Computers, statistics, and the grouping of rune forms

Espen S. Ore, Fiona J. Tweedie, and Craig Dougan

Published in: Deegan, Marilyn, Jean Anderson and Harold Short, Eds., DRH 98 (Digital Resources for the Humanities 1998), (OHC No 12; ISBN 1 897791 13 5), Office for Humanities Communications, King's College, London, pp. 117 - 127


From 1993 to 1995 the Norwegian Research Council (NRC) funded a project at the Norwegian Computing Centre for the Humanities (NCCH) which aimed at developing basic tools for a transliteration system for runes based on graphic form rather than graphemic value (Ore and Haavaldsen 1996; Haavaldsen and Ore 1997). A collaboration between the University of Glasgow and the HIT (Humanities Information Technology) Centre at the University of Bergen has tested some of the suggestions from the former project.

Identifying rune forms and styles

Runic nametag
Fig. 1: K(UN)NARA NIyR 698 (B197)

The medieval nametag (KUNNARA = Gunnar owns) in Fig. 1 was found in Bergen and is dated to some time after AD 1198, since it was found above a burned layer with a known date. For many of the inscriptions found in the excavation of the old Wharf, there is no more exact dating as they have been found in rubbish dumps which were used to fill in the harbour. These particular examples relate to medieval inscriptions in the sixteen-rune futhork, but there are even more difficult problems of dating with the Germanic twenty-four-rune futhark.1)

With a lack of other, external data, the use of rune forms for stylistic grouping might be an important aid. Runic palaeography might help not only in dating inscriptions but might offer evidence of style changes based on the geographic origin of the author. Ideally we might even recognize the various hands which have been used to carve the name tags with the name 'Gunnar' and so in some cases have supporting evidence for identifying certain 'Gunnar's as being the same person.

Runic nametag, detail
Fig. 2: Detail from Fig. 1

In a paper published in 1965 Bengt Loman discussed the runes used in an inscription from Rök, Sweden as a graphemic system, and introduced the idea of minimal pairs of runes which could be established based on a small set of features such as high or low stave position in the rune forms (Loman 1965). In Fig. 2 the difference between the 'K' and the 'N' rune is the direction of the twig (small side line), or its angle on the main stave - or the vertical placement on the main stave. The difference between the 'N' and 'A' runes is in the angle of the twigs compared to the base line, and between the 'K' and 'A' runes in the position of the twigs relative to the stave - or to the text base lines. The angles and positions relative to the text's base line are the deciding factors and not necessarily the positions and angles relative to the main staves: in so-called 'staveless' runes (also known as Hälsingerunes) this is shown in practical use. In his work from 1965 Loman compares a larger group of inscriptions from Norway and Sweden with his study of the graphemes used in the Rök inscription, and claims that they all belong to one graphemic system which, according to Loman, is different from the system used in contemporary Danish inscriptions. Later runologists have accepted the basics in the system suggested by Loman (e.g. Spurkland 1991), and so we decided to build on similar criteria, although with a finer mesh in our sieve at first so as to be able to check if the comparison could be as simple as suggested. Thus we will compare more data from each rune than Loman's typology suggests.

Our first aim, therefore, was to show that distinctive factors of a sort similar to those used by Loman can be recognized by analysis of image data. The next step was to see if a difference between styles could be established. This would mean that rune forms could be grouped in such a way that the differences between groups could be shown to be statistically significant. If such groups were found, we could then look for group combinations. If the N-runes in a population of runic inscriptions fall into two groups or types, N1 and N2, then the next test would be to see if there were other runes, for example A-runes, which also fell into groups, and if so, whether there would be any correspondence between the rune types: would inscriptions with N-runes belonging to type N1 have A-runes which belonged to A1 rather than A2?

The short result of our experiments so far is that within the main collection of samples from Bergen there are not clear correspondences between groups, but at the same time that there are inscriptions which stand out as 'abnormal' and that some of these do so in a systematic way.

The analysis - data collection

Relative values and fractions
Fig. 3: Relative values and fractions used for comparing rune forms

Loman's and later scholars' criteria for defining runic graphemes have been based on abstract models of the graphic forms: by this we mean that no absolute measures have been used. We have decided to follow this approach. Whether this is acceptable or not, or whether the forms change with size is something that has to be tested. A simple example of how relative measures are obtained can be seen in Fig. 3 where HK1 is the fraction H2/H1. Angles are calculated from x and y position measures of connection points and end-points of lines. With this relative measuring it should not make any difference how we obtain the measures. Some are taken using measuring tools in the Image software distributed by NIH,2 and some are taken by hand from prints. All measures are normalized to a coordinate system with origo in the upper left corner, but apart from that no transformation is performed. These pixel-based measures are stored in a database where each record holds data from one individual rune. The fractions and angles are computed automatically before they are exported for use with the statistical software.

Tests of the selected relative measures were performed in the first half of 1998. From around fifty inscriptions about 221 individual runes were collected. Most of the inscriptions were of a fairly similar type: name tags. In addition there were some other kinds of inscriptions including futhorks: inscriptions with the runic alphabet. The individual rune forms selected are (when the runes are seen as alphabetic characters): A, E, F, H, K (+G), L, M, N, O, T, U, and Æ. Of these F, H, M, and O have two twigs; K, L, N, and U have twigs on the right side of the stave; A has a twig on the left side; and Æ has a twig which crosses the stave in a way that makes it possible to interpret the form as a development from the form of the A-rune. The H-rune has two twigs crossing each other more or less in the middle of the stave, and the O-rune has two twigs on the left. The E-rune in these inscriptions has a dot at middle height in the stave.


The variability found in the data obtained from the inscriptions can be partitioned into two sections: the variability between characters, that is what differentiates a K-rune from an A-rune, for example; and the variability within characters, that is how K-runes, for example, differ amongst themselves, whether on the same inscription or not. An internal report by Dougan et al. (1998) details how classification of runic characters can be carried out using a subset of the variables considered. In this paper we shall concentrate on the variation found within each rune to examine whether styles of carving can be identified.

We shall investigate each rune by performing cluster analysis: a technique where the interest is in identifying groups of data points, where no previous knowledge of groups is available. It will be suitable for this situation as we wish objectively to find groups within the data. We detail the results from each rune in turn below.


This cluster analysis is shown in Fig. 4.3) Here there appear to be three clusters, apart from runes from B026 (5 and 6) and B051 (10) which are completely different. The first is made up of runes from B011 (2) and B023 (5), the third from the samples from B106 (14 and 15), and the remainder make up the central cluster.

F-runes cluster analysis
Fig. 4: Cluster analysis of the F-runes


O-runes cluster analysis
Fig. 5: Cluster analysis of the O-runes

The cluster analysis for these runes is shown in Fig. 5.4) Here three runes, B026 (2), B086 (6), and B216 (12) stand out from two main clusters. The other O from B026 is observation 1.


These runes split into two clear clusters, with characters from inscription B171 being outside both. The first cluster contains characters from B086, B176, B206, and B246, while the second contains three Us from each of B106 and B251, as well as runes from B121 and B146.


It appears that most of these runes fall into a cluster, with B116, B081, and B006 outside. Different physical surfaces may affect the measurements for B006 and B081. B116 is on the back side of what looks like a tally stick.

T-, N-, M-, A-, L-, K-, and Æ-runes

No clusters are apparent in these runes. In some cases, for example B046, runes from the same inscription are similar, while in others, notably B026, the letters have very different styles. Runes from B081 and especially B026 appear as outliers in several analyses.

Perhaps disappointingly, few of the runes considered gave rise to clusters of inscriptions. Indeed, in only a few cases did runes from the same inscription appear similar. In the case of several inscriptions, physical constraints are likely to have affected the carving. For example B006 is carved on a cross, while B081 is carved on the curved surface of a bowl.

B026 side a
Fig. 6: FUÞOR B026 (part of side a)

B026 side c
Fig. 7: FUÞOR B026 (part of side c)

However, the case of inscription B026 is of interest. In the runes that appear on this inscription (each character appears twice in the sampled data) one of the runes (an 'o') stands out from the others, while the other rune appears amongst the other examples of that character. The difference in the appearance of the runes on the two sides shown in Figs 6 and 7 may be an example of a teacher's display and a learner's experiments. The o-rune (second to last in both figures) shows a non-standard form in the 'teacher's' inscription while the 'student's' inscription shows a more normal form for Christian times in Bergen (there is no dating for this inscription). Side b of this inscription has not been used in the statistical comparison but the o-form is worth looking at (see Fig. 8).

B026 side b
Fig. 8: FUÞOR B026 (part of side b)

The 'o' here might represent an intermediate form between the non-standard but well-carved one in B026a and the standard but rough form in B026c. The inscriptions in B152 and B026a both have a non-standard o-rune - non-standard in medieval Bergen that is. To consider objectively the classification of the o- and f-runes from B152, we carried out a discriminant analysis on these data. Discriminant analysis concentrates on data from a known group, that is, data from runes that we are sure are 'o's, or 'f's, and then uses this information to predict the group of new data, here the o- and f-data from inscription B152. As combinations variables which are highly correlated cannot be used within discriminant analysis, the variables used here were Size, Top, and angle for both twigs, as well Twig 1's location on the Stave. To estimate the error rate that would be expected when considering new observations, cross-validation was carried out, and the discriminant function correctly classified 96.7 per cent of the data, that is twenty-nine out of thirty runes. The mis-classified observation is an 'o' from inscription B216 (12 in Fig. 5) which is classified as an 'f'. It would seem that the function is a good classifier of these characters. The new data, from inscription B152, was then presented to the discriminant function. Both characters were classified as being 'o's.

Clusters of o- and selected f-runes
Fig. 9: Cluster analysis of o-runes and particular f-runes and Angle for both twigs, as well as Twig 1 location on Stave.

Number 2 = B026a, number 15 = 'o' from B152, and 16 = 'f' from B152. These three runes are from inscriptions accepted as non-normal in a medieval Bergen context based on traditional palaeographic evaluations.

MIyR 670
Fig. 10: BOTLAIFRA NIyR 670 (B152)

It has been suggested (see for instance NIyR) that inscription B152 has been written by a person from Gotland. Both the name 'Botlaifr' and the rune forms have been considered abnormal in a Bergen context. In B026 we find that the 'teacher' inscription also shows a rune 'o' with the twigs placed to the right and not to the left of the stave. The 'student' inscriptions on the other hand place the twigs on the left - although in one (B026b) pointing up to the left instead of the expected down to the left.6)


We have seen that the statistical analysis of shape can highlight similarities and differences within and between runic characters, objectively confirming hypotheses based on philological grounds. While no obvious clusters have been found within most of the runes, the analysis has highlighted the heterogeneity of the B026 and B152 samples.

Variation between runes can be of two different kinds: the first is where there are small differences, which can be found between individual runes of the same value (the length of a twig in one 'a' may be slightly longer than the length in another in the same inscription). This kind of variation has rarely been found in such a way that it is possible to claim that forms belong to different styles, given that the variation within texts written by the same hand is large enough to allow the variants to co-exist. In the other kind of variation it is uncertain whether the forms are indeed variants, or are actually different types. The 'o'-runes in B152 and B026a as opposed to a more standard Bergen-form as in B026c seem clearly different. But for historical reasons one can argue that both go back to a form with the twigs crossing the stave, and this makes the form in B026b especially interesting. In the analysis of the rune forms, left or right placement of the twig(s) on the stave is only one factor, so we suggest that the analysis gives 'the correct' answer when it places the 'o' and 'f' among the 'o'-s in the overall analysis. We are planning further work based on this.

The data used for this project will be made available for downloading on the World Wide Web,7 and we suggest future research where corpora of rune forms are constructed in which comparable numbers of rune forms from different locations are compared. The runes from the Bergen excavations are mainly on wood and should be compared with other wood inscriptions both from Norway and from Scandinavia. A special comparison should probably be made both within inscriptions on stone and between inscriptions on different media. Where possible we also suggest corpora built from inscriptions with known dates.


1 'It is a sad fact that among the inscriptions executed in the older or Germanic futhorn;ark, ... , there is not a single one that is HISTORICALLY datable' (Antonsen 1998).

2 NIH Image is a public domain image-processing and analysis program for the Macintosh. It was developed at the Research Services Branch (RSB) of the National Institute of Mental Health (NIMH), part of the National Institutes of Health (NIH).

3 Fig. 4 numbers: B011: 1, 2, 3; B023: 4; B026: 5, 6; B046: 7, 8, 9; B051: 10; B056: 11; B066: 12; B086: 13; B106: 14, 15; B117: 16.

4 Fig. 5 numbers: B026: 1, 2; B066: 3, 4, 5; B086: 6; B106: 7; B116: 8; B171: 9, 10, 11; B216: 12, 13; B251: 14.

5 Fig. 9 numbers: B026: 1, 2; B066: 3, 4, 5; B086: 6; B106: 7; B116: 8; B171: 9, 10, 11; B216: 12, 13; B251: 14; B152: 15, 16.

6 A very tempting explanation is that the 'teacher' has learned to carve runes outside Bergen while the 'student' is used to the Bergen way of carving runes.


Antonsen, Elmer H., 'On Runological and Linguistic Evidence for Dating Runic Inscriptions', in Klaus Düwel (ed), Runeninschriften als Quellen interdisziplinärer Forschung (Walter de Gruyter, Berlin/New York: 1998).

Dougan, Craig, Tweedie, Fiona J., and Ore, Espen S., Runes: Can Nice Statistical Groups be Formed for Different Styles of Runes?, undergraduate project report (Glasgow, 1998).

Haavaldsen, Anne and Ore, Espen S., Runes in Bergen, Centre Report no. 71 (Norwegian Computing Centre for the Humanities, Bergen: 1997), Electronic edition at

Loman, Bengt, 'Rökrunerna som grafematiskt system', Arkiv för Nordisk Filologi 80 (1965), 1-60.

Ore, Espen S. and Haavaldsen, Anne, 'Computerizing Rune Forms', paper given at the International Conference on Medieval Epigraphy (St Hilda's, Oxford, 1996, now published:
Espen S. Ore & Anne Haavaldsen, 'Computerizing Rune Forms' in Roman, Runes and Ogham - Medieval inscriptions in the insular world and on the continent, eds. John Higgit, Katherine Forsyth and David N. Parsons, pp. 129-133, Shaun Tyas, Donnington, 2001)

Norges innskrifter med de yngre runer (NIyR) VI:1 1980. VI:2 (1990).

Spurkland, Terje, En fonografematisk analyse av runematerialet fra Bryggen I Bergen, Ph.D. thesis (Oslo, 1991).


Figs 1, 2, 6, 7, 8, and 10 are scanned from photos taken by Aslak Liestøl, The University Museum of National Antiquities, Oslo and published with permission from the Museum.

This version of the paper has been edited for the WWW on December 9. 2002, Espen S. Ore