I think that's sort-of true, and is one implication of an exoself of sufficient breadth / magnitude that other people care about it, or that it even incorporates them in some fashion s.t. they become part of each other in important ways.
But there are also much "smaller" variants that are interesting to me. For instance, a friend of mine, the most talented hacker that I know, has turned his house into an extension of himself -- both how the place is designed, how it's decorated, and the million little hacky features where he's built to augment it. To go into his house is to enter a part of his Being. You're very aware of being present in the heart of a respirating meta-organism, part of it.
This guy is pretty amazing and stands a reasonable chance of being remembered in 100 years for other things, but this would still be a beautiful and impressive type of exoself even if that weren't true.
this territory is moderated
That sounds fascinating and intriguing. And it adds color to your exoself idea with a very concrete example. A physical extension of a person that made their house an extension of their body or mind.
I was thinking more of a metaphysical extension of one's being captured in art or writing where a person's physical being, which inevitably withers, is replaced by a metaphysical embodiment of their mind which if done well has the potential for immortality. When one thinks of Socrates for example, although he did not write a single word, Plato captured his dialogues in a timeless manner where we have a very good sense of who he was shaped by Plato's writings that survive.
There are more abstract examples, such as Euclid, who gave us Elements, which laid the foundation for mathematics. His writing tells no story with no characters, but the progression of his theorems are so elegantly structured that we get a sense of the greatness of his mind - or exoself.
And of course, Satoshi gave us Bitcoin which has every possibility of surviving for centuries and positioning his exoself among the very greats in history.
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