Pentimal system

Pentimal system

The pentimal system ( _sv. 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 to runes.

The notation is similar to the older Roman numerals for numbers up to 9 "(I - VIIII)". Unlike the Roman notation, 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.

The widest use of the notation is in presenting the golden numbers, 1 - 19 on Runic calendars ( _sv. runstavar, _no. kalenderstavar, also known as "clogs"). [ [ think - rune calendars] ] 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 letters of Younger Futhark represented the numbers from 1 to 16 with three special runes used for the numbers 17 to 19. The "Computus Runicus", originally from 1343, but collected and published by Ole Worm in the 17th century, used this alphabet notation. [" [ Computus Runicus - The Runic Calender From Gotland From 1328.] " Described by Ole Worm]

Most runic texts, including the Viking age runestones, use no numeral system; instead, numbers are simply spelled out.

Positional notation

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 2004.

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", [ [ Transcription of Spirit Pond Number 3] , lines 3 and 8] 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.

The use of this otherwise unknown numeral system has been seen as evidence that the North American rune stones are hoaxes.


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