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Could you give examples of some questions of which you think that they could be prevented by this sort of captcha?
I looked at some of the captchas, five or so, they were all high-school level or at best basic calculus; question below this level are IMO rare.
In any case, I do not think this would work well. (Even if the site could have it at no effort for anybody, I'd be against it.)
Clearly the sentiment has been expressed before. See, e.g., the last comment (as of this writing) in this thread: http://meta.mathoverflow.net/discussion/203/captcha/
Essentially, we've discussed measures like this (but not exactly this) before, and the very strong feeling (at least on my part...) has been that every tiny little hurdle we put in front of real mathematicians using the site is way more costly to us that dealing with inappropriate questions.
At the moment I count only two closed questions on the front page; by historical standards that's actually really good. It might be useful to have a discussion again about people's impressions of the level of inappropriate questions, and what, if anything we should be doing about it. It is possible to deal more robustly with off-topic questions --- e.g. users can flag for moderator attention, suggesting immediate closure or deletion, and this might slightly speed up their disappearance. That said, closures these days usually don't involve the moderators at all.
I agree with Scott. The potential costs far outweigh the minor benefits; and if you think we get a lot of off-topic questions then you have been living a blessed life on the Internet so far...
I wouldn't either. And it might turn away mathematicians whom we'd otherwise like to attract.
In another thread I suggested the idea of a two tiered arrangement of questions. The tier most viewed by the community would be the "research" tier, while it would be possible to have other questions relegated to the "other" tier and still be viewed by those of the community who wished to see them. New users could post to the "other" tier and request a sponsor to move it to the research tier. While the standard cries of "But we can't change the software!" and "Why give new research mathematicians any more hurdles?" could be given, I would like to see a consideration of this idea. I think it would address the issue brought up by the the thread and, if properly thought out, could be a direction we want a new platform to go.
I can imagine at least two disadvatanges to such a system, but I prefer other eyes consider this and wish to hear other points of view.
Gerhard "Ask Me About System Design" Paseman, 2011.08.10
I see there's general consensus against this proposal, so I won't go on arguing in its favour. Besides that, the measures suggested by grp in the thread linked above address the same problem in a less radical way, and seem to have more appreciation.
@angelo: in any case, I wasn't suggesting solving calculus problems at the time of posting, but when registering, so only once in a user's lifetime.