Fundamental obstructions

[riceissa]

see:

• https://agentfoundations.org/item?id=1129
• http://lesswrong.com/r/discussion/lw/ok6/the_i_already_get_it_slide/dw8a
• http://johnsalvatier.org/blog/2017/the-i-already-get-it-slide
• https://www.facebook.com/groups/aisafety/permalink/768960229934760/
• https://ai-alignment.com/directions-and-desiderata-for-ai-control-b60fca0da8f4

I haven't done enough enough theoretical computer science or math to understand this intuition, but it would be nice to have more examples of these "fundamental obstructions".

I'm not sure about the venue; maybe LW or LW Wiki would be fine.

[riceissa]

see also Paul's comment on this page, which seems like it's describing the same or similar thing:

This is a more general pattern in theoretical research. When you first start to attack a hard problem you often notice many promising lines of attack. Somehow in every line of attack, there will be at least (and often exactly) one thing that doesn't quite work out. Terence Tao has described this as feeling like "enemy movements" or something like this (though I can't find the quote). It is generally not possible to cross such gaps until you actually understand them. Once you do, instead of looking for a path from premises to conclusions you look for any gap in the chasm that seperates them. Once you've found the gap, it's often easy to go from premises to the gap and then from the gap to your conclusions.

[riceissa]

From Tao's "Be sceptical of your own work":

In a related spirit, if you are trying to prove some ambitious claim, you might try to first look for a counterexample; either you find one, which saves you a lot of time and may well be publishable in its own right, or else you encounter some obstruction, which should give some clue as to what one has to do in order to establish the claim positively (in particular, it can “identify the enemy” that has to be neutralised in order to conclude the proof).

[riceissa]

See also this comment by Tao, where he says:

I also wanted to add one more comment, which is that expositions of proofs of existing results, while important, are only one side of the story. It is just as important to talk about non-proofs; naive arguments, conjectures, or theories which fail, but for an instructive reason. These failures “identify the enemy” and allow one to truly appreciate the strength of the successes. This, I think, is perhaps the least developed area of mathematics exposition currently; nobody wants to talk about failure.

[riceissa]

maybe more at https://www.google.com/search?q=terence%20tao%20%22fundamental%20obstruction%22 and similar searches