"You can't step in the same river twice."

I heard that sentence in that form a while ago. I took it to mean that you cannot redo the past. You cannot step in the same river again, because the water is not the same.

Entropy, ever stubborn, allows no mulligans.

But when you examine the sentence in its original form, it seems to say more than that.

The original form that is closer to source (Heraclitus) is, "No man can step in the same river twice. For it is not the same river, and he is not the same man."

Time changes both the stage and the actor.

The second part of that sentence also brings up the question of identity. Am I the same man I was, say, seven years ago? Am I same man I was last night?

There is a very interesting thought experiment in metaphysics called The Ship of Theseus. So it goes that Theseus the great Greek hero sailed in his ship and did many heroic deeds using said ship. When he passed, the ship was put on display. People from near and far came to admire the ship. Over the years, the wooden planks of the ship rotted and were replaced, until a time came when not a single original plank used to build the ship remained. Is it still the Ship of Theseus? You could argue this paradox both ways.

Yeah, identity is a paradox. It does not survive the passage of time. What is perhaps worse is that it can be replicated and the very act of replication immediately destroys any notion of identity.

This computer being used to type this post is unique. It is My Computer. Or so it seems. If someone took all the data in this computer and copied it into identical hard drives, and put those hard drives into identical hardware, and shuffled them, how would someone tell which was the original computer? The computers themselves could not tell the difference (if they could think) since they would have identical outputs.

If someone took all the memories I am holding in my head and implanted it in a thousand bodies, which one is Me? Since the memories are identical, each one of those thousand Me's would unequivocally state that it was Me. And they would be equally correct. Or incorrect.

Therefore the paradox.