Vigesimal

The vigesimal system or twenties (Latin Vicesimus, the Twentieth ') is a number system, the number used as the basis twenties.

A possible explanation for the existence of this system is that for counting and arithmetic in addition to the fingers and the toes were used. Another explanation is the turning of the hands.

• 3.1 Garifuna

• 4.1 Nahuatl: Twenties unit with four of five units
• 4.2 Mayan languages ​​: Twenties unit with two tens units
• 4.3 Number of words for Twenties powers
• 4.4 counting in fives and twenties units

Dissemination

The vigesimal system has been applied consistently in the cultures of Mesoamerica, which is why the number of words in the languages ​​of the local language based on Federal and had simple names for the Twenties powers. With the enforcement of the decimal system in the Spanish colonial period, this counting method has been largely lost even with speakers of indigenous languages ​​in Mexico, but is locally still counted ninety-nine to twenty or even to traditional Numerals.

In Europe, there are just as many languages ​​traces of a Vigesimalsystems, but is nowhere counted in twenties units of the number ninety-nine out.

The vigesimal system is also found in other languages ​​of the Eurasian space. These include:

• Ainu, a language isolate spoken in northern Japan
• Burushaski, a language isolate spoken in northern Pakistan
• Georgian, a South Caucasian language. This language group is isolated so far, as no relationship could be demonstrated to the same language group, not even to other Caucasian languages ​​.

European Languages

The German linguist Theo Vennemann, according to the European vigesimal vaskonischen ( Basque ) origin, which he equates with Alteuropäisch. It went into other European languages ​​as a substrate, that is, in many Celtic languages, French and Danish.

After Menniger the European vigesimal system, however, is of Norman origin and has established itself with the spread of the Normans in the Middle Ages in Northwest Spain, Portugal, France and the British Isles.

Remains a possible Vigesimalsystems are also found in Etruscan, where the words for 17, 18 and 19 transferred literally " 20 less 3 ", "20 less 2" or " 20 minus 1 " mean.

In the old British monetary system twenty shillings were a sterling.

In his speech I have a dream Martin Luther King used the formulation Five score years ago for " a hundred years ago " as an allusion to a (originally from the withdrawn Bible ) similar phrase in the Gettysburg Address Abraham Lincoln ( four score and seven years ago).

Basque language

The Basque has a vigesimal system with numbers up to 99. That's the name Hogei 20, 30 hogeita hamar ( "Twenty and Ten " ), 31 hogeita Hamaika ( "Twenty and Eleven " ), 32 hogeita hamabi ( "Twenty and Ten - Two "). It is counted in twenties units: 40 berrogei ( " double - Twenty " ), 60 hirurogei ( "Three - Twenty " ) and 80 laurogei ( " four-twenty "). The intervening full ten are - similar to the Mesoamerican languages ​​- expressed by adding " Ten ": 50 berrogeita hamar ( " double - Twenty and Ten " ), 70 - hirurogeita hamar ( "Three - Twenty and Ten " ), 90 - laurogeita hamar ( " four-twenty and ten" ). From the hundreds of Basque numbers follow a decimal: 100 ehun, berrehun 200, 300 hirurehun etc.; at the higher powers of ten mila (thousands, cf span mil) and milioi ( million, Spanish Millón ) interprets the word shape indicates a borrowing from Spanish or Vulgar Latin.

Celtic languages

The Celtic languages ​​have traditionally up to the number 99 on a vigesimal; the figures are formed as in the Basque same principle.

Irish language

In Irish, traditionally seen in the vigesimal system with twenty ( fiche ) as a base. Forty is daichead (→ dhá fhichead 2 × 20), sixty is trí fichid (3 × 20), eighty is ceithre fichid (4 × 20). Thirty fiche is a dyke (20 10), fifty is daichead a dyke, 99 is ceithre fichid a Naoi Deag (4 × 20 19). In the official standard, however, the decimal system is favored today.

Welsh language

The Welsh language traditionally used as twenty ( Ugain ) as a base. Deugain are twice twenty ( ie 40), trigain three score ( = 60) and pedwar Ugain four times twenty ( = 80). The intervening multiples of ten are formed on the basis of each smaller multiples of twenty: Deg ar hugain is thirty ( " ten to twenty " ), deg a thrigain seventy ( " ten to three times twenty " ) and deg a phedwar Ugain ninety ( " ten to four times twenty "). Contrast Fifty is hanner cant ( " half a hundred "). Until the introduction of the decimal system in the monetary system in 1971 was papur chwigain ( six twenties ), the colloquial name for the ten shilling note ( = 120 pence ). In the second half of the twentieth century, then the decimal system was compared with the traditional vigesimal generally preferred.

Breton

Since the Breton is closely related to the Welsh, the vigesimal system is used as in this. So say 40 as in Welsh, daou - ugent, 60 tri - ugent and 80 Pevar - ugent. 30 has its own name Tregont while fifty hanter - kant ( " half a hundred " ) is called. 70 and 90, however, the respectively smaller multiples of twenty are as in the other Celtic languages ​​on the basis formed, thus similar in French: dek ha tri - ugent ( " ten and three times twenty " ) and dek ha Pevar - ugent ( " ten and twenty four times ").

Danish language

The Danish number system is probably pre- Indo- European origin and extends well back 3500 years ( or even more), that is, to the Late Bronze Age. It is based - similar to the Basque, Celtic and French number system - on a vigesimal system, the only backward but finds application. While the Scandinavian neighbors ( the Norwegians and Swedes ) and the Germans all apply almost alleinherrschende in Europe today decimal number system, change the Danes when counting from the number 50 ( up to and including 99) of the conventional decimal into a vigesimal counting. However, for the numerical notation of the Danish number system uses only the decimal Arabic numerals. Since about the mid-20th century, a shortened form typographical spelling and pronunciation of these numbers has prevailed. From it can be seen that today's final -s of the numbers from 50 to 99 represents a rudiment of the original Auslautes - sindstyve.

The altdänische word shall find '(- sinds - is the genitive form represents ) is multiplied by, and the word tyve, ' called to be the number 20 This results in the unfamiliar Dezimalsystemanwender Danish numerical values ​​from 50 to 99, the hereinafter be illustrated by two examples:

• Halvtreds [ indstyve ] = halv - tre shall find tyve (literally: half - three * times twenty) = 2 ½ x 20 = 50
• Nioghalvfems [ indstyve ] = og ni halv - fem shall find tyve (literally: nine and half - five * times twenty) = 9 4 ½ x 20 = 99

Some partially obsolete Danish terms that still stems from the time of acting in kind, allow conclusions to be originally in everyday common vigesimal. So the Danes use even today (as well as the French and Celtic peoples descendants ) - in addition et Dusin ( a dozen ) - terms such as et snes ( a stairs / sidewalks; = 20), et skok ( a shock, such as eggs, 3x20 = 60), and et ol ( a Wall / choice / Oll; 4x20 = 80).

French language

A partial vigesimal found for example in standard French: Up to 60 ( soixante ) and 70 ( soixante - dix ), the decimal system is being used. Is then counted in twenties blocks:

• 80: quatre - vingts ( twenty four )
• 90: quatre - vingt- dix (four times twenty plus ten)

In Old French the vigesimal the left in Paris Hôpital des Quinze - Vingts, which takes its name = 300 hospital beds has from the original 15 × 20 was also true for even larger numbers, cf.

However, the Vigesimalzählung does not apply to the spoken in Belgium and Switzerland, French as well as for regional variations in France: There are variants septante (70) octante / huitante (80) and nonante (90 ) used the obsolete in standard French of France or regionally applicable, with quatre - vingts (80 ) is used in Belgium, however.

Resianisch

The resianische dialect of the Slovene language used in contrast to the neighboring Slovenian and Friulian dialects from the vigesimal 60: 60 is trïkart dwisti (3 × 20 ), 70 is trïkart dwisti nu DESAT (3 × 20 10 ), 80 is štirikrat dwisti ( 4 × 20) and 90 is štirikrat dwisti nu DESAT (4 × 20 10 ).

Albanian

In Albania, there are ruins of a Vigesimalsystems. So there 's the number for twenty njëzet ( NJE "one" zet " twenty "); dyzet is forty ( dy " two "). In dialects still exist Trizet " sixty " and katërzet " eighty ". The other numbers for the tens are formed according to the decimal, eg tridhjetë " thirty " ( tre " three " dhjetë " ten ").

Caribbean

Garifuna

The Garifuna, an indigenous American language in Central America, has borrowed almost all number words from the French; it runs the vigesimal system up to the number 99 through consistently. From 100, the decimal system is being used.

Mesoamerican languages

In Mesoamerica was twenty commonly used as base of the number system and the formation and letters of calendar data. The number of words of the Mesoamerican languages ​​, which formed as a non- genetically related languages ​​together a Sprachbund, based just like the Mayan numbers consistently on the Twenties system. These languages ​​counted in addition to the Mayan languages ​​and Nahuatl Aztec. Simple words for large numbers did not exist for hundreds and thousands, but for the powers Twenties Twenty Four Hundred, Eight thousand and so on.

Is interesting to note that the number of words Mayathan and unrelated Nahuatl are all put together differently here but both build consistently on the twenties of magnitude.

Nahuatl: Twenties unit with four of five units

From the structure of the Nahuatl numerals is grateful that a twenty story from four of five units. So makuili "Five " is attributed to the root ma - ( maitl "hand" ), while the numbers six through nine from chiko ( " opposite [ s hand ]") and the words for one composed by four ( chikuasen, chikome, chikueyi, chiknaui ). For the multiples of five - ten ( majtlaktli ) and Fifteen ( kaxtoli ) - there is again his own words, where majtlaktli (ten ) is also associated with maitl "hand" in context. The number of episodes 11-14 ( majtlaktli sett, majtlaktli omome, majtlaktli omeyi, majtlaktli onnaui ) and 16-19 ( kaxtoli sett, kaxtoli omome, kaxtoli omeyi, kaxtoli onnaui ), however, are composed directly from these Zahlwörten and the words for one to four. As with the appearance of the Mayan numerals - a line forms a group of five, four strokes a Twenties unit - the counting to four hands and feet together with twenty fingers and toes is thus clear even at the Nahuatl numerals.

Mayan languages ​​: Twenties unit with two tens units

In contrast to the Nahuatl have the numerals in Mayathan and other Mayan languages ​​as a subunit of twenty not five, but ten (see eg Thirteen to Fifteen: oOX Lahun, kan Lahun, ho ' Lahun composed of Lahun " ten " and oOX, kan, ho ', " three, four, five "). The Twenties system with the subunit Ten we find also in the Mayan Languages ​​of Guatemala (eg in the Quiché language and the Cakchiquel language ), however, the number of words in detail, such as on the order of one, twenties and four hundred, formed differently. The numbers close to those in the same 13-19 Mayathan ( One "Ten ", see eg Thirteen to Fifteen on Quiché: oxlajuj kajlajuj, olajuj from oxib, kajib, job and lajuj ), but follow the Quiché and Cakchiquel also eleven and twelve completely regular this system ( Quiché julajuj, kablajuj against Mayathan buluk, lahka'a ). In the Quiché and Cakchiquel exist two number words for " twenty ", for a k'alh (corresponding k'áal in Mayathan ), on the other winaq, which is also " human " means, so all the fingers and toes of a person. Also in other Mayan languages ​​, there are two number words for " twenty ", such as in the Tzotzil tob and vinik.

In addition, have or had these two Mayan languages ​​a special word for eighty, jumuch or jumútch (ju - as a prefix " A - "). From the data written to the Quiché Popol Vuh as a different system from the Twenties Special Education on this basis omuch, " five Eighties " for " four hundred" occupied. In previous Cakchiquel grammars we find counting methods, in which the basic component of the number word is the next multiple of twenty and is at the end, while in more recent grammars of the basic component of the number word is the nearest multiple of twenty and is at the beginning. In addition, earlier was more common and mostly used k'alh winaq in later language levels.

As an example of the different composition of number words with the same base of a Twenties system, the numbers -seven and Fifty-seven are: 37 says in Mayathan Uk Lahun Katak hun k'áal ( "Seven [ and ] Ten and A [ times ] - Twenty ") in Cakchiquel and Quiché identical Juwinaq wuqlajuj ( " A [ times ] Twenty Seven [ and ] ten" ), in Nahuatl, however Sempouali onkaxtoli omome ( " A [ times ] Twenty and Fifteen and Two "). 57 is, in turn, in Mayathan Uk Lahun Katak ka ' k'áal ( "Seven [ and ] ten and two [ times ] - Twenty " ), in the ancient Cakchiquel language Wuqlajuj roxk'alh ( "Seven [ and ] ten [ for counting ] before three [ times ] - Twenty " by oxk'alh " Sixty " ), in the modern Cakchiquel and Quiché identical Kawinaq wuqlajuj ( " two [ times ] twenty [= man ] Seven [ and ] Ten " ), in Nahuatl, however Ompouali onkaxtoli omome ( "two [ times ] Twenty and Fifteen and Two ").

Number words for Twenties powers

Count in fives and twenties units

This table shows the Maya numerals and number words on Mayathan, Nawatl in modern notation and classical Nahuatl.