The runestones turned their text towards the road – half of the inscriptions within 45 degrees of the road, against a quarter expected

Gunnar Ekholm (1950) asked where the runestones were raised. Torun Zachrisson (1998) has related them to farm, boundary and grave field, Lydia Klos (2009) has argued that most were raised at grave fields, and Shane McLeod (2014) has objected that this overstates the grave fields at the expense of other places, such as the roads. Johan Bollaert (2016) compared stones along three Viking-Age roads with other stones in the same districts and found that the stones by the roads more often have striking ornament and more often belong to monuments of several stones, which supports that they were raised to be seen.

What is missing is a measure of how the inscription itself was turned. A stone may stand by a road but turn its text another way. The aim here is to test whether the inscription was turned towards the road, towards the farm or towards a particular point of the compass, with the information on the inscription's direction that the register gives for some stones.

The hypotheses, measures and rules of interpretation were written down in an analysis plan on 29 October 2026, before any direction had been computed. The plan has the SHA-256 checksum cd73b962457fde0e… (see Data and code). Before locking only the number of records was known: 456 records in the register give a direction, 369 concern a single stone with one direction, 219 of these stand in place, and 88 of the 369 mention a road with a compass point.

The plan tests four hypotheses with Holm correction: H1 that the directions are not evenly spread over the compass, H2 that the inscription is turned towards the road, H3 that it is turned towards the farm and H4 that bridge and road stones are turned towards the road more than others. A hypothesis holds when Holm p is below 0.05 and the direction is the same with p below 0.05 in both halves.

The plan did not contain the project's fixed sensitivity analyses, which are built for associations between two traits and not for directions. The corresponding steps for directions were therefore fixed in an addendum plan on 31 October 2026 (SHA-256 4da9710de49fa2b6…), before they were computed. Two of the steps, the halves and the source of the road, were already in the main plan. A check of re-erected stones was made after the main run on 29 October with a different word list; in the addendum plan the word list was locked before the step was computed.

• The stones. Swedish Viking-Age runestones in the Scandinavian Runic-text Database (Rundata) that still stand in place and have a known location, and whose record in the Swedish National Heritage Board's register of ancient monuments concerns just that stone and gives one direction with the words "faces" and one of sixteen compass points: 219 stones. Runestones only.
• The road. First the register's own statement of the stone's position relative to a road ("5 m E of road"; the road then lies in the opposite direction): 69 stones. Otherwise the nearest registered route or road marker within 500 metres. 123 stones with a road in all.
• The farm. The nearest registered village or farm site within one kilometre: 94 stones.
• The directions are computed as bearings from the stone, with north as 0 degrees and the compass points in steps of 22.5 degrees.
• The halves are the project's fixed division parish by parish.

4.1 The measure. For each stone the cosine of the angle between the inscription's direction and the direction to the road is computed: 1 when the inscription faces the road straight on, 0 when it faces sideways and −1 when it faces away. The mean over the stones is compared with 9,999 shuffles in which the inscriptions' directions are redistributed among the stones within the same province, so that each province's general pattern of directions is kept. The test is one-sided. The share of stones within 45 degrees of the road is also reported; if the direction were random it would be a quarter.

4.2 The other hypotheses. H1 is tested with Rayleigh's test of uniformity (Mardia & Jupp 2000). H3 is tested like H2 against the direction to the farm. H4 compares the mean cos towards the road between bridge and road stones and the others, with the label shuffled within the province, two-sided.

4.3 Correction and replication. Holm correction (Holm 1979) over the four tests. Each hypothesis is also tested in each half on its own.

4.4 The sensitivity analyses under the addendum plan: the halves; without one province at a time (provinces with at least ten stones with a road; significance required only where at least two thirds of the stones remain); the parish as the unit, with one value per parish; one stone per secure carver; without re-erected stones; without stones the National Heritage Board's register Runor (2020) gives as moved; with today's rule for moved stones; only roads from the register text; and only registered routes and road markers. A step holds when the mean cos lies above the expected value and p is below 0.05.

4.5 Deviations from the plan. None.

5.1 Towards the road (H2). Of the 123 stones with a road, 50 percent turn the inscription within 45 degrees of the road. The mean cos is 0.37 against 0.01 expected, p = 0.0001, the lowest value 9,999 shuffles can give, and Holm-corrected p = 0.0004. Half A: 71 stones, mean cos 0.45, p = 0.0001. Half B: 52 stones, mean cos 0.26, p = 0.019. H2 holds by the plan's rule. In plain words: of the stones where we know where the road ran, half turn their text towards the road, within 45 degrees either way; if the direction were random, a quarter would.

5.2 The compass, the farm and the bridges (H1, H3, H4). The directions are spread evenly over the compass: Rayleigh's test p = 0.49. West is the most common (37 stones), then north (26), east (25) and south (25); 32 percent face south, south-east or south-west. Towards the farm: mean cos 0.01 against -0.02, p = 0.30. The bridge and road stones (9 with a road) are not turned towards the road more than other stones: p = 0.86. None of these holds.

5.3 The sensitivity analyses. All hold:

• Half A (71 stones): mean cos 0.45 against 0.04, p = 0.0001.
• Half B (52 stones): mean cos 0.26 against 0.05, p = 0.016.
• Without one province at a time: without Uppland (62 stones left, half, so only the direction is required) mean cos 0.50, p = 0.0001; without Södermanland (92) 0.29, p = 0.0001; without Östergötland (113) 0.36, p = 0.0001.
• The parish as the unit, 76 parishes (123 stones): mean cos 0.36 against 0.02, p = 0.0001.
• One stone per secure carver, 20 carvers (93 stones): mean cos 0.38 against 0.03, p = 0.0001.
• Without re-erected stones, 14 removed (109 stones): mean cos 0.43 against 0.02, p = 0.0001.
• Without stones Runor gives as moved, 10 removed (113 stones): mean cos 0.35 against 0.01, p = 0.0001.
• With today's rule for moved stones none of the 123 counts as moved; the result is the same as the main test.
• Only roads from the register text, 62 percent within 45 degrees (69 stones): mean cos 0.49 against 0.07, p = 0.0001.
• Only registered routes and road markers, 28 percent within 45 degrees (80 stones): mean cos 0.16 against 0.01, p = 0.020.

The addendum plan's word list for re-erected stones hits 29 of all 219 stones; the check after the main run, with a wider word list, hit 58. Both give the same result.

What the finding says. Those who raised the runestones turned the text towards the road. It holds in the whole material, in each half, without Uppland, parish by parish and with one stone per carver, so it does not depend on a few places or workshops. It also holds without the stones that have been re-erected, which could otherwise have been turned towards today's road. That the directions are otherwise spread evenly over the compass and do not follow the farm shows that it was the road, not the sun or the home, that decided how the stone was turned.

Against earlier research. The result gives a measure to the idea that the stones by the roads were raised to be seen (Bollaert 2016) and to McLeod's (2014) objection that the roads have been underrated. It does not contradict that many stones were raised at grave fields (Klos 2009): a stone can stand at a grave field and turn its text towards the road past it.

Weaknesses, in order of weight.

1. The road is often today's road. The register text gives the road at the time of the survey. With only registered older routes and road markers the association is weaker (28 percent within 45 degrees, p = 0.020) but goes the same way. Where a later road follows the old line both measure the same thing; where it does not, the association becomes weaker, not stronger.
2. The selection. Only 219 stones have a direction in the register, and we do not know what decided which stones received such a statement.
3. Re-erections. The word search does not catch every stone that has been re-erected. The result is, however, stronger without the stones it finds, not weaker.
4. The resolution. The directions are given in sixteen compass points, that is in steps of 22.5 degrees.

What would overturn the finding. If the association disappeared when the roads were measured on the oldest land-survey maps, or if a new survey of more stones' directions gave an even distribution relative to the road.

The runestones turned their text towards the road: half of the inscriptions face within 45 degrees of the road, against a quarter if the direction were random, and the association withstands every sensitivity analysis. The carvers wrote for those who passed by. The next step is to measure the roads on the maps of the seventeenth and eighteenth centuries.