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144/JAIN STUDIES AND SCIENCE
NUMERATE, INNUMERATE AND
INFINITE Shirsaprahelika (The Top riddle)
Mahapragya, while giving a discourse on the arithmetic of the Vedic Era, mentioned about the specialty of the Sirsaprahelika, the maximum number, described in the Jain canonical texts. Yajurveda, 17/2 mentions up to Mahasankha in which 20 digits are included. An intermediate number of ten kharabas is also prominent, which is obtained by raising 10 to the power of 12 i.e. 1012. In that mathematical text, the counting progress as ikai (unit), das (ten), shata (hundred), sahasra (thousand),..., kharaba, dos kharabas,..... shankha, das shankha, mahashankha. Whereas, in the Jain ancient literature, the biggest number, called Shirsaprahelika, comprises 54 digits followed by 140 zeros. The maximum number, therefore, contains 194 digits. However, in another text, the Shirsaprahelika is recognized as a number having 250 digits. By any means, the biggest number as quoted in the Vedic era, is very small in comparison. The modern sophisticated mathematics also acknowledges the importance of large numbers such as Shirsaprakelika and has regarded it as an important discovery. We shall therefore, discuss the interesting part of Jain Arithmetic regarding the maximum and the minimum numbers.
In the Jain Texts, there is description of the numerate, the innumerate and the infinite in defining the time periods. The ultimate finest unit of time has been called as 'Samaya' (instant). The period from an instant (Samara) up to the Shirsaprahelika is calculable, thus all numbers in between are called numerate. It is interesting to find that among the numbers smaller than the Shirsaprahelika, an intermediate number, Eighty Four Lacs, has been given special importance.
In deriving the biggest number, first the counting up to a number of eightyfour lacs was done. This number was named 'Purvanga'. After this, eightyfour lacs have been multiplied by eighty four lacs, i.e. eighty-four lacs have been squared. The number thus obtained was named Pura'. When the number "Purva', is multiplied by eighty-four lacs again, the result was called *Trutitanga'. In this sequence, there are twenty eight such places. Progressing in this manner, the ultimate number, 'Sirsaprahelika' can be denoted as follows:
(8400000)28 or (84x 103)28
Although the time-period up to the ‘Sirsaprahelika' is sufficient for all practical purposes, the calculable and numerate periods beyond this limit are
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