Pentadic numerals (Swedish : Pentadiska siffror/runor/talsystemet) are a notation for presenting numbers, usually by inscribing in wood or stone. The notation has been used in Scandinavia, usually in conjunction with runic calendars and inscriptions in runes.
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The notation is similar to the older Roman numerals for numbers 1 to 9 (I, II, III, IV, V, VI, VII, VIII, IX). [1] Unlike the Roman notation, there are only symbols for numbers one ("I") and five ("U"), protruding off the side of a vertical stroke, or stem, which has no numeric value by itself. In some inscriptions the notches are placed horizontally on a vertical stem or stav of the rune; on other inscriptions the stave is horizontal and the "I" and inverted "U" rise off of it.
The number 4 is represented by four vertical lines on the horizontal stem, 5 is represented by what looks like a half-turned letter U, resembling the letter "P" in combination with the stem. 10 is represented by two turned U's opposing each other. More numbers up to 19 or 20, can be represented by a combination of I's and U's branching off of a stem, similar to how Roman numerals are represented by combinations of I's and V's. [lower-alpha 1]
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 ). [2] 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 improvised for the numbers 17, 18, and 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. [3]
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 pentadic runes. A copy of the note was first published by the Institute for Dialectology, Onomastics and Folklore Research in Umeå in 2004. [4]
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, [5] 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 Kensington Runestone is a slab of greywacke stone covered in runes that was discovered in central Minnesota, United States, in 1898. Olof Ohman, a Swedish immigrant, reported that he unearthed it from a field in the largely rural township of Solem in Douglas County. It was later named after the nearest settlement, Kensington.
Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five digits on either hand.
A rune is a letter in a set of related alphabets known as runic alphabets native to the Germanic peoples. Runes were used to write Germanic languages before they adopted the Latin alphabet, and for specialised purposes thereafter. In addition to representing a sound value, runes can be used to represent the concepts after which they are named (ideographs). Scholars refer to instances of the latter as Begriffsrunen. The Scandinavian variants are also known as fuþark, or futhark; this name is derived from the first six letters of the script, ⟨ᚠ⟩, ⟨ᚢ⟩, ⟨ᚦ⟩, ⟨ᚨ⟩/⟨ᚬ⟩, ⟨ᚱ⟩, and ⟨ᚲ⟩/⟨ᚴ⟩, corresponding to the Latin letters ⟨f⟩, ⟨u⟩, ⟨þ⟩/⟨th⟩, ⟨a⟩, ⟨r⟩, and ⟨k⟩. The Anglo-Saxon variant is known as futhorc, or fuþorc, due to changes in Old English of the sounds represented by the fourth letter, ⟨ᚨ⟩/⟨ᚩ⟩.
The Elder Futhark, also known as the Older Futhark, Old Futhark, or Germanic Futhark, is the oldest form of the runic alphabets. It was a writing system used by Germanic peoples for Northwest Germanic dialects in the Migration Period. Inscriptions are found on artifacts including jewelry, amulets, plateware, tools, and weapons, as well as runestones, from the 1st to the 9th centuries.
A Runic calendar 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 other. Special days like solstices, equinoxes, and celebrations were marked with additional lines of symbols.
The Computus Runicus was a runic calendar produced in 1328 and found on the Swedish island of Gotland. A transcription/description of the text - called Computus Runicus - was published in 1626 by the Danish physician and antiquarian Ole Worm (1588–1654).
Jera is the conventional name of the j-rune ᛃ of the Elder Futhark, from a reconstructed Common Germanic stem *jēra- meaning "harvest, (good) year".
The Stentoften Runestone, listed in the Rundata catalog as DR 357, is a runestone which contains a curse in Proto-Norse that was discovered in Stentoften, Blekinge, Sweden.
The Scandinavian Runic-text Data Base is a project involving the creation and maintenance of a database of transliterated runic inscriptions. The project's goal is to comprehensively catalog runestones in a machine-readable way for future research. The database is freely available via the Internet with a client program, called Rundata, for Microsoft Windows. For other operating systems, text files are provided or a web browser can be used to interact with the web application Runor.
Cipher runes, or cryptic runes, are the cryptographical replacement of the letters of the runic alphabet.
A number of runestones have been found in Oklahoma. All of them are of modern origin dating to the 19th century "Viking revival" or were produced by 19th-century Scandinavian settlers.
The Spirit Pond runestones are three stones with alleged runic inscriptions, found at Spirit Pond in Phippsburg, Maine in 1971 by a Walter J. Elliott, Jr., a carpenter born in Bath, Maine. The stones, currently housed at the Maine State Museum, are widely dismissed as a hoax or a fraud.
The Italy runestones are three or four Varangian runestones from 11th-century Sweden that tell of warriors who died in Langbarðaland, the Old Norse name for south Italy. On these rune stones it is southern Italy that is referred to (Langobardia), but the Rundata project renders it rather anachronistically as Lombardy.
Counting rods (筭) are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
The Sønder Kirkeby Runestone, listed as runic inscription DR 220 in the Rundata catalog, is a Viking Age memorial runestone that was discovered in Sønder Kirkeby, which is located about 5 kilometers east of Nykøbing Falster, Denmark.
Danish Runic Inscription 48 or DR 48 is the Rundata catalog number for a Viking Age memorial runestone from Hanning, which is about 8 km north of Skjern, Denmark. The runic inscription features a depiction of a hammer, which some have interpreted as a representation of the Norse pagan god Thor, although this interpretation is controversial.
Runic alphabets have seen numerous uses since the 18th-century Viking revival, in Scandinavian Romantic nationalism (Gothicismus) and Germanic occultism in the 19th century, and in the context of the Fantasy genre and of Germanic Neopaganism in the 20th century.
A runic carving is defined as a runic inscription in stone or other material, according to the definitions of the Swedish National Heritage Board. The term refers to both prehistoric and medieval runic carvings in raised stones or on blocks, on rock slabs, early medieval tombstones and "Eskilstuna coffins" with runes, runic carvings in materials other than stone, e.g. in plaster on churches, as well as historical and recent runic carvings. Viking Age runic carvings are often memorial inscriptions, usually after dead relatives. The runic inscription has usually been arranged in ribbons, which are often shaped like elongated animal bodies with head, feet and tail. The carving surface is often adorned with crosses and animal ornaments. Sometimes the runic carvings have also been decorated with more complicated image representations. Older, Old Norse, runic-carved stones usually lack ornamentation and have the text arranged in horizontal or vertical rows. Early medieval tombstones and "Eskilstuna coffins" with runes are given the property value "in grave context". Early medieval tombstones and Eskilstuna coffins without runes are registered under the relic type gravvård.