shminux comments on Problematic Problems for TDT - Less Wrong

36 Post author: drnickbone 29 May 2012 03:41PM

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Comment author: shminux 23 May 2012 08:37:36PM * 1 point [-]

I wonder if there is a mathematician in this forum willing to present the issue in a form of a theorem and a proof for it, in a reasonable mathematical framework. So far all I can see is a bunch of ostensibly plausible informal arguments from different points of view.

Either this problem can be formalized, in which case such a theorem is possible to formulate (whether or not it is possible to prove), or it cannot, in which case it is pointless to argue about it.

Comment author: Vladimir_Nesov 23 May 2012 09:58:45PM 2 points [-]

Either this problem can be formalized, in which case such a theorem is possible to formulate (whether or not it is possible to prove), or it cannot, in which case it is pointless to argue about it.

Or it's hard to formalize.

Comment author: shminux comment score below threshold [+] (13 children)

Comment author: TheOtherDave 23 May 2012 11:04:28PM 0 points [-]

So, what ought one do when interested in a problem (decision theory or otherwise) that one does not yet understand well enough to formalize?

I suspect "go do something else until a proper formalization presents itself" is not the best possible answer for all problems, nor is "work silently on formalizing the problem and don't express or defend a position on it until I've succeeded."

Comment author: shminux 23 May 2012 11:31:15PM * 1 point [-]

How about "work on formalizing the problem (silently or collaboratively, whatever your style is) and do not defend a position that cannot be successfully defended or refuted"?

Comment author: TheOtherDave 24 May 2012 12:28:02AM 2 points [-]

Fair enough.
Is there a clear way to distinguish positions worth arguing without formality (e.g., the one you are arguing here) from those that aren't (e.g., the one you are arguing ought not be argued here)?

Comment author: shminux 24 May 2012 01:21:51AM 2 points [-]

It's a good question. There ought to be, but I am not sure where the dividing line is.

Comment author: Vladimir_Nesov 23 May 2012 10:40:50PM * 0 points [-]

You check the arguments using mathematical intuition, and you use them to find better definitions. For example, problems involving continuity or real numbers were fruitfully studied for a very long time before rigorous definitions were found.

Comment author: shminux 23 May 2012 11:26:16PM * 0 points [-]

You check them using mathematical intuition, and you use them to find better definitions.

Indeed, you use them to find better definitions, which is the first step in formalizing the problem. If you argue whose answer is right before doing so (as opposed, say, to which answer ought to be right once a proper formalization is found), you succumb to lost purposes.

For example, "TDT ought to always make the best decision in a certain class of problems" is a valid purpose, while "TDT fails on a Newcomb's problem with a TDT-aware predictor" is not a well-defined statement until every part of it is formalized.

[EDIT: I'm baffled by the silent downvote of my pleas for formalization.]

Comment author: TheOtherDave 24 May 2012 12:53:32AM 1 point [-]

[EDIT: I'm baffled by the silent downvote of my pleas for formalization.]

If I had to guess, I'd say that the downvoters interpret those pleas, especially in the context of some of your other comments, as an oblique way of advocating for certain topics of discussion to simply not be mentioned at all.

Admittedly, I interpret them that way myself, so I may just be projecting my beliefs onto others.

Comment author: shminux 24 May 2012 01:24:28AM 2 points [-]

as an oblique way of advocating for certain topics of discussion to simply not be mentioned at all

Wha...? Thank you for letting me know, though I still have no idea what you might mean, I'd greatly appreciate if you elaborate on that!

Comment author: TheOtherDave 24 May 2012 04:54:43AM 7 points [-]

I'm not sure I can add much by elaboration.

My general impression of you(1) is that you consider much of the discussion that takes place here, and much of the thinking of the people who do it, to be kind of a silly waste of time, and that you further see your role here in part as the person who points that fact out to those who for whatever reason have failed to notice it.

Within that context, responding to a comment with a request to formalize it is easy to read as a polite way of expressing "what you just said is uselessly vague. If you are capable of saying something useful, do so, otherwise shut up and leave this subject to the grownups."

And since you aren't consistent about wanting everything to be expressed as a formalism, I assume this is a function of the topic of discussion, because that's the most charitable assumption I can think of.

That said, I reiterate that I have no special knowledge of why you're being downvoted; please don't take me as definitive.

(1) This might be an unfair impression, as I no longer remember what it was that led me to form it.

Comment author: shminux 24 May 2012 02:38:36PM * 3 points [-]

Thank you! I always appreciate candid feedback.

Comment author: David_Gerard 24 May 2012 12:27:58PM 0 points [-]

My general impression of you(1) is that you consider much of the discussion that takes place here, and much of the thinking of the people who do it, to be kind of a silly waste of time, and that you further see your role here in part as the person who points that fact out to those who for whatever reason have failed to notice it.

It's too easy for this to turn into a general counterargument against anything the person says. It may be of benefit to play the ball and not the man.

Comment author: Luke_A_Somers 30 May 2012 03:49:34PM 1 point [-]

Anything the person says? In respect to most things it would be a total non-sequitur.

Comment author: TheOtherDave 24 May 2012 12:38:19PM 0 points [-]

Yes, I agree. Perhaps I shouldn't have said anything at all, but, well, he asked.

Comment author: Douglas_Knight 25 May 2012 12:52:53AM 1 point [-]

Which issue/problem? fairness?

Comment author: shminux 25 May 2012 05:35:09PM * 1 point [-]

The fairness concept:

the reward is a function of the agent's actual choices in the problem (namely which box or boxes get picked) and independent of the method that the agent uses to choose, or of its choices on any other problems.

should be reasonably easy to formalize, because it does not depend on a full [T]DT algorithm. After that, evaluate the performace of [a]DT under a [b]DT-aware Omega Newcomb's problems, as described in the OP, where 'a' and 'b' are particular DTs, e.g. a=b=T.

shminux comments on Problematic Problems for TDT - Less Wrong

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