Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

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mathematical theory and describes the various units of simile measures for n easuring distances and time (from minutest to the biggest) with the help of wł ch the universe and all the fluents and their events are measured. It also gives the description of the Number measure.'
The minutest distance is the distance-space occupied by an ultimate particle (paramāņu) and is called a pradeśa, that is, a space point, while the biggest distance is a rajju (or a jagaśrèni=7 rajjus) which is equal to asamkhya yojanas which in turn has been estimated to be equal to nearly 8 miles of the modern times. Similarly the smallest time, viz., "samaya” or "instant" has been defined as the time taken by a paramāņu in moving from one space point to the next space point with minimum velocity; this unit of time is indivisible while the biggest practical unit of time is called 'acalātma' and is equal to 18431 x 1090) years.* In fact these texts also describe the system of infinite time measures. The two sets relating to distance and time are connected as follows** on the basis of cardinality :
Log, (Angula) = [(Log, (Palya)]2 where Angula' means actually the number of Pradeśas' in one Utsédhasūcyāngula (angula) while "Palya' means the number of 'Samayas' in one “Palya' (actually palyopama).
This chapter also gives the description of the Number measure, including the concept of infinity. In fact the Jaina School needed a quantitative analysis of Karmic events and for it the concept of mathematical infinity was necessary. Twentyone types of numbers (including three types of samkhyāta, nine types of asamkhyāta and nine types of ananta, thus including eighteen types of infinities) were given, ranging from unity to the cardinal number of the indivisible-corresponding-sections of omniscience (all knowledge or Kevala-jñāna). Thus while the concept of infinity has been perfected by modern western mathematicians only recently, in India this had reached its climax even before the early centuries of the Christian Era.
Proceeding further to Chapter 4, the author throws further light on some salient features of mathematics discovered in another important Jaina work of Dhavala' whose author Virasénācārya (8th century A. D.) was fully conversant with the place value system of notation, laws of indices, logarithm of a number to base 2 (called ardha cheda), general laws of logarithms, function of function-etc. Thus the principle of logarithm
*According to the Svetämbara, texts, this unit is called Sirsa-Prahelikā and
is equal to (8428 x 10140) years. **As given in other relevant texts.
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