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