in which, not being well-read, i am sidetracked by reading.

.. 68 references and counting,

which means i've reading reviews, checking up on facts,
and occasionally hunting down and browsing through articles.

there's a lot i never learned.

---

i'm not a very well-read mathematician .. not by my own standards, at least. sometimes i wish i were born earlier, when the analysιs of metric spaces was in its true nascence or before.

this field follows a long history, from many traditions.

when i was a graduate student, it had already begun to take shape. subsequently one can now train a student in purely metric ways and avoid classical formulations altogether .. not that one should.

for example, in heιnonen's lectures on analysιs on metric spaces, the first discussion of capacιty (chapter 7) doesn't really do justice to the history. by this i mean that the "mod=cap" theorem feels tautological. the definitions make it so.

in contrast, at the time it required nontrivial efforts by gehrιng and zιemer to prove the "mod=cap" theorem in the classical setting. the point is that one had to construct a function with the right gradιent, not just an upper gradιent ..

.. never mind the rich geometry one can do with capacities. in some sense, they are the analytιc cousins of hausd0rff measures; you can even study rectifiabilιty of sets in terms of capacitιes.

i've been feeling the same way about many other topics, which puts me at an impasse:

1. there's no time for me to re-learn the past. there's two more years of postdoc left, and one more year before i fill out the job applications.
   
   
2. without some awareness of the past, and how some constructions came to be, i have that much less intuition with how to proceed, much less pose well-motivated problems.
   
   if you learn only axiomatic definitions, then how do you escape pseudo-problems arising from the continual manipulation of axioms?

---

oddly enough, i had meant to write this not to as an uneasy invective, but as something positive. what i really wanted to say was this:

the more i read about them,
the more i am impressed with euclιdean spaces. (-:

more entertainment, from math reviews.

mathematics can be a culture where we use "trivial" to dismiss anything we know how to prove. i never liked that word, to be honest.

some concepts are just hard to understand, at first, and some are just hard.

to quote the review of Gromoν's paper "Fιlling Rιemannian manιfolds" (1983) -

"This paper presents a wide investigation touching various aspects of geometry and contains numerous results.
      ..
The paper contains not only the proof of the inequality (1) itself but also new notions and approaches which allow the author to connect various important concepts and to give them new interpretations."

all well and good.
as for the last line, though,

"The paper is difficult to read."

sometimes you just have to admire honesty. (-:

stay up late enough, work hard enough, and you will see ghosts.

after back-&-forth debates on whether to add another section or project [1],
after making one section shorter, then longer, then another section longer,

i've finally made it to the crucial number: 15 pages.
somehow, i also accrued 54 or more references [ln(3)].

i'm not even sure if my thesis has that many references .. [2] but for the current task, most of these have been earned by recent, constant searches on mathscιnet, clicking on lists of references and reading article reviews.

---

at some point in the evening -- or night, or perhaps early morning, it doesn't matter -- i started reading one review, and i could swear that i had read it before. on the other hand, the terminology was too new to me, and the exposition had too many surprises for me to have seen them before.

it was just disarmingly familiar;
maybe i just needed sleep or coffee, or food,
and in their absence i wilted towards false thoughts.

nonetheless, i was consumed. i read on.

by the end, it made sense -- not the math, of course, that's too great a feat for a mind like mine -- but as for why i "remembered" ..



.. the advisor had written the review.


i had recognised him,
two paragraphs in.

odd, but fitting. even dead, he still finds a way to be helpful .. or at least to young, far less well-read researchers like me. (-:

---

[1] yes, i was arguing with myself. to my credit, however, i didn't make up separate voices for each side of the argument, nor acted them out with toy figurines. sometimes one must draw the line somewhere.

[ln(3)] as of last count, it was 54. it may still increase ..

[2] .. i just checked: 44 references, including one non-mathematical, so 43.

on competition (or: why i am absent from events, lately)

a month ago i was ready to register for a 10k race. the last one i ran would have been about 9 years ago, or so. even then, i didn't like my finishing time.

call me curious;
this year, i was willing to attempt the challenge.

the starting gun went off today, at 9am, but i didn't hear it.
i was at home, typing and pausing and re-typing.

---

every fall, the department sponsors a picnic in one of the city parks. for postdocs, the entry fee is $5, a nominal thing. i missed it last year.

from what i heard:

they supply the food,
they even splurge for the liquor license.

last week i told some friends and colleagues that i was going,
but as it happened, i lied.

i'm at home, typing and pausing and re-typing.

---

i know that the chances of my obtaining an N$F grant are slim, especially when you think about the competition.

yes, i've even accounted for "junior researchers" and within the area of analysιs.

just as in the case of community road races, i never win within my age group. there are always faster people.

i know that i don't look very appealing on paper. i need to change that, especially since the job search is only a year away.

---

at any rate, i'm still willing to try. it's making my life hell for a few weeks, but i'll still try. i'm even curious as to how far i'll get.

my work is frustrating, but i like it, and there's some worth in trying to explain why .. if only to an anonymous panel. if there is a good reason why not to like it, then maybe they'll tell me.

the stakes are low, and i'll make the gamble.

besides, if it weren't this, i'd probably be miserable about something else.

heck, 10k races aren't easy, either;
i always feel awful, afterwards.

more from ρaul 9raham: on writing.

maybe i've spent too many hours awake, typing away on an N$F grant proposal, but this recent essay of paul gr@ham struck a chord in me.

That's not even the worst danger. I think the goal of an essay should be to discover surprising things. That's my goal, at least. And most surprising means most different from what people currently believe. So writing to persuade and writing to discover are diametrically opposed. The more your conclusions disagree with readers' present beliefs, the more effort you'll have to expend on selling your ideas rather than having them. As you accelerate, this drag increases, till eventually you reach a point where 100% of your energy is devoted to overcoming it and you can't go any faster.

lately, i've been writing to persuade. specifically, i want the government to give me money. then again, i look at my writeup and i realise,

it looks too much like a paper or a lecture.

there's a bad habit of "polishing" a research article. as a general rule, technical writing is concise writing. i'm guilty of this. often i ask myself, even in casual conversations,

what is the best (read: most efficient) way to say this?

as a result, often reading a research article is like decoding, trying to figure out what the author was really thinking.

it's rare that someone writes in roughly the same order in which one discovers the proof of a theorem. that sort of exposition is left for talks and lectures.

if only temporary, une raison d'etre ..

this grant application writing has been among the busiest times in my life- the busiest i remember since the postdoc job search.

teaching .. that was always annoying, at first stressful,
but it wasn't busy- not this busy.

---

this is odd to say, but i think i'm going to miss this period of time. it gives my life an unparalleled purpose, even a superficial meaning.

it's like surviving, living only for revenge.
after that, one has to learn how to be a person again.

it's nice to be appreciated, sometimes.

i learn something new, every day. for instance, i just learned that today is national post-doc appreciation day.

then again, back in 2005, i could have enjoyed a full graduate student appreciation week.

come on.
was it worth defending that thesis, after all?

5 whole days .. imagine: i could have saved them up,
one for each year of grad school .. \:

[sighs]

oh well.
at least i make twice as much money as i did then. (;

last minute citations.

at this point, it wouldn't be unreasonable to switch the start page on my web browser to MathScιNet. apart from a few email checks, it's the first page i visit upon loading firefox.

as you can imagine, i'm deep into writing the research part of the N$F grant application, and there are a lot of sources to cite.

also, yes: i should have listened to everyone who warned me.
i should have started this on august 1st ..

a catchy title, but ..

i must have missed this arXiv preprint the first time:

Lιon and Man -- Can Both Win?
Authors: B. 8ollobás, I. Lεader, M. Waltεrs

my immediate thoughts:

1. i wonder if this has relevance to the sτochastic game approach to PDE. this could even be done on mεtric spaces!
   
   
2. velocιraptors would have been much cooler. q:
   

anyways, the associated abstract:

This paper is concerned with contιnuous-tιme pursuit and evasιon games. Typically, we have a lιon and a man in a metric space: they have the same speed, and the lιon wishes to catch the man while the man tries to evade capture. We are interested in questions of the following form: is it the case that exactly one of the man and the lιon has a winning strategy?

As we shall see, in a compact metric space at least one of the players has a winning strategy. We show that, perhaps surprisingly, there are examples in which both players have winning strategies. We also construct a metric space in which, for the game with two lιons versus one man, neither player has a winning strategy. We prove various other (positive and negative) related results, and pose some open problems.

"wait, wait .. don't tell me .."

odd. at the moment i cannot remember the exact definition of a currεnt, in the sense of Fεderer and Flemιng.

i suppose that's the risk of

1. always assuming that a currεnt has finite mass, and not remembering the general case;
   
   
2. having learned the theory of currenτs on meτric spaces first, instead of the classical theory.
   

the definition from this wiki seems reasonable, if a little vague. it's almost exactly the same as how one defines distrιbutions, which is pretty reasonable ..

---

i guess my memory is bad, that's all. next thing you know, i'll forget the definition of a manιfold.

as found on the arXiv: Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds (by Juha Heinonen & Stephen Keith)

i would never have expected any preprint of the advisor on the arXiv. from the way i remember him, it wasn't quite his style.

nevertheless, it was a pleasant surprise to see one:

Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds, by Juha Heinonen & Stephen Keith

Abstract: We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in Rⁿ. The condition is a Sobolev condition for a measurable coframe of flat 1-forms. In combination with an earlier work of D. Sullivan, our methods also yield an analytic characterization for smoothability of a Lipschitz manifold in terms of a Sobolev regularity for frames in a cotangent structure.

In the proofs, we exploit the duality between flat chains and flat forms, and recently established differential analysis on metric measure spaces. When specialized to Rⁿ, our result gives a kind of asymptotic and Lipschitz version of the measurable Riemann mapping theorem as suggested by Sullivan.

so: thank you, stephen.
it's nice to see the advisor live on, in some way.

in case you must chat in $$'s ..

i wouldn't say every day, but most days i learn something new.

as for today, i learned ..

1. .. about Wolff potentials (of measures), i.e.
   
   
   and how they come up in PDE, occasionally.
   
   
   
2. .. that there is a LaTeX-based web chat program called MαthIM.
   
   since nobody claimed the name yet, i have started a chatroom called quasiworld and posed a random question that came to mind, some months ago.

i admit, we don't exactly study real-world phenomena, but .. seriously?

just earlier i stumbled onto this headline @ io9:

"why we should study zombie attacks"
by lauren davis.

i scoffed immediately.

is that what biologists are studying these days?
i guess cancer research isn't paying off ..

.. but then, unfortunately, i read on:

Patrick J. Kiger, a journalist and blogger for the Science Channel, has been criticized for focusing on technologies in his column Is This a Good Idea? that currently exist only in the realm of speculative fiction. To answer those critics, Kiger looks at the recent study by mathematicians in Ottawa as to the best response to a zombie outbreak. (more)

[sighs]
one more thing to explain or deny, i guess.

from the sounds of it, though, it seems that the writer of the previous article meant "mathematical biologists" --

In a paper published in Infectious Disease Modelling Research Progress, a team of mathematicians from Carleton University and the University of Ottawa have created a series of mathematical models to explore the effects of a zombie outbreak and determine the best course for human survival. (more)

and, in their defense, they at least have style --

For the purpose of the paper, the team limited their models to the George Romero slow-moving zombies, and created separate models for zombie infections that cause the infected to resurrect immediately after contact with a zombie and for zombie infections with a 24-hour incubation period.

does that mean that the fast-moving zombies of "28 weeks later" will be a topic of future research? q-:

tuesdays, then and now.

i like tuesdays. at some point i decided that they were my favorite day of the week.

---

my teaching schedules have always avoided tuesdays. when i was a graduate student, i was always given a M-W-F or a M-W-Th. as a postdoc, the trend continues; in fact, it's hard to have an alternative schedule here.

tuesdays make fine mornings.

waking up, i put the pot of coffee on, knowing that i needn't worry about drinking it in a hurry. even if i show up to the office, it wouldn't be until after lunch.

heck, i can make myself lunch!
i can turn on the radio and work in my pajamas.

my books are at home. i've enough paper around to become the bogeyman whom trees tell their children about. if i need to look up a paper, i can access mathscinet through a university proxy.

the only thing i miss about my office, actually, is my chalkboard. paper just isn't the same; neither are marker boards. [1]

---

on the other hand, i always seem to have seminars or meetings on thursdays.

for 2 years straight, as a graduate student i'd meet the advisor on thursday afternoons before the study seminar. at first it was an hour, but our discussions would regularly run over. i suppose i was generally to blame when thursday seminar would start a few minutes late; we would wait for him. \-:

so after a while, they became 1 1/2 hour meetings. of course, that didn't really solve the problem of being late.

i guess i've always had a tendency to ramble. q-:

so yes, i could have said the same thing about thursdays, but it was more than about teaching. you see, thursdays were mornings that i spent trying to make myself "make sense."

sure, i'd collect ideas over a week and work out details, but there's nothing like a meeting to separate the wheat from the chaff.

i can't count the number of times when an idea made sense in my own head, and when i'd try explaining it to the advisor, it would suddenly become complete nonsense.

tuesdays were the tranquil sorts of concentrated research days. i didn't need a good idea right away. i had time to wonder.

[1] there is something nice, though, about being able to put a marker board atop your dinner table, and drawing right on the surface. it makes me feel like a vandal!

an auspicious sign.

this was my cookie fortune earlier, from dinner:

"you will receive some high prize or award."

i suspect that the cookie fortune gods don't mean the fields medal.

then again,
i am applying for an nsf grant, this year .. (-;

---

ah, but fortune favors the prepared mind,
so it's back to writing i go!

on p@ul gr@ham's "list of N things" article.

having spent 5 years as a graduate student, i have developed my share of procrastinate activities.

among my favorites was reading webpages which consisted of lists of a fixed number of (mildly) interesting items.

here are examples from a glance @ digg, just now:

10 ugly truths about modern journalism,
4 sites where you can download old pc games for free,
top 10 tactics for protecting your stuff,

and that's only from the first two pages!

---

interestingly enough, in his latest article, p@ul grah@m has attempted to explain this phenomenon. he makes some good points, but there is one point which was hinted but not fully expressed:

for mathematicians like me, the title is catchy: it's a finite, explicit number. one knows that, up to a few clicks, the article or link will take only a fixed amount of time.

in contrast, the generic link/article can be anywhere from 1 to 8 pages -- new york times articles vary in size, with this variety. it is an inherent investment of attention and interest which, for we impatient moderns, may be too costly ..

.. especially when we have work to do, and allow ourselves only a 5-minute break.

not about maths, but mathematicians discussing maths.

there is a pleasant article/slideshow by seed magazine of 13 well-known mathematicians and their working philosophies on maths.

of these, my favorite excerpts:

"[W]hen you get started, to really become a mathematician, the key step is to realize that at some point you have to stop reading books. You have to think on your own. You have to become your own authority."
(alaιn connεs)

"In applied math, you must always worry whether you are paying attention to the data or whether you are forcing reality into a mathematical straitjacket."
(davιd mumf0rd)

"As mathematicians, we play and dream but we don't cheat. You can't cheat in mathematics. Truth is so important."
(Marie-Francε Vιgneras)

"I came across one of my old papers the other day and I could barely understand it. I thought, 'Wow this guy is good! How could he think of that?'"
(Davιd Harold Bla¢kwell)

one mind, divided against itself, cannot stand?

this term, i teach my first class at 11am. there have been enough classes that i've noticed something:

whenever i work on research before heading off to teaching, my lectures become slightly erratic:

one day, it would be a persistent problem with missing negative (-) signs,

another day, it would be forgetting to discuss some arithmetic facts earlier in the lecture -- despite having arranged them carefully in my lecture notes -- and remembering only, in the midst of an example.

maybe my research self and my teaching self cannot co-exist peacefully!

---

on a related note, the last few mornings have been productive. each day i'm a little closer to proving this one theorem ..

eventually, you get the hard questions.

when i had worked as a TA, years ago, i deferred all the "hard" (that is, administrative) questions to the head instructor. there was even one prof who told me explicitly,

"i don't mind being the bad guy.
if students complain, send them to me."

as a graduate student, i might have run my own calculus class, but my students knew that i was nobody important. they didn't ask me the hard questions.

now i'm dr. so-&-so, the head instructor .. and there are always student emails in my in-box.

[sighs]

i suppose it happens to everyone, sooner or later.

ah .. geek humor. (:

"Jim Buckmaster is tall and thin, Newmark is short and round, and when they stand together they look like a binary number."

from why craiglist is a mess
by gary wolf, wired magazine.

an old memory: endings and beginnings.

by the time it turned august, 6 years ago, i was ready to move and start graduate school in mathematics. it was in my future. i was sure of it!

my bags and boxes were packed, fit neatly into the trunk and most of the backseat of a 4-door sedan. most of those were books, and of these, most of them i'd never read again; i didn't know how to plan very well, back then.

there was one last thing, before driving away: one last meeting with one of my profs, one last chat about ideas and research.

---

it had been an eventful summer for me, full of new travels. those were my first conferences; he had suggested them. i learned a lot. among other lessons, i discovered that i truly knew nothing.

sometimes i hated being right. (i had my suspicions.)

i hadn't seen that prof since may, but upon walking into his office and greeting him, that gap of time seemed utterly imagined. he asked me about finland and about utah, whom i had met there, what i thought about the kinds of analysis that i've seen.

even in that last hour, i still learned a few last intuitions. i confessed that i understood very little and asked him a handful of the things that i didn't know.

so we talked mathematics for a while.

after a while, he cautioned me: "where you're going, they're very geometric, very abstract. make sure you always know the beginnings of the theory, the motivations. always ask!"

i nodded.

a moment passed, and then he asked, "they're not going to make you take algebraιc geometry there, are they? it's not one of the required first-year courses?"

i assured him no, but i learned later that it wasn't a silly question. that would be true for half the students i'd meet in grad school, but not for me.

i had an agenda, you see.
i was determined to become an analyst.

---

before my ph.d.,
before i had an advisor,
i had a mentor.

there was never any formal agreement, just some unspoken understanding. he always listened, he offered before i could ask; he still does. without him, i doubt i'd have become a mathematician.

so, for those profs, postdocs, or instructors who interact often with undergrads: your mentoring matters.

it's frustrating, i imagine. undergrads, american or otherwise, aren't especially known for their professionalism.

for a few of us, though, it's made all the difference.

it's nice to know that i'm not alone in my postdoc confusion.

except for the wife & child, i can imagine myself saying the same thing ..

from Ph.D. Comics by Jorgε Cham.