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JAIN MATHEMATICS AND KARMAVAD/149
increment in the powers rather than addition and multiplication. Let us look at the following table -- Numerical terms between 1&100 = hundred
Numerical terms between 101&1000 = nine hundred
Numerical terms between 1001&10000 = nine thousand
Numerical terms between 8400000 & shirshprahelika = ?????
The entire purpose thus becomes clear. It was the ingenuity of those scholars who circumvented the cumbersome problem of unmanageably large number of terms at the higher end of the counting. So, simple unity increment or multiples were replaced with the powers which reduced the number of numerical terms between 8400000 & shirshprahelika to only 28! How practical!
We have discussed the special features of Jain Arithmetic with regard to the biggest numerate number, the importance of the number 84 Lacs and the probable reasons for squaring the 84 Lacs in expanding the numerates. These discussions establish the independent development of Jain Mathematics. There is one more aspect of Jain Arithmetic about 'zero' which is equally interesting - whatever exists may be near to or tending to zero but cannot be "pure zero'. Entities and realities can be infinitesimally small but cannot be pure zero. This concept is another example of their practical approach towards mathematics. It is a matter of serious contemplation as to why 'zero' finds no place in the Jain Agam Literature?
Tending to Zero but not Zero
The mathematician, Euclid assigned no dimension to the finest point of the space. Although, any dimension (length, breadth and height) is obtained by joining these dimensionless points in the space. Similarly, the scientist, Newton, used to treat the finest particles of matter, the atoms, as having zero dimensions. But Einstein, while making use of the Gaussian geometry, has compared the finest point of space with other micro particles. Similarly, in Jain literature, the finest forms of the six realities (mattereals) have been compared and a definite relationship is being established. For instance, mutual equivalence has been established among the finest part of matter, paramanu - the dion, the finest part of akash, Pradesh, and the finest part of time, samaya. Hence the finest part of elementary tattvas of nature cannot be reduced to zero. They all may be defined to be infinitesimally small-tending to zero - but cannot be zero.
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