Xannat at 00:22, 14 April 2026

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{{Short description|Method of recording numbers using words}}
The '''Bhūtasaṃkhyā system''' is a method of recording numbers in [[Sanskrit]] using common nouns having connotations of numerical values. The method was introduced already in astronomical texts in antiquity, but it was expanded and developed during the medieval period.<ref name="Sircar">{{cite book|last=D.C. Sircar|title=Indian Epigraphy|publisher=Motilal Banarsidass Publishers Private Limited|location=Delhi|year=1965|edition=1|pages=228–234|isbn=81-208-1166-6}}</ref><ref>{{cite journal|last=David Pingree|date=September 22, 2003|title=The logic of non-Western science: mathematical discoveries in medieval India|journal=Daedalus|publisher=American Academy of Arts & Sciences|volume=132|issue=4|pages=45–53|jstor=20027880|doi=10.1162/001152603771338779|s2cid=57559157|doi-access=free}}</ref><ref>{{cite book|author=Kim Plofker|author-link=Kim Plofker|title=Mathematics in India: 500 BCE–1800 CE|title-link=Mathematics in India (book)|publisher=Princeton University Press|location=Princeton, NJ|year=2009|pages=47–48|isbn=978-0-691-12067-6}}</ref>
A kind of [[rebus]] system, bhūtasaṃkhyā has also been called the "concrete number notation".<ref>{{cite book|last=Kim Plofker|title=The mathematics of Egypt, Mesopotamia, China, India, and Islam: a sourcebook |editor=Victor J. Katz|editor-link=Victor J. Katz|publisher=Princeton University Press|year=2007|pages=420–421|chapter=Mathematics in India|isbn=978-0-691-11485-9}}</ref>

For example, the number "two" was 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 the meaning "earth" could be used to signify the number "one" as there is only one earth, etc.

In the more expansive examples of application, concepts, ideas and objects from all parts of the Sanskrit lexicon were harvested to generate number-connoting words, resulting in a kind of [[kenning]] system for numbers.
Thus, 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 term ''[[anuṣṭubh]]'' has been used to signify "eight" as it is the name of a meter with eight syllables in a foot.<ref name="Sircar"/> 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 there is a tradition of "thirty-three gods" (''[[trāyastriṃśa]]deva'') in certain Hindu and Buddhist texts.<ref>Beginning with [[Atharvaveda]] [https://www.sacred-texts.com/hin/av/av10007.htm 10.7] ("([[:wikt:स्कम्भ|Skambha]]) in whose body are contained all three-and-thirty Deities"), with references in various Upanishadic, Puranic and Sutra texts.</ref>
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.<ref name="Sircar"/>

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 decimal place value system into the scheme, where digits are named in ascending order. As an example, in an 18th-century inscription from [[Kalna City|Kalna]], a year is given as ''bāṇa-vyoma-dharādhar-indu-gaṇite śāke'' which means "In the Śāka year enumerated by arrow [5], sky [0], mountain [7] and moon [1]", that is, "Śāka 5-0-7-1" = Śāka 1705 = AD 1783.<ref>{{cite book|last=Richard Solomon|title=Indian epigraphy: a guide to the study of inscriptions in Sanskrit, Prakrit and other Indo-Aryan languages|publisher=Oxford University Press|year=1998|pages=173|url=https://books.google.com/books?id=XYrG07qQDxkC&q=epigraphical+%2B+bhutasankhya&pg=PA173 | isbn=978-0-19-509984-3}}</ref>


The earliest evidence of this system is found in [[Yavanajataka]], a versification of a Greek astronomical text dated to the early centuries CE.<ref>{{cite book|last=David Pingree|title=The Yavanajātaka of Sphujidhvaja|publisher=Harvard University Press|year=1978|series=Harvard Oriental Series|volume=48 (2 vols)}}</ref>
Limited use of Bhutasamkhya is seen in some [[Purana]]s, for example Bhagavata Mahatmya of Padma Purana (6.66) uses the word '''nagaaha'' to refer to "seven days",<ref>{{Cite web|last=Mahatmya|first=Bhagavata|date=8 July 2021|title=Bhagavata Mahatmya|url=https://srikrishnakathamritam.files.wordpress.com/2015/05/part-1-a-journey-towards-the-insight1.pdf|url-status=live|archive-url=https://web.archive.org/web/20210709184829/https://srikrishnakathamritam.files.wordpress.com/2015/05/part-1-a-journey-towards-the-insight1.pdf |archive-date=2021-07-09 }}</ref> i.e. ''naga'' "mountain" is used as a synonym of "seven" (because of the "seven principal mountains" or ''kula-giri''), a usage already found in medieval recensions of the [[Surya Siddhanta]]. It is found throughout the Indian Buddhist [[Kalacakra Tantra]] literature.

==See also==
* [[Aksharapalli]]
* [[Āryabhaṭa numeration]]
* [[Katapayadi system]]

==References==
{{reflist}}

==External links==
* [https://sanskrit.iitk.ac.in/jnanasangraha/sankhya/bhoota '''Bhūtasaṅkhyā''', a Bhūtasaṅkhyā encoding-decoding system]

==Further reading==
* For a list of words commonly used for the representation of numbers in ''bhūtasaṃkhyā'' system see:
** {{cite web |url=https://sanskrit.iitk.ac.in/jnanasangraha/sankhya/bhoota/list |title= Bhūtasaṅkhyā
|last=Terdalkar |first=Hrishikesh |date= |website=Sanskrit Activities at IIT Kanpur |publisher= |access-date=January 2, 2023 |quote=}}
** {{cite book|last=D.C. Sircar|title=Indian Epigraphy|publisher=Motilal Banarsidass Publishers Private Limited|location=Delhi|year=1965|edition=1|pages=228–234|isbn=81-208-1166-6}}
** {{cite book|author = P. V. Kane | title = History of Dharmaśāstra Volume 5 part 1 | pages = 701–703 | year = 1968 | url = https://archive.org/stream/KhistoryOfDharmasastraancientAndMediaevalReligiousAndCivilLaw/Kane_A-History-of-Dharmasastra-v5-1toc_1958#page/n713/mode/2up}}
** {{cite book|author = C. P. Brown | year = 1869 | title = Sanskrit Prosody and Numerical Symbols Explained | pages=49–54 | url = https://archive.org/stream/sanskritprosody00browgoog#page/n64/mode/2up}}
* Related Video [https://www.youtube.com/watch?v=nY6Aro93ZOY]

[[Category:Indian mathematics]]

Bhutasamkhya system - Revision history

Xannat at 00:22, 14 April 2026