bitterness.

for a while i believed that if i don't write much about the job search, then i won't be bothered as much by it. that's not the case.

i think about the future often.

it makes me uneasy, just as it did months ago and years ago.
the only difference is that there's nothing i can do about it now.

the most i can do is keep working and enjoy the remaining time left in this postdoc.

i think a lot about the things that i should have done differently. i never used to think about questions like:

is this a good area of research to work in?
what will make me more competitive for future grants or jobs?

even now, these questions don't come naturally to me.
it takes active effort for me to concentrate on them.

i don't know if i'm particularly bad at it either, or if this is a weakness for most mathematicians. in every other discipline, academic or not, this kind of naiveté probably destroys careers.

what i really want to say is that:

i feel betrayed by the economy and all the university departments that have slashed their budgets and kept their hiring freezes;

i'm envious of those lucky few who tie up all the job offers from the top-tier schools, even if i stand no chance of making those short lists;

i'm angry with myself, with my foolish idealism and delusions. i curse those mistakes and oversights that cost me more than i know.

sometimes all i feel is bitterness.

the dark knight returns.

lately i feel like batman again.

that's not a good thing:
i mean it in the sense of the recent film the dark knight.

---

i really thought that i was being a nice guy, fool that i was. the midterm for my proofs class will be 5 problems. i promised the students this.

on the other hand, i told them what two of the problems were, so that they can prepare unambiguously for them:

1. one problem will be just definitions, no proofs: it is pure memory.
2. another problem will be one of two possible theorems that we have already proved in class. they can memorize and regurgitate them, or they can understand the proof and therefore rebuild it in an intuitive fashion.

at first i thought that the certainty would be relieving. already i get the feeling that the students are mad at me:

why do we have to memorise these definitions?
it's so unfair!

sure, that's one viewpoint.

on the other hand, say that i did not give them this certainty.

say that you don't bother remembering what a bιjection is.

say i ask you a problem where you have to prove things about bijections. if you don't even know the definition, are you any better off?

[sighs]

i already have a bad feeling about this ..

well, at least this day is done.

this morning at 7:30am i woke up tired. looking in the kitchen, i had only enough coffee grounds to make 3/4 of a proper cup.

[sighs]

later there would be two lectures to give, as well as a third substitute lecture; all of them, different courses.

[winces]

i agreed to cover for a fellow postdoc, you see.

that said, this favor better not be in vain;
he'd better nail that job interview ..!

by the time i was half-way through the 3rd lecture (the proofs course), i was exhausted. at one point i thought the proof i was giving the students had a hole in the strategy.

fvck.
stupid, stupid, stupid ..!

rather than have them stew in uneasy confusion while i'd try to patch it on the fly, i decided to set it aside. i promised them a complete proof next time, explained that most people don't remember all the proofs they learn, and went on to prove corollaries.

if that's true for "most people,"
then why am i still mad at myself?

in the end, though, the proof was right. i was just too tired to see it.

---

this post came out more frustrated than i'd like it to be. today was just a day worth forgetting. what i really wanted to say was that i worked all weekend.

thinking about it now,
i doubt that sounds any better.

there is a good part, though. remember when i said that i was looking for another theorem, something interesting enough to make a decent paper?

i think i found one. it took a weekend, scratching away hours from exam grading and lecture writing, but i think it works.

i can't wait to write it up in $\LaTeX$ tomorrow ..!

a veces, el sueño de la razon produce monstruos ..

having gone to bed at 1am or so, last night, this morning i woke at 6am and couldn't go back to sleep.

on the bright side, i finally had enough time to go back and read through a paper i've read before, but years ago. i was also sleepy enough to be patient and take my time, dwell on the details.

there's a lot i've forgotten.

odd:

in the mornings, it takes me 1-2 cups of coffee to be awake enough for small talk. on the other hand, i can still think about math in that half-conscious state.

on that note: have any of you ever woken up, with a solution to a problem right away? myself, i've only had the experience of waking up and realising that an idea couldn't possibly work.

excuses, excuses.

every time a student emails me, days before an exam and citing a medical emergency, two things come to mind:

1. they better have their hospital papers with them.
2. i think about my own accident-prone life. in the last 10 years, i've
   
   fallen off a mountain, as well as a hill,
   been hit by a car,
   elbowed in the throat,
   slipped and nearly fell into an icy stream (a few times),
   crashed my bicycle countless times, in several countries,
   held for hours under airport security,
   been hospitalised for days, due to a freak infection,
   (unknowingly) went canoeing in alligator-infested waters,
   and nearly arrested by the finnish police.

i might be missing some other sporadic situations.
at any rate, life happens: there better be proof, that's all.

---

in other news, life is busy. i can see why tenured faculty have ph.d. students. sometimes you have plenty of ideas but no time to work them out.

in honor of st. valentine's day,

(from xkcd #55, but now available as a t-shirt)

on a related note, march 14th isn't just pi day but a day of reciprocation:

Custom dictates that women give chocolate to all of the important men in their lives — from fathers and schoolteachers, to office colleagues and of course boyfriends — so women will probably spend more this year to keep up appearances.

But in Japan, there's no such thing as free chocolate. The confectionery industry has deemed March 14 "White Day," when men are supposed to return the favor and give candy to women.

(the article continues @ NPR.)

---

on an unrelated note, my monday lectures are generally out of sorts, especially my proofs course.

today i couldn't seem to get my mind straight on what i wanted to prove. also, it bothered me that i couldn't find an easy proof of
$$\left(1+\frac{1}{n}\right)^n \;\leq\; 3$$ for large values of n .. or without limits, anyway. (to explain, i covered bernοulli's inequality and wanted to relate it to what you can say about the number e.)

maybe it's because i work on the weekends, which is a wonderfully uninterrupted time to do research, and it takes me a day to get back to being "responsible."

speaking of which, there's never enough time to get anything done .. [sighs]

every beginning has an ending.

from xkcd:

two thoughts:

1. that webcomic would make a really cool cookie fortune. it's even the right size!


2. some years ago, i spent hours trying to debug one particular subroutine in a programming project. in the end and to my dismay, it was because i forgot to close a set of curly brackets: {}.
   
   since then, i stuck to the habit that if i ever type an open bracket, then immediately afterwards, i'll type the corresponding closed bracket:
   

   {
   {}
   {\em}
   {\em manifold}

   i do the same thing with HTML tags:
   

   <i>
   <i></i>
   <i>manifold</i>

   trauma and paranoia shape our habits, sometimes.

emails, memories, letters.

the more i look through this naοr-neιman preprint, the more interesting it gets.

---

in other news: today i received an email reply from flemιng (of federεr-fΙeming's ιntegral and nοrmal currents) which is really cool. it reminds me of fine memories:

when i was still a graduate student, at one meeting with the advisor he excitedly showed me a letter he just received from flemιng, regarding his "nοnsmooth caΙculus" survey article.

the advisor had this deep respect for traditions, as i recall. i never asked him how large of a part he played in the ahlfοrs centennial; i wonder now.

it's cold, and i'm thinking about snowflakes.

lately it seems like all i write about is teaching. i suppose that's where the recent frustration comes from, especially with this class that is new to me.

as for research frustrations, i can handle those. this line of work is so full of setbacks (and occasionally, advances) that i've developed a sense of humor about it.

---

that said, before the teaching rants begin anew, here's a little problem that came to mind today. it's nothing serious (not for research or anything) but right now i can't seem to answer it.

given a metrιc space $(X,d)$ and a number $0 \leq \epsilon \leq 1$, we call $X^\epsilon := (X,d^\epsilon)$ the $\epsilon$-snowflake of $X$.

it's not hard to show that $X^\epsilon$ is also a metrιc space; usually one finds such a problem in textbooks.

question: is the real line the snowflake of some metrιc space? what about the plane, or other Euclιdean spaces? for those experts out there: if the answer is yes, then can one choose the metrιc space to be doubling?

(epilogue: the answer is easy. thanks for the comments, guys.)

as for how it came up, i was thinking about embeddings of metric spaces, including the recent result discussed in a preprint of naοr and neιman. apparently assοuad's embedding theorem now works with a fixed dimension, regardless of the snowflaking parameter $\epsilon$.

roughly speaking, the doubling condition on a metrιc space is a finite-dimensιonality condition. so the naοr-neιman result suggests (to me) that one shouldn't have to push too far from the dimension of the given space in order to embed it.

it would be easier, if this social gathering had prerequisites ..

this morning i remembered:

tonight is a dinner party.
the host, a fellow postdoc, invited me.

fair enough; the usual crowd is used to my teaching rants.

then i thought about it: his sig.other is studying in the school in public health at our university. other students, of a professional kind, will be there as well.

ver well, then: don't rant in front of the students. it's bad form.

i thought further:

i might be the only non-applied mathematician there. most of the postdocs in this department are mathematicaΙ biοlogists.

did he invite the logician? probably not;
no butch-&-sundance ending, then.

crap. there's no way out of this, is there?

they'll ask .. they always ask: so what do you do? what is theoretical maths, exactly?

so i'll have to explain myself non-rigorously, using plain language and concrete examples, while not sounding like a physicist or a computer scientist .. and without becoming too dry and boring.

[sighs]

oh well. at least it's a dinner party, not being stuck in a row of seats in an airplane ..

good teaching involves mentoring, but ..

teaching this theory course is like teaching for the first time again. it's hard to figure out what they don't know how to do.

for example, take definitions:

over several office hours, i think a handful of my students have started to appreciate them as a (necessary) starting point. for problems in naive set theory, sometimes it's best to consider an arbitrary point in a given set, walk through the logic, and slowly assemble our conclusion.

while grading quizzes, however, quite a few papers seem to demonstrate this arcane manipulation of symbols. admittedly, set operations and relations like

$\cup$, $\cap$, $\setminus$, $\subseteq$

are like arithmetic, but only after one proves theorems akin to rules of arithmetic!

i suspect that they are too used to computing without reflecting on their computations.

ideally, i'd sit each of them down for a "how to write a proof" tutorial.

we'd introduce ourselves. i'd figure out the student's background to determine how to fit my explanations in a form they'd most readily understand.

i'd choose a theorem. then we'd "go in reverse" -- dissect the proof, learn where it came from, how it was written.

then i'd choose a related theorem with a slightly different proof, and go forwards: think about why it's true, jot down some ideas, write down a good proof.

let me emphasize: ideally. i have 30 students in this course alone; in my other course, 64 students are learning linear algebra from me.

there's just no time.

i don't have the energy.

maybe some students don't want to learn how to write a good proof: they could be applied persons or future high school teachers [1] and to them, this theory course is just another hurdle between them and what they really want to do.

then again, for those (few?) potential mathematicians sitting in class:

shouldn't someone tell them that they can't learn everything just by sitting passively in lectures?

shouldn't someone tell them that there is a craft to proof,
that maths is a language that requires practice for fluency?

shouldn't someone tell them that one doesn't become a mathematician by accident, and that discipline is just as important as curiosity?

i've never been good at telling others what to do.

---

teaching this course involves, i think, an understated responsibility of mentoring. i used to say that i'm too young to be someone's mentor ..

.. but that's not it. forget age: i'm too impatient and reluctant to be anyone's mentor. so far i think i'm teaching this theory course competently, but not particularly well.

[sighs]

i guess, at some point in my life, i'd have had to teach a course like this. inevitably it'd be a learning process for me .. and, of course, it happens in my last semester as a postdoc at this university ..


[1] honestly, that's no excuse. the fact that one of my students might be training the next generation of young people is a reason for why he/she should know how to write a good proof .. not against.

the pigeοnhole principle is ubiqitious.

as an example of the pigeοnhole princιple today, i told my theory class that

"there is no injection from $\mathbb{N}_{26}$ into $\mathbb{N}_8$.

"many of you probably think that this is a strange example. it's not .. rather, it wasn't always strange. most of you probably have iPhοnes or BΙackberries or a phone that has a QWERΤY keyboard.

me, i have an old fashioned flip phone, and i suffer T9 faιl a lot .. i once tried to text someone a hug but gave them a 4th instead."

borrowed from d1m5um (so, not my photo)

a few chuckles ensued. (-: