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Jack comments on Take heed, for it is a trap - Less Wrong
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Comments (187)
Zed, you have earned an upvote (and several more mental ones) from me for this display of understanding on a level of abstraction even beyond what some LW readers are comfortable with, as witnessed by other comments. How prescient indeed was Bayesian Bob's remark:
You can be assured that poor Rational Rian has no chance when even Less Wrong has trouble!
But yes, this is of course completely correct. 50% is the probability of total ignorance -- including ignorance of how many possibilities are in the hypothesis space. Probability measures how much information you have, and 50% represents a "score" of zero. (How do you calculate the "score", you ask? It's the logarithm of the odds ratio. Why should that be chosen as the score? Because it makes updating additive: when you see evidence, you update your score by adding to it the number of bits of evidence you see.)
Of course, we almost never reach this level of ignorance in practice, which makes this the type of abstract academic point that people all-too-characteristically have trouble with. The step of calculating the complexity of a hypothesis seems "automatic", so much so that it's easy to forget that there is a step there.
I think this is actually too weak. Hypothesis specification of any kind requires some kind of working model/theory/map of the external world. Otherwise the hypothesis doesn't have semantic content. And once you have that model some not totally ignorant prior will fall out. You're right that 50% is the probability of total ignorance, but this is something of a conceptual constant that falls out of the math-- you can't actually specify a hypothesis with such little information.
Yes, that's exactly right! It is a conceptual constant that falls out of the math. It's purely a formality. Integrating this into your conceptual scheme is good for the versatility of your conceptual scheme, but not for much else -- until, later, greater versatility proves to be important.
People have a great deal of trouble accepting formalities that do not appear to have concrete practical relevance. This is why it took so long for the numbers 0 and 1 to be accepted as numbers.
I disagree with this bit. It's only purely a formality when you consider a single hypothesis, but when you consider a hypothesis that is comprised of several parts, each of which uses the prior of total ignorance, then the 0.5 prior probability shows up in the real math (that in turn affects the decisions you make).
I describe an example of this here: http://lesswrong.com/r/discussion/lw/73g/take_heed_for_it_is_a_trap/4nl8?context=1#4nl8
If you think that the concept of the universal prior of total ignorance is purely a formality, i.e. something that can never affect the decisions you make, then I'd be very interested in your thoughts behind that.