The asaṃkhyāta (innumerable) is classified into three types:
1. Parīta Asaṃkhyāta (P. A.)
2. Yukta Asaṃkhyāta (Y. A.)
3. Asaṃkhyāta Asaṃkhyāta (A. A)
Each of the above is again of three types:
1. Jaghanya (Minimum)
2. Madhyama (Middle)
3. Utkṛṣṭa (Maximum)
In this way, there are nine types of asaṃkhyāta. Let us consider each of them one by one.
1. Jaghanya Parīta Asaṃkhyāta (J. P. A.)By adding one to U. S. we get the value of Jaghanya Parīta Asaṃkhyāta (J. P. A.).
Thus
J. P. A. = (U. S.) +1
2. Madhyama Parīta Asaṃkhyāta (M. P. A.)The numbers from [(J. P. A.)+1] to [(U. P. A.)-1] are called M. P. A., thus
[(J. P. A.)+1] ≤ M. P. A ≤ [(U. P. A.)-1]
3. Utkṛṣṭa Parīta Asaṃkhyāta (U. P. A.)[(J. Y. A.)-1] is called U. P. A.
U. P. A. = [(J. Y. A.)-1]
4. Jaghanya Yukta Asaṃkhyāta (J. Y. A.)J. P. A. raised to itself[1] is called J. Y. A.
J. Y. A. = (J. P. A.)
5. Madhyama Yukta Asaṃkhyāta (M. Y. A.)The numbers from [(J. Y. A.)+1] to [(U. Y. A.)-1] are called M. Y. A, thus
[(J. Y. A.)+1] ≤ M. Y. A. ≤ [(U. Y. A.)-1]
6. Utkṛṣṭa Yukta Asaṃkhyāta (U. Y. A.)[(J. A. A.)-1] is called U. Y. A.
U. Y. A. = [(J. A. A.)-1]
7. Jaghanya Asakhyāta Asaṃkhyāta (J. A. A.)There are two definitions.
(I) By raising J. Y. A. to itself[2] we get the value of J. A. A.
(J. A. A) = (J. Y. A)(J. Y. A)
(II) By squaring[3] J. Y. A., we get J. A. A.
It means,
J. A. A. = (J. Y. A)2
8. Madhyama Asaṃkhyāta Asaṃkhyāta (M. A. A.)The numbers from [(J. A. A.)+1] to [(U. A. A.)-1] are called M. A. A.. It means,
[(J. A. A.)+1] ≤ M. A. A. ≤ [(U. A. A.)-1]
9. Utkṛṣṭa Asaṃkhyāta Asaṃkhyāta (U. A. A.)We get four definitions of Maximum Asaṃkhyāta Asaṃkhyāta:
I. By raising J. A. A. to itself and subtracting one from it[4] gives U. A. A. It means
U. A. A. = {(J. A. A)(J. A. A)-1}
II. Firstly, the square of J. A. A. is squared. Then, the following sets of asaṃkhyāta magnitude[5] are added in the above result. Then again obtained magnitude is squared three times. Then one is subtracted from the result. What we obtain is the magnitude of U. A. A.[6] The sets added are[7]:
(1) The total number of ākāśa-pradeśas (space-units) of the loka.[8]
(2) The total number of pradeśas of the dharmāstikāya.[9]
(3) The total number of pradeśas of the adharmāstikāya.[10]
(4) The number of pradeśas of a single jīva (soul).[11]
(5) The adhyavasāya-sthānas[12](the number of states of subtlemost consciousness) which are the cause of the sthiti-bandha (bondage qu duration of karma).
(6) The adhyavasāya-sthānas[13] which are the cause of the anubhāgabandha (bondage qu intensity of karma).
(7) the indivisible units of the mental, vocal and bodily activities (yoga).[14]
(8) The total number of samayas of one kālacakra (timecycle).[15]
(9) The total number of pratyekaśarīrī jīvas (the souls whichare possessed of individual body).[16]
(10) The total number of the bodies of the anantakāyika (nigoda) jīvas (the souls which are possessed of common body).[17]
Thus, if the total number of all the above ten sets is p, then
U. A. A. = {(J. A. A)8+(p)8}-1
III. The third definition of U. A. A. is as follows:[18]
Firstly, the number J. A. A. is made to undergo three times the operation called vargita-saṃvargita (in short, V.-S.).[19] Then the following six sets are added to the result:
(1) The total number of pradeśas of the dharmāstikāya.
(2) The total number of pradeśas of the adharmāstikāya.
(3) The total number of pradeśas of the loka-ākāśa (cosmic space).
(4) The total number of pradeśas of one jīva (soul).
(5) The number of pratyeka vanaspati jīvas which are pratiṣṭhita.[20]
(6) The number of pratyeka vanaspati jīvas which are apratiṣṭhita.[21]
Now, the magnitude which is thus obtained is again made to undergo three times the operation of V.-S. and the following four sets of asaṃkhyāta magnitude are added:
(1) The total numebr of samayas of one kalpakāla (one utsarpiṇī and one avasarpiṇī).
(2) The adhyavasāya-sthānas which are the cause of the anubhāgabandha (bondage qu intensity of karma).
(3) the indivisible units of the mental, vocal and bodily activities (yoga).
(4) The total number of samayas of one kālacakra (timecycle).
Now, the magnitude which is thus obtained is again made to undergo three times the operation of V.-S. Now, one is subtracted from the magnitude thus obtained. The result thus obtained is
U. A. A..
Thus, if J denotes the Jaghanya Asaṃkhyāta Asaṃkhyāta, then by thrice operating V.-S., we get
Now, if the magnitude added first is m1, then we get
If we call this magnitude j′ then operating thrice V.-S., we get
Now, if we add the magnitude m2, we get
If we call this magnitude j′′ then
IV. The fourth definition of U. A. A is as follows:[22]
Firstly, make J. A. A. undergo the operation V.-S. J. A. A. times. The magnitude thus obtained is again made to undergo the same operation that many times. the magnitude thus obtained is again made to undergo the same operation that many times.[23]Now, the aforementioned six sets of asaṃkhyāta magnitude (see. pp. 377--378) are to be added to the result obtained. Again, the obtained magnitude is made to undergo the operation 'śalakātrayaniṣṭhāpana'. Now, the aforementioned four sets of asaṃkhyāta magnitude (see. p. 378) are added to the magnitude thus obtained. Again the obtained magnitude is made to undergo operation 'śalakātrayaniṣṭhāpana'. Now by subtracting one from the magnitude thus obtained we get what is called U. A. A..
yāvat pramaṇao yo rāśirbhavet svarūp asaṃkhyayā. sannyasya tāvato vārān, guṇito'bhyāsa ucyate.. - Lokaprakāśa, 1.165
Jaghanyayuktā saṃkhyātaṃ prāgvadabhyāsatāṃitam.
hīnamekena rūpeṇa yuktāsaṃkhyātakaṃ guru..
etadeva rūpayuktasaṃkhyāsaṃkhyakaṃ laghu. - Lokaprakāśa, 1.173-174
jahaṇṇaeṇaṃ juttāsaṃkhejjaeṇaṃ āvaliyā guṇiyā aṇṇamaṇṇabbhāso
paḍipuṇṇo jahaṇṇayaṃ asaṃkhejjāsaṃkhejjayaṃ hoi. Aṇuogadārāiṃ, Sūtra 593.
jaṃ taṃ jahaṇṇaṃjuttāsaṃkhejjayaṃ taṃ sayaṃ vaggido ukkasajuttāsa
ṃkhejjayaṃ adicchidūṇa jahaṇṇamasaṃkhajjāsaṃkhejjayaṃ gaṃtūṇaṃ paḍidaṃ. - Tiloyapaṇṇattī, 4.310
jaghanyayukāsaṃkhyātaṃ vargitaṃ rūpavarjitam.
Utkṛṣṭaayuktāsaṃkhyātaṃ prāptarūpaiḥ prarūpitam..
ekarūpeṇā yuktaṃ tadasaṃkhyāsaṃkhyakaṃ laghu.
(This is the opinion of Karmagrantha). - Lokaprakāśa, 1.186-187
jhaghanyaāsaṃkhyāsaṃkhyātaṃ bhavedabhyāsatāḍitam.
ekarūponitaṃ jyeṣṭhāsaṃkhyāsaṃkhyātakaṃ sphuṭam..- Lokaprakāśa, 1.175
jahaṇṇam asaṃkhajjāsaṃkhejjayaṃ jahaṇṇaya asaṃkhejjāsaṃkhejjyamettā
ṇaṃ rāsīṇaṃ aṇṇamaṇṇabbhāso ruvūṇo ukkosayaṃ asaṃkhejjāsaṃkhejjayaṃ hoi. - Aṇuogadārāiṃ, Sūtra 595.
We do not exactly know to which kind these sets of asaṃkhyāta belong, but probably they belong to Madhyama Asaṃkhyāta Asaṃkhyāta
Lokaprakāśa, 1.188-196
his definition is as per the version of Karmagrantha. Also, see Anuyogadvāra Sūtra ed. by Ātmārāmji Mahārāja, Uttarārddha, p. 243 footnote
The definitions of these sets of asaṃkhyāta magnitude are given in the technical terminology of the Jain philosophy; one has to refer to treatises of Jain philosophy to understand their exact meaning. (Cf. Technical Terms of Jain Philosophy by Ācārya Mahāpraja).
The total number of pradeśas of each dharmāstikāya, adharmāstikāya, lokaākāśa and a single jīva (soul) are the same. Jain-Siddhānta-Dipikā, 1.25.
"asaṃkhyayāḥ pradeśāḥ dharmādharmalokākāśaikajīvānām."
The association of the karma-pudgalas with soul is called 'bandha' (bondage). The determination of the duration of such bondage is called sthitibandha and that of the intensity of such bondage is called anubhāgabandha. There are asaṃkhyāta (innumerable) intermediate states of duration and intensiy of karma between the maximum and minimum duration and intensity of karma respectively. The cause of these states are basically the adhyavasāyas (subtlemost states of consciousness (soul)) which are also asaṃkhyāta (innumerable). They are innumerable times the number of pradeśas of the lokākāśa (cosmic space).
Yoga (activities) of mind, speech and body are undertaken with the vīrya (energy) of soul. The number of prativiṣiṣṭa (maximum) number of indivisible units of the vīrya imagined by an omniscient is also asaṃkhyāta (innumerable).
1 kālacakra = 20x107x107 sāgaropamas. See Appendix II (supra pp. 350-353) for the total number of samayas in 1 sāgaropama.
There are two types of mundane souls:
(i) Pratyekaśarīrī Jīva : The jīva (soul) which is possessed of its own individual body is called Pratyekaśarīrī Jīva. The total number of such souls is asaṃkhyāta (innumerable).
(ii) Anantakāyika (Nigoda) Jīva : When infinite number of souls occupy a single body (which is common to all), they are called anatakāyika jīvas or nigoda. The number of such bodies is also asaṃkhyāta innumerable).