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Saturday, March 31, 2012

The World of Valmiki-17

The World of Valmiki-17

Mathematics and measures
रक्षसां भीमकर्माणां सहस्राणि चतुर्दश ।
निहतानि शरैस्तीक्ष्णैः तेनैकेन पदातिना ।
अर्धाधिकमुहूर्तेन खरश्च सहदूषणः ॥३/३४/१०॥
 Fourteen thousand Rakshasas along with Khara and Dushana were killed within a muhurta and a half by sharp arrows by (Rama) singly standing on the ground.


चतुरङ्गुलमात्रोऽपि नावकाशः स विद्यते ।
रावणान्तः पुरे तस्मिन् यं कपिर्न जगाम सः ॥५/१२/१७॥
There was not even a space of four angulas which was not searched by the monkey.


शतैः शतसहस्रैश्च कोटिभिश्च प्लवङ्गमाः ।
अयुतैश्चावृता वीराः शङ्कुभिश्च परन्तप ॥
अर्बुदैरर्बुदशतैः मध्यैश्चान्तैश्च वानराः ।
समुद्रैश्च परार्धैश्च हरयो हरियूथपाः ।
आगमिष्यन्ति ते राजन् महेन्द्रसमविक्रमाः ॥४/३८/३१-३६॥
The monkeys and their chiefs will come in hundreds, hundred thousands, crores, ayutas (10 thousands), shankus, arbudas (10 crores), one hundred arbudas, madhyas, antas, samudras and parardhas
[ Govindaraja quotes: एकं दशशतं अस्मात् सहस्रं अयुतं ततः परं लक्षम् । प्रयुतं कोटिमथार्बुदवृन्दे खर्वं निखर्वं च ॥ तस्मान्महासरोजं शङ्कुं सरितां पतिं त्वन्तम् । मध्यं प्रार्धमाहुः यथोत्तरं दशगुणं तथा ज्ञेयम् ॥ arbuda=10 kotis; vrinda=10 arbudas; kharva=10 vrindas; nikharva=10 kharvas; mahasaroja=10 nikharvas; shanku=10 mahasarojas; samudra=10 shankus; anta=10 samudras; madhya=10 antas; parardha=10 madhyas. परार्ध is ten to the power of nine Crores! Tirtha apparently errs in explaining samudra and parardha. Bhaskara's Lilavati calls वृन्द as अब्ज: एकदश शत सहस्रायुतलक्षकोटयः क्रमशः। अर्बुदमब्जं खर्वनिखर्वमहापद्मशङ्कवस्तस्मात् ॥ जलधिश्चान्त्यं मध्यं परार्धमिति दशगुणोत्तराः संज्ञाः ॥ Valmiki's conversion table is different and perhaps in error- See below ]


शतं शतसहस्राणां कोटिमाहुर्मनीषिणः ।
शतं कोटिसहस्राणां शङ्कुरित्यभिधीयते ॥
शतं शङ्कुसहस्राणाम् महाशङ्कुरिति स्मृतः ।
महाशङ्कुसहस्राणां वृन्दमिहोच्च्यते ॥
शतं वृन्दसहस्राणां महावृन्दमिति स्मृतम् ।
महावृन्दसहस्राणां शतं पद्ममिहोच्च्यते ॥
शतं पद्मसहस्राणां समुद्रमभिधीयते ।
शतं समुद्रसाहस्रं ओघ इत्यभिधीयते ॥
शतमोघसहस्राणां महौघा इति विश्रुतः ।६/२८/३३-३८॥
The learned consider a hundred of a thousand hundreds as koti. A hundred of a thousand kotis as Shanku; A hundred of a thousand Shanku as Mahashanku; A hundred of a thousand Mahashanku as Vrinda:  A hundred of a thousand vrinda as Mahavrinda; A hundred of a thousand mahavrinda  as Padma; A hundred of a thousand Padma as Samudra; A hundred of a thousand Samudra is Ogha; A hundred of a thousand Ogha as Mahougha. [ Each unit is ten to the power of five times the previous unit. Consequently Mahougha is ten to the power of forty five times hundred=10 to the power of 47 ! ]

रक्ताक्षाः सुबहुव्यामा नीलाञ्जनचयोपमाः ।
शूलानुद्यम्य खड्गांश्च निशितांश्च परश्वधान् ॥६/६५/३८॥
Red-eyed Rakshasas who looked like heaps of black anjana and who were of several Vyaamas in height ( came) holding sharp parashvadhas and Sulas and swords. [A Vyama is the distance between the tips of middle fingers when the two arms are fully extended in line.]

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