Pentimal system

The pentimal system (Swedish: pentadiska siffror) is a notation for presenting numbers, usually by inscribing in wood or stone. The notation has been used in Scandinavia, usually in conjunction with runes.

The notation is similar to the older Roman numerals for numbers 1 to 9 (I, II, III, IV, V, VI, VII, VIII, IX). Unlike the Roman notation, there are only symbols for numbers one ("I") and five ("U"). In inscriptions the notches are placed vertically on the stem or stav of the rune. The number 4 is represented by four horizontal lines on the stem, 5 is represented by what looks like an inverted letter U. 10 is represented by two U's opposing each other. Numbers up to 19, or even 20, can be represented by a combination of I's and U's, just like the Roman numerals are represented by combinations of I's and V's. (A Roman 10 is represented by two V's opposing each other).

The widest use of the notation is in presenting the Golden Numbers, 1 - 19 on Runic calendars (Danish: kalenderstave, Swedish: runstavar, Norwegian: kalenderstavar, also known as clogs).[1] The numbers are commonly found in Modern Age and possibly Early Modern Age calendar sticks. It is unknown if they were in use in the Middle Ages, let alone in the Viking Age. On older runic calendars, a different notation for representing the Golden Numbers was used; the 16 runes of Younger Futhark represented the numbers from 1 to 16 and three ad hoc runes were used for the numbers 17 to 19. For example, the Computus Runicus manuscript, originally from 1328, but collected and published by the Dane Ole Worm (1588-1654), uses this futhark notation, and not the pentadic numerals under discussion here.[2]

Positional notationEdit

Edward Larsson's notes from 1885 show the use of "pentadic" runic numerals to replace the Arabic numerals in representing dates.

In some peculiar instances runic numbers have been used as numerals in a base ten positional system, replacing the Arabic numerals. It is unknown if this use existed before the 19th century.

The oldest authenticated use of this notation is in the notes of an 18-year-old journeyman tailor, Edward Larsson, that are dated to 1885 in pentimal runes. A copy of the note was first published by the Institute for Dialectology, Onomastics and Folklore Research in Umeå in 2004.[3]

This positional notation however appears on two unrelated sets of rune stones allegedly discovered in North America. The first is the Kensington Runestone found in 1898; the second are the three Spirit Pond runestones found in 1971. All refer to pre-Columbian Norse exploration of the Americas.

The authors of the North American rune stones do not seem to understand the positional notation or the concept of zero. The rune for 10 is used interchangeably for 0, 10, and <1,0> with little consistency. The inscription stone from Spirit Pond contains the sequences ahr:011 and ahr:00,[4] which have been read as year 1011 and year 1010 respectively. It is unclear if the notation can represent all numbers unambiguously; for example, it may not be possible to distinguish 1010 from 100.

See alsoEdit


  1. ^ - rune calendars.
  2. ^ Computus Runicus - The Runic Calendar From Gotland From 1328. Described by Ole Worm
  3. ^ Tryggve Sköld (2003). "Edward Larssons alfabet" (PDF). DAUM-katta (in Swedish). Umeå: Dialekt-, ortnamns- och folkminnesarkivet i Umeå (Winter 2003): 5–6. ISSN 1401-548X. Archived from the original (PDF) on 2010-08-17. Retrieved 2009-06-02.
  4. ^ Transcription of Spirit Pond Number 3, lines 3 and 8

See alsoEdit