The Enigma Of The Universe : Computation of Rajju

Published: 13.11.2014
Updated: 19.07.2015

A rajju is a linear astrophysical measure used in Jain Cosmology. It consists of asaṃkhyāta (innumerable)[1] yojanas. Some efforts have been made by scholars to compute the value of a rajju in terms of modern astrophysical measures. The efforts made by C. T. Colebrooke are very important.[2] We try to compute rajju on the definition provided by him.

According to Colebrooke, a rajju is the distance which a Deva flies in six months at the rate of 20,57,152 yojanas in one ‘kṣaṇa’. Prof. G. R Jain has calculated the value of rajju from this definition, by taking, ‘kṣaṇa’ as ‘prativipalāṃśa’ which is equal to 1/54,00,00 minutes.[3]

Taking 1 yojana = 4000 miles, Prof. G. R. Jain has covered the distance covered in 1 kṣaṇa, i.e., 2057152 yojanas into miles thus:

x = 2057152 yojanas
  = 2057152 x 4000
  = 8,228,608,000.......... (1)

Further, he has calculated prativipalāṃśa (kṣaṇas) in 6 months thus:

t = 6 x 30 x 24 x 60 x 54000.......... (2)

Then substituting the values from (1) & (2),

1 rajju = distance covered x time
  = x x t
  = 8,228,608,000 x 6 x 30 x 24 x 60 x 540000 miles
  = 1.15 x 1021 miles

Prof. G. R. Jain has found out the value of one rajju on the basis of the volume of the universe of Einstein’s model. He writes:[4]

“If we take the Einstein’s value of the radius of the finite universe, we can arrive at the order of magnitude of a rajju thus:

Radius of the universe = 1,068 million light-years.

One light-year = 5.88 x 1012 miles.

∴ Volume of a spherical universe, i.e., (4/3 x 22/7 x r3)

= 4/3 x 22/7 (1068 x 106 x 5.88 x 1012)3 cu. miles

= 1037 x 1063 cu. miles

i.e., 1,037 followed by 63 ciphers or 67 digits in all.

“Now if 1,037 x 1063 be equated to 343 cubit rajjus, we get: 1 rajju = 1.45 x 1021 miles, whereas if equated to 239 cubic rajjus, we get: 1 rajju = 1.63 x 1021 miles, a quantity of the same order of magnitude as before.”

The values of one rajju found on the basis of the definition given by C. T. Colebrooke and on the basis of Einstein’s universe are almost very close to each other. But there are some questions which do not allow us to accept them:

  1. The value of one rajju as described in canonical texts is asaṃkhyāta (innumerable) yojanas, whereas this value is less than 1022 yojanas.[5]

  2. In the definition given by C.T. Colebrooke, kṣaṇa is given, but Prof. G.R. Jain has substituted kṣaṇa by prativipalāṃśa. Prof. G.R. Jain is not sure about the meaning of kṣaṇa. In the footnote on p. 92 of his book, he quotes Hindu Purāṇas which give yojana equal to 100/11 miles and kṣaṇa = ¼ second. In fact, it seems that kṣaṇa should really mean the smallest unit of time, i.e., samaya.

  3. Prof. G.R. Jain has made the radius of curvature of universe, which was estimated by Einstein, the base of his calculation of the magnitude of a rajju. But. Prof. G.R. Jain has himself admitted:[6] “The dimensions of the universe have been estimated by Einstein on the basis of a spherical finite universe, whereas the shape of the finite universe according to Jaina is anthropomorphous with infinite pure space on all sides.”

Considering these odds, it is very difficult to make an exact comparison between the modern determination of the size of the universe and the determination of the ancients’. However all that has been said above reflects credit on the work of ancient thinkers.

“Modern theories of the universe regard the universe as expanding although the final word has not yet been pronounced on this point.”

Thus, it can be said that the value thus found by Prof. G. R. Jain is not dependable. Also, because now we know that the modern theories have accepted the universe as “expanding one”, and therefore, there is no fixed value of the radius of curvature of the universe.

Thus, both the values of rajju found by Prof. G.R. Jain become unacceptable because of the uncertainties of scientific figures and the absence of exact interpretation of the ancient terminology. C.T. Colebrooke has only given the definition, but not calculated the value of rajju. Thus, we can say that computation of rajju still remains unaccomplished. Here, we make an attempt to compute the value of rajju. There are two possible ways for this, one of which is to make use of the definition given by C.T. Colebrooke.


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Title: The Enigma Of The Universe Publisher: JVB University Ladnun English Edition: 2010 HN4U Online Edition: 2014

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Some texts contain  footnotes  and  glossary  entries. To distinguish between them, the links have different colors.
  1. Asaṃkhyāta
  2. Deva
  3. Einstein
  4. JAINA
  5. Jain Cosmology
  6. Jaina
  7. Purāṇas
  8. Rajju
  9. Samaya
  10. Space
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