Numeration

The numeration indicates the mode of representation of the Nombre S. Aussi, it relates to the words, the gestures and the signs which made it possible different the Peuple S to state, of mimer and to write these numbers.

Representation of a quantity

Pilot quantity

An old technique makes it possible to represent a quantity without the intervention of the writing nor of the language. By symbolizing each element by a stone or a token, that makes it possible to record a quantity using an equivalent quantity. In this manner, by comparison of the quantities, element by element, it is possible to determine if a herd is complete, or if the number of animals which it includes/understands increases, decrease or remains stable.

Symbolization

The numbers can be represented by signs, words or gestures. A whole of rules of use of the signs, words or gestures representing the numbers define a Numbering system.

Characteristics

Type of numeration

The cardinal, or arithmetic numeration, corresponds to the Représentation of the Quantité S, the Proportion S or the sizes. The ordinal numeration corresponds to the representation of the row of elements of whole of elements.

Character of a numeration

To count, one adds successively units, and one groups them per packages each time a certain value is reached. In the same way, at the end of a certain number of packages, one groups these packages out of larger packages, and so on. Ideally, the number of elements of each package, which gives the character of numeration, is identical. In practice, it is not always the case. Thus, the Maya Numeration, of character vigesimal, in order to approach the calendar, is irregular, the Babylonian Numération, of sexagesimal nature , is presented in the form of a combination of systems, and remains thus accessible.

Many systems were used by varied people and at times.

a Binary system (bases 2) used in languages of South America and Oceania.
a quinary Système (bases 5) was used among the first civilizations, and until the 20th century by African people , but also, partially, in numerations Roman E and Maya.
a octal Système (bases 8) is used in pame north (northern pame), with the Mexico, and in yuki, California.
a Decimal system (bases 10) was used by many civilizations, like the Chinese as of the first times, and, probably, the Proto-indo-Europeans. Today, it is most widespread by far.
a duodecimal Système (bases 12) is used with the Nepal by the people chepang. It is found, because of his advantages as regards Divisibilité (by 2,3,4,6), for a certain number of Monnaie S and current Units of Account in Europe with the Moyen-âge, partially in the Anglo-Saxon countries in the imperial Système of unit, and in the trade. It is also used for to count in month.
a Système vigesimal (or vigesimal, bases 20) exists with the Bhutan in language dzongkha, and was of use at the Aztèques and, though irregular, for the Maya Numération. Some think that it was also used by the Gaulois or the Basque S in the first times, but one is unaware of actually if their numeration had a decimal or vigesimal carcactère.
a sexagesimal Système (bases 60) was used for the Babylonian Numération, like by the Indians and the Arabs in Trigonométrie. It is currently useful in measurement of time and the angles.

Commonly, one speaks often basic instead of character. These concepts are close, but, in a rigorous way, the base applies only to one exclusively positional notation strictly and. Certain number bases are used in scientific disciplines, in particular in numerical electronics and data processing. To consult the article Base (arithmetic) for more details.

Anthropology of numeration

Among different the human cultures, many traditional numbering systems rest on numbers 5,10 or 20. That can be explained by the fact that in much of cultures one uses counting on the 5 Doigt S of the Main, on the 10 fingers two hands or the 20 fingers of the hands and Orteil S of the Pieds. Thus in Shuar, number 10 says “two hands”.

However, certain numbering systems can be more limited much. Thus, in Munduruku, there does not exist linguistic symbol to represent cardinal higher than 5.

Applications

To number

To number consists in allotting a number to each element of a whole of elements. Although the numbers are generally numbers, they do not represent a quantity. However, these numbers can allow an ordered relation of the numbered elements. In this direction, classification is connected then with an ordinal numeration.

To number

To number consists in naming the quantity of elements of a whole of elements.

To count

Compte R consists in reciting an ordered succession of words, called numbers. To count elements consists in one by one putting elements of a whole of elements in correspondence with the successive numbers. It is to some extent about an ordered classification. To count elements at the same time requires to know to recite the natural entireties in the order, to know to point (hand, glance,…) elements, and to know to coordinate motricity, the sensitive activity (visual or tactile) and the language.

To count

Dénombrer consists in determining the quantity of elements of a whole of elements by the means of counting. To count a whole of elements thus amounts counting them and numbering them. Thus, a child, for example, can count when the technique of counting is acquired and that it knows that the last word employed represents the quantity of the counted elements.

To measure

Mesurer consists in determining a quantity, a dimension or an intensity, generally using a Measuring instrument, this last, generally, defining or being related to a Measuring unit, being able itself to be fixed by a standard.

To calculate

Calcul er consists in carrying out operations.

To enter

To enter consists in being interested in a quantity or its fluctuations, by the means of an account or an accountancy, by considering the arrivals and the departures, the entries and the exits, the profits and the losses, the receipts and the expenditure, etc

Anecdotes

Several fictional numerations were imagined:

the Numeration Bibi of Boby Lapointe;
the Numeration Of neither of the saga Myst, basic 25, used by civilization Of nor;
the numeration Shadok, quaternary, using the figures Ga, Drunk, Zo and Meu.

See too

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