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Doug_S.2 comments on Just Lose Hope Already - Less Wrong
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"Never give up" is bad advice?
Probability of success if you continue: small. Probability of success if you give up: zero.
Small is better than zero, am I right?
On the other hand, this analysis only matters if the cost of failure is no worse than the cost of giving up. The "rational" thing to do would be to give up if and only if (probability of success * utility of success) + (probability of failure * utility of failure) < (utility of giving up).
There are a lot of things that one can achieve through sheer persistence, but there are others that, well, you can't do, period. The trick is to be able to tell the difference. I suspect that I'm not going to be a star athlete no matter how much I practice, but I just might qualify for the Pro Tour some day.
The point of this post was to show that persisting at something while being irrational can only cause harm. Of course, "Never give up" is not bad advice, but Eliezer's advice is be rational and accept defeat when you need to.
You're ignoring the probability of succeeding at something else. If you're still doing this, it's zero. If you give up, it's not.
Of course, that can also be considered a cost of failure, in which case you didn't ignore it.
Edit: This is equivalent to counting opportunity cost as a cost of failure that's not a cost of giving up, so maybe you weren't ignoring it.
In addition, as Eliezer's earlier post about the math proof shows, if the original reason that led you to believe you could do something was shown to be false, you should almost certainly give up. It's very unlikely you were right for the wrong reasons. If, knowing what you know now, you would never have tried, then you should probably stop.
This ignores the case where your "original reason" was an attempt to formalize some informal reason. If your error is in the formalization process and not in the reason itself, being right for the wrong reason is a plausible scenario.
And what a trick it is!