Concept of Infinity in Jainism

   Introduction

                 

    Infinity  is an intriguing word. The dictionary meaning is unmeasurable or endless. Mathematics tells us as a distance where all parallel lines meet. As a number it can be described as a never ending sequence of zeros preceded by one. We call our space as infinite space. The numbers of atoms in the universe are infinite. So also are the total number of life forms in the universe. Then the question arises that which one is higher ? Is the space more infinite or the atoms or the life forms? Science fails to provide us with a satisfactory answer. But in Jainism this subject is treated very admirably. After all the answer is directly attributed to the omniscient. When we  read this subject , we not only can appreciate the magnitude of  intricacy that Jainism nurtures within its folds, but also the greatness of the omniscience which has described all this in so clear terms without having any scientific tools at its disposal. One can truly appreciate  the meaning of term direct knowledge or clairvoyance when one reads the  extent to which the details are described in Jain scriptures. How else do we explain that while  Dr Jadish Basu discovered that trees are life forms in 20th century , Jainism was already talking of five types of single sensed jivas( life forms) including vegetations  as early as 1st century ( which is the earliest when the scriptures were transcribed from oral to written form). It is mind boggling to note that Jainism describes nine types of innumerables followed by another nine types of inifinities which are extensively used for the purpose of describing relationship of one quanity with respect to another. In fact Jain scriptures are loaded with several charts describing “Alpabahutva” which deal purely  with relationship of one number to another in terms of quantity , size, period  etc.. Can you imagine that in Jain mathematics 216 is such an important number that it is given a name called “Pannatthi” which is named after the figure 65 which is part of the number 65536 which it represents. The value of 232 is called “ Badaal” after the figure 42 which is ten digit number. Further 264 is a very important number named “Ikathhi” after the figure 18 with which the number begins and is a twenty digit number. While western world takes credit for invention of Log tables , the Jain mathematics freely used numbers to the base of 2 and uses terms like “ardhchheda” which imply log of a number to the base of two. There is a major reason why Jainism did not bother about publicizing their findings. The entire effort of the scriptures including mathematics is directed towards realization of the soul and nothing else. Knowledge of these subjects aided their understanding of the self, universe and their relationship. For them mathematics was just a tool while soul was the goal. In this paper we will present the various types of infinities that Jainism uses and give a glimpse of the highest infinity.

The organization of numbers

In Jainism the numbers are described in three categories. Samkhyat ( numerable) , Asamkhyat (Innumerable)  and Anant( infinite).

Samkhyat(Numerable):  While counting begins with 1, the number 1 is not treated as Samkhyat since the square of 1 does not increase the number and subtracting square root of the number from 1 makes it zero. Hence the minimum Samkhyat is 2. The maximum Samkhyat is cleverly assigned as 1 less than Minimum Asamkhyat. All the intermediate numbers are called Madhyam(medium) Samkhyat. Thus the numerable numbers fall into three types as Min, Max or Intermediate. The only important thing to note is that the maximum Numerable is also a very very large number as will be seen when we try to compute the minimum Innumerable. The following chart presents the organisation of numbers in Jainism.

The Innumerables

Asamkhyat ( Innumerable) :  These are three types: 1. Paritasamkhyat  2. Yuktasamkhyat  3. Asamkhyatasamkhyat , each of which have Min. Max and Intermediate. Thus there are nine innumerables.

Note : In this article I have tried to simplify the language as much as possible to make it easier to understand. English equivalents are used wherever possible. Where no equivalent exists , I have used original Hindi words.

Min Paritasamkhyat : The process for computing this number involves imagining four wells of 1lakh yojan diameter and 1000 yojans deep. ( 1yojan=4kosa=9miles).  Let us name them as A,B,C and D. Then the  well A is filled with mustard seeds such that it overflows and forms a conical shape on top and cannot take any more. The number of seeds required to do this has been computed to be a 46digits number(say X). Now first seed is dropped into an island of 1lakh yojan diameter , second into sea surrounding the first  in a concentric shape having 2lakh yojan width, then third into a concentric  shape  island surrounding the sea having 4lakh yojan width and so on. Thus the last seed will fall on island/sea having width of 2^X yojan. Once all seed of well A are exhausted then drop one seed in well B. Now imagine a well having  diameter equal to the sum of all seas and islands where seeds were dropped  and depth of 1000 yojan. The diameter of this well is sum of the series  Y=2⁰+2¹+2²+2³+……..+2^X. Now fill this well in the same manner that well A was filled with mustard seeds. Then continue the process of emptying these seeds in ever enlarging concentric seas and islands. When all seeds are emptied then another seed is dropped into well B. Continue in this manner till well B is overflowed with seeds. Now drop one seed into well C and empty well B. Now start again by emptying seed of the well with diameter Y into alternating concentric seas and islands. When it is emptied one seed is dropped into well B. In this manner when well B is filled another seed is again dropped in well C. Continue this process till well C is filled, then one seed is dropped into well D. Restart with emptying of well B and C. Continue the process till well D overflows. At this stage the number of seeds  filling the massive size of concentric seas and islands which correspond to the final well  is equal to Min Paritasamkhyat. Let this be denoted as JP.

The number Min Yuktasamkhyat is computed as JY= JP^JP.

The Max Paritasamkhyat is = JY-1    Between Min and  Max Paritasamkhyat all numbers are intermediate Paritasamkhyat.

The Min Asamkhyatasamkhyat is computed as JA= JY².

Max Yuktasamkhyat = JA-1  Between Min and Max Yuktasamkhyat all numbers are intermediate Yuktasamkhyat.

The Max Asamkhyatasamkhyat is = Min Paritanant-1  . All numbers between Min and Max Asamkhyatasamkhyat are intermediate Asamkhyatasamkhyat.

                                                The Anants

Note : In this chapter several new words and units are used to describe the unit of time , length etc. Effort is made to minimize it with objective of conveying the essence of the process without cluttering with details.

Min Paritanant:   Let min Asamkhyatasamkhyat be denoted as x

Compute   y =  x^x^x     then z = y^y^y    then  A = z^z^z

All the numbers y, z and A are intermediate Asamkhyatasamkhyat only.

Into this number A are added four times spacial elements of Lokakash ( universe) which are Asamkhyat.( The spatial units of the entire universe is described in scripture as Asamkhyat only in number and not Anant. Each spatial unit is the space occupied by an atom. This atom is far smaller than the atom that we know)  Further added are Number of vegetation form Jivas( life forms) which are Asamkhayata times of Lokakash number. Thus we arrive at a number B

Now compute   C = B^B^B   ,   D =C^C^C   ,  E = D^D^D

Even now the number E is intermediate Asamkhyatasamkhyat.

Into this number E now we add four quantities.

1.   Number of time elements( samay) equivalent to 20 kodakodiSagar years. Here Sagar is a imaginary unit of measurement of time of very large order, and samay is the smallest unit of time in Jainism which is far far smaller than second. Kodakodi means 10¹⁰. 20 KKsagar is denoted as Kalpa kala which is one life cycle of time.

2.   The sthitibandha adhyavasaya sthana which are asamkhyata times of item 1.

3.   Anubhaga bandh adhayavasaya sthana which are asamkhyata times of item 2.

4.   Number of Max avibhaga praticcheda of Yoga which are asamkhyata times of item 3.

It will be futile to explain these four quanitities in this paper since each needs elaborate explanation. Suffice to say that these are very large asamkhyata numbers.

Addings these four quantities would still generate an intermediate asamkhyat number F.

Now compute E = F ^ F^F  This number is the Min Paritanant.

Min Yuktananta is computed as  = ( Min Paritanant ) ^{Min Paritanant} 

Max Paritanant=  Min Yuktanant- 1   and the intermediate numbers are intermediate Paritanant.

Min Anantanant =  (Min Yuktanant )² = G

Max Yuktanant = Min Anantanat- 1   and in between numbers are Intermediate Yuktanant

Intermediate Anantanant =  From Max Anantanat-1    to  Min Anantanat+1

Computation of Max Anantanat :

Compute H= G^G^G = Intermediate Anantant number

Into this add six quanities

1)   Number of liberated souls( Sidhhas) which is infinite times smaller than total souls(Jivas) of the universe.

2)   Entire Nigod Jiva quantity ( these are single sensed Jivas which are miniscule and occupy the entire universe in miniscule size and also live dependent upon vegetation. Their unique feature is that infinite jivas live and die together occupying the same body). These are infinite in numbers.

3)   Vegetation jivas inclusive of Nigod Jivas.

4)   Pudgala  ( Matter) quanity which is infinite times the Jivas quantity.These are the numbers of atoms in the universe.

5)   Number of samay ( time units) of past present and future which is infinite times that of 4.

6)   Number of spatial elements of Alokakash which is infinite times that of 5. ( Lokakash is the universe where all jivas reside and is a bound space which Alokakash is unbound infinite space surrounding Lokakash ). Together they form Akash or the space as described in Jain scripture.

Thus we obtain a quantity K

Then compute L = K ^ K^K = Intermediate Anantanant

               Into this add quality units of Agurulaghu Guna of Dharma and Adharma dravya. ( This too need not be explained here. These are also infinite numbers)

                   So we arrive at a number = M

          Compute N = M ^M^M   which is still medium Anantanat

The scripture says that in spite of doing all this we have not arrived at the number representing Max Anantanant. So what do we do ? So they say Substract N from the Max Anantanat and add the resultant back to N , thus you will arrive at Max anantanat.

For example you want to count upto 1000 and have managed to count upto 100 only. So substract 100 from 1000 and add the resultant 900 into 100 to arrive at 100. What it symbolizes is that inspite of this exercise the number N is far less that Max anantant. 

What does Max Anantanat represent ?

We have already counted all the known quanitites in the process of computing Max anantanant. These were as follows:

1)   Number of Jivas in the universe(life forms)

2)   Number of matter units in the universe(atoms)

3)   Number of spatial units in the lokakash and alokakash

4)   Number of time units of past present and future.

Then what has not been accounted for ? Which is still higher than these numbers ?

The answer is exceedingly interesting . What is not accounted is the number of units of knowledge. As per scripture, the Jiva is never devoid of knowledge, even though he is in the lowest single sensed state called Nigod. If he has no knowledge then he becomes inert like matter which is not possible. In spite of his continuous transmigration in different births  he still continues to  have the capability of knowing and seeing (consciousness). Only  his knowledge is obscured due to accumulated karmas but the capability of knowing exists since that is his nature.The amount of knowledge is least in single touch sensed nigod form to highest in human form which is six sensed.   Now the knowledge content is measured in units of avibhaag praticcheda which is nothing but smallest indivisible quantity of knowledge or in other words units of knowledge.

 The knowledge content of Nigod jiva ( which is the lowest of the life forms which one can take) is infinite times less than the knowledge content in a single letter of vocabulary! Even then  his knowledge units are infinite times higher than that of six quantities we have just added in the computation of Max Anantanant !!

One wonders why the knowledge content of most smallest of Nigod jiva is measured as  such a large number. There is reason for it. There are infinite jivas in the single sensed state itself and their knowledges are not equal and keeps varying as a function of time. In fact the increases are infinitesimal, finite, innumerable to infinite times of the least units. If lowest state was ascribed a value unity then others would have been increasing by a number unity divided by infinity in fraction form. In Jain system   the least number itself is infinite and increases in the single sensed jivas itself , then to two, three, four and five sensed jivas  . This increase goes on till we arrive at knowledge pertaining to single letter called Akshar Gyan.

          Here onwards the knowledge can be measured in terms of number of letters , words or sentences. Hence it is called Sruta Gyan since this can be contemplated in mind and passed on orally. Interestingly the quantity of this knowledge is arrived as 2⁶⁴-1. This is so because 64 is the number of letters in Hindi language and 2⁶⁴-1 forms the total number of non repetitive letters that can be formed with 64 letters. Hence total knowledge cannot exceed this number which itself is a very high number.

          Jainism describes three types of knowledge above Sruta Gyana. While knowledge with senses is called Indirect knowledge, these three are called direct knowledge wherein the soul knows directly without any sensory tools.  One is Avadhi Gyana which enables one to know about objects directly, the second is Manahparyaya Gyan or Clairvoyance which enables higher order saints to  know about objects in someone’s mind directly. The third is the Keval Gyan or Omniscience which was the subject of this paper. The knowledge of the liberated soul when all  karmas are shed is capable of knowing and seeing all the knowables. The omniscient knows all the smallest modifications of the entire lot of six dravyas ( elements of the universe) pertaining to past present and future at the same time . The Max Anantanat denotes the number of units of knowledge it contains. No wonder it is far far higher than any number we could imagine. This knowledge is the inherent property of soul which was obscured in the worldly state depending upon his karmas. Once the soul is liberated , all the knowledge is unobscured and once he knows all, he has no perturbation since he does need to know anything. It may also be noted that Keval Gyan is far far more than the Sruta Gyan or the knowledge we can gain through words , since the amount of knowledge the omniscient can pass on is only a fraction of what he knows and further what can be transcribed is still a fraction of what is received.

          It is important to note at this stage that while science does talk about the infinite universe size or the age of the universe and the quantum of matter in the universe but they are unable to venture beyond this. Hence they do not talk of the soul leave apart the direct knowledge and its quantum. Therefore this is one infinity which is untouched by science. On the other hand Jainism has delved deep into this subject even in first century !

Interestingly  the knowledge units are not dependent upon our universe. As per scripture , the knowledge capability is so high that several universes also would have been known had they been there. It means that knowables are limited because they are part of the universe but knowledge of omniscience is unlimited.

That is infinity for you.

Note : For those who are interested to learn more on the subject are advised to read “ SamyakGyan Chandrika : JivaKanda” written by Pandit Todarmal

                                                                The End 

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