Sri Krishna himself answers this in the Gita. He is not there as the physical Krishna since He declares Krishna as one of his vibhutis, – ‘I am Krishna among the Vrishnis, Rama among those who have paurush….’.
Nor is he the Atman that is present in all. He declares Himself to be both Kshara and Akshara as the Purushottama, the Avatar.
The problem is that a certain class of Advaitins does not understand the concept of Avatarahood, the Divine becoming human, not in a general sense but in the specific sense of the Divine Himself assuming a human form. This idea or conception is unique to the Gita and developed later in the Puranas. The Vedas do not speak of the Avatar and hence a typical Vedantin misses its significance, which Sri Krishna describes as one of the Secrets. The Vedas hint at the possibility of the Avatar but only in a very general sense. It is the Gita that develops it fully. As with all Scriptures, the Gita has to be seen in its totality and not specific verses alone.ย
The Avatar doesn’t leave the earth ever. That is why we see several seers have had the darshan and guidance from Sri Krishna including Surdas, Mirabai, and more recently Sri Aurobindo himself.
Affectionately,
Alok Da


