Ostensive Expression of Measures in ANUYOGADHARHAIM 

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ABSTRACT

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Unlike modern Numerology based abstract measurements ancient Indian and especially Jaina mathematical expressed were designed ostensive kind of measurements.A peculiar system of measurement was in use during those days.

The measures used to weigh or measure different kinds of things were not only simple and understandable but were also perfect and unique. The Jaina āgama text ‘Ānuogadharāin‘ contained with elaborate explanations are different kinds of measures used in those days, which owes its own importance for the cultural study our Indian heritage.

Jainism is a spirituality based religion and philosophy. In fact all Indian schools are such. Hence all the mathematical issues found in scriptures are not merely for economic transactions but for exploring the state – of – facts i.e. world and worldly components including the abstract phenomenon like soul.

The significant quality of Indian and Jaina mathematical expressions and measurements is that they could measure every inch of this universe and indicated about all the locations through their own measurement units.

The purpose of exploring the universe and its different locations was to
develop detachment(Vairagya) towards worldly hankerings. Since lokajiuina, i.e. the knowledge of the world is one of the causes of Vairiigya, it helps one to understand his position in the world and make efforts to evaluates the self on still higher level of existence.

Hence mathematical issues are useful in the description of the universe, in astrology and in social transactions also mathematical issues are found. The measurement units of were used, defined and developed in their own system.

The modern numerology based on mathematics has employed numbers as the units of all measurements and calculations. What really a numbers is?

It is defined as- ‘it is functional, subjective and anonymous phenomenon. It belongs to logical world but functions in actual world.’

It is defined as the “an arithmetical value representing a particular quantity and used in counting and measurements and making calculations.” 

Its existence is in logical world but functions in actual world. Logically existing numbers are helpful to apprehend the state – of – fact. The knowledge gained by numbers is inferential rather than direct. For eg., When
one utters the word, centimeter, inch’, kilometer, kilogram or litre etc. we realize that all of them are measuring units that are purely abstract and known by mental faculty. Although there are scales that shows what a centimeter is but it cannot be shown directly as ‘see, this is one centimeter.’ Numbers in themselves doesn’t have any physical properties.

We can never say number 7 is white or grey or it smells bad. They have pragmatic value but not the existential value. Hence modern measurement units do function in the sphere of material world but we can never prove its objective reality.

On the contrary, when we look into the Indian and Jaina manuscripts, we find that mathematical calculations are used to determine the state-of-fact but are not completely abstract phenomenon but it is ‘ostensive‘. By ostensive, it is meant false or duplicate display that means to show the measure through some physically existing object whether it is one and the same or alike’.

It is defined as to show or confront you with an instance or instances of the word’s denotation”?
It is pointing out something to understand the objective world. Through the display of some object measurement units are standardized.

Showing pink colored ice cream and a mountain if it is told to imagine about a pink ice mountain, it is easy to think of it by imagination. Similarly in Jaina scriptures, the measurement-units are quite common commodities used by the people in general hence they are easily apprehensive’. Sometimes imagination
is also required to measure such as in multiplication or division. Hence Jain

manuscripts display the truth that in ancient times ostensive kinds of units of measurements were used. One of the manuscriptsis Anuyogodvara,which has described about the measurements units at length. Using this text we can know about various such measurement units.

In Prarnan adhikara, there is a mention of four kinds of pramauas (measurements )

1. Dravya pramana	2. Ksetra pramana
3. Kala pramana	4. Bhava pramana

Among these four, except Bhava Pramana all the three empty ostentation for measurement.

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I. Dravya Pramana

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It is sub divided into two types-
a. Pradesanispanna – It counts from one atom to infinite pradesas, Here the ‘atom‘, the fundamental unit of objective world has been held as the unit of measure.

b. Vibhaganispanna- Measure based on different kinds of divisions.

Dravya Pramana is of four kinds.

1. Mana- Used to measure solids (Dhanya prarnana) and liquids (Rasa pram aua)
In those times, to measure solids and liquids kg or liter units were not used. They used for dhanya pramana the measurements like Asati, pasati   upto tula.

Here, Asati means ‘handful of i.e. as much’ the inverting downward ones palm pick up the grain etc. palmful of grains is called as an asati and then with the addition or multiplication of this asati, other measurement units are formed.

It goes upto tula. Liquids are measured by pal a which in the series of units begin from paramanu. Here the Paramanu (atom) itself is the unit of measurement. Generally it is also defined very clearly that ‘the thirtieth part of the subtle fibers that are seen in the sunrays beamiag from a window or any thin curtailed space is called as paraman u. 

But in Jaina tradition, there is a different definition. There is a mention of two kinds of pararnanu.

Vyavaharika (empirical), and Param arthika (transcendental). The empirical is a gross form of paramanu that can be imagined. Hence such paramanu is used as the primary measurement unit and then pala is one of the units formed by the further addition of param anus. Whole class of measurement units are used to measure the liquids kept in various kinds of pots named as driti, kalasa, ghata, kudika etc. 

2. Unmana is useful in weighing powders like kurnkum, sugar powder, dry molasses powder etc. It begins with the Ardha-karsa and ends upto bhara, Karsa is a stone determined for measuring. Sarsapa, gunja, dhanyadla. are all fruits that are used as measuring units. It lastly goes llpto khari and baha.

3. A vamana is again to measure areas like plots, fields etc. In this casehath is used to measure home plots, danda for fields, dhanusa for roads, nalika for wells and valleys, and aksha for walls. Finally it goes to rajju, which is used to measure the length and breadth of the universe.

4. Ganita – It is a kind of measuring system which is completely based on money and other countings for economic transactions.

Ganyate sankhyayate yat tat ganimam
It goes from 1,2,3.4   upto srrsa prahelika.” Here, a thing to be noted is that upto sirsa prahelika, there is a system of counting but beyond that every measure and calculation is based on ostentation. Such are the concept of palyopama, sagaropama, utsarpini and avasarpini and finally ardha-pudgala­ paravartana.?

The most complicated phenomena of palya, sagara and rajju have been explained so beautifully that just by the listening or reading that ostensive expression, a clear picture of their vast duration can be pictured in the mind.

S. Pratimana- It is used to weigh the gold, diamonds, pearls and other valuable things. Although they can be included in the dravya pramm).a but since they are generally not sold in kilos or liters, a special system of gunja and ratti etc. is used to weigh them.

n. Ksetra Pramana-It includes the measures like afigula, hatha, gau, dhanusa, yojana etc. These are all ostensive expressions. This measure is very interesting to understand the structure of anything in general.

For example –

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Lets observe another series-

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6 afigula	1 foot (Pada)
12 foot	1 vitasti
24 vitasti	1 hand (hath a)
48 hand	I kukshi
96 kukshi	1 dal).c;la
200 danda	1 dhanusa
500 Dhanusa	1 gavyuta
4 gavyuta	I yojana

These are the terms of the things lying in their own periphery of transaction
and were used by the people in general. Hence they were very easy to understand and also to use.

 

It is quite interesting to know that having no technological support they could manage measure not only the worldly things but also the hell and heaven are measured up to the end of the universe.

Even the length and the breadth of the people residents in hell or heaven or other alien countries and void space of this universe also has been measured by their intuitive knowledge. Some times they have used the purusa i.e. human body .itself to measure the depth of valleys or any down slanting locations like there is mention of usage of such words in paniniya Kalina Bharatvarsha. For example dvipurusika, trihastika khai, etc.

In Paniniyakalina Bharatavarsa, it is mentioned that there is a mention about barter system prevailing in those days.” In the chapter on pramana and unmana, there is a description of different kinds of weighs- used in those days. some of them seem similar to those that are found in Jaina agamas. Like adhaka, drona, Khari etc. It also illustrates the measuring units as referred in Astadhyayl, such as-

1. mas a	a coin or a weigh made up of silver and copper
2. Nisapava	it is equal to three ratti
3. Sal).a	it is equal to 20 ratti
4. Bista	it is equal to 80 ratti
5. Anjali (handful)	16 karsa, It was also called as kudava
6. Kulija	may be equal to prastha
7. 4 prastha	1-1 adhaka
8. 4 adhaka	1 drona
9. 4 drona	1 khari,
10. 20 drona	1 kumbha
11. 10 kumbha	1 mana

III. Kala Pramana

In Bhagavai, the kala pramana has been described from samaya to sirsaprahelika. From samaya to slrsaprahelika are the units of countable time. here some higher levels of time measuring units have been called as ‘ovamiya‘ (illustrative) kala. Under this category comes the

(1) Palyopama (pit-measured time-unit)

(2) Sagaropama (ocean measured time-unit)

Its starting point is pararnan u. The param anu is the first unit of measurements.” The paramanu is of two kinds- subtle and empirical. In the present context, subtle paramanu is not considered.

An infinite number of subtle paramanus make one empirical atom. It cannot be cut or pierced even by sharpest weapons. It is applicable to both empirical and transcendental atoms. Here empirical atom is intended. 

Palyopama is again explained ostensively that- ‘a pit’ one yojana long and one yojana wide and one yojana deep- is filled tightly with the pieces of the hair of a New born baby one to seven days old. Now if one piece of hair is taken out of the pit in one hundred years, the period taken for emptying the pit is called palyopama.”

Sagaropama is defined as

eesim pallanam, kodakodi havejja dasaguniya 

tena sagaropamassa uekkassa bhave parim anarp 

Ten crore and crores of this palyopamas make one sagaropama. Crores of sagaropamas together constitute one ufsarpinl or avasarpini. Then the number comes to the innumerable, uncountable and ultimately it reaches up to the infinite. Hence the period of one utsarpini and one avasarpini together makes the 20 crore & crore sagaropamas.”

Hence, in conclusion it can be said that the use of ostentation in measurement is quite unique in Indian and especially Jaina system of measurement. -Use your hand or objects available around you and measure whatever in objective world.

No calculators or computing support is needed. Use of addition, subtraction, and multiplication is more prevalent in those texts than division and other mathematical calculations. Hence it remained always simple for general public to understand and apply mathematics.

No highet complications of mathematical issues are found at least in the case of measurement. Hence I believe that it is right time to organize seminars in such issues. It is ostensive expressions which is unique and unparallel in any other belt of the world.

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BIBLIOGRAPHY 

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Abhidhāna Rājendra Koșa of Vijaya Rajendra suri,Ed. by Bhupendra Suri, Jain Prabhakara Yantralaya, RatIam, 1991.

Anuogadārāim, Ed. by Ācārya Mahāpragya, Jain Vishva Bharati Institute, Ladnun, 1996.

Anuogadvārasūtram, Ed. by Misrimalji Maharaj, Trans. by Kevala Muni, Agama Prakashana Samiti. Byavara,1987.

Bhagavai, Part-2, Ed. by Ācārya Mahāpragya, Jain Vishva Bharati University, Ladnun, 2009.

Concise Oxford Dictionary, Ed. by R. E. Allen,4th edn., Oxford University Press, Oxford, 5th reprint 1994.

Hospers, John., An tntroduction to Philosophicol Analysis, Allied Publishers
Pvt. Ltd., New Delhi, 1971, 15th print 2002.

uminator of Jaina Tenets, ( English Trans. of Jaina Siddhanta Dipika of Acaryasri Tulsi), Translated by Satkari Mukherjee, Ed. with notes by Nathmal Tatia & Mahendra Muni, Jaina Vishwa Bharati Prakashana, Ladnun, 1995.

Jainendra Siddhanta Kosa, Part-Z, ed by Jinendra Varni, Bharatiya Jfianapitha, New Delhi, 7th edn., 2004.

Thanam, Chapter Vll, by Acarya Mahapragya Jain Vlshva Bharati, Ladnun, 1996.

Vasudeva Sharana Agraval., Paninlkalina Bharatvarsa, (A cultural study of Astadhyayi) Chaukhamba Vidyabhavan, Varanasi, 1969.

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References 

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I. Concise Oxford Dictionary-, ed by R.E. allen. 4th edn .•Oxford University Press, Oxford. 5th reprint 1994. p. 813.

2. Hospers. John.-, An introduction to Philosophical Analysis”’. Allied Publishers Pvt. Ltd., New Delhi. 1971. 15th Print 2002. p. 56, 57.•

3. Anucgadaraim,- ed by Acarya Mahapragya, Jain Vishva Bharati Institute, Ladnun, 1996, P. 221.
4. .Op Cit.
5. Sarngadhara Samhita-, p. 4. “, jalantaragate bhanau yatsuksmam drsate raja tasya trinsattamo bhagan, paramanu sa kathyate” As quoted in Anuogadaraim, P. 241.

6. Ibid. p. 222

7. Ibid. p. 224. Cf . Anuogodarrsutram, ed by Misrimalji Maharaj, p. 237.

8. It comes to be the number –7582632530730 I0247157973569975699756964062189668480-
80183296 with 140 zeros appended to it. The whole number consists of 194 digits. Up to this, there is mathematical calculations; subject of mathematics; beyond that the period of time are to be measured through comparisons or ostentation.

9. Iainendra Siddhanta Kosa-, Part-2, ed by Jinendra Varni, Bharatiya Jnanapitha, New Delhi, 7th edn.,
2004. p. 217.

10. Paainikaliua Bharatvarsa-, P. 244.

11. Op cu.

12. Ibid-, p. 240-242.

13. Bhagavai-, Part-2, ed by Acarya Mahapragya, Jain Vishva Bharati University. Ladnun, 2009, p.429.

14. Ibid-, P. 432 satthena sutikkhena, Chettum va jam kira na sakkii lam paramiinum siddhii, vadanti iidim pamiiniiiiruim
15. Anuogadarairn. P.24 J. Note: Acarya Mahapragya, In his critical notes .propagate that though atom is indivisible unit in Jaina philosophy but modern scientific sophiscated tools have devided the atom and propounded it to be divisible. To resolve this contradiction we must accept that the subtle atom cannot be devided but gross and empirical atom has parts, hence it is divisible. Cf. Bhagavai, P. 435

16. Ibid-, p.436.

17. Ibid, p.434.

18. Op. Cit.,P. 434