We can try to assume that a horcrux is literally a fragment of a soul, in the Hofstadterian sense. It is then indeed an abstract algorithm (or a set of them), and it need not include memory and separate intelligence, although it would include personality and feelings.
Extrapolating on what we know about how the Source of Magic interprets things, we should expect inanimate object horcruxes to be generally passive, while alive horcruxes to incorporate the algorithms into their own minds, although still somewhat separate.
[It'd be cool to read about how a horcruxed software would behave.]
The next discussion thread is here.
This is a new thread to discuss Eliezer Yudkowsky’s Harry Potter and the Methods of Rationality and anything related to it. This thread is intended for discussing chapter 85. The previous thread has long passed 500 comments. Comment in the 15th thread until you read chapter 85.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author’s Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.
As a reminder, it’s often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: