thaane kaatuvai Arunachala
The ‘I’ that shines as I am is the meaning of (all) philosophy (thattuvam means philosophy). Since you are that I Arunachala, show me your resplendent form.
‘I’ is the form of wisdom (gnana swarupam). In all the changing states such as sleep, dream and waking state, this I shines through constantly as witness of jiva. Since Arunachala remains as ‘I’ in the heart of all beings, Bhagavan says ‘thaane thaane’ (I-I).
Thaane kaatuvai (you yourself show me) = since the jiva (soul) loses its light on merging with the Self, it shines as the effulgent self.
‘I’ is the attributed self and I am is the place of Brahman. Remaining as yourself is the bliss of the self (brahma anubhavam). Bhagavan as asking not to slip into the jiva bhavam (ordinary state of jiva) and remain as the Self (as Arunachala).
Note: In Tamil, I and I am both are conveyed by ‘naan’. Eg: I am here = naan Inge irukkiren, I came here = Naan ingot vandhen. ’Thaan’ usually refers to the ego state.