[HN Gopher] Math Overflow users resolve PhD thesis crisis
___________________________________________________________________
Math Overflow users resolve PhD thesis crisis
Author : DarkContinent
Score : 470 points
Date : 2020-08-04 12:55 UTC (10 hours ago)
(HTM) web link (mathoverflow.net)
(TXT) w3m dump (mathoverflow.net)
| fizixer wrote:
| 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.
| thaumasiotes wrote:
| 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.
| lifeisstillgood wrote:
| The walled garden sweet spot
|
| 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.
| Dirlewanger wrote:
| 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.
| munificent wrote:
| I look at this as a fundamentally hard problem of information
| design. You have a series of posts to present to a reader.
| Which posts do you give primacy to?
|
| If your reader already knows most of the context and has read
| the previous posts, then "re-posts" are bad, long-running
| threads are good, and they just want to see the latest
| updates.
|
| If your reader is coming to the material cold, a "re-post"
| may be completely new to them, and posts that presume pages
| and pages of existing context are completely impenetrable.
| You want to lean towards fresh, short threads.
|
| The challenge for designing a forum then is balancing the
| competing needs of those users. You can make some progress by
| tracking on a per-user basis which comments they've already
| seen. Reddit does that (maybe just for gold accounts?) where
| new comments are blue. That makes it pretty easy to skim
| through a comment thread and see just the new leaves.
|
| But there's still the question of how to sort the threads
| themselves. It might be interesting if that sorting was also
| user-specific. Maybe deprioritize threads that you've seen
| but not interacted with, and prioritize "live" threads that
| you've participated in and are still changing.
| gowld wrote:
| SO is a garden, not a walled garden.
| neves wrote:
| 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.
| Shog9 wrote:
| 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.
|
| [0]: https://meta.mathoverflow.net/questions/969/who-owns-
| mathove...
|
| [1]: https://archive.org/details/stackexchange
| lifeisstillgood wrote:
| Re: MathOverflow Inc - I had not only not heard of this, but
| never even considered it was possible :-)
|
| Yes, I think I am wrong to use the term walled garden, but
| it's hard to think of something else.
|
| In a "platonic ideal" of the internet everyone would have
| their own internet connection, and a server and say post
| their own interesting queries and somehow others would find
| and answer them.
|
| Perhaps search was assumed to solve it all then.
|
| But the universe is much more "clumpy" than that so people
| will gather around certain locations, in nature they are
| natural oasis.
|
| Perhaps we should drop the walled garden idea - gardens,
| walled or otherwise need tending and upkeep and that passed
| the ability of one or two people to do in their spare time
| somewhere around 1991 on usenet.
|
| Tending a garden is a costly affair.
|
| I think perhaps walled city might be a better term? It
| implies the "never leaving" which is what facebook seems to
| aspire to.
|
| perhaps a better analogy is "chargeable car parking". :-)
| Shog9 wrote:
| This is yet another one of those situations where the use
| of a dying metaphor[0] hurts communication; you wall up a
| garden to protect what is inside from the harsh conditions
| outside: wind, cold, vermin... The implication is that the
| people in the garden are delicate flowers who would be
| destroyed by the conditions on The Greater Internet if they
| were to be exposed.
|
| The antonym to the walled garden is the open garden or
| field, with hardy plants able to withstand and even thrive
| in the local atmosphere. They're still _cultivated_ -
| weeded, fertilized - but there 's no need to create a
| microclimate to just to accommodate them.
|
| In this context, Facebook does make some effort toward
| walling off their gardens, but... As you note, Facebook's
| primary goal isn't protecting it's _dominating_ - Facebook
| is just as happy to own major portions of the 'Net in
| pursuit of this goal, and more than a little reluctant to
| provide any real protection beyond what is absolutely
| necessary.
|
| Beyond that... We all garden. From little personal websites
| and blogs, to big community gardens[1] like Wikipedia,
| Reddit, Stack Overflow, and even Hacker News. We plant, we
| harvest, we tend these plots, alone or together, but make
| little effort to isolate them from the larger world -
| indeed, we generally recognize that the strength of the Web
| is based on its interconnections, its inherent ability to
| draw together different sources of information.
|
| [0]: https://www.orwell.ru/library/essays/politics/english/
| e_poli...
|
| [1]:
| https://meta.stackexchange.com/questions/349513/feedback-
| for...
| supernova87a wrote:
| 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.
| jfkebwjsbx wrote:
| 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
| generationP wrote:
| 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.
| tgb wrote:
| 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.
| generationP wrote:
| I thought this was only an issue in K-12, as anyone in
| research math considers the domain and the target to be part
| of a function, and then the problem disappears: The function
| R \ {0} -> R, x |-> 1/x is not just piecewise continuous but
| continuous on-the-nose. The function R -> R, x |-> 1/x
| doesn't exist. The function R |-> some completion of R, x |->
| 1/x is continuous or not depending on which completion you
| choose (the one with two infinities or the projective line).
|
| But I do recall a similar confusion happening with "piecewise
| linear" (the question is whether the pieces have to fit
| together).
| nicoburns wrote:
| > I thought this was only an issue in K-12, as anyone in
| research math considers the domain and the target to be
| part of a function
|
| Anyone is research math does consider the domain and target
| to be part of the function. Alas, that doesn't mean that
| they'll actually write down which domain and target they
| have in mind.
| gowld wrote:
| f doesn't even have either of a right or left limit at 0.
|
| f is maybe (piece-wise) continuous _over what pseudo-domain_?
| R or R\\{0}?
|
| You could axiomitize that an infinite discontinuity is like
| an unbouned function as x->infinity, but then how would you
| avoid 1/x being regular continuous?
|
| I think you are claimokg that a set being incomplete "at the
| end" is different from a set having a hole in the middle --
| that the question of continuity presumes _connected_ sets.
| That 's not standard but might be an appropriate assumption
| for the context of your paper.
|
| Anyway, arguing over terminology is boring unless it raises
| conceptual issues. The point is to communicate, which has at
| least 2 stakeholders. Clarify your terms and move on.
| tgb wrote:
| I think you missed the point of the example, which is that
| people rarely clarify this because to the author their
| definition seems obviously correct. I made it 90% through a
| PhD without having considered that there could be more than
| one possible meaning for "piece-wise continuous".
|
| The domain is R in this case. The less-restrictive
| definition would be that f is piece-wise continuous if
| there are a discrete set of points .. < x_0 < x_1 < ...
| with f continuous on each interval (x_i, x_{i+1}). The
| alternative definition is that, plus requiring that the
| restriction of f to those intervals have limits at the
| endpoint. For piecewise smooth function, there's an even
| larger variety of possible meanings, yet it's often stated
| without clarification.
| thaumasiotes wrote:
| > The less-restrictive definition would be that f is
| piece-wise continuous if there are a discrete set of
| points .. < x_0 < x_1 < ... with f continuous on each
| interval (x_i, x_{i+1}). The alternative definition is
| that, plus requiring that the restriction of f to those
| intervals have limits at the endpoint.
|
| This sounds kind of surreal; putting them in shorter
| terms, we have two rival definitions for "piecewise
| continuous":
|
| 1. A function f is piecewise continuous if there exist
| one or more intervals over which f is continuous.
|
| 2. A function f is piecewise continuous if there exist
| one or more intervals over which f is (1) continuous, and
| (2) bounded.
|
| I agree that it sounds obvious which of those is more
| appropriate as a definition of "piecewise continuous"...
|
| (It also worries me that the definition you give requires
| the intervals to be adjacent, but doesn't require that
| more than one interval exist. A function that is
| continuous over (-2, -1) and also over (1, 2), but not
| anywhere else, would meet this definition, but you
| wouldn't be able to include both of those intervals of
| continuity in the set of endpoints.
|
| I would prefer to either have two sets of endpoints, such
| that we end up saying f is continuous over (x_i, y_i),
| (x_{i+1}, y_{i+1}), etc. (if we want to allow for
| intervals of discontinuity), or to say that the intervals
| (-inf, x_0) and (x_n, +inf) also count (if we don't).
|
| However, if we take that second approach, and we go with
| the definition of piecewise continuity that requires the
| function be bounded over every interval, we've just
| defined functions like f(x) = x as being not piecewise
| continuous despite the fact that they are continuous.)
| Ericson2314 wrote:
| The idea is that what 1/x is is intuitively simple enough,
| so we should have some standard terminology for it.
|
| And saying left and right limits is -infinity or +infinity
| really also isn't that weird. I'm pretty sure other metric
| spaces can be likewise extended and end up with similar
| algebraic laws as the "extended real numbers". Again this
| isn't very profound, but is good for education and
| efficient communication, and so should be perused.
|
| Finally, it's interesting that measure spaces with infinite
| measure is already a thing that people. I would like to see
| more connections with metric and measure spaces; e.g. we
| can have an n-point metric which is defined using the
| measure of the (n-1)-simplex. Just as regular metric spaces
| have a "triangle inequality", 3-point metric spaces should
| have a "tetrahedron inequality", and n-point metric spaces
| should have a "(n-1)-simplex inequality". Again, this is
| not profound, but good for communication, and connections
| between definitions help one compress everything for better
| mental storage.
| gus_massa wrote:
| I teach math in the first year of the university and it's not
| a good moment to discuss about the subtle details of topology
| and definitions. So every time someone ask me that, I reply
| "It is not continuous for _all_ the real numbers "
| OskarS wrote:
| 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
| generationP wrote:
| Sure you can embed any group in a permutation group, but that
| doesn't mean the two notions behave identically in all
| respects. For example, two groups being isomorphic is not the
| same as two permutation groups being isomorphic, as the
| latter come with their embeddings.
| wenc wrote:
| 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.
| sadfev wrote:
| Your comment is a lifeline to me in this difficult time.
|
| Why are we not resourceful in normal time?
| Enginerrrd wrote:
| I wish I knew the answer to this. When everything is totally
| screwed up and on fire and I need to get something done by
| 5:00 today that would normally take a week and a half, by
| God, it becomes apparent every millimeter of fat that can be
| trimmed and I can usually scrape together what's needed by
| then. Then the deadline is over and I get a similar project
| the next day and it's back to taking 5 days to finish.
|
| There are real quality differences between the two scenarios,
| but they aren't nearly as bad as what you'd think they are.
| The reality is that I can just work a lot more efficiently
| when stressed. If I could do that all the time I'd be able to
| work 3 hours a day and remain as productive.
| mordymoop wrote:
| The "point" of gradual school should be taking long walks
| with friends from completely different departments, talking
| about abstract ideas that aren't related to your work at all.
| Maybe later in the shower you realize some subtle connection
| to your work that gives you an idea for an innovation, but
| maybe not. The point of graduate school is play. The switch
| from "play" to "product" is difficult but necessary. Both
| phases are important to the budding PhD. You need to
| demonstrate the ability to think creatively AND the ability
| to process that creativity into a deliverable. That's the
| value of a PhD. If you're interested in a focused grind to a
| specified finish line, skip graduate school.
| YeGoblynQueenne wrote:
| Because in normal time we spend most of our time reading HN
| rather than working on our urgent stuff.
| infogulch wrote:
| Whelp that's my signal to get back to work.
| dleslie wrote:
| It's not typically sustainable to operate at such high levels
| of stress, but the stress brings with it a myriad of hormones
| and behavioural adaptions that, for some people, aid in
| sustaining focus and effort.
| lotsofpulp wrote:
| It's selection bias. There are probably far more instances
| where rushing through causes problems than there are where
| rushing through doesn't.
| gandalf013 wrote:
| Hobbes: Do you have an idea for your project yet?
|
| Calvin: No, I'm waiting for inspiration. You can't turn on
| creativity like a faucet. You have to be in the right mood.
|
| Hobbes: What mood is that?
|
| Calvin: Last-minute panic.
| [deleted]
| foepys wrote:
| > 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.
| pvarangot wrote:
| In my humble experience this force of human will also gets
| early stage startups a second chance or saves them from
| sudden death regularly.
| mjklin wrote:
| The book "Godel, 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.)
| dmch-1 wrote:
| 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!
| supernova87a wrote:
| 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.)
| supernova87a wrote:
| I might offer a corollary as an practice to adopt (in the
| absence of the above possibility) -- learn to enable your
| research to have visible incremental gains on a known path
| every day, rather than hoping (hoping!) for some amazing
| breakthrough at the end.
|
| Amazing breakthroughs have high risk, and make it highly
| likely you'll have a crisis when it doesn't happen.
|
| And what I mean is that, even if you don't know what the
| answer is going to be at the end of your research, you must
| think about, or have an idea about, the _format_ of what that
| amazing answer is going to be. Write the outline of your
| thesis and "ghost out" what the major charts will be. Write
| the intro sentences of each chapter -- what are they? (and I
| don't just mean the boring review of the field part, but your
| findings part)
|
| You should know what major finding, plot, or table your
| research is going to output. What are the columns and rows of
| that table, or axes of that plot? How many data points are
| required? How many of them can already be guessed? Where is
| the surprise going to be? What is the conclusion going to be?
|
| For most graduate research, the finding is not an amazing
| field-changing big bang. Few grad students are that
| fortunate. Or at least most of the bulk of the work will be
| of that sort. You should be able to predict what the answer
| is going to look like from past work, and the error bars.
|
| Draw out the answer you're aiming for, now. If you can't even
| articuate what the answer will _look like_ , you may be in
| for a bad time, so work on fixing that. It will also push you
| and your advisor to be specific about what the output of your
| thesis will be.
|
| Your future self will thank you.
| newen wrote:
| One of my professor's recommendation was to write the
| actual paper that you want to write, introduction, related
| works, methods, discussion, conclusion, leaving the
| figures, tables, etc. blank, before you actually start
| doing the experiments.
| mkl wrote:
| This reminds me of Simon Peyton-Jones's (of Haskell fame)
| seminars on How to Write a Great Research Paper:
| https://www.microsoft.com/en-us/research/academic-
| program/wr...
|
| There are multiple slightly different versions of the
| seminar (another is linked below that one), but
| unfortunately they all came out after I'd finished my
| PhD, and I didn't hear that advice from anyone else.
|
| The process I arrived at after losing time on failed
| projects was basically "fail fast": find the simplest
| quickest way to demonstrate that your idea _won 't_ work,
| and do that. Then find the next simplest, and so on,
| until either it works or you've proven it doesn't and
| moved on.
| supernova87a wrote:
| Many advisors don't push their students to do this, and
| they should. Or they haven't had enough practice to know
| to do this. Or they're not taking their responsibility
| seriously enough.
|
| An effective PhD advisor/thesis isn't wandering the woods
| to find something. It's a guided coaching exercise, with
| an outcome in mind. If your advisor doesn't know this,
| maybe time to find a new advisor...
| Twisol wrote:
| > An effective PhD advisor/thesis isn't wandering the
| woods to find something. It's a guided coaching exercise,
| with an outcome in mind. If your advisor doesn't know
| this, maybe time to find a new advisor...
|
| You don't know me, but I really needed to hear this. I
| left grad school essentially because of a dearth of
| coaching. Thank you for framing this so succinctly.
| mensetmanusman wrote:
| This is amazing advice I hadn't heard before, it rings
| very true.
|
| I remember after my first paper was finished and
| submitted, and wow, it seemed easy to bang out papers
| after that, all you needed was four to five figures :)
| kiba wrote:
| _For most graduate research, the finding is not an amazing
| field-changing big bang. Few grad students are that
| fortunate. You should be able to predict what the answer is
| going to look like from past work, and the error bars._
|
| Does it ever works that way for field changing big bang
| ideas? Every human achievement was built upon the back of
| previous achievement and works, either by you or someone
| else.
| thomasahle wrote:
| > You should be able to predict what the answer is going to
| look like from past work, and the error bars.
|
| If you basically know the answer in advance, chances are
| you are not doing very interesting research.
|
| The worst work I have done has been of this sort. The best
| has had me completely change my view of (mathematical)
| reality multiple times during the process.
| supernova87a wrote:
| Well, I'm of course emphasizing empirical fields. Maybe
| you're in one of those heavily theoretical fields.
| thomasahle wrote:
| In emperical fields as well I would assume the purpose of
| doing experiments is that you don't already know what the
| result will be. I accept that this may be a idealised or
| naive...
| supernova87a wrote:
| I'm not talking about the exact result, right? Just that
| someone engaging in research should know what the format
| of the plot/table/output should look like, how much work
| is needed to populate that table, and what kind of
| conclusions will come out of it.
|
| If you (the general "you") are in industry breakthrough
| territory, you're an advanced student and my advice isn't
| for you. Otherwise, I think it's a good practice.
| thomasahle wrote:
| > what kind of conclusions will come out of it.
|
| Fair. I think considering what possible conclusions could
| come is certainly important. I worried about your
| original post suggesting actually writing the conclusion
| in advance.
| JamesBarney wrote:
| Hmm this is different than my experience when my co workers
| had kids. Usually their productivity dropped due to being
| sleep deprived and not having the time on nights and weekends
| to come up to speed on any new technology.
|
| Not that I minded, just saying that time constraints and
| sleep deprivation seemed to have the effect you'd except from
| them.
| alfonsodev wrote:
| productivity at work is harder to measure than academic
| achievements, also different setup and motivations in play.
| iateanapple wrote:
| > Usually their productivity dropped due to being sleep
| deprived
|
| High levels of sleep deprivation is only common for the
| first few months.
|
| > not having the time on nights and weekends to come up to
| speed on any new technology.
|
| This tends to be a problem on teams that don't properly
| evaluate costs of new technology and so churn like crazy
| for very minor productivity increases.
| keithnz wrote:
| it wasn't about coworkers.... when people are working they
| often get paid the same no matter what their productivity
| is, so the motivations are different
| hprotagonist wrote:
| grad students and coworkers have very different priorities.
| bigfudge wrote:
| This happened to me. I typed the last paragraph of my thesis
| shortly after my wife went into in labour. It was very
| satisfying to hear it printing while I was filling the
| birthing pool in our living room!
| QuercusMax wrote:
| Before I got engaged to my wife(who was a year ahead of me in
| college) I had plans to do some kind of individualized honors
| project across 2 or 3 different majors (physics / math / CS).
|
| I very quickly found myself reprioritizing how quickly I
| could graduate and find a job (since my wife's field didn't
| have many lucrative career prospects).
| mensetmanusman wrote:
| This was me, had a 1 year old at my thesis defense on Mass
| Ave :D
| cacois wrote:
| This rings so true to me. I got engaged during the last 6
| months of my PhD student tenure, and lo and behold, I
| defended my thesis in the same month we got married. In the
| same vein as above, the added perspective and fire under me
| resulted in a number of novel solutions to problems that
| probably would have been major issues in the past, including
| a full change in direction of my research conclusions after
| realizing a substantial issue in the practical application of
| the technology.
|
| I credit my now wife with the (passive) motivation to shave
| at least 6-12 months off my time in grad school.
| chrisseaton wrote:
| Lol my wife had a baby while I was doing my PhD... was a
| less-than-ideal way to structure your life I'll admit. Do not
| recommend.
| ColanR wrote:
| > What's the minimum I need to do to get out of here? Not,
| "What amazing interesting thing could I explore?"
|
| I totally get it, but it makes me sad. That line, right
| there, probably explains why it's so few people who actually
| get to make the big discoveries.
| no_identd wrote:
| >"the faculty will not accept asymptotics"
|
| the hell does that mean?
| impendia wrote:
| (Math professor here).
|
| 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."
| mywittyname wrote:
| If you don't mind, could you explain the practical difference
| or the reasoning behind such a requirement? Are there
| situations where boundaries appear to be asymptotic but the
| exact solution shows this not to be the case?
| boyobo wrote:
| I mean, maybe they need to exponentiate the bound or
| something. e.g. 2^(4n) is much much much worse than 2^n.
|
| The sentence did strike me a little wierd though.
| rrobukef wrote:
| I re-implemented a quasi-polynomial algorithm.
| Experimentally, it shows exponential behaviour. Back-of-
| the-envelope calculation shows this behaviour can continue
| until the input size is >>10^21 before the asymptotic bound
| asserts itself. (For comparison, input size 30 is
| unfeasible)
| Ragib_Zaman wrote:
| Which algorithm?
| truthwhisperer wrote:
| (try to be funny) depends if you are on the university
| where 2+2 can also be 5 depending on your feelings
| impendia wrote:
| Once again, I don't understand the Math Overflow poster's
| exact situation.
|
| But roughly speaking, imagine you have two functions f(t)
| and g(t), which are described in completely different ways,
| and you want to prove that f(t) = g(t). If you try and
| fail, then you might instead aim for a proof that the
| difference between f and g is bounded, or that f(t) =
| O(g(t)) and vice versa, or that the limit of the ratio
| between f and g is 1, or something along these lines.
|
| In many cases, such partial results are also of interest.
| In general, partial successes in math are considered to be
| successes.
|
| But in some cases, partial results aren't really considered
| all that interesting -- or perhaps are known already or can
| be obtained very easily.
| ReedJessen wrote:
| This kind of "social media" gives me faith in the ability of
| humanity to survive and thrive in the future.
| oconnor663 wrote:
| A neat comment on the accepted answer:
|
| > 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...
| finolex1 wrote:
| As an aside, looks like one of the comments in the Math
| Overflow link above was made by Terence Tao himself
| oconnor663 wrote:
| Oh neat!
| thechao wrote:
| 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.
| nicoburns wrote:
| > > There's so much to learning where the sharp bits of math
| are; proofs are the razor-thin path through the briar patch.
|
| As a student representative for my undergraduate mathematics
| course, I got really pissed off at lecturers for exactly this
| reason: they'd write out a perfect correct proof on the
| whiteboard, but wouldn't explain where it had come from or
| how people had arrived at the solution. We were left to
| figure that out on our own.
|
| They then complained that students were rote-learning for
| exams, rather than coming to a full understanding of the
| material. I'm not sure what they were expecting, given that
| that's exactly how they were teaching it.
| nwallin wrote:
| My discrete mathematics professor was like that. He would
| regurgitate a proof onto the whiteboard. Then he'd do it a
| few more times with proofs of other things.
|
| He has an identical twin brother, who is also a math
| professor at the same college. The regular professor was
| out for a day, and his brother came in to teach the class.
| His teaching style was completely different. "Ok, we need
| to prove X. Where should we start?" and would sit on the
| table and look at us with an inquisitive look on his face.
| Then learning happened.
|
| Everyone's mind was blown. Most people didn't realize it
| was a different person. Then on Thursday it was back to
| same-old same-old.
|
| I still don't know shit about discrete math.
| hackermailman wrote:
| This is what Putnam seminars are like, the whole class goes
| through problems together. A few of them are on Youtube,
| maybe more will show up as everything is remote now.
| truantbuick wrote:
| > There's so much to learning where the sharp bits of math
| are; proofs are the razor-thin path through the briar patch.
|
| This is an excellent metaphor using beautiful language. Did
| you just coin this yourself or is it pre-existing?
| thechao wrote:
| I guess this is mine? I would hesitate to believe I made it
| up, but I don't remember it from anywhere. If you don't
| feel comfortable with that, then credit it to Michael
| Starbird, who was my first Moore-method professor 20-odd
| years ago.
| mslm wrote:
| Just felt the same way about the portion after the
| semicolon; it's quite catchy as well! Please give a
| reference or else if I use this later I'll have to say it
| came from "some guy on hackernews".
| AnimalMuppet wrote:
| Cite it as "thechao on HN", not just as "some guy".
| (Unless thechao gives you something more specific.)
| theossuary wrote:
| It reminds me of this math overflow answer:
| https://mathoverflow.net/a/338620
|
| 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
| jb775 wrote:
| Wisdom of the crowd in action.
|
| 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?
| leokennis wrote:
| Low quality comment, but this once again confirms what I already
| knew: I suck at math.
| truthwhisperer wrote:
| Maybe I don't understand but he should have been now in the
| position to have already a few accepted publications. I'm mean
| this seems strange to me a few weeks before due date or is his
| supervisor on covid break? Don't get this honestly. Or is this a
| paid phd?
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