I attach the entire Hindu concept of time reckoning for your convenience.
Dr R Brahmachari,
Jun 25, 2011
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Yuga and māhāyuga in Hindu time-reckoning
Yuga is used in three contexts and achieving three levels of precision in Hindu calendrical or astronomical computations:
- Yuga: Reckoning real (or, elapsed) time: yuga refers to a duration of 12,000 years
- Pānkta yuga: Reckoning auspicious time for performance of yajña: Pānkta yuga refers to a duration of five years
- Māhāyuga: Reckoning astronomical computational time: māhāyuga refers to a duration of 4,320,000 years.
Yuga (in the Mahābhārata and the Mānava Dharma śāstra) has a total duration of 12,000 years. Yuga is divided into four parts: Kṛta,Treta, Dvāpara, and Kali, with lengths of duration in the ratio 4:3:2:1
A second definition of yuga is related to five years (pānkta), of which samvatsara (year) is of 360 days (Rgveda). For purposes of determining the timing of yajña, taittirīya brāhmaṇa (TB 3.4.11 and TB 3.10.4 ) give the names of all the five years of yuga as: samvatsara, parivatsara, idāvatsara, idvatasara, and vatsara. The five-year yuga of vedānga jyotiṣa (VJ) consists of 62 cāndramāsa (synodic months, i.e. description of the moon’s phases), 1830 days and 1860 tithis (1/30th part of a synodic month) and was taken to commence at the winter solstice. At the time of VJ, winter solstice occurred at the beginning of the first tithi of the śukla pakṣa of the month of māgha…This five-year grouping of yuga is to bring into reckoning the two adhimāsa (intercalary months) in a yuga. The sun and the moon are supposed to occupy the same position at the beginning of each subsequent yuga and all the happenings would be repeated in the subsequent yugas in the same way. The five-year group has the associated scheme of two adhimāsas. It occurs in texts such as Mahābhārata (pañcame-pañcame varṣe dvau māsāvupajāyate; MBh 4-47), and kauṭilya’s arthaśāstra (pañca samvatsaram yugam iti; atharva jyotiṣa 22.214.171.124). (Achar, N., 1997, A Note on The five-year Yuga of the vedānga jyotiṣa, http://www.ejvs.laurasianacademy.com/ejvs0304/ejvs0304.txt) kālajñānam pravakṣyāmi …yajñārthakālasiddhaye, “I shall describe [systematically] the science of time for the purpose of determining the appropriate time for [different] yajñas .” (Rgjyotiṣa 2.3)
A third definition is Māhāyuga = 360 samvatsara X 12,000 years = 4,320,000 years; Kalpa = 1000 Māhāyuga (Brahma’s day). Names of 30 Kalpas are found in the Matsya Purāṇa (290.3-12)
In an encyclopaedic work, which is recommended reading for any scholar interested in the study of history of mathematics and astronomy, Kaushal Vepa recounts the antiquity and precision achieved in Hindu astronomical studies, and cites Sūrya Siddhānta to explain the technical time-reckoning terms used in Hindu civilization tradition (Vepa, Kaushal, 2010, The origins of astronomy, the calendar and time: a critique of the conventional western narrative, McGraw-Hill Open-publishing, p.184):
lokānām antakṛt kālah kālonyah kalanātmakah
sa dvidhā sthūlasūkṣmatvān mūrtaścāmṛta ucyate
The time which lapses is the real time, and other kind of time is for the purpose of computations. They are of two kinds, the gross one is used for real or elapsed time use and the firm one for the purpose of computations. (Sūrya Siddhānta 1.10) [Note: Sūrya Siddhānta uses the least count of kala or minute of the arc in a circle of 21,600 kala to arrive at precision in astronomical computations.]
With this elucidation of real or elapsed (sthūla) time distinquished from computational precision (sūkṣma) time, many misconceptions and textual misinterpretations which have arisen in arriving at chronologies of Hindu civilization events related to yuga stand resolved.
Yuga is elapsed time of 12,000 years and is used to reckon historical time [as in the itihāsa (historical) text of Mahābhārata]. Māhāyuga is used for astronomical computations related to the movement and location of celestial objects.
I am grateful to Narahari Achar and Kaushal Vepa for their insightful observations on ancient Hindu astronomical texts.
June 24, 2011