Pentimal system is a notation for presenting numbers, usually by inscribing in wood or stone. The notation has been used in

Scandinavia Scandinavia is a subregion#Europe, subregion of northern Europe, with strong historical, cultural, and linguistic ties between its constituent peoples. ''Scandinavia'' most commonly refers to Denmark, Norway, and Sweden. It can sometimes also ...

, usually in conjunction to

rune Runes are the letters in a set of related alphabets, known as runic rows, runic alphabets or futharks (also, see '' futhark'' vs ''runic alphabet''), native to the Germanic peoples. Runes were primarily used to represent a sound value (a ...

s. The notation is similar to the older

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

for numbers up to 9 ''(I - IIIIV)''. Unlike the Roman notation, the

tick Ticks are parasitic arachnids of the order Ixodida. They are part of the mite superorder Parasitiformes. Adult ticks are approximately 3 to 5 mm in length depending on age, sex, and species, but can become larger when engorged. Ticks a ...

s are placed vertically on a 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 if I's and U's. The widest use of the notation is in presenting the

golden numbers A golden number (sometimes capitalized) is a number assigned to each year in sequence which is used to indicate the dates of all the calendric new moons for each year in a 19-year Metonic cycle. They are used in computus (the calculation of th ...

, 1 - 19 on

Runic calendar A Runic calendar (also Rune staff or Runic almanac) is a perpetual calendar, variants of which were used in Northern Europe until the 19th century. A typical runic calendar consisted of several horizontal lines of symbols, one above the ...

s, also known as ''

clogs Clogs are a type of footwear that has a thick, rigid sole typically made of wood, although in American English, shoes with rigid soles made of other materials are also called clogs. Traditional clogs remain in use as protective footwear in a ...

''). The numbers are commonly found in

Modern Age The modern era or the modern period is considered the current historical period of human history. It was originally applied to the history of Europe and Western history for events that came after the Middle Ages, often from around the year 1500 ...

and possibly

Early Modern Age The early modern period is a historical period that is defined either as part of or as immediately preceding the modern period, with divisions based primarily on the history of Europe and the broader concept of modernity. There is no exact date ...

. It is unknown if they were in use in the

Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and ...

, let alone in the

Viking Age The Viking Age (about ) was the period during the Middle Ages when Norsemen known as Vikings undertook large-scale raiding, colonising, conquest, and trading throughout Europe and reached North America. The Viking Age applies not only to their ...

. On older runic calendar, 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 Year 1343 ( MCCCXLIII) was a common year starting on Wednesday of the Julian calendar. Events January–December * January 14 – Arnošt of Pardubice becomes the last bishop of Prague and, subsequently, the first Archbishop of P ...

put collected and published by

Ole Worm Ole Worm (13 May 1588 – 31 August 1654), who often went by the Latinized form of his name Olaus Wormius, was a Danish physician, natural historian and antiquary. He was a professor at the University of Copenhagen where he taught Greek, Latin ...

in the 17th century used this notation. Most runic texts, including the Viking age

runestone A runestone is typically a raised stone with a runic alphabet, runic inscription, but the term can also be applied to inscriptions on boulders and on bedrock. The tradition of erecting runestones as a memorial to dead men began in the 4th centur ...

s use no

number system A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...

, instead numbers are simply spelled out.

Positional notation

In some peculiar instances runic numbers have been used as numerals in an base-ten positional system, similar to the Arabic numbers. It is unknown if this use existed before the 19th century. The oldest authenticated use is in the notes of an 18-year-old journeyman tailor, Edward Larsson, the contain the date 1885 in runes. A copy of the note was published by the Institute for Dialectology, Onomastics and Folklore Research in Umeå in 2004. This positional notation however appears on two unrelated sets of rune stones allegedly discovered in

North America North America is a continent in the Northern Hemisphere, Northern and Western Hemisphere, Western hemispheres. North America is bordered to the north by the Arctic Ocean, to the east by the Atlantic Ocean, to the southeast by South Ameri ...

. The first is the Kensington Runestone found in 1898, the second are the three Spirit Pond runestones found in 1971. Both refer to pre-Columbian Norse exploration of the Americas but are modern day hoaxes.
-
-
-
- Snow, Dean R. (October/November 1981)
"Martians & Vikings, Maldoc & Runes"
''

American Heritage Magazine ''American Heritage'' is a magazine dedicated to covering the history of the United States for a mainstream readership. Until 2007, the magazine was published by Forbes.

'' 32(6). Archived fro
the original
on September 29, 2007. Haugen, Einar (1974). "The Rune Stones of Spirit Pond, Maine". ''Visible Language'' 8(1).

Positional notation

References

See also