Sunday, October 13, 2013

Sunday: I ended up being lazy. Then I mocked someone semi-famous. Finally, I did unnecessary math.

I had intended to make spaghetti for dinner, but discovered last night that my butter had gone bad.  "I have never had butter go bad," you say?  You apparently don't buy butter and then leave for a month allowing it to go bad.  So congratulations for eating your butter faster than I do.

Since the butter was no good, I had to go out today anyway to get more butter, but then I became lazy and waited around until I had become too hungry to wait to get groceries and then make dinner and then eat. So, burger time.


You may have noted that that last one isn't really fair, because I've kind of expected NF and CNF not to be writing in the exact same article.  Therefore, I don't see any other option than to conclude that Niall Ferguson is kind of a shitbag.  Maybe he's an incompetent shitbag, and me calling him a liar isn't fair either.  


And now, after sorting out links for that mess, something else has struck me.  That rating system isn't just arbitrary and stupid, it's mathematically arbitrary and stupid.  If you wanted to rate the quality of twitter feeds, how would you do that?  First thing that would be nice would be if we have an accuracy value.  Like, the fraction of tweets that were true or helpful or something.  Next thing that you need to include is something to account for how much they tweet.  If you tweet zero, you spread zero information no matter how correct you are, so more tweets that are true is better than fewer tweets that are true.  Next, you need some sort of network effect.  If you tweet, but no one listens, you're only marginally above not tweeting at all when it comes to spreading information.  So, you get the product of these three things, or something like:
U = (a + k) N F
where U is the utility of the feed, a is the accuracy, N is the number of tweets, F is the number of followers, and k is the fraction of tweets containing "cats," in a very general sense (basically, any tweet pointing out something cute to look at.  Puppies would work too, but because internet).

You probably also need to fold in a time decay term, something of the form N = \int \rho(t) dt; U(t) = (a + k) F * \rho(\tau) exp(-(t - \tau) / \kappa).  The idea here being that something wise you said three years ago is probably less important right now than something wise you said seconds ago.  Then again, this invites switching to a(t) as well.  I may be right in what I say today, but two years from now added information may change this fact.  This means that the present utility rating is like
U(t) = \int (a(\tau)|_t + k) \rho(\tau) exp(-(t - \tau)/\kappa) d\tau F

Shit.  F.  That's not constant either, is it?  I'm going to stop here because I'm be lazy today and assume all followers do the responsible thing and scan the entire tweet archive to become as up-to-date as all previous followers.  Therefore, we don't need to bother with anything else and F is simply F(t).  This now tells us the utility at time t, based on a distribution of past tweets at times \tau < t.

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