Alphasyllabic numeral systems are a type of

numeral systems A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbo ...

, developed mostly in

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

starting around 500 AD. Based on various alphasyllabic scripts, in this type of numeral systems

glyph A glyph () is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface, of an element of written language. A g ...

s of the numerals are not abstract signs, but syllables of a script, and numerals are represented with these syllable-signs. On the basic principle of these systems, numeric values of the

syllable A syllable is a unit of organization for a sequence of speech sounds typically made up of a syllable nucleus (most often a vowel) with optional initial and final margins (typically, consonants). Syllables are often considered the phonological "bu ...

s are defined by the consonants and vowels which constitute them, so that consonants and vowels are - or are not in some systems in case of vowels - ordered to numeric values. While there are many hundreds of possible syllables in a script, and since in alphasyllabic numeral systems several syllables receive the same numeric value, so the mapping is not

injective In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies . (Equivalently, implies in the equivalent contrapositiv ...

Alphasyllabaries

The basic principle of the Indian alphasyllabaries is a set of 33 consonant-signs, which are combined with a set of about 20 diacritic marks that indicate vowels of the

brahmi script Brahmi (; ; ISO: ''Brāhmī'') is a writing system of ancient South Asia. "Until the late nineteenth century, the script of the Aśokan (non-Kharosthi) inscriptions and its immediate derivatives was referred to by various names such as 'lath' o ...

s, these produce a set of signs for syllables; unmarked consonant-signs denote the syllable with the inherent vowel ''’a’''.

Indian alphasyllabic numeration

Starting around 500 AD, Indian astronomers and astrologers began to use this new principle for numeration with assigning numeral values to the phonetic signs of various Indian alphasyllabic scripts – the

s. Earlier 20th-century scholars supposed that the Indian grammarian

Pāṇini , era = ;;6th–5th century BCE , region = Indian philosophy , main_interests = Grammar, linguistics , notable_works = ' (Sanskrit#Classical Sanskrit, Classical Sanskrit) , influenced= , notable_ideas=Descript ...

used alphasyllabic numerals already in the 7th century BC. Since there is no direct evidence for any alphasyllabic numeration in

until about 510 AD, recently this theory is not supported. These systems, known collectively as ''varnasankhya'' systems, were considered to be distinct from other Indian systems – i.e.

brahmi Brahmi (; ; ISO 15919, ISO: ''Brāhmī'') is a writing system of ancient South Asia. "Until the late nineteenth century, the script of the Aśokan (non-Kharosthi) inscriptions and its immediate derivatives was referred to by various names such ...

kharosthi numerals The Kharoṣṭhī script, also spelled Kharoshthi (Kharosthi: ), was an ancient Indo-Iranians, Indo-Iranian script used by various Aryan peoples in north-western regions of the Indian subcontinent, more precisely around present-day northern ...

- that had abstract numeral-signs. Alike the alphabetic systems of Europe and the Middle East, these systems used phonetic signs of a script for numeration, but they were more flexible than those. Three significant systems of them:

Āryabhaṭa numeration Āryabhaṭa numeration is an alphasyllabic numeral system based on Shiksha, Sanskrit phonemes. It was introduced in the early 6th century in India by Āryabhaṭa, in the first chapter titled ''Gītika Padam'' of his ''Aryabhatiya''. It attr ...

katapayadi system ''Kaṭapayādi'' system (Devanagari: कटपयादि, also known as ''Paralppēru'', Malayalam: :ml:പരല്‍പ്പേര്, പരല്‍പ്പേര്) of numerical notation is an ancient Indian alphasyllabic numeral s ...

, and the

aksharapalli Aksharapalli () is a certain type of alphasyllabic numeration scheme extensively used in the pagination of manuscripts produced in India in pre-modern times. The name ''Aksharapalli'' can be translated as the ''letter system''. In this system t ...

numerals. Alphasyllabic numeration are very important for understanding Indian astronomy, astrology, and numerology, since Indian astronomical texts were written in

Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...

verse, which had strict metrical form. These systems had the advantage of being able to give any word a numerical value, and to find many words corresponding to one given number. This made possible the construction of various

mnemonic A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imag ...

s to aid scholars and students, and would have served a prosodic function.

Structure

Structure of the Indian alphasyllabic numeration systems differs basically from one another. Though in each of the systems consonants and vowels are ordered to numeric values, thereby each syllable has a numeric value, but on the base of each system's own rules. In various systems the V, CV, CCV syllables receive different values, and the methods, how the numbers are represented by these syllables, are quite different. *

system operates on the additive principle, so that the number's value, which is represented in it, is computed as the sum of each syllable's numeric value. In his mapping, the consonants are ordered from 1 to 25, then by tens from 30 to 100. Each successive vowel is ordered to the different exponent of 100. In

’s the diacritic signs, which mark vowels, multiply the value of the syllable’s consonant by the given power of 100. Direction of his script is right to left, which reflects the order of the Sanskrit lexical numerals. *In

, syllables have the numeric values only from 0 to 9. To each V, CV and CCV syllable is given a value between 0 and 9. In this way each number between 0 and 9 are ordered to several syllables. Unlike Aryabhata's system, changing the vowel in the syllable doesn’t change the syllable’s numerical value. The number’s value, which is represented in this way, is given as positional number with one syllable on each position. Direction of this script is right to left. *In

system, syllables were assigned the numerical values 1–9, 10–90, but never as high as 1000. According to S. Chrisomalis there was never a single regular system for correlating signs with numeral values in this system. It was used widely for paginating books, aksharapalli numerals were written in the margins from top to bottom.S. Chrisomalis 2010: p. 212.

Systems

Katapayadi system ''Kaṭapayādi'' system (Devanagari: कटपयादि, also known as ''Paralppēru'', Malayalam: :ml:പരല്‍പ്പേര്, പരല്‍പ്പേര്) of numerical notation is an ancient Indian alphasyllabic numeral s ...

Aksharapalli Aksharapalli () is a certain type of alphasyllabic numeration scheme extensively used in the pagination of manuscripts produced in India in pre-modern times. The name ''Aksharapalli'' can be translated as the ''letter system''. In this system t ...

References

Sources