Bhutasamkhya system

Bhūtasaṃkhyā system is a method of recording numbers using ordinary words having connotations of numerical values. The method was popular among Indian astronomers and mathematicians since ancient times. Sanskrit was the language from which words were chosen to write numbers in the bhūtasaṃkhyā system. The system has been described as the "concrete number notation" for the representation of numbers.

The number "two" can be associated with the word "eye" as every human being has two eyes. Thus every Sanskrit word having the meaning "eye" was used to denote "two". All words synonymous with "earth" could be used to signify the number "one" as there is only one earth. Concepts, ideas, and objects from all facets of Indian cultural experience – mythological, puranic, literary, religious, etc. – were harvested to generate number-connoting words. As an illustration, every Sanskrit word indicating an "arrow" has been used to denote "five" as Kamadeva, the Hindu deity of love, is traditionally depicted as a warrior carrying five arrows of flowers. The Sanskrit word anuṣṭubh has been used to signify "eight" as it is the name of a meter with eight syllables in a foot. Any Sanskrit word for "tooth" could be used to denote 32 as a grown-up man has a full set of 32 teeth. Terms implying "the gods" were used to indicate 33 as it is believed that the number of devas (gods) is 33 crores.

Single words indicating smaller numbers were strung together to form phrases and sentences for representing arbitrary large numbers. This formation of large numbers was accomplished by incorporating the place value system into the scheme. While decoding numbers encoded in the bhūtasaṃkhyā system, one should bear in mind the specialty of the Indian method of writing numbers. The various digits were written from left to right; that is, the digit with the lowest place value is written as the left most digit. The various digits of a large number are arranged from left to right in the increasing order of the place value. This specialty, succinctly indicated by the Sanskrit adage aṅkūnāṃ vāmato gatiḥ, has been extended to the bhūtasaṃkhyā system also. As an example, consider a certain number used extensively in Indian astronomy. Varahamihira (505 – 587 CE), an Indian astronomer, mathematician, and astrologer, encoded this number in bhūtasaṃkhyā as kha-kh-āṣṭi-yamāḥ. The individual words in this are "kha", "kha", "aṣṭi" and "yamāḥ" and they denote the numbers "0", "0", "16" and "2" respectively in that order. To obtain the modern equivalent of the number indicated by kha-kh-āṣṭi-yamāḥ, the four numbers have to arranged in the reverse order, namely, in the order "2", "16","0" and "0". Placing these four numbers side by side we get the number 21600. Incidentally, the number 21600 is the number of minutes in a full circle.

A potential user of the system had a multitude of words to choose from for denoting the same number. The mapping from "words" to "numbers" is many-to-one. This has facilitated the embedding of numbers in verses in Indian treatises on mathematics and astronomy. This helped in memorising large tables of numbers required by astronomers and astrologers.

The system has also been used extensively in epigraphical inscriptions in the Indian subcontinent for inscribing dates and years. As an example, in an inscription from Kalna, the date is given in bhūtasaṃkhyā system as bāṇa-vyoma-dharādhar-indu-gaṇite śāke which means "In the Śāka year enumerated by the arrows [5], the sky [0], the mountains [7] and the moon [1]", that is, in Śāka 1705 = AD 1783."

The earliest reference employing object numbers is a ca. 269 CE Sanskrit text, Yavanajātaka (literally "Greek horoscopy") of Sphujidhvaja, a versification of an earlier (ca. 150 CE) Indian prose adaptation of a lost work of Hellenistic astrology.

See also

• Āryabhaṭa numeration
• Katapayadi system

Further reading

• For a list of words commonly used for the representation of numbers in bhūtasaṃkhyā system see:

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