The Enigma Of The Universe ► 3 ►Jain Cosmology ► (2) Universe: Size and Shape ► Computation of Rajju ► 1. Computation of Rajju based on Colebrookes’s Definition

Posted: 14.11.2014

As suggested before, let us interpret kṣaṇa as samaya which is the ultimate indivisible unit of time.[1] Now, for calculating the number of samayas in 6 months, first we have to find out the number of samayas in 1 āvalikā. This number is equal to [2]-

Jaghanya-Yukta-Asaṃkhyāta (i.e., J. Y. A.)

This number is described as [3]-(Jaghnya Parita Asaṃkhyāta) raised to (Jaghnya-Parita-Asaṃkhyāta), which we can write as (J. P. A.) (J. P. A.). where J. P. A. is equal to-Utkṛṣṭa Asaṃkhyāta + 1 (i.e., the highest numerable number + 1).[4]

Now, again it is very difficult to compute the value of this number.[5] However, we can replace the Utkṛṣṭa asaṃkhyāta by the number -

x = Śīrṣaprahelikā

Which is the highest numerable unit of time.[6]

As mentioned above,

J. P. A.

= Utkṛṣṭa saṃkhyāta + 1

Now, J. Y. A.

= (J. P. A.) (J. P. A.)

 

= (x + 1) (x + 1)............. (1)

There are two variants in Shvetambara traditions which give differently the value of x.

The value given by the Synod at Māthurī is - (84,00,00028)

= 758,263,253,073,010,241,157,963,569,975,696,406,218,966,808,080,183,296 x 1040

= 7.58 x 10193 approximately.

According to the version of the Synod at Vallabhī, this number is - (84,00,00028)

= 187,957,179,550,112,795,419,009,699,813,430,770,797,465,494,261,977,747,657,257,345,718,681,6 x 10180

= 1.87 x 10249 approximately.

We may use the lower value (as we are trying to find out the lower limit of the value of one rajju), i.e., that given by Māthurī synod.

Again, neglecting one which is much much less than Śīrṣaprahelikā, and substituting the value of Śīrṣaprahelikā in equation no. 1 we get,

J. Y. A. = (7.58 x 10193)(7.58 x 10193).

Using the table of the units of time, we find that

1 Muhūrta (= 48 minutes) = 1,57,77,216 Āvalikās

6 months = 5,400 muhūrtas.

Then a rajju, which is the distance travelled in six months at the speed of 20,57,152 yojanas per samaya, will be

           = 5,400 x 1,67,77,216 x (7.58 x 10193)(7.58 x 10193) x 20,57,152 yojanas.

The approximate calculations of the above multiplication is given

1 rajju = 1.86 x 10{(1.47 x 10196) + 17} yojanas.

Now 1 yojana = 8,000 miles

∴ 1 rajju = 14.88 x 10{(1.47 x 10196) + 20} miles-----(1-A)

or, in terms of light-years, since,

1 light-year = 5.88 x 1012 miles

1 rajju = 2.91 x 10{(1.47 x 10196) + 8} light years-----(1-B).

Then, the volume of the universe, which is 343 cubic rajjus, will be

= 11.35 x 10{(4.41 x 10196) + 65} cubic miles, if the first value (1-A) is taken.

In the terms of cubic light-years, the volume will be

= 8.45 x 10{(4.41 x 10196) + 27} cubic light years according to (1-B).

In the above calculations, we have taken

1 yojana = 8,000 miles.

However, according to the Digambara tradition,

1 yojana = 4,000 miles.[7]

If we take this value, then the above values will be -

1 rajju = 7.44 x 10{(1.47x10196)+20} miles

1 rajju = 1.45 x 7.44 x 10{(1.47x10196)+8} light years

Volume of loka will be

            1.42 x 10 {(4.41x10196)+65} cubic miles

1.05 x 10 {(4.41x10196)+27}  cubic light years

Footnotes:
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