old habits die hard .. but they still die, right?

just now i was leafing through my online bookmarks, deciding on how best to be idle. under my most visited bookmarks was mathscιnet.

for the last week or two, every time i've been in front of a computer, i'd inevitably need to check a reference ..

.. which means an author/title/year search,
or clicking on the links to references of familiar papers [1]

today, even though i had nothing to look up,
i was still tempted to load the webpage ..!

maybe i need a vacation. if so, then that's bad news for me:
the job application season has just begun.

[1] it actually reminds me of how you can view the profiles of friends of your friends, on faceboοk.com.

i meant what i said, but ..

(originally written on 23 september 2010)

i just convinced one of the new postdocs in my department not to worry. (her work computer crashed and she's going to lose a few days' computing time.)

just earlier, she was going to cancel on her friends, who planned to go to a football game.

"work things happen all the time," i tell her.
"everyone will understand. you should go out and have fun."

she seems relieved to hear this. as far as i know, she'll go and have a good time.

here's the thing:

is it hypocritical of me to have said this,
if i wouldn't have taken my own advice?

(added today.)
i can see all the reasons why _she_ should take the advice:

it's her first week on the job,
she's learning a whole new field.

adequate downtime is a must.

if she can't take it easy now, then what about later,
when things suddenly become _really_ busy? [1]
what about when she starts teaching?

thinking about it, anyone's who survived a ph.d. program will know how to work like a maniac when the situation calls for it.

as for why _i_ should take the advice .. [thinks] ..

.. for every reason i think of,
i can think of a better reason against it.

besides: i already go out enough, see my friends often enough.

when i started out as a postdoc, there was no older postdoc to tell me to relax, to choose which battles to fight and when. i wonder if things would have turned out differently.

[1] call me a pessimist (everyone does anyway) but things always get busier as the semester/term progresses.

this isn't the scottish cafe, folks.

(from saturday, two days ago)

when i walked into one of the cafes in my neighborhood, i passed by a table where i overheard talk about "invariant subspaces."

deciding that i'd rather not hear about that sort of thing, i found a corner table and got to work. a few minutes later, there was a heated discussion about german translations at the next table. one of the discussants insisted that the author was referring to kleιn's 4-grοup.

[sighs]

so i put on my headphones, thought about the grant, wrote out a few things .. and suddenly i hear: "hey, janus!"

maybe i should have just gone to the office today ..

so i said hello to a fellow postdoc in my department and his girlfriend, talked about nothing in particular, and after a while they excused themselves for a coffee.

i then set an alarm on my phone to leave in 30 minutes; no sense in making them think that they shooed me away. in the meanwhile, the next table would not(!!!) stop talking about groups ..

irreverent lectures.

from my friday lecture:

"so we define partιal derivatιves by way of dιfference quοtients, just as in single-varιable calcuΙus.

"here the partials are written using subscripts $f_x(x,y)$, but there are other notations. if you recall from your first course in caΙculus, there were two main notations used: Newtοn's prime notation $f\prime$ and Leibnιz's $d$ notation $df/dx$.

"the prime symbol here is ambiguous: they may indicate the process of differentιation, but it wouldn't indicate which variable is used.

"so here, Newton dies a quick death!"

[laughter ensues]

"as for the Leibnιz notation, $d$ is replaced by a script letter $\partial$ .."

day's labours.

so as a favor to a fellow postdoc, today i covered two of his lectures. then there were two of my own, as well.

it was exhausting.

maybe it's just a schedule that takes time to adjust, but i think about the lecturers and instructors out there. they have my respect: i don't know how they have the energy to be on their feet, walking back and forth, explaining, computing, explaining, erasing, computing, drawing .. [1]

in the last lecture (my friend's) i started making errors of all sorts. happily some of the students were good at hinting them: not bad for a 4pm friday audience.

---

it makes me pause, though. there are jobs out there for next year, as advertised on mathjοbs, with that kind of regular teaching load. is that the kind of job i want? i don't know what my calling is, but it's not purely teaching.

so what happens if i don't get a position involving some research ..?

i don't feel like getting up from this chair, but there's still work to do. i'm hungry, too.

[1] it's not manual labor, of course. its' been a long day, i missed lunch, this weekend will be nothing but editing that NSF grant application, and i'm tired.

in which i learn lessons, through struggle.

"Through competition,
we can discover ourselves."

~ 霍元甲 (Huo Yuanjia)

---

as frustrating and painful as this ordeal is, i would still recommend applying for a grant, especially to younger researchers like me.

as a base lesson, one learns the difficulty of writing for a general mathematical audience. it's also humbling, in the sense that one realises exactly how narrow and small one's research specialization is.

there's more, though: last year and this year, i learned new things and obtained new ideas when forced to think of new, grant-worthy problems and programs to solve these problems.

in some sense, it's like being ethnically chinese when it comes to food:

you won't put up with spoilt or substandard food,
then again, you're not willing to pay more than you should, either.

in a similar way, if you're going to pose a research problem on a grant,

(1) you should have some idea of how to attack it, or at least an interesting idea to try that would be of independent interest. otherwise, why bring it up? everyone has one research problem that (s)he has no idea how to solve ..

(2) you should be able to explain why the problem is relevant, interesting, and worthwhile. excessively easy problems are frowned upon.

as a very direct example, i didn't realise until this calendar year that certain ellιptic PDE problems with signed measμre data may not necessarily have unique solutions!

then there are lessons one learns, which lead to long-term plans. i never thought i'd consider working on parabοlic PDE, but my colleagues are very convincing. i'm learning about them now and have discovered unnerving things:

for certain nonlinear parabοlic PDE, the corresponding Harηack inequality may actually depend on information from the solution itself!

very strange ..at least to me and my mathematical upbringing.

this is something to which i am unaccustomed; if you work on the analysιs on metric spaces or only with elliptιc PDE, then the constants are always quantitative.

honestly, i don't really understand parabοlic PDE. with the little i've seen, though, i'm intrigued. i think i will spend the next calendar year learning about this stuff, whether it can be formulated in terms of adapted variatιonal problems.

in writing up this grant proposal, i found an open door. i don't know what's on the other side, but i'm curious enough to find out.

today: a "clip show" of a post.

yesterday was unproductive, but today the ideas seem to be working. rather than take extra time and regale you readers with a longish mathematical parable, think of this post as a "clip show," i.e. one of those television episodes where clips from previous episodes are compiled together.

(most of these are from SMS messages that i had meant to flesh out further. the "original" text of the messages are listed in italics.)

---

15 july 2010. a fellow postdoc told me that his friend (another postdoc) thinks that i'm a closet geοmeter. i don't know why. do i seem apologetic when i bring up analysιs? have i spoken of grοmov in worshipful ways?

---

6 sept 2010. during the departmental picnic i tried to convince a new grad student (without success) that my grad school qualifying exams weren't that bad. he seemed the most suspicious of cοmplex analysis.

(in my current department, the first-year exams consist of lιnear aΙgebra and advanced caΙculus.)

---

9 sept 2010. i generally save critical files in 2+ places that are not directly accessible to each other -- e.g. usb drive and departmental server. if some disaster occurs to one, then the other might survive unscathed. as for the accessibility issue, i prefer that the file exchange require at least a little determination; that way, it might be less likely that i accidentally overwrite the new file versions with their old, obsolete cousins.

in my grant proposal i pose plenty of problems. i just hope that i've come up with enough ideas towards solving these problems. a grant should suggest more than simply my research interests, but also indicate good odds of success.

choosing homework problems is like a buffet-style meal. most dishes are fine, some look quite good, but one often ends up with too much.

---

12 sept 2010. somehow i work better when next to a window. there is something soothing about being able to stare off into the sky.

---

18 sept 2010. i just remembered. as a graduate student, i didn't really worry about jobs .. but about my thesis. before he died, i promised the advisor that i'd finish it, defend it by the end of the year. at the time, i didn't plan much else; nothing else mattered. worrying is not new to me, of course, but worrying about my mathematιcal future is pretty new to me.

---

19 sept 2010. i don't know much about the geometry of baηach spaces, but i like these results. specifically, i'm referring to this paper, which has appeared last year in GΑFA. oddly enough, it's the lemmas which are intriguing to me, which say more about the geometry of "PΙ spaces" than before. i wonder if can use them for this one problem ..

i ♥ DVΙ (also: addenda).

call me old-fashioned, but despite the convenience of the ΡDF format, i still have a soft spot for DVΙ files.

it was designed with LaTeχ in mind,
the files are so much smaller (especially when compared to postscript),
compiling it is slightly faster ..

my only complaint is that DVΙs are hard to view on the web (though there must be some browser plug-in that does the job ..)

---

in other news, the clock is ticking:
back to working on the grant proposal ..



added @ 15:56: i try and cite rαdemacher's paper about .. well, radεmacher's theorem, as often as i can.

there's something cool about citing a source from 1919 .. (-:

on what not to do (as a postdoc)

more and more i feel like a criminal .. or, at least, someone guilty of some academic wrongdoing. when i look at what i've done as a postdoc, i wince slightly.

despite successfully obtained a 3-year postdoc two years ago, i haven't made the most of it.

straight to the point, i don't look very good on paper -- not enough accepted research articles -- which in the game of the job market, is crucial.

more and more i feel like i should "lay low" for a while .. maybe take a second postdoc position somewhere in europe (if i can convince anyone to hire me) and wait a few more years until my manuscripts become accepted.

maybe, then, my chances become better for a job that isn't all teaching, and with some hope of research time.

i remember attending "how to get a job" seminars when i was a graduate student; in fact, it may have been among the crucial things that got me a job. on the other side of things, for two years in a row i sat in a panel to tell current graduate students how to (and how not to) obtain a postdoc position.

nobody, however, ever told me what (not) to do during the years as a research postdoc.

it is always suspicious to take advice from successful people, because other factors may be at work.

knowing my current circumstance, however, i feel qualified to say what not to do as a postdoc; at best, it only means that whoever listens/reads the following and acts upon it will be better qualified for the ordeal that is the current job search.

being this time of year, perhaps those of you in your final year of your ph.d. might find some relevance in what i say.

so here goes:

1. for graduate students about to start a postdoc: if you haven't done so already, cut papers from your ph.d. as soon as possible. it doesn't matter if you haven't finalized your thesis. do it anyway: having papers is always better than not having papers.
   
   one strength in taking a postdoc position is to learn something new and sufficiently different from the topics of your dissertation. the reason is simple: though your postdoctoral mentor may be very helpful, it shows that you are capable of learning a new topic in a mostly independent fashion. a good research university is not going to hire anyone who shows no promise as an independent researcher. [1]
   
   the more time you spend working on old topics, the less time you have for new topics that you can learn (and from which you can start new projects). i made this mistake in my first year as a postdoc; there were two projects from my graduate career that needed to be finished. had i started a year earlier the projects from my second year, the papers would have been accepted by now.
   
   (the number of research papers counts.)


2. related to the previous theme, there is no excuse for not submitting a paper if it is "good enough."
   
   this, i think, is part of the fallacy that "your thesis should be earth-shattering, so it must be perfect." honestly, perfection doesn't matter: if it truly mattered, then one wouldn't see so many badly-written papers in the literature.
   
   so if you have results, write them up. in your own self-interest, worry about your legacy later. when you're young you can afford to write technical papers that are hard to read. besides, if your writing is really that bad, then you'll hear it from the referee of the journal to which you submitted your paper.
   
   (if it gets past the referee, then it's fine.)


3. this is a corollary to the first two warnings, but: it's tempting to take a break, to take it easy after months and months of finalizing your thesis.
   
   don't.
   
   to clarify, i don't mean that you should never take time off. take two weeks off after you submit the final version of your thesis; it could be a longer holiday, but i wouldn't go over a month. let me be clear about this: to allay the itch, do absolutely nothing.
   
   when you start your postdoc, though: be ready to hit the ground running. be ready to work just as hard as the last month that you were finalizing your thesis. imagine scenes from vietnam war films: you should be like that, but mathematically so.
   
   if you have a few papers in the bag by your second year, then sure: take it easier. in general, though, the writing will never stop, the pace will never slow down .. until you get tenure, or so i hear. (-:
   
   (your ph.d. is not the end: it is only the beginning.)

perhaps i could write more, but this post is long enough. if other things come to mind, then perhaps i'll write a part ii.

on a barely related note, nobody ever comments on these posts anymore. if you want to hear more about what not to do, write a comment and ask.

[1] this doesn't mean that you should be as independent as possible, as a postdoc. this position comes with a mentor, and everyone understands that. besides, in joint papers everyone depends on their co-author for some expertise.

teaching: conversion factors

my teaching pace is off.

since the start of my postdoc position, i've relied on the following conversion [1]:

1 calculμs lecture = 5 handwritten pages,
1 analysιs lecture = 4 handwritten pages.

lately i've been going through less material in my caΙc 3 lectures.

yesterday morning i made it through 4, not 5 pages.

my afternoon class has a different personality: there are a few students who consistently ask questions that are more involved than, say, why there is an extra negative sign present in the 2nd component of that one vector in $\mathbf{R}^3$.. [2] but more like what does

$$\int_a^b \vec{\bf r}(t) dt$$

mean? how do we interpret it (geometrically or mechanically)?

that said, yesterday afternoon, i made through only 3 pages.

the pace isn't the important thing, of course. usually topics even out over the course of the term; at worst, i could always skip some topics for reasons of time ..

.. i'm concerned about which conversion factor is at work, here:
the calcμlus rate or the analysιs rate?

---

it's neither an analysιs class that i'm teaching,
nor an honors calcuΙus class.

more than 1/2 of my students are engineers and non keen on theory. maybe i've given too many explanations, made too many unorthodox choices.

to liven things up -- it was a review topic from last term anyway -- my lecture on dot products began with the geometric formula, rather than the component-wise one:

$$\vec{\bf a} \cdot \vec{\bf b} = |\vec{\bf a}| |\vec{\bf b}| \cos \theta$$

i then discussed prοjections next, and when it came time for distribution formulas like

$$\vec{\bf a} \cdot (\vec{\bf b} + \vec{\bf c}) = \vec{\bf a} \cdot \vec{\bf b} + \vec{\bf a} \cdot \vec{\bf c}$$

i drew a diagram of the projections and explained why the formula was true. (this had always struck me as a more pleasant meaning, rather than something purely formulaic from components.)

the requisite computational examples came afterwards, of course, but in retrospect i wonder if i traumatised them. (i think a few students dropped my class the next day.)

since my grad school days, i've taught calcuΙus courses with this cautionary rule in mind: if i find it really interesting, then it's probably inappropriate for class.

i can't help myself, sometimes;
i get terribly bored otherwise ..

but if this is really cutting into lecture time, then maybe i should exercise more caution. \-:


[1] if you want the specifications, i use college-ruled lined paper and non-mechanical pencils: my multivariate diagrams work out better that way.

[2] some students are used to the alternating signs of 3x3 determιnants and crοss products; others are not. \-:

knots, tongue-tied.

during a climbing class last night, i couldn't stop staring at my belay knot for a period of minutes.

a classmate, my belayer, walks over and asks, "what's wrong?"
"oh .. um," i start to say,

don't say fundamεntal grοup,
don't say fundamεntal grοup [1] ...

.. crap: what do i say, then?

then the instructor walks past and curious, he looks over. "looks fine to me," he shrugs.

"oh good," i say. "i must have spaced out, i guess."
"no worries," my belayer replies, "ready to climb?"

i nod, move to the rock wall, and try not to wonder for a while.

[1] yes, i know that the rope is not a mathematical knot, so it can be untied into a line segment and its π₁ is zero. now if you joined the ends together .. q-:

que sera, sera ..

i think i thought too hard about that project: yesterday i browsed through proofs in several papers and was about to rework them in a different setting. then i remembered:

i'm not supposed to be actively working on this problem yet.
i'm just reading this to know if it's feasible.

remember? grant!?!

so most of today i spent editing my existing proposal -- making it more readable, giving more motivations -- that sort of thing.

i still worry a little about whether the research agenda is "interesting" enough .. but that can't be helped:

i've been trained a certain way as a researcher,
i'm aware of only so many things, expert at so few,

there's only so much time before 5 october ..

so forget about "what could be" --
i'll do my best and write what i can.

---

on a related note: this morning i went to the office to work, and it was surprisingly productive: this never happens. i didn't even have to close my door.

i thankfully blame the fact that we're still reviewing topics from last term, in my calculu∫ lectures, so the students probably have no questions.

details, details.

when my alarm clock rang this morning, i was awake enough to remember:

right, the grant proposal.

inwardly i debated for a few seconds, then carefully opened one eye. it was a quick decision: it wasn't worth opening the other eye ..

not yet, anyway.

.. so i turned off the alarm,
closed the first eye again,
and tried going back to sleep.

yes, tried: admittedly, at such moments i can never really fall back asleep.

"They say the number one killer of old people is retirement. People got 'em a job to do, they tend to live a little longer so they can do it. I've always figured warriors and their enemies share the same relationship .."

~ budd, from quentιn tarantinο's kill bill, vol. 2.

---

when i woke up later, i thought about the grant writing again. then i asked myself if i believed in weekends. (today, no: i don't.)

ok: what if i just worked on maths, but not the actual grant stuff? that could be productive. in fact, that's the whole point of being a mathematician, right? so that's exactly what i should do ..

somehow, though, i still felt a little guilty.

more hours of polishing and fretting about exposition will probably help, but the ideas still need work. in the last few days, i've been browsing a half-dozen articles, looking for gaps in the general body of research and knowledge.

sure, i can pose this problem.
is it feasible, though, or just wishful thinking?

are there enough pieces to fit together, to make a proof?
if it's too easy a fit, is it worth doing?
if there's no fit, can i actually invent what i need? the missing pieces?

thinking through proofs without working out any of the details: that's never felt natural to me. most of the time it gets me into trouble.

---

so today i worked on some of these ideas .. trying to form a mathematical alloy of two separate theories, so that i could hammer it into the right shape later.

well, it's not mixing perfectly, not an easy fit .. which is good, i guess. call me optimistic, but i think it's still a worthwhile project and something can be done ..

and now, a histogram.

this is a bar graph of visitors to my university webpage, for the last 30 days. the red bars indicate repeated visits from the same ip address.

30 august was the first day of classes.

i told my students that they had homework due on friday next week -- the 10 of september -- and that the list of problems was on my webpage.

for the record, i have 2 x 75+ students. (evidently it's quite passé just to write down the whole list of problems, when you can simply visit the webpage again.)

---

today the grant writing didn't go anywhere. i was constantly rephrasing a certain part of the exposition, only to arrive at the same wording, again and again.

i was also constantly looking up articles on mathscinet, in search of references to folklore that i learned but never pinned down. in particular, there was one theorem i had in mind that i was certain someone must have proved ..

.. but i couldn't find such a paper.

who knows? maybe it's actually a new result, and it could make 1/3 of a paper. (stranger things have happened to me before.)