This reminds me of my Ph.D. crisis. (which I'm sure many former grad students can relate to)
I was in my 6th year. All my friends had graduated, and my stipend had run out. I was 2 weeks away from submission and discovered that one of my assumptions was wrong, which potentially distorted/invalidated all my studies -- to fix these studies would have potentially delayed submission for months. It was a very subtle assumption violation (and it wasn't even that wrong) and my committee probably wouldn't even have noticed. I was tempted to sweep it under the carpet and not let it keep me from graduating.
But I knew it was wrong. I felt that if I sacrificed my integrity then, the moral failure would mark me for life. No one would know -- but I would know. So I decided to fix the issue, re-do the studies and live with the reality that I would have to delay my defense.
Turns out when you're desperate -- and many grad students can attest to this -- a resourcefulness that you never thought you had kicks in ("where were you during all my years of grad school?"). I don't remember how, but I somehow managed to wrangle new studies out in 3 days (which would have previously taken me months). I made the deadline in the end.
The lesson I learned was that committing to doing the right thing has its costs, but in some cases it also forces one to explore attacks never previously considered. Asking on MathOverflow is one such attack.
There's another (slightly kinder) version of this:
When people go to grad school, then during their studentship get married and have a kid -- suddenly their productivity goes up dramatically and output per time increases by many factors. What happened?
It turns out when you have self-motivating reasons to get out (and a target on your head from your spouse to earn some money for godssake), you find ways to focus on what's important and drop the rest.
No more idling away for hours on silly ideas that don't get you closer to handing in your thesis. No more trying random libraries that get your code to run 2% faster. No more goofing around after 6pm with other students just because you have the time -- you have to get home and be a breadwinner for your family. You have to get shit done.
You start to ask, "even if I don't know exactly what the thesis will say, how should it be organized and what kinds of conclusions will make up the writing? And what experiments do I need to fill in those charts/paragraphs, and no more?" What's the minimum I need to do to get out of here? Not, "What amazing interesting thing could I explore?"
Limits and constraints sometimes free the mind dramatically. The side effect is maybe you don't get to explore ideas that go nowhere, but that's a discussion about the purpose of the PhD and for another topic I guess.
(And sometimes, if you think, well I don't have a kid, so what's the rush? Well, someday you might have a spouse, a kid, and every day of time you left in grad school is a day for your future self -- and family -- and $$ -- left behind in time. Work to free your future self... now, while you have the time.)
> Turns out when you're desperate -- and many grad students can attest to this -- a resourcefulness that you never thought you'd had kicks in
This is getting millions of students through high school, college, and university every year.
Everybody has at least one thing they pushed back for way too long and then developed almost super-human-like abilities to do it. Doesn't guarantee a good grade, though.
Good on you for doing the right thing. We have far too little thinking like this in the world.
It reminds me of a story I heard from a businessman that was walking with an associate down the street. He stopped at one of those old metal newspaper dispenser machines to buy a paper. For those that don't know, the way they work is once you have put in your quarter the machine opens up and all the papers are just stacked in there.
His associate asked him to grab a newspaper for him. So he pulled out one paper, closed the machine and put in another quarter and then pulled out another. The associate asked, "Why didn't you just grab a second paper for free? It's just a quarter." The businessman's response was, "If I'm willing to sacrifice my integrity for a quarter, how much easier will it be to sacrifice it when something serious is on the line?"
My laptop broke down just hours before I had to submit the thesis. It was the day of the deadline. I did have printed copies of the thesis (I had to submit printed copies), however I discovered bad typos on the front page. But, my laptop was down with the only digital version in it. In the end, I corrected the typos using a photocopier. I overlayed the typos with corrections on cut out pieces of paper, and photocopied. It was quite a struggle, but I made it!
I wrote a special chapter where I discussed my results with myself and ended up suggesting someone takes a closer look if interested.
The jury was initially 6 people, 1 refused to review a thesis where the candidate discusses with himself because it breaks tradition. The others were quite happy, with one of them referring to my discussion and thanking me for the time she gained with it and which allowed her to spend more time with friends.
For some small issues it is sometimes better to tell it upfront and highlight hiw genius the rest of the thesis is.
I discovered that the proof of a fundamental proposition in my maths PhD thesis had a mistake in it two weeks before my viva, after I had submitted. Not sure if that was a better or worse time to discover it! After a rather stressful few days, I managed to reprove it and took the correct proof along to the viva. The examiners were 'well, the result was obviously correct so we weren't worried about it'!
The book “Gödel, Escher, Bach” was printed with a special process only available at one printer far away from where Hofstadter was living, and was extremely time consuming. At the last minute the whole thing had to be redone, so he had to get on a plane, print a few pages, then fly back to his job. This took several months. (He talks about it in the 20th anniversary edition.)
> From OP's point of view this could be viewed as glass half-full rather than glass half-empty. Their dissertation results hold unequivocally on the sphere and might hold on the torus, though it is an open problem if they do. It is certainly legitimate to study what follows from a given conjecture being true. It could even be spun as a feature rather than a bug of the dissertation. If the results in fact fail on the torus then you know that the conjecture must be false. Potentially, it could open up a fruitful avenue of attack.
When Terence Tao writes stuff like this, I'm always very happy that I got to experience the Moore-method for learning math (at UT Austin). A group of us would be dumped into a class with a common topic and we'd just have to prove things (topology, algebra, analysis) ... on the blackboard, in front of everyone. The best work we did was when something started going wrong and then we'd all start arguing about the proof, building count-conjectures on the fly and riffing on the math. The worst work was when someone went and found a proof ahead of time and just showed the answer. There's so much to learning where the sharp bits of math are; proofs are the razor-thin path through the briar patch.
It was only later that I found out that history, the study of art & literature, and philosophy can all teach you the same thing. The important part is that you're interested in the topic.
I suspect the reason OP's thesis worked out okay is because his intuition wrt the problem is correct, even if his formulation was a bit off. Very cool, sounds like a good mathematician to me
Stack overflow and it's cousin sites have many serendipities like this - and I happily conjecture this happens more here than facebook or twitter.
I think the reason is that despite being a walled garden (ie proprietary) it still has a promise to open up the content and makes effort to moderate and grow the community - in other words what they are really selling is not the SEO but the sweet spot between "anyone posts anything" of an "ideal" internet where no rentiers exist but no one can find anyone else, and the much more corporate hand of Facebook.
I am not sure reddit exists in this sweet spot either - mostly because there is just sooo much reddit.
A couple relevant bits of info about MathOverflow:
- The site is operated by Stack Overflow/Exchange, but is owned by MathOverflow, Inc a non-profit corporation[0]. As such, it retains the right to exist independently of the Stack Overflow company - to my knowledge, it is the only public Stack Exchange site for which this is true.
- Like all public Stack Exchange sites, authors retain ownership of their work, which is published under a CC-BY-SA license. Regular archives are uploaded to Archive.org and can be obtained there or via Bittorrent[1]
In short, not a walled garden, and not Stack Overflow's garden.
I always say that the wonder of the Internet is the collaborative Wikipedia, not Facebook walled garden. Stack Overflow network of sites is another of the great Internet wonders. Non technical people can not grasp how fantastic they are. Younger developers do not imagine a world without SO.
As a private company, probably someday they will lost their techno-utopian magic (as Google already lost). It will be a very sad day.
Both reddit/SO and say, classic forums, each have their own method of content discovery (reddit/SO always prioritize new items, forums push you to long-running threads), but both have their blind spots. With reddit you can end up with a lot of duplicates because a subreddit's dashboard decays stuff pretty fast based on the frequency of posts. It makes long-running discussion impossible. With forums you can have your long-running discussions, but you sometimes have to wade through page after page to find those specials nuggets of info.
PG recently tweeted something relevant to this thought [1]
"Twitter is a few people saying interesting things amidst a much larger number saying mean or mistaken things. So are books. But you don't suddenly get sentences from bad books in the middle of reading one of the good ones. Maybe this gets fixed in version 2 of social media. Maybe version 2 is halfway between the randomness of Twitter and the predictability of Substack."
StackExchange sites feel like sites that you can browse without them trying to get you addicted and trying to stop you leaving. They do have the sidebar which sometimes shows interesting content but it doesn’t feel optimised for addiction or stickiness - more genuine discovery.
I’m not sure what sort of advertising they do on other stack exchange sites if any, but sticking to a job board on SO makes it so much more pleasant to read than a social feed throwing random junk products at you every few minutes until you go away.
As far as notational clusterfucks go, crossing numbers (along with the three standard definitions of a ring) are one of the best-known ones to still be biting people on a regular basis. ("Positive" and "natural number" are sufficiently well-known that people are careful.) But imagine how it felt to do group theory back when "group" could mean any of "abstract group", "subgroup of GL(n)", "finite group", "monoid", "semigroup" and combinations thereof.
The simplest gotcha I know is: is f(x) = 1/x piece-wise continuous?. This is calculus 1 level material and yet author's disagree significantly on this point, sometimes without specifying it! Some say yes, others would require f to have finite left and right limits at every point. This mattered for a point of my thesis and my advisor was very unhappy with me calling these function piece-wise continuous.
The way I was taught was that back in the olden days, "group" always referred to groups of permutations (and the operation was always composition), and it was Cayley that introduced the much more general and abstract notion of groups that we use now. He could do that because it's relatively trivial to prove that the the two definitions are basically the same: every group is isomorphic to some group of permutations according to Cayley's theorem: https://en.wikipedia.org/wiki/Cayley%27s_theorem
OP is incredibly fortunate. Or maybe mathoverflow is that active/supportive.
As a STEM grad student (not in math), I had more than a couple such moments of crises, when I posted my questions on various stackexchange websites. I got either useless replies, or no replies.
Mathoverflow is different from most of the other SE sites in that it's only for research level questions. There is a separate site, math.stackexchange, for other math-related questions.
I have to say also that this type of crisis is not surprising (unfortunately) for math, or similar highly theoretical, loner fields. I can guess that the student asking the question is not being very open with his/her advisor, has worked and struggled for long hours alone, thinking they have to solve it on their own, and is not super communicative and checking in about important aspects of the thesis. Because he/she thinks it has to be a surprise "breakthrough" result -- a heavy obligation of the field's expectations.
No responsible advisor would let the work get to such a state, so late in the game. Major fault of the advisor too, here.
Advisors are also very much at fault, not just students.
The last year of my PhD I ended up being pretty much alone because my advisor had changed research topics a year before and therefore was not interested nor up to date, so any of her inputs were not very useful.
A couple friends of mine also struggled with their advisor because he actively avoided communication for some reason. I guess he had a personal or health issue.
So even on good faith, advisors can end up making students life quite stressful for one reason or another
I was contacted by someone in a PhD thesis crisis who wanted me to provide speech samples they were apparently missing. The thesis was due imminently.
As far as I could tell, the analysis was already done -- but my samples were needed for some other reason. I was kind of bemused by the idea that the analysis would be invalid with nothing behind it, but valid with unrelated data behind it.
My insight was an eng. student whose novel outcome of a maths model in Fortran on a mainframe depended on his not understanding what uninitialised arrays were. This was in the 80s.
There was no interesting novel outcome: he was random-sampling prior states of memory.
I felt very bad for him, it was mid-stage. I didn't hear how he resolved it.
The other side of this is the crisis which only emerges in the viva. I was working in Leeds uni in the 80s and overheard an external discussing a case he had: it was obvious the results were fraud. They made the student and his supervisor to the sums in the room, on the blackboard. He didn't get his thesis.
I was in a PhD crisis, but I did not post it anywhere. Not sure if it is allowed to ask for outside help.
Although now I have finished the thesis without that part (it should have become an additional chapter). Perhaps I should post it around (although that might spoil it for a paper)
Consider n polynomial equations in variables x_1, .., x_n, with constants a_1,..,a_n, b_1,..,b_n, c_1,...,c_n:
Under which circumstances exists a (unique) solution for x_1,..,x_n in terms of the constants?
I have found a recursive approach that results in a quadratic equation, containing only a single variable x_i (and the constants). (It is too much for a comment, here is a PDF: http://benibela.de/tmp/quadratic-equations-recursion.pdf )
For example for n = 2, it is very simple: x^2_1 (a_2 b_1 - a_1 c_2) + x_1 (a_2 d_1 + b_2 b_1 - a_1 d_2 - c_1 c_2) + b_2 d_1 - c_1 d_2
This gives 2 solution. But I do not know what happens if the terms cancel each other out. Like if a_2 b_1 - a_1 c_2 = 0, there would only be one solution. But since the full solution in the pdf is so complex, I do not see which constraints would lead to cancellation there.
---
And that is not the full problem I was trying to solve. In the full problem there are constraints on the a, b, c, d. There is a given graph, and depending which nodes are connected in the graph, the constants are the same. Like if node 3 and node 7 are connected, then b_3 = c_7 und c_7 = b_3. (even more complex though). And then the question is, do these constants cancel in the solution of those equations? And the final problem we want to solve: which graphs lead to exactly one solution, and which graphs lead to no solution of the equations?
Ambiguous and poorly explained. (Note the question immediately afterwards asking for clarification.) But probably something along the general lines of "My advisor said that, if my main theorem is an asymptotic estimate instead of an exact formula, then this would not be judged to be novel/strong enough to earn a Ph.D."
On the surface, I agree: there's an interesting problem that's worth solving, and a purely artificial limit is forcing people to do a bang-up job at solving it.
But if you dig a bit deeper, I can see two counter-arguments:
1. The real risk -- by which I mean "the risk I have most often observed in the wild" -- is that a Ph.D expands to fill the time it's given, without ever wrapping up and producing a publishable result. This happens so often that it's practically expected in some places.
2. Having a deadline, oddly enough, also serves as a catalyst for birthing an idea... for "pinching it off" as the expression goes. At some point you have to stop planning and start executing. You can see the deadline as a forcing function.
Ph.Ds are needlessly traumatic and procedural in many ways, but I'm no longer sure that hard deadlines are a net negative.
I feel like this wisdom isn't tapped into enough. We're often burdened with individual tasks and challenges while utilizing crowd knowledge is looked down upon or seen as an inferior solution finding mechanism. e.g. Imagine if companies worked together to figure out self-driving cars rather than compete?
[+] [-] wenc|5 years ago|reply
I was in my 6th year. All my friends had graduated, and my stipend had run out. I was 2 weeks away from submission and discovered that one of my assumptions was wrong, which potentially distorted/invalidated all my studies -- to fix these studies would have potentially delayed submission for months. It was a very subtle assumption violation (and it wasn't even that wrong) and my committee probably wouldn't even have noticed. I was tempted to sweep it under the carpet and not let it keep me from graduating.
But I knew it was wrong. I felt that if I sacrificed my integrity then, the moral failure would mark me for life. No one would know -- but I would know. So I decided to fix the issue, re-do the studies and live with the reality that I would have to delay my defense.
Turns out when you're desperate -- and many grad students can attest to this -- a resourcefulness that you never thought you had kicks in ("where were you during all my years of grad school?"). I don't remember how, but I somehow managed to wrangle new studies out in 3 days (which would have previously taken me months). I made the deadline in the end.
The lesson I learned was that committing to doing the right thing has its costs, but in some cases it also forces one to explore attacks never previously considered. Asking on MathOverflow is one such attack.
[+] [-] supernova87a|5 years ago|reply
When people go to grad school, then during their studentship get married and have a kid -- suddenly their productivity goes up dramatically and output per time increases by many factors. What happened?
It turns out when you have self-motivating reasons to get out (and a target on your head from your spouse to earn some money for godssake), you find ways to focus on what's important and drop the rest.
No more idling away for hours on silly ideas that don't get you closer to handing in your thesis. No more trying random libraries that get your code to run 2% faster. No more goofing around after 6pm with other students just because you have the time -- you have to get home and be a breadwinner for your family. You have to get shit done.
You start to ask, "even if I don't know exactly what the thesis will say, how should it be organized and what kinds of conclusions will make up the writing? And what experiments do I need to fill in those charts/paragraphs, and no more?" What's the minimum I need to do to get out of here? Not, "What amazing interesting thing could I explore?"
Limits and constraints sometimes free the mind dramatically. The side effect is maybe you don't get to explore ideas that go nowhere, but that's a discussion about the purpose of the PhD and for another topic I guess.
(And sometimes, if you think, well I don't have a kid, so what's the rush? Well, someday you might have a spouse, a kid, and every day of time you left in grad school is a day for your future self -- and family -- and $$ -- left behind in time. Work to free your future self... now, while you have the time.)
[+] [-] foepys|5 years ago|reply
This is getting millions of students through high school, college, and university every year.
Everybody has at least one thing they pushed back for way too long and then developed almost super-human-like abilities to do it. Doesn't guarantee a good grade, though.
[+] [-] jjeaff|5 years ago|reply
It reminds me of a story I heard from a businessman that was walking with an associate down the street. He stopped at one of those old metal newspaper dispenser machines to buy a paper. For those that don't know, the way they work is once you have put in your quarter the machine opens up and all the papers are just stacked in there.
His associate asked him to grab a newspaper for him. So he pulled out one paper, closed the machine and put in another quarter and then pulled out another. The associate asked, "Why didn't you just grab a second paper for free? It's just a quarter." The businessman's response was, "If I'm willing to sacrifice my integrity for a quarter, how much easier will it be to sacrifice it when something serious is on the line?"
[+] [-] dmch-1|5 years ago|reply
[+] [-] sadfev|5 years ago|reply
Why are we not resourceful in normal time?
[+] [-] unknown|5 years ago|reply
[deleted]
[+] [-] BrandoElFollito|5 years ago|reply
I wrote a special chapter where I discussed my results with myself and ended up suggesting someone takes a closer look if interested.
The jury was initially 6 people, 1 refused to review a thesis where the candidate discusses with himself because it breaks tradition. The others were quite happy, with one of them referring to my discussion and thanking me for the time she gained with it and which allowed her to spend more time with friends.
For some small issues it is sometimes better to tell it upfront and highlight hiw genius the rest of the thesis is.
[+] [-] jvvw|5 years ago|reply
[+] [-] mjklin|5 years ago|reply
[+] [-] oconnor663|5 years ago|reply
> From OP's point of view this could be viewed as glass half-full rather than glass half-empty. Their dissertation results hold unequivocally on the sphere and might hold on the torus, though it is an open problem if they do. It is certainly legitimate to study what follows from a given conjecture being true. It could even be spun as a feature rather than a bug of the dissertation. If the results in fact fail on the torus then you know that the conjecture must be false. Potentially, it could open up a fruitful avenue of attack.
Kind of reminds me of Terence Tao's post on what solving big problems looks like: https://terrytao.wordpress.com/career-advice/be-sceptical-of...
[+] [-] thechao|5 years ago|reply
It was only later that I found out that history, the study of art & literature, and philosophy can all teach you the same thing. The important part is that you're interested in the topic.
[+] [-] finolex1|5 years ago|reply
[+] [-] theossuary|5 years ago|reply
I suspect the reason OP's thesis worked out okay is because his intuition wrt the problem is correct, even if his formulation was a bit off. Very cool, sounds like a good mathematician to me
[+] [-] lifeisstillgood|5 years ago|reply
Stack overflow and it's cousin sites have many serendipities like this - and I happily conjecture this happens more here than facebook or twitter.
I think the reason is that despite being a walled garden (ie proprietary) it still has a promise to open up the content and makes effort to moderate and grow the community - in other words what they are really selling is not the SEO but the sweet spot between "anyone posts anything" of an "ideal" internet where no rentiers exist but no one can find anyone else, and the much more corporate hand of Facebook.
I am not sure reddit exists in this sweet spot either - mostly because there is just sooo much reddit.
[+] [-] Shog9|5 years ago|reply
- The site is operated by Stack Overflow/Exchange, but is owned by MathOverflow, Inc a non-profit corporation[0]. As such, it retains the right to exist independently of the Stack Overflow company - to my knowledge, it is the only public Stack Exchange site for which this is true.
- Like all public Stack Exchange sites, authors retain ownership of their work, which is published under a CC-BY-SA license. Regular archives are uploaded to Archive.org and can be obtained there or via Bittorrent[1]
In short, not a walled garden, and not Stack Overflow's garden.
[0]: https://meta.mathoverflow.net/questions/969/who-owns-mathove...
[1]: https://archive.org/details/stackexchange
[+] [-] neves|5 years ago|reply
As a private company, probably someday they will lost their techno-utopian magic (as Google already lost). It will be a very sad day.
[+] [-] Dirlewanger|5 years ago|reply
[+] [-] gowld|5 years ago|reply
[+] [-] lukeplato|5 years ago|reply
"Twitter is a few people saying interesting things amidst a much larger number saying mean or mistaken things. So are books. But you don't suddenly get sentences from bad books in the middle of reading one of the good ones. Maybe this gets fixed in version 2 of social media. Maybe version 2 is halfway between the randomness of Twitter and the predictability of Substack."
[1] https://twitter.com/paulg/status/1290738446059950080
[+] [-] mcintyre1994|5 years ago|reply
I’m not sure what sort of advertising they do on other stack exchange sites if any, but sticking to a job board on SO makes it so much more pleasant to read than a social feed throwing random junk products at you every few minutes until you go away.
[+] [-] generationP|5 years ago|reply
[+] [-] tgb|5 years ago|reply
[+] [-] OskarS|5 years ago|reply
[+] [-] fizixer|5 years ago|reply
As a STEM grad student (not in math), I had more than a couple such moments of crises, when I posted my questions on various stackexchange websites. I got either useless replies, or no replies.
[+] [-] iflp|5 years ago|reply
[+] [-] supernova87a|5 years ago|reply
No responsible advisor would let the work get to such a state, so late in the game. Major fault of the advisor too, here.
[+] [-] jfkebwjsbx|5 years ago|reply
The last year of my PhD I ended up being pretty much alone because my advisor had changed research topics a year before and therefore was not interested nor up to date, so any of her inputs were not very useful.
A couple friends of mine also struggled with their advisor because he actively avoided communication for some reason. I guess he had a personal or health issue.
So even on good faith, advisors can end up making students life quite stressful for one reason or another
[+] [-] thaumasiotes|5 years ago|reply
As far as I could tell, the analysis was already done -- but my samples were needed for some other reason. I was kind of bemused by the idea that the analysis would be invalid with nothing behind it, but valid with unrelated data behind it.
[+] [-] ggm|5 years ago|reply
There was no interesting novel outcome: he was random-sampling prior states of memory.
I felt very bad for him, it was mid-stage. I didn't hear how he resolved it.
The other side of this is the crisis which only emerges in the viva. I was working in Leeds uni in the 80s and overheard an external discussing a case he had: it was obvious the results were fraud. They made the student and his supervisor to the sums in the room, on the blackboard. He didn't get his thesis.
[+] [-] benibela|5 years ago|reply
Although now I have finished the thesis without that part (it should have become an additional chapter). Perhaps I should post it around (although that might spoil it for a paper)
Consider n polynomial equations in variables x_1, .., x_n, with constants a_1,..,a_n, b_1,..,b_n, c_1,...,c_n:
Under which circumstances exists a (unique) solution for x_1,..,x_n in terms of the constants?I have found a recursive approach that results in a quadratic equation, containing only a single variable x_i (and the constants). (It is too much for a comment, here is a PDF: http://benibela.de/tmp/quadratic-equations-recursion.pdf )
For example for n = 2, it is very simple: x^2_1 (a_2 b_1 - a_1 c_2) + x_1 (a_2 d_1 + b_2 b_1 - a_1 d_2 - c_1 c_2) + b_2 d_1 - c_1 d_2
This gives 2 solution. But I do not know what happens if the terms cancel each other out. Like if a_2 b_1 - a_1 c_2 = 0, there would only be one solution. But since the full solution in the pdf is so complex, I do not see which constraints would lead to cancellation there.
---
And that is not the full problem I was trying to solve. In the full problem there are constraints on the a, b, c, d. There is a given graph, and depending which nodes are connected in the graph, the constants are the same. Like if node 3 and node 7 are connected, then b_3 = c_7 und c_7 = b_3. (even more complex though). And then the question is, do these constants cancel in the solution of those equations? And the final problem we want to solve: which graphs lead to exactly one solution, and which graphs lead to no solution of the equations?
[+] [-] no_identd|5 years ago|reply
the hell does that mean?
[+] [-] impendia|5 years ago|reply
Ambiguous and poorly explained. (Note the question immediately afterwards asking for clarification.) But probably something along the general lines of "My advisor said that, if my main theorem is an asymptotic estimate instead of an exact formula, then this would not be judged to be novel/strong enough to earn a Ph.D."
[+] [-] unknown|5 years ago|reply
[deleted]
[+] [-] rvieira|5 years ago|reply
I knew I could take this route but never did it. This is a bit of a mockery of the whole purpose of a PhD thesis (it has to be your work primarily).
This is just an advanced version of posting homework questions on the internet.
[+] [-] thom|5 years ago|reply
[+] [-] omginternets|5 years ago|reply
But if you dig a bit deeper, I can see two counter-arguments:
1. The real risk -- by which I mean "the risk I have most often observed in the wild" -- is that a Ph.D expands to fill the time it's given, without ever wrapping up and producing a publishable result. This happens so often that it's practically expected in some places.
2. Having a deadline, oddly enough, also serves as a catalyst for birthing an idea... for "pinching it off" as the expression goes. At some point you have to stop planning and start executing. You can see the deadline as a forcing function.
Ph.Ds are needlessly traumatic and procedural in many ways, but I'm no longer sure that hard deadlines are a net negative.
[+] [-] ReedJessen|5 years ago|reply
[+] [-] blickentwapft|5 years ago|reply
[+] [-] leokennis|5 years ago|reply
[+] [-] unknown|5 years ago|reply
[deleted]
[+] [-] miqarifa|5 years ago|reply
[deleted]
[+] [-] jb775|5 years ago|reply
I feel like this wisdom isn't tapped into enough. We're often burdened with individual tasks and challenges while utilizing crowd knowledge is looked down upon or seen as an inferior solution finding mechanism. e.g. Imagine if companies worked together to figure out self-driving cars rather than compete?
[+] [-] alentist|5 years ago|reply
[+] [-] truthwhisperer|5 years ago|reply
[deleted]
[+] [-] noumantariq477|5 years ago|reply
[deleted]