The Enigma Of The Universe : ANANTA (INFINITY)

There are three main types of ananta (infinity).

1. Parita-Ananta (P. An.)

2. Yukta-Ananta (Y. An.)

3. Ananta-Ananta (An. An.)

Each of the above three types are sub-divided into three subtypes:

1. Jaghanya (Maximum)

2. Madhyama (Medium)

3. Utkṛṣṭa (Maximum)

Now let us consider these nine types of ananta as described in the Jain philosophy.

1. Jaghanya-Parita Ananta (J. P. An.)

By adding one in U. A. A., we get the value of J. P. An.. It means,

J. P. An. = (U. A. A.+1)

2. Madhyama Parīta Ananta (M. P. An.)

The numbers [(J. P. An.)+1] to [(U. P. An.)-1] are called M. P. An.. It means

[(J. P. An.)+1] ≤ M. P. An. ≤ [(U. P. An.)-1]

3. Utkṛṣṭa Parīta Ananta (U. P. An.) [(J. U. An.)-1] is known as U. P. An.

U. P. An. = [(J. U. An.)-1]

4. Jaghanya Yukta Ananta (J. Y. An.)

By raising J. P. An. to itself (abhyāsa-guṇita), we get the value of J. Y. An..^[1] It means

J. Y. An. = (J. P. A_n.)^{(J. P. An.)} 5. Madhyama Yukta Ananta (M. Y. An.)

The numbers [(J. Y. An.)+1] to [(U. Y. An.)-1] are called M. Y. An., It means

[(J. Y. An.)+1] ≤ M. Y. An. ≤ [(U. Y. An.)-1]

6. Utkrsta Yukta Ananta (U. Y. An.)

[(J. An. An.)-1] is called U. Y. An.. It means

U. Y. An. = [(J. An. An.)-1]

7. Jaghanya Ananta Ananta (J. An. An.)

There are two definitions of J. An. An..

1. By raising J. Y. An. to itself (abhyāsa-guṇita), we get the value of J. An. An..^[2] It means-

                J. An. An. = (J. Y. A_n.)^{(J. Y. An.)}

2. By squaring J. Y. An., we get the value of J. An. An..^[3] It means

                J. An. An. = (J. Y. An.)² 8. Madhyama Ananta Ananta (M. An. An.)

Its definition is in two versions:

1. All the numbers from [(J. An. An.)+1] onwards are called (M. An. An.).^[4] It means

M. An. An. ≥ [(J. An. An.)+1]

2. The numbers from [(J. An. An.)+1] up to [(U. An. An.)-1] are called^[5] M. An. An.. It means-

[(J. An. An.)+1] ≤ M. An. An. ≤ [(U. An. An.)-1]

9. Utkṛṣṭa Ananta Ananta (U. An. An.)

According to Shvetamber (canonical) tradition, there is no existence of U. An. An..

According to the Digambara tradition and the Karmagrantha, we get different definitions of U. An. An.. Again, in the Digambara tradition, we get three different definitions based on different definitions of V.-S. and difference in the sets of the infinite magnitude to be added. The fourth definition is of the Karmagrantha (which however is not believed to be canonical work in the Shvetambara tradition). We give here all the four definitions:

1. Firstly, J. An. An. is squared three times (i.e., it is raised to the power eight). Then the following six sets of infinite magnitude^[6] are added to the result obtained:

(1) The total number of vanaspatikāyika jīvas (vegetable bodied souls) of the whole universe.

(2) The total number of nigoda jīvas.

(3) The total number of siddhas (liberated souls).^[7]

(4) The total number of paramāṇus (ultimate atoms) of the whole universe.

(5) The total number of samayas of all time.

(6) The total number of pradeśas of the whole alokākāśa (supra-cosmic space).^[8]

Now, the magnitude thus obtained is again squared three times. Then to the magnitude obtained, the modes^[9] of the kevalajāna (omniscient knowledge) and the kevaladarśana (omniscient intuiion) are added. The magnitude thus obtained is called U. An. An.. There does not exist any object of this magnitude, and hence, it is of no use in empirical world.^[10]

2. The second definition of U. An. An. is as follows:^[11]

Firstly, J. An. An. is made to undergo operation V.-S. three times. Then the aforementioned six sets of ananta (infinite) magnitude are added to the magnitude obtained. Again, the obtained magnitude is made to undergo operation V.-S. three times. Now, to the magnitude thus obtained, the avibhāgī pratīccheda (indivisible units) of the agurulaghuguṇa (the quality of self sustenance) of the two dravyas (substances)- dharmāstikāya and adharmāstikāya- are added, and again the magnitude obtained is made to undergo the operation V.-S. three times. The final result thus obtained is denoted as 'U. An. An.'^[12] This magnitude is equal to the (modes of) kevalajāna (omniscience). The mathematical computation which was made in the third definition of U. A. A. (see pp. 378-379) will be repeated here.

Thus, if J = J. An. An.

m₁ = the sets added first time

m₂ = the magnitude added second time

then,

III. The third definition of U. An. An. is given as follows^[13]:

The only difference in the II and III definitions is that instead of operation V.-S., here we use the operation 'śalakātrayaniṣṭhāpana'.

Here, the same mathematical computation is to be made as in the fourth definition of U. A. A.

Thus, if

J₁ = J. An. An.,

Then, by administering operation śalakātrayaniṣṭhāpana', we get the magnitude J₄.

Now, if m₁ = the sets added, then

J₄ + m₁ = J′₁

Then, we can find the value of in J′′1 in the same way. Thus, we get

J₄` + + m₁ = J₁" and so on up to J₄".

Then, U. An. An. = J₄"

IV. The fourth definition of U. An. An. is given as follows^[14]

The only difference in the III and IV definition is that here, after getting the value of J′₄ -1, the ananta (infinite) bahubhāgas (indivisible units) of kevalajāna (omniscient knowledge) and kevaladarśana (omniscient intuition) are to be added to it. If it is denoted by m₃, then

U. An. An. = J′′₄ + m₃

This number is also in the form of bhājana (container) and not actual dravya (real substance). It means that there is no such object in the universe which has this magnitude.

Thus, even if there is difference in the different definitions of U. An. An., but one thing is unanimously accepted that the value U. An. An. is only virtual, there being no substance actually existing, which has this magnitude.

Further research in the concept of ananta in Jain philosophy and that of infinity (α) in the modern mathematics is needed to evaluate the Jain philosophical view.