So, a couple people asked for an explanation, so here goes:
t_s basically serves as "gravity" to make older posts fall down the page. Why Dec 8, 2005? Maybe that's when they launched. Anyway, what t_s does in the function is equate a 10-fold increase in points with being submitted 12.5 hours (that's 45,000 secs) later. So a 1-hour-old post would have to improve its vote differential 10x over the next 12.5 hours to maintain it's rating to compensate for elapsed time. If a post's vote differential increases more than 10x in 12.5 hours, its rating goes up.
As for where the numbers come from, I'm pretty sure they're tuned by trial-and-error. It's really hard to predict voting patterns beforehand (ie how fast should items "fall" from the main page?)
The log function is there because your first 10 upvotes should have more weight than the 101st to 110th upvotes. The way the formula is written (and assuming 0 downvotes), your first 10 upvotes have the same weight as the next 100 upvotes, which have the same weight as the next 1000, etc. Again, the base of the logarithm is somewhat arbitrary, and can be tuned by trial and error.
And needless to say, if you have more downvotes than upvotes, your rating is negative. That's about it.
(note: I'm just reading the page and interpreting the algorithm - I don't have any special insight into how they chose these particular constants)
Edit: Time since Dec 8, 2005 is an elegant way of doing it. My first (crude) thought would've been to use "time since posting" to determine gravity, but that requires keeping track of what time it is now. This method is completely independent of the current time. So nicely done.
It's the other way around. yts goes up as the posts are made a greater and greater distance in the future from 12/08/2005. That means that the ratings of new posts are pushed UP, rather than older posts being pulled down.
Yeah, you're right. I simplified it since posts falling down is easier to conceptually understand. New posts start out with a higher rating, and an old posts needs to boost its rating 10x to be at the level a posts starts out at 12.5 hours later.
No, ratings don't change without votes being cast. But new posts automatically start out with a higher rating, so a post must grow its (positive) vote differential by 10x to "keep up" with the new posts. The rating increases as a log of the vote differential, so the votes need to increase exponentially, not the rating. The vote differential increasing by 100x would result in an increase of 2 rating points (this is what a logarithm means).
A new post submitted on June 8, 2008 would have started out with about 1753 rating points, and this number grows by a little less than 2 every day. So it's not that big to store.