The carver had the last word

Viðhugsi had this stone raised in memory of his good father. He lived in Ågersta. Here the stone shall stand between the farms. May the man who is skilled in runes interpret the runes that Balli carved.

So it reads on a runestone at Ågersta in Uppland, carved some time between 1050 and 1080 to judge by its ornament. The father's name can be interpreted in two ways, but there is no doubt about the carver: Balli puts his name last, after a challenge to anyone who can read. He was not alone. On the earliest runestones the carver is almost never named, but on the last ones the carver's name stands on more than one stone in three, and nearly always at the very end. The last word, which a generation earlier was often a prayer to God, became the carver's.

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The last word changes hands

We went through the 1,292 runestones in Sweden that have a legible text in the Scandinavian Runic-text Data Base. On 182 of them the carver wrote his name, with a carver's formula such as Balli risti, Balli carved. Nine signatures in ten stand among the last five words of the text. The prayer – God help his soul – usually comes last as well. And on the 36 stones that have both a prayer and a signature, the signature comes after the prayer, on every single one. The carver has the last word, after God.

So we can follow how the texts end. 740 of the dated stones have a surviving ending.

Around 1035, in the style group Pr2, 27 % of the texts end with a prayer and 12 % with the carver's name. A generation later, in Pr3, they are equally common, 22 % each. In Pr4, around 1085, the balance has turned: 7 % end with a prayer and 22 % with the carver's name. Among the last runestones, in Pr5, 38 % end with the carver's name and 3 % with a prayer.

The signature spreads

Counting all dated stones, not only those with a surviving ending, the carver's name stands on 3 % of the earliest (RAK) and on 38 % of the last (Pr5).

Our model compares stones by the same carver and in the same area. With it the share rises from about 6 per cent around the year 1000 to 28 per cent in the early 1100s – an increase of 22 percentage points, probably somewhere between 10 and 36.

The last bar needs an explanation. 28 of the 32 stones in Pr5 were carved by one and the same carver, Œpir, who signed about one stone in three that he made. That bar is therefore largely his. But the increase is not down to him: without Œpir's stones the share rises from 3 % in RAK to 23 % in Pr3 and 19 % in Pr4.

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Our hypothesis – and two tests

That carvers sign more and more often is known, especially in Uppland, and Magnus Källström has studied the signatures thoroughly (2007). What we add is the measurement with carver and area held constant, and the observation that the signature takes over the last place in the text just as the prayer leaves it. That calls for an explanation.

The nearest explanation is that rune carving became a trade: carvers with many commissions put their name on the work, as a master's mark – perhaps as advertising. That explanation has two consequences that can be tested.

Did the signature push the prayer aside? If the carver's name replaced the prayer as the ending of the text, a stone with a prayer should rarely have a signature – they would compete for the same place. We compared stones within the same style group (804 dated stones). A stone with a prayer was signed just as often as a stone without one from the same time. The odds ratio is 1.1, in practice no difference, and it probably lies between 0.6 and 1.9 (p 0.69: a difference of that size easily arises by chance). The prayer and the signature were chosen separately. The last word changed hands because prayers became fewer and signatures more frequent, not because one pushed the other aside.

Did the signature follow demand? If the signature was a master's advertisement, it should be most common where many stones were raised, for there were the most patrons and the most carvers to compete with. We counted how many runestones stand within ten kilometres of each stone and split the stones into three equal groups, from the sparsest districts (at most 22 stones within ten kilometres) to the densest (more than 55). In the later style groups, Pr3 to Pr5, when the signature was common, the share of signed stones is almost the same in all three: 25, 24 and 24 %. In a model with style group and province there is no association (p 0.29). The signature was not more common where the market was largest.

It followed the carvers. What makes the difference is the carver. Œpir put his name on 38 % of the stones we can read, Balli on 37 % and Ásmundr on 27 %. Fótr, who was active at the same time and also has many stones, signed 10 %, and Gunnarr, one of the early carvers, 3 %. Having many commissions did not by itself lead to a signature. It was something some carvers did and others did not.

So we state the hypothesis more sharply:

The signature spread as a custom among the carvers – from master to apprentice and between carvers who worked side by side – not in answer to the patrons' demand.

The tests have their limits: the number of stones within ten kilometres is a rough measure of demand, and the style groups divide time into steps of about twenty-five years.

How the hypothesis can be tested further

1. The carvers' network. If the signature was passed on between carvers, carvers who worked together or learnt from each other should sign about equally often, wherever they worked.
2. The words of the signature. The formulas vary – risti, hiogg, markaði – and sometimes praise follows, as in Balli's challenge to the rune-skilled. If a custom spread, the wording should follow the carvers' schools rather than the provinces.
3. The carver's own career. If signing was something a carver learnt or grew into, the share of signed stones may rise within one carver's career. That requires each carver's stones to be dated more finely than the style groups allow.
4. The costly stones. If the signature was a selling point after all, it should be more common on the largest and most elaborate stones. The stones' measurements exist for part of the material.

Caveats

• The dating rests on the ornament and is approximate, and the style groups were worked out for the stones of Uppland and Södermanland.
• Signatures are found by searching for carver's formulas in Rundata's normalised text, and a damaged text can hide a signature. So we follow the ending of the text only on stones whose ending survives.
• Many carvers are known precisely through their signatures, and unsigned stones have been attributed to them by style. The share of signed stones per carver therefore rests on the scholars' attributions.
• The last style group, Pr5, consists largely of Œpir's stones.
• An association in time is not a cause. The hypothesis explains the pattern, but other explanations are possible – for example that more people could read, so that a name on the stone found more readers.

See for yourself

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On how the prayer left the stones: The prayer fell silent – but the cross remained.

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.

Sources and data

• Scandinavian Runic-text Data Base (Rundata), Department of Scandinavian Languages, Uppsala University. Open Database License.
• 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.
• Källström, M. 2007. Mästare och minnesmärken. Studier kring vikingatida runristare och skriftmiljöer i Norden. Stockholm Studies in Scandinavian Philology, New Series 43. Stockholm: Stockholm University.
• Holm, S. 1979. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, pp. 65–70.
• Wood, S. N. 2017. Generalized Additive Models: An Introduction with R. 2nd edn. Boca Raton: CRC Press.
• Photos: Wikimedia Commons, with photographer and licence in the captions.