What is the meaning of Narayana?
I quote the following from the book Manusmriti:
He thought deeply, for he wished to emit various sorts of creatures from his own body; first he emitted the waters, and then he emitted his semen in them. That semen became the golden egg as bright as the sun with his thousand rays; Brahma himself, the grandfather of all people, was born in that egg. 'The waters are born of man' so it is said; indeed the waters are the children of the primordial man. And since they were his resting place in ancient time, there he is traditionally known as Narayana ('Resting on those born of man').
Narayana means resting on those born of man. Water is born of man. Therefore Narayana means resting on water.
The actual verse from Manusmriti:
Verse 1.10 [Meaning of the term ‘Nārāyaṇa’]
आपो नारा इति प्रोक्ता आपो वै नरसूनवः ।
ता यदस्यायनं पूर्वं तेन नारायणः स्मृतः ॥ १० ॥
āpo nārā iti proktā āpo vai narasūnavaḥ |
tā yadasyāyanaṃ pūrvaṃ tena nārāyaṇaḥ smṛtaḥ || 10 ||
Water is called ‘nara,’ — water being the offspring of nara; since water was the first thing created by (or, the original residence of) that being, he is, on that account, described as ‘nārāyaṇa.’ — (10)
(Sanskrit text, Unicode transliteration and English translation by Ganganath Jha)
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