When it claims 96 per cent about a word it has barely seen, it is right in 89.

The Malt stone through the model

Then the model read the Malt stone. Here are the words it reads with at least 30 per cent probability:

Translated into modern English, the most probable reading is this. Bold means more than 70 per cent, plain text 50–70 per cent and a question mark 30–50 per cent. Square brackets stand for runes the model cannot turn into a known word with at least 30 per cent probability. A slash marks a new row:

so(?) ever(?) [titultitul] [the rune row] who [isi] [alisti] of the Æsir who is(?) / [uifrþuʀ] made [afraftasini] father / [kul] Finnr(?) fals(?) joy(?) runes and runes of eternity [suli] [alta] who [the sign] [utu] [tuuutbilikikʀ] [tuʀ] Raggi(?) / Tóli

The model confirms the core. Rows B1 and B4 ask 'who' three times. Someone 'made' something, and a 'father' is named. There are 'runes of joy and runes of eternity', and the stone ends with the name Tóli. The word for runes of eternity, ævinrúnar, the model knows only from the Edda, where it occurs in a single place, in Rígsþula.

The model also suggests something new. The rune sequence raki in row B5 may be the man's name Raggi, found on a runestone in Södermanland (48 per cent). It reads fals with 32 per cent certainty, but the nearest word it knows is falls, 'of the fall', not 'hid', as several interpretations have it.

But the model does not fill the gaps. Five rune sequences it does not know as words at all: parts of titultitul, parts of alistiąsa, uifrþuʀ, afrafta and utu. One of them is a failure of the model, not of the runes. The name Vífrøðr, uifrþuʀ, occurs on four other runestones, but not in this form and spelling, and so the model does not recognise it. Nor does the model find the eldest of the Æsir, which several interpretations read in alistiąsa. It finds only asa, 'of the Æsir' (57 per cent). For utu the model's second-best suggestion is óttu, 'at dawn', the same reading as Heltoft's 'early in the morning'. But it gets only 9 per cent when the model is forced to choose.

If we add up the probabilities of the 30 words the model recognises, we get the expected number of right words. It is about 12. With the five unknown rune sequences, that is a third of a complete reading, and we do not know for certain which third.

What the language says about the disputed runes

Six points on the stone are disputed. The model cannot see the stone, but it can say which reading the language prefers. We let it read the text with all 64 combinations of the six points and worked out what share of the total probability each reading accounts for. Every alternative started with the same chance.

The language clearly settles three of the points:

• Row B4, rune 1. Stoklund and Heltoft read a, Grønvik k. The language gives k 97 per cent. With k, the runes u and k form the word uk, 'and', a common spelling: of the 1,164 times the word occurs in Rundata, 229 are spelled that way. With a, u would have to stand alone for 'and', which it does not do a single time. Here the eye and the language disagree, and that is why this rune should be measured first.
• Row B5, runes 22–23. Grønvik reads ki, Stoklund considers il possible. The language gives ki 96 per cent, because raki can then be a known man's name.
• Row B1, rune 23. Grønvik reads i, Stoklund a divider. The language gives the divider 86 per cent.

These three results hold when we change how much weight unknown words and the Eddic vocabulary get. They stay between 82 and 99 per cent. The other three points the language cannot decide. The divider after rune 14 in row B4 gets between 51 and 65 per cent depending on the settings. For s or i in row B3 the answer turns to i (89 per cent) if the Eddic words are removed. Rune 14 in row B5 stands at half and turns with the settings. The sign that looks like three t-runes the model cannot judge at all, since it may not be runes.

The price of a complete text

Why, then, have seven scholars arrived at seven different texts? Probability theory has a simple answer. A complete reading requires every word to be right at the same time. The probability of that is roughly the product of the words' probabilities, and it shrinks fast. For the model's most probable reading it is about 2 in a hundred quadrillion, a number with 16 zeros after the decimal point. That is less likely than winning the top prize in the Swedish Lotto two weeks in a row. And that is with the five unknown rune sequences left as unknown.

If we force the model to make a known word of every rune sequence, the text becomes complete, but the probability drops to a number with 21 zeros after the decimal point. Something also happens to the content. The name Vífrøðr is the one thing all seven interpretations agree on. It becomes vefr Þórr, 'Thor weaves', because the name's spelling is not in the model's vocabulary. Thor gets 54 per cent and 'weaves' 38. The rune sequence tuʀ becomes the god Týr, with 9 per cent.

That is no argument for Thor or Týr. It shows what happens when one demands a whole text from runes that are not enough for it. Every complete interpretation is a long chain of choices. The chain is never stronger than the product of its links, and where the links are weakest it is easiest to fill in what one already believes.

The Malt stone's text, as far as it goes

This is what we can say, with the support of probability theory and without borrowing any interpretation. The Malt stone speaks of a father, and a man, Vífrøðr, made something. It asks 'who' three times. It speaks of the Æsir, of runes of joy and runes of eternity, and it ends with the name Tóli. The rest is a handful of words with low probability and five rune sequences that no known language material can explain.

That is less than every interpretation promises, but more than nothing. It can be tested, and it shows where the next step lies. The rune where the eye and the language disagree, row B4 rune 1, can be measured in a 3D scan. A carved branch has a V-shaped profile, a crack does not. When the stone at the Museum at Sønderskov is scanned, the model can recalculate the text with the measured runes.

See for yourself

The maps, curves and models come from Vitki, an open tool for runestone research that you can download and run on your own computer from GitHub. The method is described in METHODS.md. The probability model is in src/runlm.py, and the test and the reading of the Malt stone in scripts/runlm_calibrate.py and scripts/malt_decode.py.

Sources and data

• Scandinavian Runic-text Data Base (Rundata), Department of Scandinavian Languages, Uppsala University. Open Database License.
• The Eddic poems and Snorri's Edda from heimskringla.no (Guðni Jónsson's edition).
• Grønvik, O. 1992. Runesteinen fra Malt i Jylland. Arkiv för nordisk filologi 107, pp. 1–34.
• Heltoft, L. 2017. Maltstenens tekst. Hvordan dæmonen uddrives. [Danske Studier](https://tidsskrift.dk/danskestudier/article/view/146816) 2017, pp. 27–100.
• Fridell, S. 2024. A New Interpretation of the Malt Inscription. Viking and Medieval Scandinavia 20. doi:10.1484/J.VMS.5.142571 (read in abstract).
• Stoklund, M. 1994. Malt-stenen – en revurdering. Runrön 9, pp. 179–202 (read through Rundata, Grønvik 1992 and Heltoft 2017).
• Thuesen, K. 1990. Maltstenen. UJDS-studier 7. Copenhagen: Museum Tusculanum (read through Heltoft 2017).
• Braunmüller, K. 1992. Der Maltstein. Versuch einer Deutung. Frühmittelalterliche Studien 26, pp. 149–164 (read through Heltoft 2017).
• Samplonius, K. 1992. Zum Runenstein vom Malt. Amsterdamer Beiträge zur älteren Germanistik 36, pp. 65–91 (read through Heltoft 2017).
• Photo: Hjart, Wikimedia Commons, CC BY-SA 4.0.