The style groups' dark number

When Anne-Sofie Gräslund sorted the runestones by the shape of their rune bands and animal ornament, research gained perhaps its sharpest tool: a runestone can be dated to within a few decades without a single year in its text. The style groups today carry much of what we believe we know about the end of the Viking Age – when the carvers began to sign, when the prayers arrived, how the cross spread.

But a tool only sees what lies in its light. This article asks the question that is rarely asked: which runestones do the style groups see – and which stand in the dark? The answer is that more than every third runestone lacks a style group in the Scandinavian Runic-text Database, and that the loss is not random. The stones that are missing are systematically the damaged, the uninterpreted and the peripheral ones. And they do not behave like the visible ones.

The tool that dates the animals

Gräslund's system runs from RAK, where the rune band has straight ends and no animal head, through the bird's-eye-view Fp and the cross-band style KB to the profile styles Pr1–Pr5, where the animal is seen from the side and grows ever more slender and elongated. The order has been tested against coin-dated hoards and the stones' internal references, and it holds: when we ourselves test Uppland's runestones by seriation, as we show further down, the traits of text and content follow Gräslund's order by a clear margin. Nothing in this article questions the system. The question is what the system does not see.

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Who stands in the dark

The pattern is the same wherever one cuts. Damage weighs heaviest: whoever wants to date a damaged stone has the style group's help in about half of the cases, for a whole stone in five of six. The difference is so large that chance is excluded as an explanation – the probability that it would arise by chance is less than one in a quintillion. Nor is it a mystery: the ornament sits on the surface, and it is the surface that weathers, cracks and gets walled in. But the consequence is the same whatever the cause. The stones that are hardest to read are also the hardest to date, and every chronological conclusion rests on the whole, interpreted stones in the well-preserved provinces.

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The objects beyond the runestones belong to the picture too: grave slabs and rock faces have a style group in 29 cases out of a hundred, loose objects never. That is expected – the system is built for runestones – but it means style dating does not reach there at all.

The invisible are not like the visible

If the nine hundred stones without a style group were a random sample, the dark number would be an annoyance and nothing more: conclusions from the visible stones would hold for the invisible as well. That can be tested. The signature – the carver writing their own name – is a trait that needs no style assessment to be counted, and one research usually ties to the later style groups.

The damage must first be kept apart: a damaged stone may have lost both its ornament and its signature, and the connection then looks stronger than it is. We therefore compare whole stones only, without lost runes. Among Sweden's whole runestones with a style group, 102 of 642 are signed, 15.9 per cent. Had the whole stones without a style group had the same mix of styles, about 16 in a hundred would be signed. In reality it is 8 of 132, 6.1 per cent. So few signatures among so many stones arise by chance about once in two thousand.

The stones without a style group thus sign like the RAK stones, the group counted as oldest – not like the average. There are two readings, and both have consequences. Either the unstyled stones are not randomly spread in time but lean early – then the chronological curves drawn on the styled stones are skewed, because an early third is missing. Or the loss reflects how the style assessments were made – which stones were examined, drawn and fitted in – and then the style groups' coverage is itself a historical source that no one has read. The figures cannot tell the readings apart. But neither of them permits treating the invisible stones as if they did not exist.

RAK: the category of what is missing

The earliest group, RAK, is defined not by a form language but by the absence of one: straight band ends, no animal head. That works in Uppland, where RAK is a small minority surrounded by datable neighbours. But see what the category does to other corpora:

In Denmark virtually every styled runestone is RAK, in Norway every single one, in Västergötland and Småland three of four. If RAK is read as a date – roughly 980 to 1015 in Gräslund's chronology – nearly all of these corpora become early by definition, not by observation. For Denmark there are independent anchors pointing the same way, but in every statistical comparison between regions the circle closes: whoever counts "early" and "late" stones per region is largely counting where animal ornament was practised, not when the stones were raised. Outside the Mälaren valley, RAK is less a date than a note that there is no animal to date.

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What it means for research's conclusions

Every study that sorts runestones by style group – when signing began, when a prayer formula came and went, how the crosses spread, our own statistics included – in fact concerns the two thirds of runestones that have a style group, and that two thirds is selected by preservation, interpretation and geography. That does not make the conclusions wrong, but it makes them conditional in a way that is seldom written out.

The simplest remedy costs one line: reporting the coverage together with the conclusion. "Among the styled stones" is a different statement from "among the stones", and the reader should be told which one is being made – with numbers: how many stones carry the curve, and how many stand outside it. We have begun doing so in our own articles, and the pattern in this article is the reason.

The dark number can be lit

More can be done than reporting. Three lamps already exist:

• Seriation on the traits of text and content. We have ordered Uppland's runestones by language traits, formulas and content, without using the ornament as input, and tested the order against the styled stones: it follows Gräslund's chronology with rank correlation 0.543 and estimates style-dated stones' time with a mean error of 21 years, against 25 if one guesses the mean year. The rank correlation means the order is largely right even where the years are uncertain; the connection stands within individual districts. The gain is that the method needs no animal: of Uppland's 374 runestones without a style group, 317 receive a placement in time, with wide but stated uncertainties. The placements are shown stone by stone in Vitki's research view.
• The text model's dating. The probability model in Vitki, which reads and fills rune sequences, also dates: in cross-validated tests it hits the right century for 58.5 per cent of the runestones, and in 94.8 cases out of a hundred it is at most one epoch off. That is coarse beside the style groups' decades – but it is a dating that reaches every stone with readable text, including the nine hundred in the dark.
• What research already knows but the database does not hold. In the style field one glimpses assessments that never became proper entries: references to oral statements and printed supplements, and 73 stones carry their style group with a question mark. The literature knows more than the database. Collecting style assessments from Sveriges runinskrifter and later examinations into the database's style field would be the cheapest single way to truly shrink the dark number.

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What the figures do not say

• The dark number is the database's, not research's. We measure Rundata's style field. Style assessments may exist in the literature without standing there – but every study built on the database, our own included, still inherits exactly this loss.
• The signature comparison has two readings. That whole stones without a style group sign like the oldest ones may mean they are early, or that style assessment has passed over a certain kind of stone. Our figures cannot tell the readings apart; that requires dating the unstyled stones by another route.
• The seriation is tested in Uppland. Outside Uppland we do not yet know how well the traits of text carry a time order; within carvers the connection is weaker, as expected when a carver's active years are few.
• A style group with a question mark counts as a style group. We count generously: even uncertain assessments stand on the lit side. The dark number is thus under- rather than overestimated.

How we did it

• The material: all Viking-age inscriptions in the Scandinavian Runic-text Database (3.1, 2018). A runestone is what Rundata calls a runestone or fragment of one; a style group counts when the style field gives anything other than "?". Damaged means lost runes or lost text in Rundata's reading. Signed means Rundata marks the carver as signed (S), not merely attributed.
• The tests: the differences in style-group coverage and signing are tested with Fisher's exact test, and the signing among the unstyled against the expected share with an exact binomial test; all signing comparisons concern whole stones only. The seriation's validation is cross-validated against the style-dated stones (leave-one-out), with robustness checks without crosses, without the voyage stones, without the changing language traits, and within districts and carvers.
• The scripts: utdata/sprakprov/stilgrupper.py and utdata/sprakprov/morkertal.py in the repository; the seriation in r/chronology.R. Every figure in the article is read from the scripts' output with automatic checks.

Sources

• Scandinavian Runic-text Database (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: Stockholm University.