F3 3.2.1 Jain Mathematics and its specialty
Though Jainism has given more importance to religion and philosophy, one finds frequent references of use of mathematics in Jain literature. The science of knowledge in Jainism has been divided into 4 divisions:
Dravyānuyog - Metaphysics
Ganitanuyog - Mathematics
Charankarnanuyogaand,
Dharmakathanuyoga - Religious tales
The second division viz. Ganitanuyoga details of measurements of all the substances, time (Kāla), materials, land-areas, mountains, rivers etc. belonging to 14 Raj Lokās . They provides for the basis of Jain philosophy as it clarified the subtle measurements of each matter. If one tries to understand the matters of all 3 universes, from view point of mathematics, one can easily, appreciate the reality and perfection in the principles propounded by Tirthankaras. One can realise that the statements made by Lord Tirthankaras were so perfect and precise, that they could not be possible without the Keval Gyana- the ultimate knowledge.
The beginning of use of Jain mathematics, however is said to have been started by Aryashreejee Maharaj. Jain mathematics include the present decimle system; but in order to provide the precise measurement of various matters, they have used the measures like Palyopam, Sagaropam. The Time Wheel, Innumerable, infinite, the measure of one finger (Anguli Map), circumference, square root, Dhanush map, Baha, Jivā, etc. Which are both perfect and precise in describing the dimension of any thing- big or small.
Besides, with reference to the description of various Lokās (Areas), the details are provided regarding Sun, Noon, Nakhshatra, Islands, sea and oceans, etc. wherein various processes of Mathematics have been deployed. We find the use of mathematics in the scriptures like Surya Pratignapati, Chandra Pragnapti, Jambudwip Pragnapti etc. as well as in the critics of scriptures like Tiloy Pannati, Dhaval critic all Six continent (Shtkhandagal) Gommarsar and Triloksar etc. this study is important to realize the process of development of mathematical calculations in Ancient India. The script Suruapraganpti is also known as Ganitanuyoga (Mathematical Science). This is specialty of Jain Mathematics.
F3 3.2.3 Definition of Space Definition of Time.
Definition of Space :Molecule is a substance which is very very small which cannot be destroyed by water, fire, electricity or any other such things, which is, in itself, indestructible. A number of molecule make an atom, which is reliable unit of measurement in space. If we consider atom as a unit.
8 atoms make a Trasremu,
8 Trasremumake a Rathrenu,
8 Rathrenu make a Bal Māp,
8 Bal Māp make a Joo Māp
8 Joo Māp make a Muster Māp
8 Muster Māp make a Burlie Māp.
8 Burlie Māp make Angul Māp (a finger thick)
This Jivās who are born in Bhog Bhoomi ( a place of a pleasure i.e. Devlok) and those born in Karma Bhoomi ( a place where one has to work i.e. this world we live in), have the measurement of finger. The present day measurement of human finger measure is known as ‘Atmangul.’
6 finger measure makes one leg measure (Pad Māp). Two leg measures make one Vitasti; and two Vitasti measures make a Hast (Hand) (18 inches or 45 Cms.) 4 Hasts make one ‘Dand’ and 2000 Dands make one Kosh (about 2 miles or 3 Kmts.). All these small and big measures provide us guidance for measurement of area.
Kāl Pari Bhasha (Time explanation)
‘Samay’ is a time taken by one atom (in speed) to travel from a given point to its nearest point.
Innumerable ‘Samay’ make one ‘Aāvali’. A number of such ‘Avali’ makes one breathe. Seven breaths make one ‘Stok’ and 37.5 stoks make one Ghadi (24 minutes.)
Two Ghadies (48 minutes) make one Muhurat. Thirty (30) Mahurats make one day (24 hours) fifteen days make a fortnight and two fortnights make one month. Two months make one season (Ritu). Three seasons make one Ayan and Two Ayans make one year (12 months.)
F3 3.2.4 Form of Twelve Arās.
In both Bharatshetra and AirāvaKshetra, the time has been divided into two phases; viz. Avsarpini Kāl andUtsarpini Kāl. They move cyclically; and both of them together make a whell of time (Kāl Chakra). Both these have 6 Atās each, making together 12 Arās in a wheel of Time (Kāl Chakra).
These 6 Arās move like a wheel of a cart, and the Arās (the inside supporting system crossing each other) like those in a wheel go up and down in a sequence. In both Bharatkshetra as well as Ariavat Kshetra, the time goes on changing like Arās of a wheel. That is why, the kāl, (Time) is compared with a wheel. The six Arās make Avsarpini kāl and other six Arās make Utsarpini Kāl. Both together make a wheel of Time (Kāl Chakra)
Avsarpini Kāl is a phase of time wherein there is continuous decrease or diminishing in various aspects of life, such as- the colours of a thing, its smell, its taste, its touch sensation, the life span of human or animals, size and strength of body etc. This decrease take place not all of a sudden but very gradually. From 1^{st} Arā, it states the process of diminishing till the end of sixth Arā. After completion of 6 Arās of Avsarpini Kāl ; starts the period of Utsrpinikāl. Now, there is a gradual increase in all these things. This process of growing also stars upto completion of 6^{th} Arā of Utsrpini kāl, thus, the process of ups and downs go on, and on and on and on.
In the table below is self-explanatory. In;
Arās 1-6 : The time is known as Sushma - Shusma ; which means that people are always happy and happy only.
Arās 2-5 : It is Sushma period, wherein people are very very happy.
Arās 3-4 : It is Sushma – Dushma ; which means that people are generally happy, but the happiness is mixed with unhappiness.
Arās 4-3 : It is Dushma – Sushma ; period wherein people are usually unhappy; but there is some happiness too.
Arās 5-2 : The period is Dushma; and as such people are very unhappy.
Arās 6-1 : It is Dushma – Dushma period; wherein people are unhappy, very very unhappy and there is only unhappy and there is only unhappiness in period of time.
Avsarpini |
Utsarpini |
Condition |
Time span |
Life Span |
The body structure (Human) |
1^{st} Arā |
6^{th} Arā |
Happy-Happy |
4 Kotakoti Sagaropam |
3 Palyopam |
3 Gau (6 miles) |
2^{nd} Arā |
5^{th} Arā |
Happy |
3 Kotakoti Sagaropam |
2 Palyopam |
2 Gau (4 miles) |
3^{rd} Arā |
4^{th} Arā |
Happy-Unhappy |
2 Kotakoti Sagaropam |
1 Palyopam |
1 Gau (2 miles) |
4^{th} Arā |
3^{rd} Arā |
Unhappy-Happy |
1 Kotakoti Sagaropam and 42,000 years |
Purva Crore years |
500 Dhanushya |
5^{th} Arā |
2^{nd} Arā |
Unhappy |
21,000 years |
130 years at the end |
7 hands (10.5 feet) at the end. |
6^{th} Arā |
1^{st} Arā |
Unhappy-unhappy |
21,000 years |
20 years |
1 Hand (1.5 feet) at the end |