Time-reckoning in Iceland

before literacy



Published in Clive L.N. Ruggles (ed.), 1991. Archaeoastronomy in the 1990s. Loughborough, UK: Group D Publications. Pp. 69-76.

Introductory remark

The history of science in Iceland is a field of study which has received little attention to date. Many of the fundamental works are old and outdated, and authors with basic scientific knowledge have been sadly absent from the arena. The present paper is a partial effort to remedy this situation.

The subject matter of the paper belongs to archaeoastronomy in the sense that it deals with astronomy and time-reckoning in an illiterate society without the knowledge and instruments of classical or late medi-eval times. However, it lacks any strictly archaeological input at present. Owing to adverse climate and the limited powers of the small and scattered medieval population, only extreme luck would produce significant archaeo-astronomical findings in Iceland. Indeed, an effort was made recently to see if archaeology could bring us somewhat closer to the twelfth-century astronomer Star-Oddi, but the archaeological study turned out not to be particularly successful in this respect (Ólafsson et al. 1992).

The Vikings

Traditionally, the Vikings originating in Scandinavia in the early Middle Ages are associated with violence and brutal force. However, the views of modern scholars paint a less mono-chromatic picture (e.g. Foote and Wilson 1984; Jones 1986; 1990; Graham-Campbell 1989). The present paper relates to one aspect of this, namely the knowledge and science of the Vikings and their immediate successors in Iceland and other Scandinavian countries.

Many of the activities of the Vikings required and produced knowledge of time-reckoning and of what we would nowadays classify as astronomy. For example, their extensive travelling and trade must have involved some knowledge of astronomy. The necessity of such knowledge is generally recognised in the case of coastal navigation, but also holds for inland travel through previously unknown areas, such as the vast lands of Eastern Europe.

Inland travel and coastal navigation is one thing, but regular trans-oceanic traffic is quite another. Yet such traffic was required to support the Scandinavian settlement of Iceland and Greenland, around the years 900 and 1000 respectively, at a time when the people of Europe knew nothing of the compass or the sextant. Even with good luck the oceanic voyage would take about a week, and without it land might not be sighted for several weeks. The navigational methods used included both terrestrial and celestial observations (Einarsson 1970: 57-63; Schnall 1975, ch. 4; Marcus 1980: 100-18; McGrail 1989: 59-63). There is hardly any doubt that the knowledge written down on vellum in Iceland in the twelfth and thirteenth centuries derives to a high degree from these observations and this experience.

The need for a calendar

Turning inland, both textual sources and common sense reasoning indicate needs for certain kinds of knowledge in the community settling in the novel environment of the large island of Iceland. For instance, the Ice-landic summer is short, making it a matter of primary concern to utilise summer time as well as possible.

In 930 the Icelanders decided to establish the Althingi, a kind of parliament where an important part of the population gathered once a year for purposes of legislation and justice. Those who went there would spend two to five weeks away from home at a precious time of the year. The farms were scattered at long distances and the landscape often barely pass-able. Therefore the method previously known to the Scandinavians, to summon conventions like the Althingi by message, was not viable. It was much more convenient to have a simple and reliable calendar to help people know when to start from home so as to arrive at the same time as the others, and also to date the parliament at the time of summer when the loss of domestic labour was least harmful.

To understand the need for a calendar we may also look at the agriculture itself and its annual cycle. Certainly, the caprices of Icelandic weather and nature are such that the calendar may often be a bad guide for action. In deciding when to let cattle and sheep out on grass or when to start hay-making it is better to observe the actual signs of nature than the calendar. But there are certain kinds of annual operation where the calendar proves superior: for example, in determining when to sow the grain, something which people had tried with little success in the first centuries of settlement in Iceland. Another good example is that of deciding when to let the ram to the ewes. It is important to do this at the right time in the winter so that the lambs have the best possible prospect of growing in the short summer, without too much risk of interludes of bad weather in the spring just after they are born. When the individual farmer makes his decision on this at some point around Christmas time, he has no clear natural signs of a terrestrial nature to go by.

The calendar reform of 955

In the brief history of Iceland called Íslendingabók (The Book of the Icelanders, Libellum Islandorum), written by Ari the learned in the period 1122-33, we have a report on a calendar reform of about 955:

This was when the wisest men of the country had counted in two semesters 364 days or 52 weeks-then they observed from the motion of the sun that the summer moved back towards the spring; but there was nobody to tell them that there is one day more in two semesters than you can measure by whole weeks, and that was the reason.

There was a man called Thorsteinn the blackŠa very wise man. When they came to the Althing he sought the remedy that they should add a week to every seventh summer and try how that would work…

By a correct count there are 365 days in a year if it is not a leap year, but then one more; but by our count there are 364. But when in our count a week is added to every seventh year, seven years together will be equally long on both counts. But if there are 2 leap years between the ones to be augmented, you need to add to the sixth. (Benediktsson 1968: 9-11)

According to this, people started by counting 52 weeks or 364 days in the year. When they realised the insufficiency of this they tried the remedy of intercalating one week every seventh year (sumarauki), thus making the average year 365 days. The method chosen may seem strange to us but it is a natural consequence of the important role of the week in the original calendar.

So far the interpretation of the text seems straightforward. However, the text continues to describe the relation and adaptation of the Icelandic calendar to the Julian one, which must have been gradually introduced in Iceland in the eleventh and twelfth centuries, following formal Christianisation of the country in the year 1000. The text says that if there are two leap years between the years to be increased by a week, then the sixth year (instead of the seventh) should be increased. This is plainly wrong and would yield a worse approximation than the more simple rule of intercalating a week every sixth year. I have found it impossible to make sense of this except by assuming the Latin meaning of the num-erals. Thus 'septimo quoque anno' actually means 'every sixth year' by our count (see, e.g., Ginzel 1958: III, 66). In this way Ari's text can be interpreted so as to coincide with practice in his time, as seen from almost contemporary Easter tables (Beckman and Kålund 1914-16: 69-71; Beckman 1916: v-ix). Also, he would escape Occam's razor, since his formula would otherwise be more complicated than necessary for its accuracy.

It is interesting to consider the possible methods which Thorsteinn the Black might have used in determining his intercalation (Einarsson 1968). His farm was favourably located in the country to utilise the so-called mountain circle method (Vilhjálmsson 1989: 93), i.e. to follow the annual motion of sunrise and sunset near the horizon where he would have suitably distant mountains and other reference points in the landscape to make fairly exact observations possible. At high latitudes the points of sunrise and sunset move so fast that this method could easily be used to determine the length of the year to within a day.

Twelfth-century knowledge of the solstices and equinoxes

The story of independent Icelandic determination of the length of the year and its subsequent adaptation to the Julian calendar ends in the twelfth century. However, for the same reasons of co-ordination and timing the Scandinavians also needed to know the dates of the solstices and equinoxes. One of the sources on this matter is attributed to a twelfth-century farm labourer, Star-Oddi Helgason, who is described as a man well versed in time reckon-ing and wise in many other respects (Vilmundarson and Vilhjálmsson 1991: 459).

The text attributed to Oddi, showing his astronomical capabilities, is called Oddi's tale (Beckman and Kålund 1914-16: 48-53; Ólsen 1914). It only covers a couple of pages in print. The text is clearly of Icelandic origin and there are no parallels in medieval literature so far as I know. The tale comprises three sections treating different aspects of the annual motion of the sun. The first gives the time of the summer and winter

No. from leap year

Summer or winter solstice


Sun's direction




Jun 15





Dec 15





Jun 15





Dec 15





Jun 15





Dec 15





Jun 16





Dec 15



TABLE 1. The date of the solstices and their direction according to the first section of Oddi's tale, together with the corresponding time, given in modern terms.

solstices, from a leap year and through the subsequent three years until the cycle is supposed to close so that the story repeats itself. The second section describes how 'the solar motion increases in sight' from winter solstice to summer solstice and then 'decreases' to the next winter solstice. The third section tells us the direction of dawn and nightfall through the year. We shall here focus only on the aspect of time-reckoning, i.e. on the timing of the solstices and equinoxes.

The first section of Oddi's tale not only informs us about the date of the solstice but also the 'direction' of the sun at solstice accurate to one eighth of the circle (see Table 1). This is an indirect way of giving the time of the day to within three hours (Ólsen 1914: 13; Þorkelsson 1926: 46-47). The dates given do not coincide with the ones we are used to, the difference being due to the accumulated error of the Julian calendar in the twelfth century. Thus the dating in the text adheres to the real solstices rather than following the ecclesiastical decree of dating the solstices almost a week later (Jun 21 and Dec 21). Another Icelandic author in the thirteenth century tried to do away with this discrepancy by supposing that these later dates were valid 'in the middle of the world' (Beckman and Kålund 1914-16: 121, 175), thus betraying that he was describing an Icelandic observation and believing his own eyes better than the church.

The interval between the solstices in Oddi's tale is incorrect. The interval from winter to summer solstice is not generally the same as that from summer to winter; the difference amounted to about eight hours in the year 1100 and three hours in the year 1200 (calculations based on Moesgaard 1975: 172), thus exceeding the accuracy indicated by Oddi. We conclude therefore that this aspect of the text is more likely an exercise in the rece-nt-ly accepted Julian calendar than a report on Oddi's own observations.

The main subject of the second section of the Oddi's tale is that of the 'increase of solar motion' from winter to summer solstice and the subsequent decrease. This section implies that Oddi places the equinoxes at equal intervals from the solstices, thus dividing the year into four equal parts. This assumption for the timing of the equinoxes would have been several days in error in the twelfth century. It seems to me that in points like this, Oddi was led more by a conception of symmetry and simplicity than by exact observation.

Origins and usefulness of Oddi's knowledge

In summary, Oddi's results may quite well be some kind of crystallisation of know-ledge and motivation gained in the Viking Age. Besides this, he was living at a time and place close to the flourishing literary and cultural interest shown in the sagas.

However, as always in cases like this, we should beware of focusing too strongly on the person. There are many complicated reasons for Oddi's tale being known to us. One of the most important ones is that other people have found this kind of knowledge useful and considered it worthwhile to copy the text onto precious vellum again and again.

It is not too hard to imagine how the knowledge described in Oddi's tale would have been of use to his contemporaries in their daily fight for a living in circumstances where the optimal use of your powers may be of crucial importance. We have spoken here mostly of the first section of the tale, which was mainly useful as an exercise during the gradual introduction of the Julian calendar in Iceland. A clear understanding of this calendar has been necessary in order to adapt the old Icelandic calendar to it, which people did so well that we still have vestiges of the old calendar going strong in the country. The other parts of the tale seem mainly to have been useful for navigational purposes.

In all probability, the knowledge in Oddi's tale has not been gained through foreign books but through independent observations, maybe spanning several generations, and perhaps with a little help from oral (e.g. mathematical) information from the continent.

Imported books replace original observations

After the days of Star-Oddi in the twelfth century it seems that Iceland experi-enced a decline in the field of independent observations of nature. This coincides with increased literacy from around 1100 onwards and with all kinds of literary activities: the import of continental books, their reading and translation, the writing of old poems and new sagas and so on. At this time it gradually became easier to obtain valuable knowledge by reading books (Vilhjálmsson 1990: 41-49) instead of, for example, looking first-hand at the sky and trying to make sense of the phenomena as Oddi had done. We have thus missed the chance to see what a full-blown astronomy of the North would have looked like.


In summary, the settlement of Iceland around year 900 demonstrates that the Scandinavians had reached a level of knowledge and skill sufficient to maintain regular ocean traffic and a co-ordinated society. A considerable part of this knowledge related to astronomy and other fields of natural science. This kind of knowledge was further developed by independent observations in Iceland after settlement, of which we have here dealt with one of the best examples. However, the advent of literacy and literary interest from the twelfth century onwards made it easier to obtain knowledge from books than from first-hand observations.


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