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CuSithBell comments on The Rhythm of Disagreement - Less Wrong
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Comments (65)
How did Eliezer determine that the expected benefit of the algorithm over random chance is zero?
He didn't say that, he said the benefit gets closer and closer to zero if you modify the setup in a certain way. I couldn't find an interpretation that makes his statement correct, but at least it's meaningful.
I don't get why it makes sense to say
without meaning that the expected density of the differential does go to zero - or perhaps would go to zero barring some particular prior knowledge about the envelope distribution. And that doesn't sound like "modifying the setup" to me, that seems like it would make the statement irrelevant. What exactly is the "modification", and what did you decide his statement really means, if you don't mind?
Sorry, are you familiar with the mathematical concept of limit? Saying that "f(x) goes to zero as x goes to zero" does not imply the nonsensical belief that "x goes to zero".
Yes, I am familiar with limits. What I mean is - if you say "f(x) goes to zero as x goes to zero", then you are implying (in a non-mathematical sense) that we are evaluating f(x) in a region about zero - that is, we are interested in the behavior of f(x) close to x=0.
Edit: More to the point, if I say "g(f(x)) goes to zero as f(x) goes to infinity", then f(x) better not be (known to be) bounded above.