The Enigma Of The Universe : Digambara Tradition

We get the following mathematical description in the Digambara tradition.3 (See fig. 4 on p. 137).

1. The height (one dimension) of the universe is 14 rajjus. (Rajju is an astrophysical measure which is equivalent to innumerable yojanas. See infra pp. 159 ff. for computation of rajju).
   
   
   
   
2. The breadth (second dimension) of the universe is 7 rajjus throughout.
   
   
3. The length (third dimension) of the universe varies from point to point. Let us divide the whole universe into two parts, each of the same height (7 rajjus). Then, the lower universe is of 7 rajjus in height. The lower end of the lower universe is 7 rajjus in length, while as we go upwards, the length gradually tapers down and remains only one rajju at the upper end of the lower universe.

Thus the lower universe forms a ‘trepezial pyramid’, whose height is 7 rajjus, breadth is 7 rajjus throughout, while the lower base is 7 rajjus in length and the upper base is 1 rajju in length

Mathematically written:

Area = ½ [a+b] x h

= ½ [7+1] x 7
= 4 x 7
= 28 square rajjus.

Now Volume = Area x Breadth

= 28 x 7
= 196 cubic rajjus.

Thus, the volume of the lower universe is 196 cubic rajjus.

The upper universe is also 7 rajjus in height and 7 rajjus in breadth. The lower end and the upper end are 1 rajju in length, while in middle it is 5 rajjus in length. In this way, when we look at the fig. 4, we see that the upper universe can be divided into two equal trepezial pyramids, each of which is exactly symmetrical, with height 3.5 rajjus. (See fig. 8 & 9).

Volume = Area of the trepezium x Height

Here, the lengths of the two parallel bases are 5 rajjus and 1 rajju, and height is 3.5 rajjus. (See fig. 10)

= ½ [5+1] x 3.5
= 3 x 3.5
= 10.5 square rajjus.

The Volume = Area x Breadth

= 10.5 x 7
= 73.5 cubic rajjus.

Total volume of the upper universe = 2 x 73.5 = 147 cubic rajjus.

Thus, the volume of the upper universe comes out to be 147 cubic rajjus. When we add the volumes of the lower and upper universes, we get total volume of the whole universe:

Total volume of the whole universe = 196 + 147 = 343 cubic rajjus.

It may be seen that if the shape of the whole universe is imagined as a perfect cube, it will be a cube of 7 rajjus in each dimension.

That is, V = 7³ cubic rajjus = 343 cubic rajjus.