new and brighter colors @ leipsig leipzig.

wow. the maths preprint server at the Max Planck Institute has been re-designed. the color scheme and layout are great ..

.. and, of course, the math is good too. q:

go and have a look!



EDIT: i cannot seem to spell today.

one first step, of many.

it's done: the maths, anyway. i've thought out how to organize it all, rewrote some parts, and found lemmas that i needed to prove. then i proved them.

all six sections and the silly appendix on functional analysis that i planned are written up in LaTeX, in a file called thesis_draft5.6.tex.

it's on my computer. i've attached a copy in an email draft in my web account. another copy is on a trustworthy usb drive [1], and one additional copy was ftp'ed [2] into my university server space.

if this were a film, then armageddon would happen, the internet would collapse, and an electromagnetic pulse would wipe out all my hardware.

then again, if it were that sort of film, i might run into a secret organization with the intent of taking over the world. probably i'd also run into their arch-nemeses, who would be dedicated to keeping the world a safe place and all that idealist cr@p.

the odds would then be good that i'd get to save the world in some amazing situation with many explosions and stunts. i might even duel a megalomaniac, lose my weapon, be told the secret world-domination plan in my seeming few seconds left of life, and in the last instant, there is a distraction and seizing the opportunity, i fell the villain.

nah.

i'm sure that i could beat him more quickly than that. q:

with all of this in mind [3], i was considering burning the file onto a data cd, just in case. even my paranoia has its limits, though ..

.. and besides, i printed out a copy. i can always scan it back in, or if worse comes to worse, i can always retype it.

then again, under the margin parameters
\setlength{\textwidth}{7.2in}
\setlength{\textheight}{10.5in}
\setlength{\topmargin}{-.8in}
\setlength{\oddsidemargin}{-.5in}
\setlength{\evensidemargin}{-.5in}
it's 47 pages long.

when i add \linespread{1.5}, it grows to 64 pages.
when i switch to \linespread{2}, it's 84 pages.

yes, that would be a lot of typing, but as for fail-safe plans, it's better than re-writing it from scratch!

what remains is an introduction; i'll write it this week. tomorrow i'll read it and see if i simply wrote rubbish, make the corrections, and then give it to the supervisor.

then i'll get the red ink back, and iterate. who knows? maybe the process will even terminate. (;

[1] yes, there are untrustworthy usb drives. i own one. in one of my few conference talks, i had brought that d@mned drive with me, intending to give a PDF slide talk (not beamer). as it happened, i attach the drive, the software is loading, and then the computer in the lecture room freezes.

for a long time i thought i was just being silly in making backup transparencies. in the end, though, i turn off the beamer and give my talk on the overhead. i think everyone was impressed.

[2] short for "file transfer protocol," in case you didn't feel like googling it.

[3] for the record, i was envisioning a grey-colored lightsabre.

about web writers, techies, and philosophical discussions.

sometimes i really like reading this one writer, paul graham. he may be embedded in the real world of money and companies and building the internet and whatnot, but he writes as if he is a techie and understands techies. [1]

i might have written this before, but one of my reasons for liking his essays is that he's willing to take a chance on philosophy. never mind if he's right or not; he's giving it a shot.

as for why i'm writing this, he has a new essay up, called "how to disagree." here is how it begins:

The result is there's a lot more disagreeing going on, especially measured by the word. That doesn't mean people are getting angrier. The structural change in the way we communicate is enough to account for it. But though it's not anger that's driving the increase in disagreement, there's a danger that the increase in disagreement will make people angrier. Particularly online, where it's easy to say things you'd never say face to face.

If we're all going to be disagreeing more, we should be careful to do it well. What does it mean to disagree well? Most readers can tell the difference between mere name-calling and a carefully reasoned refutation, but I think it would help to put names on the intermediate stages. So here's an attempt at a disagreement hierarchy:

perhaps there is not much new in this, and perhaps other web writers have written such things already. also, it's short.

perhaps i should stop here, in my attempts to explain why i like this or that. these discussions go the way most philosophical arguments tend to go:

after a while, the words you use don't mean anything. they're used colloquially and not rigorously. if your company is persistent enough, then this might reduce to a first-order logic problem. then your discussion becomes a standard exercise.

more often than not, it will also lose most of its original feeling and humanness, though you can't really explain why.

this is the curse of arguing with mathematicians and techies; everything must be well-defined.

in other words, humanity is often sacrificed for the sake of rigor.

[1] i didn't make up the word "techie," but having tried several times before, i won't define it here. the term is too vague, but let me give an example or two:

if you've ever done any programming in your spare time, you're a techie;

if you've talked math at a bar before because it was natural to do so (and not because you intended to annoy someone) then you're a techie;

if you played with legos as a child, still like playing legos with your little cousins, but are careful not to build too extravagantly (so that you won't be found out), then you're a techie.

references & ignorance.

you know, this geometric measure theory book by h. federer isn't so bad. before, i've heard complaints about it and made my own complaints about it.

admittedly, the book is immense,
the generality is somewhat overwhelming,
and i wouldn't want to learn gmt for the first time by reading it,
but it's useful.

then again, i will probably continue my complaints, in years to come. the odds are good, at any rate: this blog isn't called "the (Frustrated) Over-Analyst" for nothing, you know!

---

i might even try and read some of gmt carefully, one day. lately i've told people that i study gmt, but i don't know if that's really an honest thing to say.

fraudulence seems to be an easy feeling for me: i might say that i study the analysis on metric spaces, but a moment later i realise that i don't know cheeger's GAFA paper so well,

or the Acta papers of heinonen & koskela, and of ambrosio & kirchheim,
or sobolev met poincaré by hajłasz and koskela,
and so on.

i know that i am some kind of mathematician, but i don't know exactly what kind anymore.

now the draft has gone extreme.

EDIT (26 march 08: 16:40): epilogue follows.

i think i've created a monster.

in my efforts to fill in the gaps in all my proofs, the thesis is starting to sound .. robotic. If my theorems were sub-routines and my thesis were program code, then my proofs would read like a series of procedure calls.

\begin{proof}
By Lemma \ref{metricspacecase} we see that ____ ...
As a result, from equation \eqref{lipweakconv} we obtain _____ ..
and hence, by Corollary \ref{specialcasedimtwo} it follows that _____ ..

.. blah blah blah
yakity shmakity ..

ad nauseum
\end{proof}

Now the proofs don't seem simple or clear anymore, which they really are. They're simply obfuscated by having to remember what Corollary #.# and Lemma #.#.# and Theorem #.# are ..

argh. okay.

i need a break, and to look at this from an impatient eye which will see and seek clarity in these mathematics.


EPILOGUE. i think i overreacted. too much caffeine all at once and too many hours spent thinking dwelling on the same ideas: it led me to jump to conclusions.

so i guess the quasi-draft isn't so bad, but it still needs work and .. um, an introduction.

unsteady, the draft.

every day either:

1. i find a gap in one of my proofs, which is either a missing hypothesis or a lemma that i need. it takes half or a whole day to patch the proof and look for other places where i might have made the same mistake.
   
   
2. i find that the result extends slightly. it takes quarter or half a day to deliberate if it's worth changing. if i change it, the same compatibility issues persist. i think i'll call this LaTeX-laziness:
   
   does it come free, or do i have to form a new definition or ..i hope not, but.. a new subsection in order to formulate it?
   
   what else do i have to change?
   
   if there's a lot to change, then is the new result really that interesting?!?

so i suppose that i'm waiting for the draft to stabilize. it's either that i haven't given up yet.

---

on a lighter note, yesterday i was working with partitions of metric measure spaces. i wanted to shift the graph of a function f, where the shift depended on the part of the partition. i ended up calling the infimum of f over the kth set by c_k and looking at the difference.

i then left to fetch a cup of coffee. it was only when i came back that i noticed what the paper looked like.

huh.
i had written f-c_k all over the place.

another latex question.

i know that some of you are analysts and that some of you are wise in the ways of LaTeX. so here is a question, and if it helps, i'm using the amsart package.

is there a nice way to form a half-arrow to indicate weak-star convergence in a dual Banach space?

naively i have been using the command

      \stackrel{*}{\rightharpoonup}

as a macro. it works well, except that the asterisk * makes unnecessary vertical space between the line containing the arrow and the preceding line.

any thoughts?

ethics, shmethics.

from a certain point of view, i've just bribed my officemate with a bubble tea, so that he would leave the office and me in peace.

from an alternative point of view, i decided to cheer up said officemate with a full stamp card from the bubble tea place (buy 5, get 1 free), after he alassed about the woes of the math dept computer network.

oh well. peace and quiet, now.
work beckons.

epilogue: never mind. it didn't work.

a meta-post: a blog post about .. this blog?

i think i should admit something: now i am conducting surveillance.

you see, there have been more people that i thought who actually read this blog, and regularly so. some have brought up this blog to me in person, but whom i didn't expect to know about it. it has made me curious about who actually reads the idle rants that i constantly write.

so if you scroll down this webpage, to the very bottom, there is a counter icon on the right-hand side. that is the counter, my surveillance device, and it records interesting statistics that you can read about here.

to my credit, i added the counter because i know of another mathematician who uses the same device for his/her own homepage. so between precedent and curiosity, i have become some type of Big Brother.

---

the statistics are interesting. some of you i expected (because .. well, you told me that you read this regularly) but other readers i cannot explain: i have never met you or heard of you. in particular, i didn't realise that anyone in the U.K. reads what i write.

so to everyone: let me thank you for bothering with me, my complaints, my insecurities, and my claims and my boasting. i think a blog is a dangerous thing: it makes one self-important, and feeling self-important one often loses ones sense of self ..

.. or at least, one's internet self. indeed, that is a type of self or aspect of self.

---

perhaps, at some point, i will write about actual mathematics again. but i feel i should be honest about surveillance. if this dismays some of you, then i apologize.

i was simply curious, and curious enough to learn about you.

almost there .. almost there ..

every week i feel like i'm almost done with the "math" [1] in my thesis ..

.. and i am. really.

it's not my fault that there's always "one more lemma/theorem." some would even say that it's a good thing, a good problem to have.

but when i say that to myself, i remind myself of "the boy who cried wolf." then i look at a calendar and count the weeks.

then i panick a little, i type a little more furiously, and i use the delete button a little more often.

earlier, i caught myself writing "clearly, it follows that .."
a slippery slope, that!

---

i do realize that writing is important. it reinforces what i already know and it improves my skill at explaining and presenting my ideas to people who would otherwise never bother with this area of mathematics. sometimes i gain new insights in how my ideas fit together.

but despite this, i miss doing new maths in the mornings.

then again, i'll probably sing a different tune when i start teaching again. \:


[1] meaning everything but the first section (the introduction) and the last section (an appendix, which is also almost done).

on mathematical conversation & my own inclinations.

lately i've been having more mathematical conversations, but i chalk it up to the anomaly of having been in the office two days in a row [1].

perhaps i should impose some sort of taxation upon my office visitors. how about this: if they visit me when i'm in the middle of a proof, then they should be forced to listen to the rest of it!

nah.
too risky. q:

---

in mathematical conversations i do a lot of listening. i've decided that it's either

1. because of youth and a lack of understanding about most subjects,
   
   
2. because of selective apathy and a lack of true curiosity about most subjects,
   
   
3. because i've nothing interesting to say about most subjects and it's easier to hear what others have to say.
   

this translates, of course, to "either i don't know, i don't care, or otherwise i'd bore you: you go first."


it's fascinating to watch someone who's really excited about a particular theorem or a problem, especially amongst the crowd here in ann arbor.

so many people,
truly willing to learn,
truly caring about what they do.

it's more likely that people would ask me questions, rather than the converse. i'm not a sage or oracle; i just don't often think of questions.

some people have a knack for questions, but not me. i've no mind for good questions or research problems, not yet at least.

---

when i work on math, it's not quite problem-solving. sometimes i think i've lost that skill; i've certainly lost any skill at exam-taking, at least. when i work on math, it reminds me of creative writing instead.

i start somewhere and it's like writing a good opening line: a beginning. i might do a simple example, which is like one scene unfolding, with un-introduced actors in media res. the plot thickens: is there a back story to the scene, what we just witnessed? or is it just a random event and should we leave it alone?

come on. it's never a random event.

and so it goes; that's how i do math, at least before i felt i had to write a good thesis. (:


[1] which is not entirely true. the office is more like a base of operations. i always intend to remain at my desk, be diligent, and work, but often it doesn't go as planned. often i set my coat and bookbag down, and then i'm due somewhere else.

in fact, often the only plans which work out involve coffee.

hours of the day, and night.

i lost my nerve again, which explains why i'm up and still LaTeXing.

earlier this morning i jotted down some notes for two of the three final theorems that i'll add to my thesis. i think i've vowed that these will be the final ones.

after them will be an introduction, and if that is ever finished then the supervisor can look at the draft, dip it in red ink, and figuratively tear it to shreds.

i suspect that the draft won't be very good, so it's probably for the best.

in the afternoon, i stopped by the office to continue to work. i was discovered, however, by colleagues. sometimes i wonder if they lie in wait, only to be disappointed more days than not.

i guess i am hard to find.

at any rate, this encounter led to a coffee, pleasant mathematical conversation, and korean food for dinner.

then i called another colleague and chatted for a bit.

all good times.

it wasn't until i went home at midnight that i counted the hours, decided that i did too little, and succumbed to paranoia. so now you have it: why i was just LaTeXing five minutes ago ..

.. and why i'm blogging now.

---

it will be a good day when the thesis is done and the defense is done. then i can worry about looking ridiculous while giving conference talks in front of peers! q:

addendum @ 4:30am: finally. one theorem down (albeit with a less than stellar exposition) and two theorems to go!

when to quit ..

argh. the contents of the thesis are almost done. i'm only including extra and interesting results now.

what really kills me is the constant line of inquiry:

"wait. i think i can prove something better .."

then i work a little, and a little while later,

"wait. is that really true?"
it would be really cool if i could add it to the draft."
"okay: let's see if it's true .."

but, of course, it's too hard to resolve immediately. i forget that it took months of careful thought before many of the results that i've written down took their current form.

so don't be fooled, when you're near the finish line:

when it's typed and when you can mechanically type more,
everything will look easy, so beware.

related to "tales from the road"

ye gods, he was right:

    if you google "maτh j0b rum0r wiki,"
    this blog is hit #6!
    (rather, a previous post about the rumor wiki.)

this does not bode well;
soon, here there may be trolls ..!   \:

"tales from the road" (conference day: 2.5 of 3)

i always feel guilty whenever i leave early from a conference.

it's like leaving a party early, which doesn't mean anything. for the sensitive host, however, it could indicate that the participant has better things to do and is willing to abandon his friends in favor to do them.

    then again, i do have a thesis to finish;
    that's pretty important.

still, guilt persists. \:

---

i wasn't the first to leave this last conference, though. a friend of mine (who knows who s/he is, and will remain unnamed) left first for the AMS Sectional this weekend @ NYU.

looking now at the special session for Isoperimetic Problems & PDE, i can see why.

it does look very interesting!

so if you're reading this, friend, don't feel guilty:
i'd have done the same thing, if my thesis were finished, too! (;

"tales from the road" (conference day: 2 of 3)

yes, i lifted the title from the ongoing series from ph.d comics. i remember being excited about the first mathematical conferences i attended, and at some point i became blasé about them.

i blame this, however, on having attended too many conferences as a passive participant: quite often i was neither a speaker nor collaborating with friends.

i think that will change now.

this past conference was a bit of fun, catching up and talking math with friends and familiar faces. so over the next few days i'll rant and ramble about some thoughts i had, but in no particular order of days.

this will explain why there was no "(conference day: 1 of 3)" post, yet. i might write one later.

at any rate, my first thoughts:

---

1. it seems like everyone who reads this blog (and who knows me personally) has their own story about how they stumbled upon it. i've always preferred that people find this archive of rants by their own accord and not by my advertising it as good reading ..
   
   .. which it isn't. it's not a bad way to waste time. then again, i could recommend better wastes of time than this! q:
   
   at any rate, i like the stories of discovery, so this website will remain unadvertised for a very long time.
   
   
2. i'd like to wish good luck to all my friends who are on the market this year and have not heard from schools yet. being new to all of this, i don't know what to say, except that it will work out.
   
   that, and it's still early.
   don't let the rumor wiki dismay you!
   
   
3. this morning (day 2 of 3) i thought that there would be coffee at the conference and resolved to have one before the first talk.
   
   while brushing my teeth in the hotel room, i stared longingly at the mini-coffeemaker, but resisted.
   
   i walked past a coffee urn in the hotel lobby. then i retraced my steps, stared carefully at it, slowly raised my hand towards it .. but then jerked it away and walked past the urn again.
   
   over breakfast at a diner, i chose against having any, in favor of conference coffee.
   
   and once we made it to the conference building, i looked at the tables outside of the lecture room: plain white tablecloths ..
   
   .. no coffee. full of breakfast, no caffeine, little sleep ..
   arghhhhhhhhh. this can't be happening ..
   
   .. but of course, it did. it wasn't until midway into the second talk that i could keep my eyes open for longer than a minute without closing them and drifting off.
   
   [sigh]
   hence: a lesson learned.
   don't fight it: drink coffee when you can!

the new blood.

recruitment weekend here in ann arbor is an Event.

prospective grad students come from all over the states to visit our department, because the ball's in their court. they come to have a careful look, in order to decide whether this will be their ph.d. experience after all.

---

as a prospective i enjoyed that weekend. a friend of mine and i were both accepted and traveled together, which i suppose is partly unfair. the point is to meet new people and fellow "prospies," which R and i did.

then again, i remember:

* playing quite a few games of table tennis,

* sitting in on a first-year algebra class; it was just to know how hardcore these guys were, with their algebra; it wasn't much, but i scared easily then.

* sneaking out to have a beer before the event-sponsored dinner;

* working on a problem set at the corner coffeehouse, while waiting for the airport shuttle. (that was before it became an espresso royale.)

---

four years ago, i was a first-year and talked about my immediate experiences, which is what a prospy should know. it was strange, though, meeting my successors, and i think i made too much of it. i don't think i was very helpful.

three years ago, i was a second year and told the prospies about a more long-term view of grad school -- that there was life after quals, and that there would be research and the frustrations following research .. but not to worry. things have a way of working out.

two years ago and one year ago, i stopped recalled my memories and talked to the prospies about grad school in general. they looked younger than ever, and someone had to give them advice regardless of where they will go for a ph.d.

since you're going to grad school anyway, watch out for this and that. don't worry about exams and class requirements and whatnot; there will always be something else to "hurry" about and you might as well enjoy yourself and be well-rested.

quals will frustrate you, but you'll get past them; you won't understand now, but one day you will. you will find an advisor, even if you don't know what you want to work on now or a year or two from now. it will work out.

---

now.

now, i can't remember the subtleties of my experiences anymore. all i remember are the frustrations and the worries, the pleasant yet unnerving surprise that i averted disaster again, somehow ..

i remember this past summer, this past fall, the recent winter.

i remember the advisor: hearing the bad news, seeing him unwell, hoping and believing but working feverishly in spite of my hope ..

i remember october thirtieth,
and i remember early december.


i'm the wrong person to talk to a prospective student.

i don't care if s/he's an analyst, even a metric analyst. heck, it wouldn't matter if s/he told me that s/he loves the geometry of the heisenberg group and currently thinking about geometric measure theory. i'd be impressed and surprised, but nonetheless ..

.. it's hard enough to keep my act together; some days i wonder if i'll really pull it off. i don't think i'm capable of advising others -- kids so young, at that -- of whether they will be successful here in this place, this town, this school, this mathematical community, is right for them.

i'm leaving soon. i'll be nostalgic and reflective, passive. they don't need to hear history. they need facts and current states of affairs. they don't need to hear from me.


besides, i'm visiting colleagues and friends in pittsburgh. happy coincidence: there's a conference and the list of speakers and participants are my people. (:

reading & name-dropping.

life will surprise you, and so will mathematics. sometimes the least likely methods become convenient and useful.

for example, i never thought that i'd ever browse through J. Milnor's paper about smooth structures on exotic spheres.

at the time ..2 years ago?.. it was relevant to my work. to understand a few of those six pages that Milnor wrote (which i still don't fully or mostly understand, to be honest) it took a few months of reading about differential geometry and re-reading several chapters from differential topology) by M. Hirsch.

speaking of which, the Hirsch book is quite good. i'd recommend it to anyone.

i never thought that the banach-alaoglu theorem would be so useful in my current work, and i never thought i'd ever need to learn about the weak-* operator topology for linear maps between dual Banach spaces.

now, to the point:

today i browsed through an article i found on JSTOR. it's J. Nash's paper on isometric embeddings of smooth manifolds.

i never thought i would read anything that Nash has written. i don't know why. maybe the film made him larger than life and reasonably handsome (if you're a fan of russell crowe, that is) and i forgot that he's a mathematician and he writes papers just like any other mathematician active in research.

[shrugs]

at any rate, it's back to work for me, and i have to find a different paper. apparently the nash paper doesn't have the result i want. q:

added @ 15:15: never mind. i don't understand basic logic, and there wasn't a reason to think about isometric imbeddings at all.

future event.

wow. the advisor's memorial conference looks to be an impressive event. all sorts of people will be attending, including many "famous" people in our little part of the mathematics universe.

i should really submit my title/abstract soon.
i keep forgetting.

also, giving a talk in that forum worries me. with an audience like that, now my talk has to be good! \:

---

added @ 15:44: i don't know what it is about my office. why am i so much more productive when i'm not working there?

added @ 16:30: it's also quite useful to have a pad of paper ready, even while typing/LaTeXing. on a conventional laptop, i find it hard to 'ad-lib' when working out a proof of something that i want to add to the file.

for me, to do math essentially means to do math on paper, or say, on a blackboard.

writing woes.

at a party, it once happened that an acquaintance of mine asked me the usual grad student greeting: "how's the work going?"

without really thinking about it, i said, "i feel like i'm a fireman, trapped in a room full of pyromaniacs."

he looked alarmed, and then i said that i didn't mean it literally. he relaxed a bit, after that.

i suspect he thought that i was accusing him of pyromania.

---

anyways, the writing is going that way. the bulk of the math has been LaTeXed, but it might as well be a laundry list of lemmas, remarks, theorems. it's unreadable.

those little paragraphs for explanation, intuition, and flow are fine, but not when you have to write several dozen of them.

also, i keep running into the vicious circle of

1. typing up a fact, then the proof,
   
2. re-reading it and finding it distasteful,
   
3. then wondering if i can improve it ..
   
4. .. and after an undisclosed amount of time, realizing that i neither know whether it's possible, nor whether i should pursue it or give up and write something i know but unsatisfactory and probably tautological.
   

argh. i'm making much of this, i know. better just to write and finish something, and finally move to the introduction.

time's running out.
i've known that for a while.

in which i offer advice on how to live unwell, but efficiently!

in my graduate career i've had plenty of ups and downs, made mistakes of all sorts, and acquired timely strokes of luck. throughout all of this, i've persisted in giving all sorts of advice to younger students ..

.. sometimes solicited, but likely, often not.

one learns little lessons in how to maintain the frugal, erratic lifestyle of the american math grad student.

---

for example, some friends and i had just finished playing basketball at the university gym. one of them says, "oh man. i haven't eaten for 20-22 hours!"

i asked him immediately, "do you have to stay up tonight? work to do?" then all of us laugh at the absurdity of such a question, so i continue:

"whatever you do, don't eat a full meal now. have a banana or something small. if you eat something substantial now, the blood will concentrate in your stomach in efforts to digest, and you'll start to nod off from a lack of blood in the brain. did you get any sleep last night?"

he shakes his head.

"then you'll certainly crash after eating. eat small portions, drink a little coffee, stay hydrated, and you'll be fine."

"huh," he thought. "good point."

---

i feel like i'm teaching others how to ruin slightly their lives. also, that last part sounded a little too much like a dialogue that plato would write!