A runic Inscription from Sigtuna
On a cattle bone from the 12th century, a rune-master carved encoded runes. The code is pretty straightforward. It consists out of a conglomerate of lines. A small space orders the lines in small groups. Every group starts with a line which is only half as long as the other lines. The encoding is similar to the encoding of the Rök-stones. The number of half lines at the beginning of a group designates the ætt. The sum of the longer lines gives us the position of the rune inside the ætt.
The decoding is unproblematic. We transcribe the runes as 3/6 1/6 2/5 1/4 3/6 which result in k y s / m k. It must be noted that the first ætt is actually Týs ætt and the third Freys.
Recently, Nordby translated the inscription as “kiss me”. This translation made it to the mainstream media, causing a small storm about the long-lost romantic nature of the “Vikings”. The inscription was placed in a bigger sociological framework. However, Nordby neglected, as fellow researchers, the findings of Klingenberg et al. Runes has also a mathematical meaning and a lot of inscriptions where mathematically encoded (gematria or isopsephy). This kind of encoding was very popular within the Greek writings and other writing-systems in the Middle East. It was German Klingenberg and before him the Swede Agrell who argued that also the runes and the runic inscriptions were ordered by mathematical rules.
This inscription too has also been ordered mathematically. The runes form two groups from 3 and 2 runes resulting in a total of 5 runes. This is the beginning of the Fibonacci sequence or the numbers of the section aureo: 2, 3, 5. The use of the sequence is found on the Horn of Gallehus, and on others artifacts from the Thorsberger Moor and the cauldron of Gundestrup. The sequence was well known in the Northern world.
There is even a more important aspect. The total numerical value of the runes is k6 + y16 + s11 + m15 + k6 = 54. This number is 2 times 27, the duration of the moon-month. This number has a protective meaning. The word laukaR has the same value 2 * 27 = 54, just as the magical expression alu like on the ring of Körlin. The writer expressed two times alu, probably hoping on a positive effect.
The on. kyss could not only mean physical “kissing”, but like the Dutch “liefkozen” means more like “to caress”, in a broader sense “to protect”. Maybe the writer didn’t want a physical kiss, but wanted the protection of the “good” gods or wanted the help of the gods to gain his love. This remains of course guessing, but is not unlikely.
The runic master had to improvise and orders the runes so that the inscription reflects a protective number. This technique has been seen in a lot of other inscription. The writer had to change the characters or leave out characters to align the inscription to the mathematical order. Even though this seems to be otherworldly for many, we find these trade-offs also in non-runic inscriptions. It is a shame that almost no researcher at all are investigating the gematric rules behind the runic inscriptions. Leaving this aspect out, reduces the inscription with its missing of sometimes false runes to a mere, faulty human to human communication. But just as in the Greek culture, the mathematical value of the inscriptions had a higher priority than the grammatical and phonological rules, resulting in apparently faulty inscriptions but with a correct value. And the same goes also for a lot of runic inscriptions.
The statement that the “codes were used in play and for learning runes, rather than to communicate” by Nordby is not really true. Of course, runic masters would have practiced, but mostly they wanted to communicate with two worlds: the human world and the worlds of the gods.
- Arntz, H., Handbuch der Runenkunde. (1944)
- Klingenberg, H., Runenschrift – Schriftdenken – Runeninschriften. (1973)
- Krause, W., Die Sprache der urnordischen Runeninschriften. (1971)
The article points out that the runes have a mathematical meaning and that many inscriptions were mathematically encoded. The runic inscription on the cattle bone is no exception – it was ordered by mathematical rules that follow the Fibonacci sequence, or the numbers of the section aureo: 2, 3, 5. The sequence was well known in the Northern world and can be found on other artifacts such as the Horn of Gallehus and the cauldron of Gundestrup.
I find it fascinating that the Vikings used math to encode their runes and that the Fibonacci sequence was known and used in the Northern world. It’s a great example of how ancient cultures used mathematics in their daily lives and how it has influenced our modern world.