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I intended to elaborate on the captcha problems in the original thread, but since it has been locked, I have no choice but to create a new thread. I think it is very important that the SE designers understand that mathematics places very unique demands on the software platform.

In the original thread Jeff Atwood speculated that a browser/network config problem might be the source of the many annoying captchas that I face (e.g. over 20 in one recent few hour period). He added that this "barely comes up" on, say, StackOverflow. The reason for that is quite simple. Mathematics has much richer structure than most other fields of knowledge. It has much deeper levels of abstraction and a much, much wider web of interconnections between various subfields. I think it is very important when teaching to point out these interesting interconnections. Sometimes these surprising and beautiful links are precisely what spurs students to study mathematics. So I often pepper my posts with links to related topics, e.g. generalizations, specializations, cryptomorphisms, etc. This can trigger a network of edits to related posts - a flurry of quick activity which furiously tickles the captcha dragon's tail.

Often times when the captcha arises it seriously disrupts my thought process. When one is trying to keep a moderately complex web of math ideas in mind to perform some related edits, having to deal with a barrage of annoying captchas can force a mental "stack overflow", i.e. short-term memory overflow. Mathematical reasoning places great demands on the pattern-matching parts of the mind. Having to swap math stuff out of mind so to recognize some obfuscated captcha text can seriously hamper one's mathematical thought processes. Not to mention time constraints. On a few occasions captchas forced me to run out of (spare) time, so I had to return to my answer later - making it much more difficult to remember what I was doing (half a minute of captcha solving time can be the straw that breaks the camel's back when your girlfriend is dragging you out the door after ten minutes of "be there in a minute" ... not to mention my young niece who, alas, overheard my cursing not "captcha" but her beloved "Casper" - the friendly ghost).

Perhaps an analogy will help. Adriaan de Groot, a chess master and psychologist, wrote a famous book "Thought and choice in chess" which explored at length how the mind works in chess grandmasters. He speculated that grandmasters reprogram certain pattern-matching parts of the mind for recognizing chess patterns - similar to what occurs in mathematics. To disprupt the mathematical thought processes with captcha's is quite analogous to forcing chess players to solve a captcha if they make too many rapid moves in succession. Of course a chess gaming site with such captcha's would never succeed. An analogous argument holds for mathematics.

So, SE designers, could you please reconsider the captcha algorithm. I think it should be easy to eliminate the above problems without sacrificing the original captcha design goals.

Note: most of my edits don't show in the edit history since they are within the 5 minute window where edits are coalesced. So it is not easy to give specific examples that show how the captcha was triggered.

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    $\begingroup$ I do not see what is the problem of simply not showing up captchas for users with sufficiently high reputation. $\endgroup$ – Mariano Suárez-Álvarez Nov 16 '10 at 19:11
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    $\begingroup$ (And I would love to change the word reputation for something with less annoying!) $\endgroup$ – Mariano Suárez-Álvarez Nov 16 '10 at 19:11
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    $\begingroup$ @Mariano Bots. Oh, and -1 for assuming Maths is different. Do you really think people give thoughtless answers on Stack Overflow? $\endgroup$ – badp Nov 21 '10 at 14:58
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    $\begingroup$ @badp, if there are bots which are able to gather sufficiently high reputation in the math site, then (i) it is a bit naive to think that such a triviallity as a captcha will stop them! and (ii) why on earth are you trying to keep those bots away? I think we want smart bots able to answer questions sensibly! $\endgroup$ – Mariano Suárez-Álvarez Nov 23 '10 at 1:22
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    $\begingroup$ @badp, I also do not agree that Maths is different---I simply do not understand why sufficiently high rep users in any of the SE sites have to deal with captchas. $\endgroup$ – Mariano Suárez-Álvarez Nov 23 '10 at 1:24
  • $\begingroup$ @badp: Math is different. It has far more levels of abstraction, far more objects, theories etc than any other body of knowledge (not being limited by physical laws). Moreover it has theories that promote analogies and interconnections (e.g. universal algebra, category theory, etc). Thus it's not surprising that when organizing math knowledge on a math site, one would employ far more links than on other sites. Alas, it is difficult to appreciate this unless one has studied math at the grad-level or beyond. $\endgroup$ – Bill Dubuque Nov 23 '10 at 1:50
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    $\begingroup$ @Bill, while all that may be true, I honestly do not see in what way it results in a difference with regards to this specific site. I keep reading T rave about an optional form to be filled in (by OPs?) providing all sort of meta information that, from the sound of it, might need a degree in library science to fill in correctly, and you about the interconnections between innumerable branches and innumerable levels... Yet all other users of this site seem to manage without both things. $\endgroup$ – Mariano Suárez-Álvarez Nov 23 '10 at 2:12
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    $\begingroup$ By the way, you should make more acquaintances among the natural sciences! The fact that biochemistry is limited by physical laws did not in the least diminish my ABSOLUTE AWE some time ago at seeing a whole aisle in a biochemistry research library devoted to a single molecule, biliverdin. I think it is a safe bet that it is simply impossible for a human to know everything there is to know about that one molecule. And the human body has uncountable many other molecules involved in its functioning!!! So, please!, let us drop the math is unique slogan... $\endgroup$ – Mariano Suárez-Álvarez Nov 23 '10 at 2:22
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    $\begingroup$ @Mariano: You do not understand the reason behind having the CAPTCHA! It is not about REP at all. Is it possible that the computer of a high rep user is hijacked? Unfortunately, this question and the upvotes it is getting just seems to show that people are upvoting without thinking. It is very very easy for a human (including the OP) to reduce CAPTCHA by just taking it a bit more slow. The reason one can afford to reduce (but not eliminate) CAPTCHA for high rep users is that they visit the site frequently enough to raise a red flag in case their account is hijacked... (cont) $\endgroup$ – Aryabhata Nov 23 '10 at 3:14
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    $\begingroup$ @Bill: btw, I forgot to ask. If you edit different posts very frequently, and are hit by CAPTCHA, why do you consider it a flaw? According to what I read, once you solve the first CAPTCHA, you are immune for at least 5 minutes. Perhaps you are just hitting a bug? From your previous comment it looks like you agree that hitting the first CAPTCHA should be by design. $\endgroup$ – Aryabhata Nov 23 '10 at 5:04
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    $\begingroup$ @Bill: Frankly I am surprised that you are so easily discouraged. Especially when the workaround is so trivial. As to your overly generic statement of what constitutes a flaw, all I can say is good luck with that, rocket science or not. $\endgroup$ – Aryabhata Nov 23 '10 at 6:05
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    $\begingroup$ @BillDubuque I'm not going to get in an e-penis measuring contest about what topic requires the most "focus" when answering. By the way, extended frequent editing is disruptive to the site, as it pushes fresh new questions down, away from the homepage. It's by design that it is hard to disrupt the home page ;) $\endgroup$ – badp Nov 23 '10 at 8:16
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    $\begingroup$ @T: anything would be more complicated and would involve more work (for someone) than what we have. I think a serious case has to be made by those propounding elaborate cataloging additions that they would help in any way with real life usage of the site. I cannot for the life in me imagine why I would search for things tagged 'homework'! I honestly think that your proposal is over-engineering a feature that will have little effect on how users use the site. Google more or less already proved that manually ontologising content is orders of magnitude worse than good searching. $\endgroup$ – Mariano Suárez-Álvarez Nov 24 '10 at 6:07
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    $\begingroup$ Honestly, I don't see much point in this discussion. On one hand, I find your proposal impracticable and---given that---in fact undesirable (bad metadata is catastrophically worse than no metadata), on the other hand, I would be extraordinarily surprised to see SE implement anything remotely similar to it. $\endgroup$ – Mariano Suárez-Álvarez Nov 24 '10 at 6:50
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    $\begingroup$ re: "anything would be more complicated" -- this is incorrect as long as the visual interface stays the same and to alter it one has to click on some unobtrusive link. For example, the Moderator Tools link would appear at the top after 10K (2K in beta) and it took me quite a while to even notice it was there. After trying it out I ignored it and used the original options. Other users might want those tools, however: it is more options without a lot of extra complexity. If the Q&A page gets cluttered with 20 more links you might have a point. $\endgroup$ – T.. Nov 24 '10 at 7:01
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About the idea that captcha "hampers math sites much more than others":

The CAPTCHA issue is a site-independent aspect of the software platform and not something that seems peculiar to a math site. It could be that it is triggered more often on math sites, and this might be for reasons of the kind that Bill mentions. Maybe. Unfortunately, citing the majestic interconnectedness of mathematics creates the impression of assigning a privileged status to math (or mathematicians, or math.SE users, or MathOverflow users). Whether or not that is the intended message, it does not play well on a site created, operated and predominantly used by non-mathematicians. If the CAPTCHA is annoying enough to require repair that problem should be solved on the basis of its annoyingness to everyone and not as a special request from the math site.

I generally agree with the points Bill has raised in many threads about math sites having a host of unusual or unique features -- but only as it concerns the Q&A function and technology that supports the Q&A. Using general aspects of the all-SE site software such as CAPTCHA to illustrate the math-is-different idea (or the is-math-different question) has led to the appearance of wanting special favors from the SE management based on a conviction that math is always an extreme outlier, or deserves unique consideration in every respect. The actual Q&A issues are more straightforward, though the technological implications of those issues are not always as easily handled as relaxing the CAPTCHA.

This is not the thread in which to explore the is-math-unique subject. But because of the volume of comments on this under the various answers it is worth mentioning that the uniqueness subject stands or falls on its own, independent of (and indeed, with very little clear relation to) any questions about CAPTCHA.

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The threat model behind the current CAPTCHA algorithm appears to be unrealistic and thus profligate.

If internals of the bot-detection routine are disclosed, there are users here (resp., on stat.SE, CS.SE, StackOverflow) who can advise on how to get better results with less annoying algorithms.

[Posting this required one CAPTCHA.]

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    $\begingroup$ are you using noscript or any other odd browser settings? There's no way posting that should have required a captcha! I almost never see captchas and I am subject to the very same captcha rules as everyone else (albeit the relaxed 10k settings are in effect for moderators). $\endgroup$ – Jeff Atwood Nov 18 '10 at 5:42
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    $\begingroup$ @Jeff: I don't know but could investigate if it is important. Like Bill, I tend to edit postings and comments multiple times after the initial sendoff. I am not concerned with CAPTCHA per se compared to the other matters of site upgrade, restoring functionality that was present in USENET, etc (you or Rob have probably seen the postings). As far as CAPTCHAs are concerned I am not personally troubled by their presence but if there is to be a focus on them, I feel that my and others' "developer time" would be better spent on the algorithm than on analyzing browser details. $\endgroup$ – T.. Nov 18 '10 at 6:40
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    $\begingroup$ "I tend to edit postings and comments multiple times after the initial sendoff" that would do it, then -- if you're editing rapidly enough. But you aren't at the 10k threshold yet, which reduces that trigger interval by 66%. $\endgroup$ – Jeff Atwood Nov 18 '10 at 7:33
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Let me provide a data point: to the best of my recollection I have never been asked to solve a captcha on math.SE or meta.math.SE. This despite the fact that I am a fairly regular user and I do sometimes edit posts several times in rapid succession. (On MO, where I think I must be one of the most active users, I have been asked to solve perhaps 10 captchas in the last year and none in several months.)

I say this not to undercut those who have experienced unpleasantly many captchas. On the contrary, it looks to me like there may be some problem with the captcha algorithms. To tell someone to look forward to 2/3 reduction of captchas with 10K reputation when other users are not experiencing any captchas at all doesn't seem fair. Or perhaps it is, but it's hard to know, since the entire captcha system seems to suffer from a lack of transparency.

If there is a cogent explanation for why this feature is needed at all, I would like to read it. Perhaps it would be worth trying out a temporary moratorium on captchas? Then we could see to what extent they are actually necessary and beneficial.

Update: I just got my first CAPTCHA on the site. I saw a question which had a maximally nondescriptive title ("How to solve this one?" or something close to that) and decided to edit the title to something more reasonable. My first chosen title spilled over onto a second line, which I decided was unnecessary, so I edited it again to shorten the title a bit, and then got a CAPTCHA. Only two edits altogether.

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    $\begingroup$ IMO, we need a good reason not to use CAPTCHA. It is annoying, but sometimes it is the price you have pay to reduce the noise (and extra manual effort in cleaning) due to spam. Besides, it is not hard to avoid. Just post more slowly. It that so hard? (You can still do the frequent edits rapidly, just press the Post button less frequently). IMO, it is ridiculous that this seems to have been blown out of proportion. $\endgroup$ – Aryabhata Nov 21 '10 at 15:29
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    $\begingroup$ @Moron: my point is that the price that people are paying seems to be unequally distributed and perhaps not completely understood. Is it clear that spam will be increased without CAPTCHA? Has it ever been tried? $\endgroup$ – Pete L. Clark Nov 21 '10 at 15:49
  • $\begingroup$ @Pete: I suggest you google Captcha. All I can say is, do you see spam on this site? I don't think turning it off is the solution. A better solution, IMO is to have instant previews. $\endgroup$ – Aryabhata Nov 21 '10 at 15:52
  • $\begingroup$ @Moron: I could just as easily cite the presence of a certain amount of spam on MO as evidence of the ineffectiveness of CAPTCHAs, but both arguments seem fallacious. Of course I have no idea what would happen if CAPTCHA was temporarily turned off, so my suggestion is somewhat in the scientific spirit and somewhat based on pure naivete. But what is causing annoyance to users of the site should not be purely brushed off. For instance, even a little advice about exactly what sort of conduct avoids CAPTCHAs would be useful. $\endgroup$ – Pete L. Clark Nov 21 '10 at 16:08
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    $\begingroup$ @Pete: Also, math.SE isn't unique (yes, contradicting this thread), IMO, with respect to CAPTCHA, if you are looking for more data. $\endgroup$ – Aryabhata Nov 21 '10 at 16:10
  • $\begingroup$ @Moron: agreed on your last point -- having looked at the discussions on meta.SE, I see that plenty of people have voiced concerns about CAPTCHAs. $\endgroup$ – Pete L. Clark Nov 21 '10 at 16:15
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    $\begingroup$ @Pete: Yes, there will always be users who are prone to editing and clicking post frequently. I have even maintained that CAPTCHA for frequent edits of the same post is pointless. I suggest you read up the existing CAPTCHA articles (I suppose google will find that for you) if you are interested in scientific data. Note: I haven't read them myself, so would be glad to hear what you find. $\endgroup$ – Aryabhata Nov 21 '10 at 16:22
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    $\begingroup$ (And yes, with all due respect to all and speaking as someone who has devoted his life to mathematics, I find arguments which proceed from the assumption that mathematics is the richest, deepest,...bestest form of human knowledge to be both unconvincing and unhelpful. If I were active on AngLeeFilms.stackexchange.com -- and let me know if such a site exists, because I would really enjoy it -- I would still hope that there would be some attention devoted to the particular needs of my community.) $\endgroup$ – Pete L. Clark Nov 21 '10 at 16:28
  • $\begingroup$ @Pete: I confess I am quite surprsied that any professional mathematician might disagree that the mathematical web of knowledge is interconnected in many more ways than in most other fields. It would not be difficult to make more precise combinatorial arguments as to why this is so. Compared to any other body of knowledge, mathematics has many more abstracted objects, many more levels of abstraction, etc. Moreover, it has meta-theories that promote the discovery of links and analogies (universal algebra, category/topos theory etc). $\endgroup$ – Bill Dubuque Nov 21 '10 at 18:21
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    $\begingroup$ @Bill Dubuque: Yes, I agree that mathematical knowledge is the richest of all knowledge in certain ways, especially having to do with abstraction. Moreover it's my favorite field of knowledge, no question about that. But others can and do find intellectual reasons to prefer their own fields (and to want to repeatedly edit their posts). Strenuously proclaiming that mathematicians deserve special treatment seems unlikely to win over outsiders, particularly SE executives. This is all just my opinion, of course. You're entitled to yours and I am not going to debate you on it. $\endgroup$ – Pete L. Clark Nov 21 '10 at 19:17
  • $\begingroup$ @Pete: I didn't "strenuously proclaim that mathematicians deserve special treatment". Rather, I pointed out one unique aspect of math that causes users of this site to stress it more than other SE sites (after Jeff remarked that no other site does such). A math "web" is more complex because it's not limited by physical laws - one can dream up any objects (modulo consistency). Such intellectual freedom has enabled mathematics to build a huge web of structures and theories. To comprehend that web requires constant (re)organization. Weaving this web here requires many edits - triggering captcha. $\endgroup$ – Bill Dubuque Nov 21 '10 at 20:49
  • $\begingroup$ I'll mention that the only times I've hit the CAPTCHA were times when I made a mistake in retagging or editing a title, and then quickly submitted a correction within a minute of having committed the bad edit. $\endgroup$ – J. M. is a poor mathematician Nov 28 '10 at 13:07
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Many a times, editing a question or answer too quickly after posting prompts a CAPTCHA.

My question to the SE staff: There is no captcha for editing comments within 5 minutes. So, why is it there for questions and answers? If as you say it is for preventing bots, then are you giving a free reign to bots for spamming with comments, but not with questions/answers?

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    $\begingroup$ In fact, the captchas gotten from editing posts 'quickly' after initial posting do not prevent bots at all... Why would a bot edit a post it has just made? The captchas are guarding us against spam bots which edit their posts! $\endgroup$ – Mariano Suárez-Álvarez Dec 4 '10 at 23:32
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    $\begingroup$ The fact that there is no CAPTCHA for comments is said to be part of the reason that minimum rep is needed to leave comments; that being said, why not make the minimum rep needed for comments be also made the minimum rep needed for the ability to edit posts without CAPTCHA fuss? $\endgroup$ – J. M. is a poor mathematician Dec 5 '10 at 0:28
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You already reached the 10k threshold, which means your captcha frequency (based on repetitive actions) is reduced by 2/3.

Additionally, as of a week ago (roughly), we instituted a 5 minute grace period after every successful captcha, so you will NEVER see a captcha more than once every 5 minutes.

If you're still running into it, that would require us to special case your account across the entire network.

I don't feel this would be a good use of our development time.

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    $\begingroup$ Jeff, is there an argument for having captchas for users with, say, >= 500 reputation? $\endgroup$ – Mariano Suárez-Álvarez Nov 18 '10 at 2:51
  • $\begingroup$ @mariano see meta.stackexchange.com/questions/3346/… $\endgroup$ – Jeff Atwood Nov 18 '10 at 3:01
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    $\begingroup$ @Jeff, that's not an argument: it's you explaining the rules. (The idea someone proposes that high rep accounts are more desirable to attackers so you need to keep having the captchas is extraordinarily silly currently in view of the fact that you get less captchas when you have more rep...) $\endgroup$ – Mariano Suárez-Álvarez Nov 18 '10 at 3:09
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    $\begingroup$ @Jeff: captchas aside, Bill raises an excellent general point about a math site having different needs from most others. Some of these can hog development time for purposes that may or may not be relevant to the average (current and future) SE 2.0 site. Is is StackExchange's intention to operate math.SE cookie-cutter style, with success defined simply as active use, or is SE willing to invest developer time into what might be unique needs of the math site? I alluded to a few of the possibilities in comments under the "mark locked threads as [locked]" discussion here in meta. $\endgroup$ – T.. Nov 18 '10 at 4:28
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    $\begingroup$ @T.. I count 44 items here meta.math.stackexchange.com/tags/status-completed ; that doesn't seem very cookie cutter to me, but perhaps we have different definitions of the words? One user, however vocal, simply isn't an adequate amount of data to justify a change so sweeping. Also remember we have already relaxed the settings twice: once for 10k users and recently with a 5 minute grace period after every captcha. $\endgroup$ – Jeff Atwood Nov 18 '10 at 5:19
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    $\begingroup$ @Jeff: yes, that link illustrates the "cookie cutter" idea perfectly. Of the 44 items, none are platform changes or upgrade based on specific needs of a math site. 5-10 don't involve the SE developers at all (e.g., requests filled by moderators to add tags or delete postings). The rest are all bug-fixes for previously decided functionality (e.g., reputation carryover from other accounts) or solving problems with TeX and graphics rendering. All are generic fixes of items that apply to various other SE sites and none modify the platform or paradigm in even a minor way. $\endgroup$ – T.. Nov 18 '10 at 6:07
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    $\begingroup$ (cont.) The question of course is whether anything beyond the current approach (ie., deriding unpaid content contributors as "too vocal" if they suggest improvements) is expected for requests whose end result is low-priority for the nonmath sites, such as adding a separate "Sources/Literature/Links" repository as part of each math.SE question. A clear indication of whether SE takes seriously the possibly unique structural or platform needs of a math site is of considerable interest here, as the votes in meta have shown -- quite vocally. $\endgroup$ – T.. Nov 18 '10 at 6:25
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    $\begingroup$ So, "special case" is now a verb :-( $\endgroup$ – Robin Chapman Nov 18 '10 at 7:29
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    $\begingroup$ @T.. the math community is "unique" in many ways. If you honestly feel you aren't getting what you need here, I encourage you to find other sites on the internet that might be more to your liking. There's no need to force a fit when you can find greater happiness elsewhere. Life is simply too short to be unhappy, and ultimately the negative energy of the vocally (and seemingly perenially) unhappy folks is a drag on everyone. Bottom line, yes, we will work with you, but if there isn't good faith on both sides, time to move on. $\endgroup$ – Jeff Atwood Nov 18 '10 at 7:31
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    $\begingroup$ @Jeff: as the meta votes in multiple discussions have indicated, a number of users have a good-faith interest in knowing whether SE would "work with [them]" in the sense of taking action on feature-requests that (although theoretically available to all sites once added) are probably, initially, or permanently of interest mostly for math.SE or a small number of similar sites like physics. I gave a simple example of adding a Sources file to questions. $\endgroup$ – T.. Nov 18 '10 at 8:02
  • $\begingroup$ @T.. we certainly weight toward changes that can help multiple communities as a simple matter of cost-benefit analysis. But I have been surprised how useful MathJax has been on multiple sites -- though we initially thought it was "just for math.se". It is an excellent example of math pushing positive changes out toward the network. It is a balancing act. $\endgroup$ – Jeff Atwood Nov 18 '10 at 8:07
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    $\begingroup$ Dear Jeff, T.. is the 7th ranked user on the site, and this is based on answers (120 of them), not questions (of which there are 2). I don't understand why you are suggesting that T.. leave the site just because of politely phrased questions about the future of the site and the SE teams medium/long-term view. Best wishes, $\endgroup$ – Matt E Nov 19 '10 at 4:26
  • $\begingroup$ @Matt E: thanks. As I see it there is a pressing matter of building a "USENET 2.0" as Jeff and Joel call it, which would be an important step forward in public-domain knowledge sharing (like ArXiv or Wikipedia). If they don't want SE to actually follow that model it is fine, but there is also a real risk that seems to be materializing of creating a troubled pseudo-USENET that carries the mantle but actually thwarts the development of the resource for another 10-15 years just as happened when the older model did not adapt to the WWW. If it were just a matter of where to talk math, MO is fine. $\endgroup$ – T.. Nov 19 '10 at 7:46
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    $\begingroup$ @Jeff Atwood: Bill Dubuque has a very high reputation; much higher than 200. And he is suffering from excessive captchas. I suspect that he is not the only one suffering from the problem. If indeed he were the only one, you could have proved it by pointing out any special habits of his that results in the problem. You haven't done that. So your answer appears to be insensitive to the experience of the OP. $\endgroup$ – user1119 Nov 19 '10 at 10:45
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    $\begingroup$ @JeffAtwood For the record, the CAPTCHA problems have not occurred in a very long time - so your developers have successfully fixed the above-mentioned problems. Thanks very much. Now how about some more powerful searching tools? $\endgroup$ – Bill Dubuque Nov 28 '11 at 23:38

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