@boagie,
I think that when Heraclitis said, “You can’t step into the same river twice,” he was not speaking about a thing/object called river, and a person/object (ego me) stepping into that objective river. He was saying that both that river and that person were two different processes, and because they continually moved and change, they could never come together at the exact same point, ever again. (He might have even likened the river to time. That is my guess.)
Now, if you hold back from these two processes, and you say both the river was an 'essential river' and the person was an 'essential person', this is entirely different, isn't it, because now you are juggling conceptual objects (both) which aren’t really living, growing and changing constantly. To bring together two conceptual objects is probably a whole lot easier to manage.
Identity is a little like this. Our identity, as an ego self, is basically manufactured like any concept, and so we feel that we can get a hold of it and even own it or even imagine that it is somehow real and permanent. But what is it outside of circumstance and imagination going about building a house of cards?
Yet we do all feel, no we know somehow, that there is something more going on than our personal autobiography, although we erroneously attribute this strong 'ME" feeling to our ego identity most of the time.
But, what is this golden thread of our essential identity, which seems to hold all of our imaginings about who we are, together?
S9