Posted: 07.11.2014

The Shvetambara tradition describes the universe in a slightly different way. Although we do not get exact mathematical description of the dimensions (in the *āgamas*), yet whatever description we get in the later works,^{[1]} we can make it the base of our discussion here. According to the works, the description is as follows:^{[2]} The height of the universe is 14 *rajjus*; as before. The length and the breadth vary from point to point but are same at the same height. It means that if a horizontal cross-section of the *loka *is made at any point, it will be a square (see fig. 11).

These are given in terms of *khanduka *which is the quarter of a *rajju*. At the lower end, the universe is 28 *khaṇḍukas *in length and breadth. Then, as the height increases, the length and breadth change. (See fig. 12).

[Fig. No. 12]

In the following table, in the first and second columns, the lengths and the breadths of the universe at the particular heights in terms of *khaṇḍukas *are given. In the third and fourth columns, the area and volumes are given respectively.

Height from the bottom (in khaṇḍukas)

Length/ Breadth (in khaṇḍukas)

Square (in square khaṇḍukas)

Volume (in cubic khaṇḍukas)0-4

28

784

3136

4-8

26

676

2704

8-12

24

576

2304

12-16

20

400

1600

16-20

16

256

1024

20-24

10

100

400

24-28

4

16

64

28-30

4

16

32

30-32

6

36

72

32-33

8

64

64

33-34

10

100

100

34-36

12

144

288

36-38

16

256

512

38-40

20

400

800

40-42

20

400

800

42-44

16

256

512

44-46

12

144

288

46-49

10

100

300

49-52

8

64

192

52-54

6

36

72

54-56

4

16

32

Total:

15296

From the above table, it becomes clear that the universe is formed of 56 rectangular parallelepipeds, each having the same height of 1 *khanduka *(¼ *rajju*), and varying lengths and breadths. (See fig. 13).

The volume of each parallopiped is obtained by multiplying the height, length and breadth, as shown in the table. The total volume of the universe comes out to be 15296 cubic *khandukas*.

Now

∴ 1

khanduka= ¼rajju, and

∴ 1 cubickhanduka= 1/64 cubicrajju

∴ Volume of the universe = 15296 cubickhandukas= cubic

rajjus

= 239 cubicrajjus.

This is referred to as the size of ‘*vargita loka*’.^{[3]} This figure, it seems, does not represent the exact volume of the universe, as the exact volume is stated to be 343 cubic *rajjus *even in Shvetambara works. For example, in *Lokaprakāśa*, the author has explicitly mentioned-‘The propounders of metaphysics (*tāttvikas*) have propounded that there are 343 cubic *rajjus *of the “*ghanīkṛta loka” *(cubified universe).^{[4]}

The description given in the *Lokaprakāśa ^{[5]}* to prove that the volume of the

The above approximation may be accepted only in approximate calculation, but are unacceptable in precise calculation.

Thus, the actual size of the length and breadth remains enigmatic. This apparent discrepancy deserves critical scrutiny, which we shall undertake in the following topic.

Footnotes: | |

[1] | We get it in the Vinayavijaya’s Lokaprakāśa, cantos XII. A similar description is made in “Der Jainismus”, a treatise on Jainism in German language, written by Helmuth Von Glassenhap. He has given a figure of ‘Weltfrau’ (loka-strī) which he has taken from the Saṃgrahaṇī Sūtra of Chandrasuri. The mathematical description made in this figure is almost similar to that which is obtained in Lokaprakāśa. Saṃgrahaṇī is found mention at various places in Lokaprakāśa. We may therefore assume that basis of Vinayavijayaji’s description is taken from Chandrasuri’s Saṃgrahaṇī. We also get some mathematical description in older treatises like Bṛhat Saṃgrahaṇī. |

[2] | Lokaprakāśa, cantos XII, verses 8 to 111; also see Der Jainismus, p. 232 |

[3] | See, Lokaprakāśa, canto XII, verses 110 to 115. |

[4] | Asmin ghanīkṛte loke praj–aptā ghanarajjavaḥ. |

[5] | See, Lokaprakāśa, canto XII, verses 116 to 132. |

[6] | Sarvasyāsya carutastrīkṛtasya bhavati dvacit. |