strike 1, 2, ...

i had high hopes for these past two weeks of traveling. among various goals, i had hoped to

1. meet the authors of papers that i've read, and discuss some ideas with them;
   
2. see the adviser again, and ask for advice;
   
3. see a postdoc acquaintance and talk some math.
   

so i was unsuccessful in all of these, but i think i realise why.

---

for 1: (X).
at a conference, everyone's out to meet someone, whether you already know them or not. the more important you are, the more likely you will be busy with co-authors and ambitious youngsters. here, tact is useless against persistence and insistence. so i learned that i have neither of those latter two qualities, or not enough of them.

so i did meet some of those authors/mathematicians, but never discussed much math with them. since it was formulated as an AND statement, it's safe to call this a failure; hence, the (X).

in some sense, conference social dynamics are a little like high school dynamics or prison dynamics. in the first few days, critical cliques form and they are nigh-impossible to break.

good luck, if you want to meet someone on day 3 of a conference (unless it's the last day and everyone's reveling). the acquaintances you make are fun and friendly, and the big shots are always busy.


for 2: (X)
i have the worst luck in the world.

the fellow grad students in my research group and the fellow (some former) students i know from other universities, they chose appropriately and attended a summer school, which happens to be the same town where the adviser was. as an untimely choice, i pick the wrong conference to attend, and become a stranger in a strange land, for a while.

others pay their visits, and then one week passes: the helsinki conference. i have an extra day to make the trip north to see the adviser -- but as it happens, the adviser's not taking any more visitors and will be flying out (by med-evac plane) to michigan, before conference end.

well, the adviser is now in MI and so am i. i guess he'll get back to me, or i'll get back to him; he has plenty of treatment and recovery to come, and there's no sense in my interrupting that.


for 3: (X).
i did see him, but we ended up talking only a little. i don't have any ideas ready, and at the stage they sat then, they weren't worth mentioning in discussion ..

.. especially in light of my fellow students (same research group) who have better, more disseminate ideas. time is short, and chances of meetings are few. let the best ideas win, i say; i'll get back to him, or anyone, when i have better (or good enough) ideas.

---

oh well. i guess conference resolutions are a bit like new year's resolutions. maybe i shouldn't have made any.

i still don't know if it was worth crossing the pond, this time around. i'm getting worse at traveling and i'm not getting any smarter or any good ideas.

sometimes i don't know anymore.

analogy, of a talk.

i heard curtis mcmullen talk today, but an acquaintance of mine overslept and missed it. when he asked me what i thought of it, i said,

  imagine someone showing you artwork, in the form of photographs. imagine also that you are extremely colorblind .. maybe you can only see a few shades of green, and you know for a fact that the photographs are in full color and fine resolution.

looking through the exhibit, sometimes the lighting is dark, and half the shots are during sunset hours, where green is impossible to see. but in the other half of the shots, what you see in green is amazing, brilliant, and insightful.

so you ask yourself: what would these look like, if you could see all the spectrum, if you had sharp eyesight, and if you could appreciate the artistic motifs and cultural references.

imagine how beautiful that could really be ..

that's what mcmullen's talk was like, i told him.

quick post: an idle self-observation.

lately i've been giving a good deal of unsolicited and unqualified advice, but it is in my nature, when meeting new and younger mathematics students.

they know me as a pessimist: i told someone yesterday that

    relax, and make time to enjoy yourself while in math grad school, because there is no reason to believe that hard work will pay off when you expect or want it to pay off.

writing, in longhand, against the clock.

i am finally being somewhat responsible. i'm writing a talk for next week .. although the flight there is tomorrow, and i should have done this earlier.

then again, it's a 20-minute talk; i'll barely have time to introduce the basic notions properly. also, more intelligent and important people will also be talking at the same time ..

(contributed talks are in parallel sessions)

.. so it's a gamble:
will i really have an audience?

it is no matter: the honorable thing is to prepare well and give a good presentation, regardless of audience.

---

i don't trust LaTeX for first drafts of talks.

the format is too slick, and every time i've drafted in LaTeX first, i run absurdly overtime.

so i'm writing a brief first draft, in longhand. it will tell me how long it takes to explain something, and i might actually plan my time well, for once.

also: pencils are very useful for this sort of thing. they provide the "Delete / Copy / Cut / Paste" options that are so tempting on LaTeX, and on computers in general!

the problem: i'm rapidly using up the paltry eraser on these mechanical pencils. i wonder if the manufacturers accounted for this, in order to force demand their way?

---

anyways, enough blogging.
there is plenty of writing to do!

how high can it go?

this is troubling:

      i've been checking the proof of a particular claim,
in order to assure that it is a theorem.
it involves Lipschitz (continuous) functions.

      every time i edit the writeup,
i spot an error, but that's not the trouble;

      so far, i can always fix them ..
      .. but the Lipschitz constant gets bigger, every time. ):


EDIT (9 august 2007): never mind.
i found an error that i can't resolve.

nature: 1,   janus: 0.

struggling against the calm; the storm soon comes.

after re-reading my previous math posts, i've decided that i sound more like a "neurotic over-analyst" than a "frustrated over-analyst."

i can't seem to concentrate on work today.

i broke my rule of "no computer/internet before noon" and i've put the radio on. it was intended originally to be a motivation in making today's worksession a little lighter, and to foster productivity.

the music has become a distraction, though, and i don't know if i have the willpower anymore to be disciplined and productive today.

this will be a busy august ..in terms of annoying trifles of life, i mean, such as moving apartments and promises to meet with incoming students. that sort of thing can cripple creative (mathematical) thought.

up, down, up .. again?!?

funny how life works. after writing yesterday's blog post last night, i left to return a few dvds to the local video store. i was walking back, thinking about what i've proven ..

.. and i realised where my flaw in reasoning lies. it's not a proof; there's a misstep.

i knew it.
i knew there was an error.
there are no such things as happy endings.

arggggh.. oh well.
i'll just let it go ..

.. but, of course, i didn't.

---

i dwelt on the obstruction for a while, reading what i wrote and shaking my head. i tried not to think about it, but thought about it anyway. i read a magazine or two but had no interest in it, and when i set down the pages i thought about the flaw again.

sometimes it's no use. i had suspected i was wrong, hoped i wasn't, and in either cased i'd have been an emotional wreck. for a moment i wondered whether one should take a psychiatric evaluation in order to qualify to be a mathematician.

the frustration can eat you alive. that's what it does to me.

how does anyone stay sane in this business? how does anyone cope with setbacks and failures and uncertainty, on a daily or weekly or long-term basis?

why does it bother me so much? why should i be a mathematician if it bothers me so much? this cannot be healthy. maybe my mind is diseased.

so i tried to let it go, and go to sleep. i don't know how i could have believed i could, but part of the point of being an adult is to try anyway ..

.. because sometimes, you don't have a choice.

---

at 1:30am, i had filled a glass of water, drank it, and went back to bed.

at 2:05am, i retreated to the toilet for a while, and went back to bed.

some time later, i had no reason to get up, but i did. i sat in my chair, at my desk, and i stared out the darkened window for a while. then, at some point, i went back to bed.

a few minutes later, it occurred to me.
well, what if the curves are C¹-smooth instead?

so i got up again, and wrote for a while:
5 pages of meandering, scratches, but i managed a rough idea.

huh. that might actually work.
the hell with it: i'm tired.
i'll work it out tomorrow.

so i fell asleep, and woke up late this morning.

---

it might work, but it probably won't. i see some possible trouble spots already, but at least i know where the argument might break down.

i think i can live with that. i wish i could tell you that it all worked out, that i proved a conjecture that isn't mine or the adviser's, but that wouldn't be true.

there are no such things as endings, happy or not,
for life goes on, and on, unsettled and unpredictable.

i wish i could tell you that i learned why i keep at it, keep at mathematics, but i still don't know why, really. i just do.

a festering idea, and silly neurotic setbacks.

so i'm supposed to be writing, and that's what i did today: staring at a LaTeX screen, off and on [1], from late morning to late afternoon ..

..then a basketball break,
in which a friend of mine broke his arm on the pavement,
and we stopped playing..

but then dinner, and more LaTeX.


"so what's the point?" you ask, "things are going. what's the big deal?"

"ah," i'd reply, "but i didn't tell you what i was writing, did i?"

---

there's an idea, which has been bugging me. it's related to the error i recently discovered in my work.

[see this previous post for details]

since that error, i haven't really trusted my own math or any of the few proofs that i've written. in fact, when working on new ideas, often i'm relieved to find several errors, because

if i made such a grievous error,
and if it cost me that many theorems and corollaries,
then i have to become better at finding those errors.

you see, i wasn't the one who found the error in my proof. someone else did, but it's not embarrassment that bothers me.

what bothers me is that by missing that error, i demonstrated that after all these years, i might not know what is a proof and what isn't, what is good math and what is bad.

if you can't tell what is good math, then how are you supposed to do good math?

---

"so, you're a fraidy-cat neurotic," you'd say, "so what?"

that's the thing, and that's where the aforementioned idea comes in. it doesn't fix the error, but if it's correct, then it proves some of my previous conclusions and corollaries.

those conclusions were based on an error-prone idea, but what i'm saying is that i found another way around, another method of proof. it's simpler and the method is more concrete than my last idea, but ..

.. i don't trust it.

the adviser is out of town ..essentially indefinitely.. so i'm on my own on this one. fool that i've been: i should have given a study seminar talk on the background of my research, last semester or before. i could then bug someone to troubleshoot my proof, and finally find that elusive error.


i've been wrong before and it could well be wrong: that's life, and that's math. not everything works out, and as the saying goes,

if all your ideas are working,
then you're not getting enough ideas.



i feel silly for saying it, but i just don't want to lose my conclusions for a second time. the first time was hard enough.

[1] i meant that i was off & on, not the screen. trust me: my laptop isn't that dependable!