advice from a friend, reincarnated.

my friend kWild [1] once told me his strategy, when packing luggage for trips:

    first i pack what i think i need,
    then i get rid of half of it.

i think i see what my friday talk look like,
and it looks to be very long and boring in its nascent form.

    so i think the next few days will be spent realising it,
    paring it down to comfortable essentials,
    and making it more visual than wordy.

    after all, pictures are a mathematician's best friends!

[1] to kWild: you may not like the nickname, but i do. q:

waiting for the story to unfold.

i've never written a novel. i don't think i ever will.

when i dabbled in creative writing, i would write short stories and little poems, but i never dared to write a novel. it's an issue of scope, and this issue follows my mathematical writing, even now.

---

the thesis is written. up to the corrections of my committee, it's done.

as for the defense talk, it's still in the works. i've written a few things down already, but i don't have a sense of the whole thing yet. it's a bad habit of mine, but it persists:

if i can't see the whole thing, then i can't write out a draft. [1]

i liken this to writing a rock-&-roll song:

if i don't have a good feeling for the rhythm and the beat, then it feels pointless to me to write down the lyrics ..

.. er. not that i write music. put another way:

even if you know how a good joke starts,
even if you remember the punchline,
it still doesn't mean that you are ready to tell it;

you have to get the middle part right.

---

it will work out. maybe i'll "see" it and write a draft tonight. admittedly, i'm curious what it will look like.

[1] writing the thesis was no different than writing a short story, and likely the talk will be no different. at any rate, this is why:

i wrote one chapter first, the main result,
then i realised that it led to another chapter.
for that first written chapter to make sense,
it took a few other chapters to explain.

put one way: it doesn't feel like i wrote a thesis. it just happened.

i wrote one chapter, kin to a short story,
then i wrote a sequel,
and then i wrote six prequels.

students and their families: it's complicated.

today i didn't do any work, really. i was too busy printing things out and making sure that the graduate school will let me have a defense next week.

i was also a little busy "graduating."

there was a ceremony in the mathematics department, where many undergraduates -- most of them, newly graduated -- arrived with their parents and siblings.

i was invited and also attended; a postdoc friend was curious and joined me. i even received a graduation certificate, and i was more pleased when i read the wording:

".. on his expected graduation date of ______."

that was something i appreciated;
you can't have mathematicians without some rigor or precision. q:

---

in this ceremony they gave a little talk about mathematical modeling in applied maths, but it was more for fifteen minutes and for some semblance of depth.

for most of the time, they did what the families wanted: they gave many awards to deserving students and said fine things about them.

i realised, then, that these are important events.

when you're a mathematician [1] for most of the day and most of the year, little human things slip from mind.

for example, we are not just ourselves, but we are our families.

i would say that mathematics is humbling, and more so in the graduate level than the undergraduate. that changes perspective between us and non-mathematicians.

as mathematicians, we often see things that we don't understand. perhaps we will, with enough time and effort, but we quickly realise that things don't come easily. there may no longer be right answers or wrong answers. there might not be any answers at all.

years of discipline and hard work pay off. on the other hand, months of unused work and failed ideas are sloughed to the side.

so perhaps it's not anything mathematical after all. maybe it's just me: i think of all the things i haven't done and couldn't do. i think of lost time, and things that might have been or never could be.

the ph.d. is near, too, and i wonder how i got here, already this close. maybe i will finish, as everyone assures me.

---

i know that my family would say otherwise. let's forget who is right and who is wrong; they will say that

of course he will succeed;
we knew all along.

how could it be otherwise?

they say such things without knowing how hard it is. somehow, our families know us. they will say what they say because they can. because we do know, because we see the risks and the difficulties, we can't .. or won't.

when [2] they are proven right, then there needs a forum, a celebration for family to say so. it is not gloating; it is a happy thing.


despite this, i avoid celebrations and instead, i reminisce. i worry about things now past and beyond worry. it's how i am.

i'm sure that it annoys my family to no end. \:

---

[1] not all mathematicians, of course. just inept ones, like me. \:

[2] or if.

enough writing; soon, talking.

there's one chapter in my thesis which i hate editing. it's not that the results are bad. in fact, my main results are in that chapter.

but it's thirty-five pages long;
whenever i edit it, it takes an eternity to finish.

---

i'm done editing: enough! there's a week and a day left before i defend.

it's time to write the talk. i've given plenty of lackluster talks, and it would be nice to finish a graduate career by giving a good one.

i have no illusions:
there are a lot of weaknesses in the writing of my thesis.

for now, though, i'll let my committee worry about them, and i'll get back to the revisions after this minor public spectacle called a defense.

[deep breath]

for most of these years, the only reason why i've stopped doing one mathematical task was because i had to start another. nothing has ever felt "finished."

sometimes you have to realize that you're becoming a little obsessive and a little crazy, and make a firm decision.

mimicry forthcoming.

another day, another defense to attend. today my friend diane defended very well, and i think i will plagiarise the presentation skills of hers, and others.

among other things,

i must remember to say things well,
write what is necessary,
and draw many illustrations.

---

there is some nontrivial part of me that enjoys drawing diagrams. i credit this for not having attended kindergarten as a child.

no matter how many people assure me that it is of little consequence,
i will always remain curious:

finger-painting? half-days?
it doesn't sound like a bad life. q:

work & play (from the onion)

wow. if you replace "botany" with "mathematics," then this becomes a very real phenomenon in my life:

"Botanists Vow Not To Discuss Botany During After-Work Drinks"
(from the onion)

there are several schools of thought on this. for example, some of us like dessert and maths, while others do prefer alcohol and maths .. q:

it's the home stretch and i'm worn out.

every time i think my thesis is ready and readable, i send the latest version to my committee chair.

inevitably, the next morning i see one consistent inconsistency in terminology, or an error in a proof or two (which is easily fixed). by the afternoon, on every other page there is something to fix.

the wheel turns once more, for more of the same. i want to say that it's not futile. admittedly, i'm somewhat convinced but not fully so.

i think i'm tired. around east hall, nobody really looks well-rested.

that might be me, though:
my eyes are tired, and that may color my vision.

---

there is a week and a half before the defense, and i still don't feel that my thesis is really ready. i feel late and behind schedule .. but whose schedule?

maybe i should say that this wasn't how i planned this year to go.

the thing is, i'm not that busy, but i expect to be busy soon. there is the defense and there will be corrections -- lots of them, i fear -- and then there will be conferences -- talks to write and talks to give.

then there are papers to write, after that;
don't i have a nervous breakdown scheduled, at some point?

[re-reads]

i'm pretty sure that i'm joking ..
but again, i'm not fully convinced.

---

i went to a fine defense yesterday: my friend john gave a good, motivating discussion on what he proved in quasiconformal geometry.

tomorrow i'll attend another friend's defense: diane'll talk about group splittings and geometric group theory.

next week tuesday, my old flatmate josé will talk about cohomology and K-theory.

then it will be my turn.

oh no. am i really an analyst anymore?

the day before i sent my thesis to the committee, i had endeavored to erase the word "rank" from all but three pages of it [1].

evidently i missed a few spots.
so today i'm doing erasing and paraphrasing.

also, i feel like i'm violating some unspoken principles which many analysts share, as well as sabotaging any readership which my thesis (or the subsequent paper(s)) may ever claim.

i mean, words like "module" and "free module" [2] and "rank" and "generator" and "homomorphism" will scare the analysts away.

maybe it would help if i add a disclaimer such as 'no, really: it's like a vector space. honest!'

on the other hand, "measure" and "Lipschitz function" and "weak-star convergence" and "rectifiability" will scare the algebraists. i can live with that, actually.

so if one believes in a two-party system for mathematics, then i am done for. fortunately, i do not! q:

---

[1] to explain, one page is to explain why "rank" is not a good word to use, and two more pages to remind the reader later (in case they forget).

[2] as far as i know, "free module" appears on one page as a necessary evil.

a rough count.

i don't know how my committee will do it.

today i started reading/editing the latest version of my thesis again, and by chapter 3 (of 8) i was ready to put it down.

so yes: i even bored myself!

as an idle curiosity (and an excuse so that i could flip the thesis pages rapidly), i was curious as to how many of each construct i had. here is the count, for now.

lemmas: 30, at least 8 of which are not mine;
theorems: 30, at least 14.5 of which are not mine;
corollaries: 14
propositions: 3, at least 2 of which are not mine;

conjectures: 1, which is clearly not mine;

definitions: 15
remarks: 18
examples: 8
figures: 0, though they would make it easier for readers.

when i say that a result is not mine, then either it has been fully proven by someone else, or it is folklore. so perhaps i should have said "partially mine" for the rest of them!

also, i didn't bother with figuring out who owns a definition, and i forgot to count "claims" (which i put in the body of proofs, in order to make them more readable).

---

curiously enough, there are no official "definitions" in chapters I and II. granted, chapter I is the introduction, but still ..

why i am paranoid: stories of drama.

when i first started to write a thesis (..which wasn't so long ago..) i had two main fears:

1. i (or someone else) would spot an error or conjure up a counter-example to one of my main theorems. the writeup would then become a meaningless list of latex symbols, the outcome of wasted months.
   
   
2. i (or again, someone else) would discover that i've been dense all along, and there are trivial/two-line proof to all of my theorems.

these fears are hard to shake off, but i like to think that this is not exactly paranoia. call it experience.

1. 13 or 14 months ago, i thought i had proven something great, and from this one result you could get so many interesting consequences.
   
   11 months ago, we found an error in my argument. we were never able to patch it explicitly, and i thought i'd have to move to a third thesis project and learn a new theory all over again.
   
   since then, you could say that my recent work has been some sort of professional vindication. as it happened, that project worked out, but unexpectedly so [0].
   
   
2. when i was applying for jobs last fall, i had no papers or preprints about my current work (..i still don't, to this day..) and in lieu of such materials, i sent a research statement to my letter-writers.
   
   one day in that fall, my supervisor and i were talking, and he mentioned that one letter-writer called him and asked him something: "i don't understand. why don't you just do <this>?"
   
   the supervisor then proceeds to tell me what <this> was. i opened my mouth a few times, then promptly shut it and thought a little more. huh. that does work. later on, the other letter-writer pointed out the same <this>.
   
   i still feel like an idiot for not having seen it. then again, if not for that suggestion, the thesis would probably be 9 to 10 chapters long, and not 8. so i'm not complaining.

just earlier i was thinking about one particular claim that should be true, but doesn't quite fit into other techniques of proof. jotting a few things down, suddenly my blood ran cold.

i sped to my bedroom, fished out my bookbag and a copy of my thesis draft from the bookbag, and leafed frantically.

i read, and re-read, and sighed;
thank god. i assumed N+1, not N.

as the saying goes (in translation, anyway):

"after you've been bitten by a snake,
even coils of rope will make you nervous."

it's going to be a nervous few weeks!

---

[0] 10 months ago, i broke a promise or two [1] and started thinking about that problem again. nothing worked: that is, none of my old ideas or new variants of those ideas.

after a while, i traced my reasons of argument to their core motivations in 1-dimensional examples. i wrote down "assume that _____" quite often and at the time, i thought that these were wholly unreasonable assumptions.

i wrote them down anyway.

it seemed like i would run out of time: 9 months ago, i flew across the atlantic and attended a few conferences. one night in england and after one too many at a local pub, i stumbled to my room and decided something.

all right: i'm going to do the most naive thing possible. this is NOT going to work, but it doesn't matter anymore. i want to know WHY.

an hour later, i couldn't figure out why it didn't "not work." deciding that it was the ale, i slept fitfully. the next conference day, during the first coffee break, i re-read what i wrote and couldn't find the breaking point. then i began to suspect something.

over two weeks and three conferences, among hyperactive social mathematicians in collaboration and good cheer, i became an antisocial ghost. i was constantly suspicious of my work and constantly expecting to be disappointed when i found the flaw.

but i never did.

from that one naive idea that i entertained, out of desperation, there appeared something interesting enough to make a thesis.


[1] that's a story for another day. i might tell it sometime.

enough typing. now: paper.

i don't plan to have my laptop on tonight. up to corrupted files through email, the thesis is now in the hands of my committee.

it's now time for comments and criticism. i have a paper copy and will add my own red ink to the pool. as for reasons why,

1. perhaps that will be the easiest way to understand the comments of others when i receive them;
   
   
2. as of now, i feel that all my editing has been local. i've worried about this-or-that section of that-or-this chapter. i've asked myself if this theorem makes sense and if its proof is correct and/or clear.
   
   as for the whole, maybe it is a monster and there are no "morals" in it, only disparate bits. it wouldn't be what i want, because there are overarching principles in this work.
   
   believe me: it's not pages and pages of cleverness.
   i'm not that good of a mathematician!

at any rate, the endgame is near. the defense is in 2 1/2 weeks, with deadlines before and after.

also, i have talk abstracts due and travels to plan. it should be an interesting 5-6 weeks ..

(well, a boy can dream, can't he?)

when the thesis is done, i will work only 8-hour days. i will also take a day off, every week. this will not be so hard, because it is difficult to be productive during the summertime.

(i strongly suspect that i alread work 8-hour days, probably shorter,
but let's not dwell on this.)


when the thesis is done, i will set aside some 2 or 3 weeks for holiday. this will be a time of great confusion.

you see, the cause will be "what do i do now?"
instead of the usual "why doesn't my proof work?"
or "did i write this? this is cr@p!"


when the thesis is done, i will kill another small tree, print out many papers and preprints, and start reading them. i will learn to be curious again, instead of tired and apathetic.


when the thesis is done, i will start talking math with others again, and this will be mathematics that have little or nothing to do with my thesis. i will branch out and learn new things in the easiest way possible:

make people teach them to me,
and bug them with questions until i understand.

dear god. this xkcd comic is not so far from the truth.

between thesis and book; more meta-blogging.

it's happening again.

as i read my thesis, each theorem sounds all right, but for some of them i wonder if something more general or stronger is true. the thesis is still intact and i won't do any major overhaul, but it's tempting ..

this morning and now, among other errands i've been leafing through weaver's book, called lipschitz algebras. i'm thinking about how things fit together and what i could add to his picture.

on an unrelated note, about books:

i have already planned that as a postdoc, i'll wait until my second paycheck before buying books that i've been meaning to acquire. i think mattila's book will be one of them, probably weaver's, and probably a gromov book. i don't know about evans and gariepy, but it's tempting.

then again, that one is expensive -- good, but expensive, and nobody is willing to part with his/her copy without good reason. it is perpetually checked out of our library.

---

also, i realise that some of you have lately arrived here from google search, partly because of my unintentional "name dropping." occasionally i list preprints or results of others that i find interesting, and that must cause some annoyance for you. sorry!

i won't say which google searches, though. my last blog post about google searches backfired, and now this blog is firmly entrenched among those hits. like many, i flatter easily and i appreciate new readers. first and foremost, however, this is my personal page of academic rants.

i wouldn't know what to do with myself if this blog became "cool." i'd probably stop saying interesting things.

if you're really that curious and want to know, then look at my surveillance data here and on the left side bar, click on "how do visitors come to my site."

no offense to algebraists, but ..

.. sometimes abstract algebra can be very, very annoying, including linear algebra.

      i now have a deep distrust of modules,
      unless they are vector spaces, of course.

---

ADDENDUM (7:35 PM). the desire to finish a thesis will make you do strange and questionable things. here are two examples.

1. turning down a dinner invitation, in order to make corrections to your thesis draft;
   
2. reading hungerford's algebra as a reference ..just in case.. even though your thesis topic consists of metric spaces and geometric measure theory.

dazed and confused, as maths go by.

my mind felt elsewhere, today. i was up late typesetting a thesis that hasn't been carefully read yet, and i wonder if i was jumping the gun.

i don't know if i slept any, last night. when i got up this morning i felt like i had just closed my eyes for a long time, still awake and waiting for the night to pass. it wouldn't do to work all night; better to wait until morning.

i wonder if it was worth the wait.

when i was typesetting this morning, i felt like a zombie and before i knew it, the second cup of coffee was gone and i needed a third.

i went without it. it made for a very difficult chapter to go through.

---

the season of thesis defenses has begun. i sat in on a friend's defense in algebraic geometry today. for five minutes i wondered what spec of a ring was -- it seems entry-level knowledge for these guys -- and felt out of place.

i play basketball with the speaker on saturdays. we're both mathematicians and i had no clue what he's talking about. everyone else seems to know his language. that's why they're there, of course; they're his colleagues.

i didn't feel stupid .. just out of place.

for the other 45 minutes, i leaned against the wall. if you haven't slept for a while, then concrete begins to feel sturdy and comfortable. to my credit, i never drowsed.

instead i drew in my spiral notebook, and convinced myself again that my idea to solve a conjecture is silly: unambiguously silly.

then i clapped when everyone was clapping. i left the room to let the committee decide -- they passed him -- and i felt distant again, as they left for a little champagne and i to my office and writing my acknowledgments.

---

later that day i listened to two hours of teichmüller theory, in a study seminar. this is a more sensible language for me, but i still have trouble.

i have to remind myself that the elements in Teich(S) are not homeomorphisms, but isotopy classes of homeo's. i wonder why it makes sense that an element in the modular group(?) is a mapping and not a class, and how it can act on an element of Teich(S).

two hmms later, i realize that post-composition is not a big deal, and then i have to see what i missed when i was busy catching up.

huh. what is an irreducible map again?
does it have anything to do with irreducible representations, in algebra?

she [the speaker] hasn't mentioned PSL₂(R) at all.
i must be wrong;
so what could irreducible mean?

all the while that silly idea comes back, and then an older, still silly idea comes to mind. it transforms slightly and i cannot think it through -- not while listening to teichmüller theory, at least.

i can't mentally draw anymore.
not when sleep-deprived, at least.

this many hours later, the newly transformed idea has merit. i see the weak part of the argument and i'm too tired to decide right now.

i should be writing instead, so that the committee has time to read the tome that i'm preparing for them.

i should be sleeping, otherwise tomorrow will be the same.

last licks, some thoughts.

now the introduction is tolerable. at the very least, i sent it to a few friends; some actually responded and i sensed no diplomacy between their words.

i'm now typesetting and making sure the chapters fit the introduction, and vice versa. this university template is slightly annoying;

too many widows and orphans, i say.

in fixing the typesetting, the page count dropped from 132 to 126 pages.
it's not done yet, either: i'm only on page 82!

then there are acknowledgments and a dedication. for once, i know exactly how to write them.



most days i feel as if i started this thing too late in the game. everyone i know who's defending this year has finished their writing and submitted their thesis.

more than that, it seems that in this field, it's good to write early: papers as well as a thesis.

---

as long as i'm on the subject, i might as well advertise a friend's preprint from the arXiv. if anything, mentioning it means that i'll be more likely it read it soon!

Geodesic manifolds with a transitive subset of smooth biLipschitz maps
Authors: Enrico Le Donne - [link]

excerpt: ".. Our main result is the following. Let X = G/H be a homogeneous space of a Lie group G, and let d be a geodesic distance on X inducing the same topology. Suppose there exists a subgroup G_S of G which acts transitively on X, such that each element g in G_S induces a locally biLipschitz homeomorphism of the metric space (X,d). Then the metric is locally biLipschitz equivalent to a sub-Riemannian metric. Any such metric is defined by a bracket generating G_S-invariant sub-bundle of the tangent bundle."

so cheers to enrico: not yet on the market, and two preprints under his belt!

go baby, go! q:

i'm finally putting my thesis into report format, under the rackham graduate school's guidelines and format. every so often i have to change the BibTeX file, because the references are slightly different in each chapter.

each time that i do so, it feels like pulling a slot machine or throwing dice in craps:

first it's 86 warnings;
then 54 warnings,
then 10 warnings,
then 8,
still 8,

come on, lucky number seven ..
and still 8 ..

right.
i must have a wrong reference or something.

EPILOGUE (12:03AM): no errors or warnings,
but 14 bad boxes, 132 pages, 46 references.

thesis writing is not eco-friendly!

every time i print out a new version of the introduction, it reads better ..which is good.. but i immediately spot a dozen errors and improvements that i can readily fix on the computer.

after enough fixes and additions, i can no longer stand to read DVI or LaTeX on the screen. i can no longer see errors, and nothing seems much different from before. on the other hand, paper is more intuitive.

i don't know why:
text should be text, right?

i still like paper much better. for example, pen marks look much better on paper than on LCD screens. i'm keen on flipping pages, back and forth: so easy! on the other hand, one must be expert at scrolling up/down to find one's way around screen text ..

.. but then again, word search options on computers are quite nice.

---

at any rate, i meant to write about how i am become a minor eco-terrorist, by printing out so many pages. i recycle them, of course, but the guilt remains.

if there's one thing i don't need, it's more guilt. the thesis is already behind schedule (read: my schedule and plans) and every day is one more failure.

never mind: the grass isn't so green.

i don't know how people can concentrate for so long on the same task. it's not that i hate thesis writing, but i've done so much of it in such a short time [1] that i've lost all enjoyment of writing that i once had.

last night i finally did it: i wrote a complete introduction. it's not very good and it needs work. however, it is something that i can properly criticize, instead of staring at empty LaTeX whitespace and thinking,

      "what if i wrote this? would it work?
      no, maybe i should write that instead ..
      .. wait. but then i would also have to write that other thing,
      so never mind: okay, should i write this?"

in other words, i've done the equivalent of shutting myself up, by way of saying

      "it doesn't matter! just write something! anything!"

so i did.

before 11pm i wrote something which fit in the outline that i wanted for an introduction. then i printed it out and stapled it to the front of a printout of the remaining sections.

      wow. a complete draft ..
      .. wait; come on. this is a complete BUT unedited draft.
      there's much work left to do ..

however, this morning i didn't do it. i woke up late and thought about some new ideas instead. i had this silly idea that i thought could prove some conjecture, and only now do i realize that yes, it is silly.

so remember when i said that i missed doing new maths? well, i have my wish now, and some more. now i recall how frustrating it can be, to see an idea fail.

ah, well. maybe it's hopeless, maybe it isn't.

it's not a complete failure, but i've thought as much as i wanted to think about it. despite the frustration, i did learn why the problem is hard.

now there's no more temptation.
now i can get back to editing without any "what ifs."

[1] technically, that's untrue. more accurately, i've worried and fretted about it a lot in a very short time. whether or not i've done very much is a highly speculative matter.


EDIT (11:39PM) : i was right. my introduction isn't very good. however, it is getting better as we speak.

the grass is ALWAYS greener.

i don't know what it is about writing which makes it so difficult for me.

maybe i have some sort of abstract "attention deficit disorder" or suffer from constant mental wanderlust. maybe i'm utterly susceptible to self-reverse psychology!

late last night, i thought to write down something, anything that i could later throw out or edit into something to add to an introduction.

i was thinking through one sentence and one particular issue -- whether or not to discuss how our proofs are limited by our tools and what is currently known -- and then it occurred to me ..

.. wait. is that really a limitation?
what if you do something like this ..?
.. so i embarked on another research idea.

as usual, it lasted long enough that there might be some promise to the idea. however, there's no time and i'm not yet clever enough to resolve the issue.

maybe this is what it means to be a "grown-up" -- being confronted with choices, one chooses the responsible option and governs one's impulses in order to be purposeful.

at any rate, enough: i must write an introduction now. i have deadlines.

i should also stop blogging so often. as much as i like to rant, there is work to do!

is he blogging about his blog .. again?

today i wrote the easy part of the introduction (to my thesis). that's the "this paper is organised as follows" part.

i still felt somewhat proud of myself, though.
as for things NOT to be proud of ..

---

i think my curiosity has gotten the better of me. in one of my recent blog posts -- specifically, this one -- i admitted to conducting surveillance about you readers. i even made a little map ..

(courtesy of google: here)

.. of places in the world where, for some reason, someone has visited this blog (as of 20 march '08). i became excited whenever i accounted a new place and diligently added it to the map, but then it occurred to me ..

i don't know anyone from there.
how did they find this blog, then?

so i looked deeper into the statistics and realised something. i think most of you have come here by accident. having procrastinated a little, i think i have reverse-engineered the right Google searches will will lead you here, unawares!

1. "maτh j0bs rum0r wiki" and "mathjobs rumors" - the one time i make an idle opinion, it lands me to hits #3 and #2 on google. judging from the keywords, most of you have come around by such a search!
   
   i can't be the only blogger with an opinion on the subject, but happily my opinion is a non-controversial (hence pointless) one and it probably won't get me in any trouble.
   
   
2. ""castles made of $and" analysis" [1] - my love of jimi hendrix has led me astray, i fear. i borrowed the song title for a really old post of mine. somewhere, out there, a jimi hendrix fan is probably seething, because s/he wanted to read about jimi's motivation for writing this song, and instead s/he encounters .. a math blog?!?
   
   
3. ""rie$z repre$entation the0rem" blog" - back in 2006, i posted some thoughts about how measures come out of nowhere when one thinks about the space of continuous functions on the unit interval [0,1] as a normed linear space (with respect to the max-norm).
   
   i am glad, however, that it takes the second page of hits before you find anything related to this blog. if you're going to discuss riesz representation, then you should at least get some actual mathematics first!
   
   
4. "blog "weak $tar"" - this is a rather recent post, actually. i had a question about LaTeX and how to represent weak-* convergence with an arrow.
   
   what makes me laugh about this search is that of all the hits to precede mine, one is a blog about Star Wars toys and on the search it describes this:
   
   "But yes, I agree that the Phantom Menance was a weak Star Wars movie."
   
   nice one! q: another concerns baseball cards, but not being terribly interested in that sort of thing, i'll let you judge the site for yourself.
   
   
5. "CAT, Topono90v" - i could swear that i've never discussed CAT(k) spaces in this blog, because i'm not that sort of geometer (see the wiki), but hit #3 is still this blog, for some reason.
   
   as it turns out, my recollection was wrong: i forgot that in that post i plagiarised m. kapovich.

other searches include "mental inertia" and "mathematics holidays," but that is enough shameless self-promotion for me. let me apologize for those of you who i lured here by false pretenses, and i hope you have not wasted too much of your time here.

in order to confirm my guesses about this, i added a little poll (see sidebar) for additional data. i ask you: fill it out only once!

[1] yes, the quotation marks are included in the Google search. it causes the search to hunt for that explicit string of letters, including the spaces.

almost the end; time for .. a beginning?!?

it always makes me uneasy, when i post this often.

it either means that i've been thinking too much about maths or that i haven't been holding enough conversations with real people in physical reality ... or that i've been spending too many nights in the office:

wireless internet + procrastination + plenty of opinions → blog post.

---

today i read the printout of my thesis and started making corrections. after a while i was starting to lose patience with it, which is strange ..

.. after all, i wrote it.

but i'm done now .. at least i've done as much as i want to do with it. perhaps the saying is true: one is never finished with a mathematics paper; after a while, one just gives up.

now the supervisor can lose his patience with it. i've sent it off, and now it's time to write an introduction.

---

i had in mind to take a quasi-day-off from writing of any sort. you see, i don't know how to write an introduction, so i plan to spend a morning or afternoon leafing through the theses of others and seeing how theirs are like.

strange. this seems the way of all things i write, for the first time:

• i needed to see what a cover letter looked like before i drafted one of my own, for jobs.
  
  
• i needed to realise that my first research statement was awful before i could write a tolerable one, and that happened only after i browsed through the statements of others.
  
  
• i suspect i'll have to do the same, the first time a student will ask me for a letter of recommendation.

perhaps it's also too late for this sort of thing, but i also had in mind to read some literature on how to write mathematics. i know that there's an essay/paper by halmos, but to those of you out there:

can you recommend good reading, about how to write?