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I've been trying to stay off meta recently, but I did want to talk about the following question:

Why is this proof of the collatz conjecture wrong

The question is now deleted, so here is a quote of the text at the time of deletion:

Ok, so there is this theorem that has been studied throughout history that says that if you pick any number you apply these steps: if it's odd you multiply it by 3 and add one if it's even you divide it by 2 after applying this you get a number to which you apply the same process and then again, and again and again and again... The theorem says that all numbers eventually go to 1.

So. If you start with an odd number it will be even in the next iteration, in the next step however there is a 50% chance of it being even again or being odd. That is because half of all integers are multiples of four, in the same way, out of the multiples of four, 50% of them are multiples of 8, meaning considering up to there, the average amount of divisions by 2 that you do on a number are 7/3 if my calculus is not flawed. This is already higher than the "3/2" multiplications by two that we do when we multiply by 3. Also, the +1 growth from every odd iteration is outgrown by the multiplicative decrease of the even numbers.

I am not an expert but I had this idea and I wanted to know if I was right or, most likely, why I was wrong because I don't believe I have produced some maths that has never been thought of.

So, to add up, looking only as far as the probabilities of the even integer (that will inevitably appear every iteration after an odd integer) being a multiple of eight, the average division coefficient by which an integer is divided is higher than the x3 coefficient of multiplication by the witch the eventual odd number is multiplied.

I thought the question was fine, if a bit unoriginal (I would be on board with finding a suitable duplicate target, and closing for that reason). The person had put some thought into the question, and wanted to understand why their intuitive reasoning didn't lead to a proof. When I arrived, the question had 4 close votes (all for the reason of missing context/details), 4 down-votes, and 3 up-votes.

It was not clear to me why this post had such a mixed reception, so I posted some comments asking for clarification as to why. User21820 replied with a helpful comment:

This question lacks research effort. For example, a quick google search brings up this Math SE thread which mentions Conway proving that a generalization is undecidable. Another quick google scholar search brings up this paper. Just looking at the graphs in the paper and the comments about the "visible kink" would strongly suggest that any such naive attempt is nothing more than naive.

Seconds after this, the post was deleted. Maybe a second after this, the poster added an extra paragraph to their question. So, I have two challenges in this situation:

  1. Is it appropriate to vote to delete a question that is merely 2 hours old, on which there is very much active discussion about its quality? I would say that, simply the fact that the asker was in the middle of editing their question indicates that this is far too soon.

  2. The asker, to me, did not strike me as particularly mathematically mature, and wanted to resolve the naive issue with their intuition. Is it reasonable to expect them to find Conway's undecidability result, either here on Google Scholar, and understand that this more advanced result answers their question?

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    $\begingroup$ Their question asks "I wanted to know if I was right or, most likely, why I was wrong". Saying previous work "would strongly suggest that any such naive attempt is nothing more than naive" doesn't actually answer the question of where their error was. I am in favour of treating honest, short, naive attempts at serious problems as proper questions (unlike crank "proofs" spanning multiple pages), especially here when someone wishes to understand their error). $\endgroup$
    – user1729
    Jul 30 at 21:35
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    $\begingroup$ (I also think that if the OP is still editing the question then it should not be deleted. There is no hurry to delete questions. If it is that bad then keep tabs on it and sort it tomorrow. Or trust that the Roomba will get it eventually.) $\endgroup$
    – user1729
    Jul 30 at 21:37
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    $\begingroup$ As for me, this type of content (vague discussions about famous open problems) is not welcome. $\endgroup$
    – quid Mod
    Jul 30 at 22:35
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    $\begingroup$ The goal of Math SE is to create a repository of narrow, focused problems about mathematics which admit (and have) high quality, authoritative answers. Math SE is not an appropriate platform for publishing new work, nor for requesting peer review of claimed results---particularly when those results claim to resolve long-standing open problems. Such questions are far to broad for Math SE. $\endgroup$
    – Xander Henderson Mod
    Jul 30 at 22:37
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    $\begingroup$ I'll note that this has come up quite recently: math.meta.stackexchange.com/q/33874/468350 . $\endgroup$
    – Xander Henderson Mod
    Jul 30 at 22:39
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    $\begingroup$ @Xander I agree it is wise to keep a lid on questions that propose new research. I didn't get that impression from this question: that the asker wanted us to peer-review a proof. The penultimate paragraph tells me not that they think they've discovered something new, but that they've discovered some gap between their intuition and mathematical reality. Of course, their choice of title doesn't convey this, but that would have been an easy fix. Either way, the "lack of context" close reason really doesn't convey this reason, especially without an additional comment. $\endgroup$ Jul 30 at 23:18
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    $\begingroup$ @TheoBendit I don't entirely disagree regarding the "lacks context" close reason. I think that either "too broad" or "not about math within the scope defined in the help center" would be more appropriate. $\endgroup$
    – Xander Henderson Mod
    Jul 30 at 23:21
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    $\begingroup$ @TheoBendit no worries we don't forbid that. The poster does not even seem to have a good grasp of what "theorem" means or what could constitue a proof. To mention "high level"in such a context strikes me as quite besides the point. $\endgroup$
    – quid Mod
    Jul 31 at 1:01
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    $\begingroup$ And has two close votes : I was aware that the question was up for only two hours, but no amount of chopping and changing was going to make the question different : claim of proof of open conjecture. So it was always going to be called off topic, even with the recent edits. The policy view is this , I implemented it. We may need more discussion of the policy, given that it has led to consternation in the recent past. My view is that we should help somebody who is willing to be helped and not be stubborn, and this OP looked receptive. The policy rules over that view, so I went with it. $\endgroup$ Jul 31 at 6:23
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    $\begingroup$ There were at least six posts regarding Collatz in the past $24$ hours, here. If we encourage them, I am sure we could get many, many more. $\endgroup$
    – lulu
    Jul 31 at 11:07
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    $\begingroup$ This site is a question/answer site helping people out of specific problems of mathematical understanding. But it is not a review site of papers , in particular not about open problems. The users here are volunteers and for posting proof trials, there are other sites with exactly this purpose. The post has , by the way , be undeleted. $\endgroup$
    – Peter
    Jul 31 at 11:10
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    $\begingroup$ @lonestudent: What's your comment for? Is there a problem with informing others who care about the site? Those are the most active participants in CURED right now. Anyone who cares about maintaining site quality have always been invited to participate CURED. $\endgroup$
    – user21820
    Jul 31 at 12:22
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    $\begingroup$ My proposal to stop deletion for 12 hours had a score of +2 when I went to sleep last night, and was deleted a few hours later. This speaks volumes. Plus, the question itself has already a close vote for being "opinion-based" (as though giving one's opinion is not permitted on meta). This reception is feeling hostile, and for the first time, I'm starting to feel censored. This sect from the CURED platform have amassed enormous power, and are clearly some of them are unafraid to abuse it. These are dark times indeed at MSE, and meta is the heart of this darkness. Don't worry, I won't be back. $\endgroup$ Jul 31 at 17:37
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    $\begingroup$ @TheoBendit I find it fascinating how whenever CURED gets brought up on meta lately (say the last 12 months) there are always broad generalities, doommongering and vague threats that CURED are the Four Horsemen of the Apocalypse, or at least their allies. You've offered cogent arguments for things you believe in in the past, so perhaps you'd be willing to present some actual evidence for your claims about this "sect" you've identified? It would be nice to see some for once! $\endgroup$
    – postmortes
    Jul 31 at 19:20
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    $\begingroup$ Question has been closed again, and deleted again. @Teresa, 16 hours ago, in a comment on the question on main, you asked people not to vote on main (but to come here to meta instead). Then, four hours later, you voted to close on main. I find this peculiar. $\endgroup$ Jul 31 at 22:52
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There is a very simple reason why we should not encourage posting about open problems by plain amateurs. If we allow just one, to be consistent we would need to allow a hundred. With the recent popularization (yet again) of the Collatz conjecture, we are already seeing a significant number of posts by people who do not even know what a mathematical argument is, much less mathematical proof. There is simply no good reason to keep such posts around, and the askers are incapable of improving it to a point that adds worth to Math SE.

For instance, in this case the asker said "probabilities become absolute as the sample (amount of steps) aproaches infinity". Ignoring the spelling error, this already shows that it is pointless to let the asker continue on and on about this idea, not to say that adequate information is easily found to fully demolish this naive idea.

If someone who actually knows some real mathematics asks a reasonable question (even about an open problem), and the answer is not easily found, there is good enough reason to keep it. But if the question has no lasting value, it does not matter whether we delete it slowly or quickly, because the asker can still see the deleted question, can still edit it, and can still self-vote for undeletion.

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  • $\begingroup$ This sort of captures what I'm thinking about as well, but I'd like to add there was quite a contrasting answer (and discussion) to this one that I saw here. I was preparing an answer along similar lines (but nowhere near as concise as this one!) and I hit upon it earlier. It apparently is the case that people would like it when others' mistakes, however odd looking, are pointed out, even if those mistakes appear on a proof of a conjecture. That's the picture they see. $\endgroup$ Jul 31 at 11:11
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    $\begingroup$ And then the justification is that "it's a common mistake" and something pointing out elementary mistakes always has a lot of takers. Anyway, I'm really happy with this answer. $\endgroup$ Jul 31 at 11:13
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    $\begingroup$ @TeresaLisbon: I can't be sure why it got many upvotes, but I suspect it was just because the post in question was long. There is a correlation between length of post and upvotes, but length does not necessarily imply quality. The problem is that anyone (including mathematically illiterate) can tell when a question is too short to be good. But you need at least a bit of mathematical training to be able to tell when a long wall of text strewn with a few mathematical formulae is in fact bogus. In turn, there is a correlation between upvotes on a question and upvotes on a meta complaint about it. $\endgroup$
    – user21820
    Jul 31 at 11:30
  • $\begingroup$ Personally I'd like a "Famous research question posts please to go stackoverflow where they can stomp them over there" policy :). Or at least a minimum reputation for Riemann Hypothesis and Collatz etc. to keep out the kooks. $\endgroup$
    – Alan
    Aug 3 at 20:11
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    $\begingroup$ @Alan: Hahaha.. Your second suggestion is an interesting one, and I wonder how well it might work (if say the threshold is 1000 rep). =) $\endgroup$
    – user21820
    Aug 4 at 7:49
  • $\begingroup$ @user21820 Unfortunately there are plenty of high-rep kooks, so that might only have limited impact $\endgroup$ Aug 8 at 9:02
  • $\begingroup$ @MorganRodgers: Yes, but even keeping out 90% might be a good start. =) $\endgroup$
    – user21820
    Aug 8 at 9:24
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I'd like to propose a policy. Please upvote only if you agree that people should follow this, and downvote if you don't.

No question should be deleted less than 12 hours after it was closed.

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    $\begingroup$ ... the reason being, of course, so that the asker has time to review the problems in their post and make the necessary changes to bring their question up to code, before their work is deleted. $\endgroup$ Jul 31 at 7:34
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    $\begingroup$ Note : I usually follow this policy. For this particular question, I informed you why I did not. So I'm going to not vote for now, but if I see a majority on this answer, then I will make sure I mend my ways. I'm sorry if the early closure prevented debate @TheoBendit. $\endgroup$ Jul 31 at 7:37
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    $\begingroup$ This has been proposed several times. $\endgroup$ Jul 31 at 7:38
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    $\begingroup$ @TeresaLisbon Thanks, I appreciate it. But, no harm done to me. We're here now. $\endgroup$ Jul 31 at 7:38
  • $\begingroup$ @TheoBendit Sure, just good to know we are on the same page. $\endgroup$ Jul 31 at 7:38
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    $\begingroup$ Say here $\endgroup$ Jul 31 at 7:41
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    $\begingroup$ @ArcticChar ... and now I wish I had put the "unless it's spam/trolling/etc" caveat. I know it's bad form to edit such posts after people start voting on them. :-/ $\endgroup$ Jul 31 at 7:43
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    $\begingroup$ @ArcticChar While I'm guessing it probably has been proposed in the interim as well, it's worth noting that the proposition you linked to will be celebrating its 7th birthday next month. The attitudes of the community could well have changed a lot since then. $\endgroup$ Jul 31 at 7:54
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    $\begingroup$ @TheSimpliFire the poster should have deleted their ill-thought proposal once they realized the blunder. On top of that it is redundant and muddies the water regarding what is actually discussed in this meta-thread. Is the problem that the question is considered as one to be removed or is it that it was removed too quickly given there was discussion going etc. Anyway I removed the comment but will remark that your parenthetical is odd in that there is of course a spectrum and I merely used some rather generic and wide-spread expletives. $\endgroup$
    – quid Mod
    Jul 31 at 10:56
  • $\begingroup$ I heavily disagree because of the word "no" and the 12 hours. I agree however partially. Questions without serious issues like abuse or spam can be hold on for a few hours to get the author the chance for an improvement. But specific circumstances require a quick deletion , for example , unjustified upvotes, ranting of the author or if the post is short from being open to a bounty. With reasonable restrictions, this rule is finally not bad. $\endgroup$
    – Peter
    Jul 31 at 11:02
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    $\begingroup$ @quid: That's interesting. I wouldn't have thought that citing an offensive statement as an example of offensive statements should be considered to be offensive... That's my opinion, anyway. Thanks for the clarification! $\endgroup$
    – user21820
    Jul 31 at 11:42
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    $\begingroup$ @ArcticChar fine. Your reaction to a policy that proposes to leave up such content for 12 hours is a bit weak then. $\endgroup$
    – quid Mod
    Jul 31 at 11:50
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    $\begingroup$ @ArcticChar as proposed, obviously and rightly so. For the old one, it's less clear. The subject was out of focus. New people arrive, old forget about it a bit. Of course it does not help at all if debates are extremely unfocused. I mean what exactly is the point of this meta-thread? It starts out as about one question mostly and pivots to a general policy on deletion. $\endgroup$
    – quid Mod
    Aug 1 at 10:10
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    $\begingroup$ @TheoBendit Currently, once a question is closed, it cannot be deleted for two days, except by users with 20k+ reputation, or if the question has a significant negative score. Generally speaking, I am in favor of quick closure and slow deletion, and am generally opposed to downvoting for the express purpose of making a post eligible for immediate deletion. As a general guideline, I am all for "wait two days before deleting", but there are exceptions: spam, abusive posts, inherently off-topic questions, and other kinds of unsalvagable posts. $\endgroup$
    – Xander Henderson Mod
    Aug 1 at 14:32
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    $\begingroup$ Naïve attempts to resolve long-standing open problems generally fall under the header of "inherently off-topic" and otherwise unsalvagable (I will not deny the possibility that someone might use such a question to ask an on-topic mathematical question, but I have difficulty imagining such a scenario). As such, I don't feel that quick deletion is a problem in such cases. $\endgroup$
    – Xander Henderson Mod
    Aug 1 at 14:34

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