A Puzzle for Student Reflection: What is the Self?

On the theory (supported by recent research) that presenting students with unsettling paradoxes and perplexities can prime them for higher performance on other learning tasks, the following might be something interesting to share with students at the beginning of a class: Macleans/Ca. has a curious feature on conjoined twins who are craniopagus (joined at the head), and the twins appear to be sharing brain functions central to the self:
There is evidence that they can see through each other’s eyes and perhaps share each other’s unspoken thoughts. And if that proves true, it will be the rarest thing of all. They will be unique in the world.

As a result, the mother finds discipline complex:

“It’s just come down to . . . you can’t discipline one without disciplining
the other. It’s just impossible.”

Those of us not craniopagus may prove to be like the blind to the sighted in relation to these twins; just as the blind can never know what the experience of green is like, we will never know the qualia of what it is exactly to experience another’s thoughts directly and to see through another’s eyes. This is not just “walking in the shoes of another” imaginatively, as when we read a novel, but really seeing through the eyes of another—of having a theatre seat in the mind of another, and that 24/7. Who, exactly, is seeing? Who is speaking? Who is thinking?:

Adding to the conundrum, of course, are their linked brains, and the mysterious hints of what passes between them. The family regularly sees evidence of it. The way their heads are joined, they have markedly different fields of view. One child will look at a toy or a cup. The other can reach across and grab it, even though her own eyes couldn’t possibly see its location. “They share thoughts, too,” says Louise. “Nobody will be saying anything,” adds Simms, “and Tati will just pipe up and say, ‘Stop that!’ And she’ll smack her sister.”

And the reporter for the Mcleans/Ca. feature concludes this way:

Their mother has come to accept each day with them as a gift and a little
miracle; its purpose still unfolding. “They’re here for a reason,” she says, as
you lace up your shoes and prepare to leave. “We just don’t know the reason
yet.” “Hug!” demands Krista. And you sweep them up, feeling their warm embrace
and two beating hearts. And you wonder about that reason all the long way
home.

What is the self, and where is it?