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It's the 5th time this happens to me. Tried to solve some simple problem for about 20 minutes (four of them were just help-asking on passages of proofs) and decide to ask for some help/hint on Mathematics. Then, when I was elaborating the question, writing down the main problem and pointing the problematic part of the thing, I just discovered that something that can do the trick. Is that usual for you?

First question here, don't know if this is a suitable place.

And if there is another tag that can fit here, please edit.

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    $\begingroup$ Its why we encourage that questions contain plenty of context. This helps everyone out, including you! $\endgroup$ – Simply Beautiful Art Jul 29 '17 at 23:52
  • $\begingroup$ @SimplyBeautifulArt yeah, that's true $\endgroup$ – Filburt Jul 30 '17 at 0:00
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    $\begingroup$ Closely related: Formulating the problem helps solving it ... $\endgroup$ – hardmath Jul 30 '17 at 3:10
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    $\begingroup$ As a tip for next time: write your problem on some scratch pad (e.g. a text editor or the sandbox), being very sure to keep explanations and your musings as clear as possible. Walk away for a few minutes, and proofread your draft again. If you still don't have a solution in mind after doing all that, then you post your question. $\endgroup$ – J. M. is a poor mathematician Jul 30 '17 at 3:57
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    $\begingroup$ Yes, this is not just usual, this is the whole point of the Feynman algorithm for solving problems. $\endgroup$ – Asaf Karagila Jul 30 '17 at 8:35
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    $\begingroup$ Yes, 70% times when my friend calls for my help he starts describing the problem and then he says "nevermind" and hangs up. $\endgroup$ – kingW3 Jul 30 '17 at 9:54
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    $\begingroup$ This happens to me all the time. Formulating a problem and your progress in a way to communicate it to someone else frequently puts things in a perspective that solves the problem. This is the whole reason that preemptively answering "what have you tried" is a healthy and useful exercise. $\endgroup$ – rschwieb Jul 30 '17 at 18:38
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    $\begingroup$ It is so common it's almost an industry standard (albeit in a different industry) to exploit it. See rubber duck debugging in software development. $\endgroup$ – Arthur Jul 31 '17 at 7:20
  • $\begingroup$ As a side note, another approach that helps me solve problems is to sleep on them. This does not mean you should think about the problem all night. In fact, you should stop thinking about the problem for the rest of the day and resume tomorrow. There have been countless times when I've solved problems in under 5 minutes after waking up which I could not manage just yesterday. $\endgroup$ – Simply Beautiful Art Aug 1 '17 at 21:51
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    $\begingroup$ A couple of years ago I blogged: “As often happens, I found the answer myself shortly after I asked the question. I wonder if the reason for this is that my time to come up with the answer is Poisson-distributed. Then if I set a time threshold for how long I'll work on the problem before asking about it, I am likely to find the answer to almost any question that exceeds the threshold shortly after I exceed the threshold. But if I set the threshold higher, this would still be true, so there is no way to win this particular game.” $\endgroup$ – MJD Aug 2 '17 at 18:28
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    $\begingroup$ This was so awesome, I decided to link it in How to ask a good question: Provide Context: Include your work. Just as a heads up. $\endgroup$ – Simply Beautiful Art Oct 26 '17 at 0:44
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Yes, this is actually rather common!

It's easy to get tunnel vision, where you're too focused on things that don't work or have a mistake stuck in your head. The mere act of switching gears to post the problem can be enough to widen your view.

Furthermore, writing out the question and elaborating on what the difficulty is can make one think more carefully about the problem than one had previously, at least when one intends to write well. For many problems, "simple" problems in particular, simply being careful about what you're doing may be enough to solve the problem.

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  • $\begingroup$ In the last case of mine, the problem was a passage on a proof. A simple trick, but with that lot of context I couldn't see it. When I elaborated the statement to fit Mathematics (with the minimum hypothesis possible), I just looked again at the problem and ... voilà $\endgroup$ – Filburt Jul 30 '17 at 13:10
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    $\begingroup$ @Filburt (the good ones) I write 3 or 4 questions per day, I post only one every month. $\endgroup$ – reuns Aug 11 '17 at 5:16
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Let me post a comment here.

I am a quite old physicist with a lot of problems and I need to express them. The problem is that my wife does not understand anything in physics, mathematics, chemistry.

So, to explain (better say, to describe) my problem, I need to shift it in rather simple terms and words in order that she, at least, looks to be understanding something.

Doing so, I solved more than a dozen of problems of mine (but in almost 60 years) !

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    $\begingroup$ "You don't actually understand something unless you can explain it to a five-year old", or so the old aphorism goes... $\endgroup$ – J. M. is a poor mathematician Jul 30 '17 at 17:26
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It's actually super common, you'll find that when explaining a problem you understand that it needs to be broken down into it's smaller problematic parts, a problem is just a collation of sub problems and putting time into thinking about those sub problems (like you do when you explain the problem to someone) is a useful trick to understand the problem better as a whole and therefore gain context and insight into a more workable solution - it's actually used as a method for solving problems. We programmers tend to call it rubber duck programming because we often explain our problem to a rubber duck and just by the act of explaining it - it helps us come up with the solution.

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    $\begingroup$ Do you have to supply your own rubber duck, or are they provided by your employer? $\endgroup$ – Gerry Myerson Jul 31 '17 at 13:05
  • $\begingroup$ Solving problems by breaking them into smaller parts is a extremely powerful tool, in programming one of such tools is dynamic programming. $\endgroup$ – kingW3 Jul 31 '17 at 13:09
  • $\begingroup$ @GerryMyerson Depends on the company! I'm pretty sure google supply rubber ducks :D could be one of those google myths though... $\endgroup$ – seanyt123 Jul 31 '17 at 13:13
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I use this technique extensively. After looking at a new problem or concept I like to take the dogs for a walk or go for a bike ride and "talk to myself."

I say, "Ok Dave, What do we know? What do we want to know? What are the links between what we know and what we want to know?"

Focusing on articulating the problem without worrying about solving the problem often brings new insight.

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It is very common in software development to show a problem to a colleague / co-worker and start to explain why you think that your program should work but, before they even say anything, you spot the problem yourself. Somehow, needing to explain the problem to another has enabled you to see what you could not spot alone. We have sometimes considered using a mannequin for this purpose. Composing a good question for this site may achieve the same.

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Situated cognition is a theory in cognitive science that explains this phenomenon: Situated cognition states that much of cognition, especially the 'higher' forms of cognition, including reasoning, decision-making, planning, and problem-solving, happens not solely inside your head, but comes about through interactions with your environment, particularly when this environment includes a symbolic language, whether this be natural language (like English), or a specialised language (math, diagrams, etc).

So, whereas we often think that our symbolic expressions are merely expressing our already completed thoughts about something, situated cognition says that these expressions are much more than that: they actually enable you to think, or at least think further, than you could without that language. Language is a powerful tool to help us think, and help us solve problems.

Indeed, imagine how much math you would be able to accomplish without the language of math ... not much at all! And think about this: why is it that when faced with a tough problem, you often find yourself talking to yourself? If all the thinking is happening inside our heads, what use is it to express those thoughts to yourself? But situated cognition says: expressing these ideas to yourself is useful, as you are engaging yourself in a dialogue, and dialogues are yet another way to interact with your environment; even if you have a dialogue with yourself, it is the act of hearing those expressions that will cue certain responses, and thus further the reasoning process.

So yes, the act of carefully formulating and describing the problem is part and parcel of the very act of problem-solving, so what happened to you is not at all surprising, and is in fact very common, and has a perfectly good cognitive explanation.

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  • $\begingroup$ Do you really talk to yourself when solving math problems? That's something I've never done. It would greatly slow me down since I can reason mentally much quicker than verbally. $\endgroup$ – Bill Dubuque Aug 8 '17 at 3:07
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    $\begingroup$ I talk to myself internally, if that counts. I don't see the need to disturb neighbors while wrestling a tough problem. $\endgroup$ – J. M. is a poor mathematician Aug 8 '17 at 3:19
  • $\begingroup$ @BillDubuque Sometimes I do, yes. But then, I am not a very good mathematician. And I should be clear that I am not saying that all thinking has to go through external language, or even using an inner voice .... but sometimes it does help. $\endgroup$ – Bram28 Aug 8 '17 at 3:19
  • $\begingroup$ @J.M.isn'tamathematician Yes, if you use an inner voice, situated cognition says that that is an internalization of something that used to happen through actual speech and hearing ... presumably the brain figured out the shortcut straight from the speech production centers to the speech processing centers, but the process is still regarded as a dialogue. $\endgroup$ – Bram28 Aug 8 '17 at 3:21

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