2. A luminous indwelling in the Divine = Transformation of the Karana sharira
3. A union of our instrumental being = Transformation of the instrument, i.e., sukshma sharira
Here is the passage from the Synthesis of Yoga to which you are referring.
‘That which is thus made manifest to our vision and experience, and the union has a threefold character. There is a union in spiritual essence, by identity; there is a union by the indwelling of our soul in this highest Being and Consciousness; there is a dynamic union of likeness or oneness of nature between That and our instrumental being here. The first is the liberation from the Ignorance and identification with the Real and Eternal, mokṣa, sāyujya, which is the characteristic aim of the Yoga of Knowledge. The second, the dwelling of the soul with or in the Divine, sāmīpya, sālokya, is the intense hope of all Yoga of love and beatitude. The third, identity in nature, likeness to the Divine, to be perfect as That is perfect, is the high intention of all Yoga of power and perfection or of divine works and service. The combined completeness of the three together, founded here on a multiple Unity of the self-manifesting Divine, is the complete result of the integral Yoga, the goal of its triple Path and the fruit of its triple sacrifice.’
(Ref. https://incarnateword.in/cwsa/23/the-sacrifice-the-triune-path-and-the-lord-of-the-sacrifice#p34)
It is against this background that we can better understand the triple union.
1. A union by identity = Atman = Brahman
Yes, it is the fundamental identity of the individual soul with the Divine Self that is being described here, the Divine Self being the Atman or Brahman. It is the universal Self, the One Self in all, that is being referred to here.
2. A luminous indwelling in the Divine = Transformation of the Karana sharira
Here it is the dwelling of the individual soul in the Transcendent Purushottama of whom it is an eternal portion, ‘mamaivansha’ as the Gita puts it. The word luminous implies a conscious dwelling in the Supreme Divine. This does not refer to the transformation which is a term reserved primarily for the nature parts or our instrumental personality. Here it is simply referring to being full of the Divine, surrounded and enveloped by the Divine Consciousness. It means that the realisation of the One Self, the soul’s essential identity will Brahman leads to Moksha but that does not necessarily mean annihilation. It attains freedom, liberation. But going further it can discover its true origin, the Paramatma, and can consciously dwell in Him, again without losing itself.
3. A union of our instrumental being = Transformation of the instrument i.e. sukshma sharira
This is the transformation of the antahkarana, the mind, of the sookshma sarira including the vital and the subtle physical, as well as eventually and eventually, the sthool sarira or the gross body including the senses and everything else.
The first leads to Mukti, the peace and freedom through liberation from the ignorant Nature. The second leads to bhukti, the delight or Ananda that comes by a constant dwelling in the Divine wherever we may be. The third is siddhi, or the perfection, not only of the soul but of nature. Our nature constituted of the ignorant trigunatmika Prakriti is transformed into the Divine Supernature or Paraprakriti.
Affectionately,
Alok Da
