the essential relationship between the two is that the "you of today" shares the memories of "you of yesterday"
except that we forget most of them, and that our memories of the same event change in time, and often are completely fictional.
Good point. The description I gave so far is just a first approximation. In truth, memory is far from ideal. However if we assign weight to memories by their potential impact on our thinking and decision making then I think we would get that most of the memories are preserved, at least on short time scales. So, from my point of view, the "you of today" is only a partial continuation of the "you of yesterday". However it doesn't essentially changing the construction of the Hypermind. It is possible to refine the hypothesis by stating that for every two "pieces of knowledge" a and b, there exists a "moment of consciousness" C s.t. C contains a and b.
"The Asymptote has property P" is "For any A there is B > A s.t. for any C > B, C has property P"
That's a rather non-standard definition. If anything, it's close to monotonicity than to accumulation. If you mean the limit point, then you ought to define what you mean by a neighborhood.
Actually I overcomplicated the definition. The definition should read "Exists A s.t. for any B > A, B has property P". The neighbourhoods are sets of the form {B | B > A}. This form of the definition implies the previous form using the assumption that for any A, B there is C > A, B.
The definition should read "Exists A s.t. for any B > A, B has property P"
Hmm, it seems like your definition of Asymptote is nearly that of a limit ordinal.
If you've recently joined the Less Wrong community, please leave a comment here and introduce yourself. We'd love to know who you are, what you're doing, what you value, how you came to identify as a rationalist or how you found us. You can skip right to that if you like; the rest of this post consists of a few things you might find helpful. More can be found at the FAQ.
A few notes about the site mechanics
A few notes about the community
If English is not your first language, don't let that make you afraid to post or comment. You can get English help on Discussion- or Main-level posts by sending a PM to one of the following users (use the "send message" link on the upper right of their user page). Either put the text of the post in the PM, or just say that you'd like English help and you'll get a response with an email address.
* Normal_Anomaly
* Randaly
* shokwave
* Barry Cotter
A note for theists: you will find the Less Wrong community to be predominantly atheist, though not completely so, and most of us are genuinely respectful of religious people who keep the usual community norms. It's worth saying that we might think religion is off-topic in some places where you think it's on-topic, so be thoughtful about where and how you start explicitly talking about it; some of us are happy to talk about religion, some of us aren't interested. Bear in mind that many of us really, truly have given full consideration to theistic claims and found them to be false, so starting with the most common arguments is pretty likely just to annoy people. Anyhow, it's absolutely OK to mention that you're religious in your welcome post and to invite a discussion there.
A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
More suggestions are welcome! Or just check out the top-rated posts from the history of Less Wrong. Most posts at +50 or more are well worth your time.
Welcome to Less Wrong, and we look forward to hearing from you throughout the site.