Monday, October 31, 2011

.. provided that ε ~ 5.6 x 107 ..

.. there are now 7 billion people living on earth today,
according to NPR and other sources, anyway. (-:

Friday, October 28, 2011

jyväskylä: then and now.

so it's been close to a week in jyväskylä again. i came with the expectation of finishing a joint project, but instead i started two new ones.
i'm glad for the work, but i worry about the future. 
at some point i'm bound to screw up the juggling routine, break another promise or two to a collaborator.

in some sense, jyväskylä was a beginning for me. i met my first co-author there, as well as two future members of my doctoral thesis committee .. a little more than 8 years ago?

 that was also when i met the advisor for the first time.

 i was fresh out of my undergraduate years, and we didn't talk much. it was only later when i'd get to know him better.

in a different timeline, where things may have happened differently, i would have spent my final semester of grad school in jyväskylä.

that was the plan, anyway: the advisor was planning a sabbatical there with his family, and we were invited as visiting scholars. it would have been a chance, i think, for us students to start building our own research connections.

 some of you know that it didn't happen that way [1] ..

.. but i suppose things worked out on the research connections front, the way the advisor would have liked.

  [1] it's almost been 4 years now, hasn't it?

Thursday, October 27, 2011

before, then, and after.

tuesday: i don't often say this, but i have a good feeling about this talk.  it might even be fun!

wednesday afternoon: ye gods.  this is the analysιs seminar, right?  it looks like the audience for a colloquium.  i've seen entire maths departments that are smaller than this ..

.. oh well: here goes nothing ..!

wednesday evening:  well, maybe 4 pages per hour [1] was a bit ambitious, especially for a chalkboard talk.  it was only after writing out the maths in chalk that i realised how technical the discussion really was.

still, i think that the talk was received well, and colleagues of mine had good things to say about the result.

when i was younger, i used to be deathly nervous of questions.  ultimately, i realised: if people are asking questions, then it means that they are listening, even willing to understand.

so questions are a good sign, after all.  besides, if you can't address the questions of the audience, then you probably didn't prepare enough for it ..

.. so: fair's fair. i've had my share of that. q-:

[1] read: "1 hour" = 45 minutes

Wednesday, October 26, 2011

if you waste a sufficient amount of time on the internet every day (like me) then you will have encountered this image/meme:

well, it wasn't the first word that i saw, but of those first four, one of them was "cotalent" ..

[see 1 line below the meridian line]

.. which sounds daunting:
a talent is a quality that, when presented, improves the impression given by the presenting person. 
co-talent, in contrast, must mean something in the opposite direction .. say, a quality that, when presented, harms the impression given by the presenting person! (-:

Monday, October 24, 2011

weekends, obsessions.

on saturday an acquaintance asked me if i worked on weekends.  not wanting to sound like a workaholic, i told her that:
"unless it's really busy,
i only work weekends when i feel like it."
she seemed satisfied that i wasn't a crazy oddball.
for my own part, i was relieved at not having to lie .. but only to stretch the truth a little.

the truth is that there are a handful of research problems that are essentially fixtures of my life.

when i wake up in the mornings, they may as well be waiting for me at the kitchen table.  odds are good that if i have nothing else planned, then i'll start thinking about them over my first cup of coffee.

i don't count them as "work" because it's easier to puzzle over them than not.  on the other hand, they're purely speculative, and i don't expect ever to make progress on them .. though i still try and i hope that, eventually, i make a small step forward ..

they're not the problems that one should think often about.  they're fun, just like how ice cream is tasty and fun .. and still not good for you.  it took me a long time .. about 3 years of a first postdoc .. to realise that it's important to have several problems at a time and of varying "levels of difficulty."

even now, i have a tough time not dropping everything entirely and running exclusively after one problem.

it's fine to like mathematics; i wouldn't be in this business if i didn't.  being a working mathematician is another thing entirely, though.  there's a rat race, just like for the rest of the world, and it helps to have something to show for your efforts.

so on weekends, i tend to work half-days on problems that border on obsession;
i'd work the full day if i didn't get tired and sick of repeated failure.

it sounds awful, when i put it that way.  for the same reasons, though, i really like rock climbing.  when you finally finish a route and reach the top, it feels like you're king of the world ..

.. which is somewhat crazy, but give me a break: i'm a mathematician. (-:

Monday, October 17, 2011


".. it is dreadfully boring to show that this formula defines a linear map TF from the space of sιmple functions of the above form into X, and we leave this as an exercise for masochists .."

from Vectοr Μeasures (p.6) by J. Dιestel and J.J. UhΙ.

Sunday, October 16, 2011

once a student, always a student.

[this was written last week on monday;
for some reason i forgot to post it until now.]

right now i'm browsing two sets of notes.  they're based on lectures that the advisor gave in the spring of 1999 .. back when Cheegεr's theorem had just come out.
looking through the topics they covered and the details, it must have been an amazing course .. maybe something worth traveling through time to have sat through [1].

i remember attending a course similar in spirit, in spring 2004, but i think i was far too young to appreciate those topics, back then ..
..  [sighs]

then again, you're never too old to learn.

lately i've been attending lectures on geοmetric measure theory, held at the uniνersity of helsιnki.  so far they have been a lot of fun .. but then again:
any course can be a lot of fun,
if you don't have to do the coursework! q-:
one of my weaknesses is that i was exposed first to a formulation of geometric measure theory on metric spaces.  as a result, i feel quite ignorant about how powerful the Euclidean theory actually is and what results are available to .. say, characterise certain classes of currents.

so, yeah: i'm thinking about a conjecture again.  i doubt i'll make any progress on it, but it's something to think about it, over breakfast and coffee.

[1] not that it would be my first choice if i were given only one opportunity to travel back in time. on the other hand, i don't think i'd have affected things enough to cause an alternate timeline to occur, or anything ..

Tuesday, October 11, 2011



this is going to sound ridiculous, but i'll say it anyway: the best thing about sequeηces is that you can always take further subsequeηces.
it's like a never-ending buffet at a restaurant;

at some point you become full, you have what you want, and you stop going back, but there is always something that you like best ..
similarly, sometimes one starts out with a less-than-optimal sequence of measurabΙe functions, but then the optimism of measurε theοry and functiοnal anaΙysis kicks in:
a sequeηce is bounded, so maybe i can take a weakΙy cοnvergent subsequeηce (i.e. Baηach-Alaοglu) ..

but i don't like the word "weak," so maybe i'll just mix up the terms a bit, and now i get nοrm cοnvergence (or Μazur's Ιemma) ..
sometimes i feel like a mathematical glutton. (-:

Thursday, October 06, 2011

on why some bibliography styles are easier on me .. even obscenely so.

this is probably an issue of the (mathematically) young [1], but the bibliography is a crucial part of many papers that i pick up and browse.
in fact, most of the time i realise that i shouldn't be reading that very paper .. but instead, the earlier papers that the author(s) cite.
as a general principle: the first paper in a topic contains the purest form of the main, recurring idea.  it may not be executed in the most efficient, general, or powerful way possible, but that's not the point:
the point is to understand how it works first,
and then to see what you can do with it ..
that said, it's very helpful for me to identify right away, in the text of the paper, which of the references contains the lemma that i just read.  it's a recurring annoyance for me to remember which paper is marked [11], and usually it means flipping/scrolling to the last page and matching up the citation number to the author/article.

it affords me more ease of thought to read [Gro96] instead and immediately remember:  

right! Gromov's gruebleen book.

on the other hand, this can cause a few .. quirks.
if you use BibTeX with the alpha style, then for single-author papers it uses the first three letters of the author's name as an identifier.

so Gromov's Metric Structures for Riemannian and Non-Riemannian spaces is [Gro96], and Cheeger's 1999 GAFA paper is [Che99].

it's an unfortunate case of typesetting, though, when i'm citing Patrice Assouad's paper, regarding embeddings of doubling spaces ..
.. so does anyone know how to fix the standard BibTeX display formatting? (-:

[1] one way to test if you're still "young" is how often you agree that a particular argument is "standard." as for myself, i still have a lot of reading .. and learning, to do.

Monday, October 03, 2011

where there is a mathematician, there is probably a cafe.

on sunday afternoon i was working at a cafe called la torrefazione earlier .. which, by the way, has great brewed coffee.

in case you were wondering about the notepad, i like writing with the longer edge on the bottom, despite the pages being lined in the orthogonal direction.

the page is otherwise too short:
the side of my hand would be on the table, not on the pad ... which in turn makes forming letters slightly harder to get right.

since the letters are small (and it would be nice to fit in something nontrivial, per page), the hand control becomes that much more pronounced ..
as for what i thought about:
in the late morning i thought about metric currents (specifically, 1-d currents in the plane) but couldn't get anywhere. it's the same obstruction, time and time again: i just don't understand BV functions well enough, at least from a geometric perspective.

as for the afternoon, that was directed towards analysιs of PDEs. i think i convinced myself that a particular strategy is NOT doomed [1] and that i should pursue it further. to do the details, however, means a much closer look at a proof ..

.. and i left my papers and computer at home. oh well: there's always the actual workweek to get work done, right? q-:
[1] the technique i have in mind isn't too strong, in the sense that it won't accidentally "prove" something that is not true in general.

Saturday, October 01, 2011

on why computers are not as complicated as you think.

with apologies to my friends who have heard me rant about this before, i nevertheless think that computers are fundamentally 1-dimensional, even painfully so.

those of you who know what a turing machine is [1] will think the idea is perfectly natural. as for the rest of you, you will have to suffer my usual amount of complaint ..

if you use an old-school text editor to compile LaTeX like me [2], then the cursor blinks at you when you stop typing. it's not as if it ever stopped blinking ..

 .. well, that i can't be sure, but it certainly blinks when you stop typing.

in fact, if you stare at it long enough, then it looks like someone is winking at you, over and over .. as if laughing at you, knowing that you don't know what to write or how to explain yourself, even though you know how to prove it mathematically forwards, backwards, and sideways.  

well, fvck you, computer.

so i found myself, having to start a research plan which is the bulk of an Academy of Finland grant application. i had ideas, but they were without structure at all, and the combination of a blank screen and a winking, subversive cursor was too much for me ..

.. so, 2 weeks ago, i pressed the off button.

a piece of paper is a pretty intuitive thing to us humans, if only because we are familiar with it from school. if you think about it as the analog version of a potential digital device .. an advanced version of a tablet or an iPad, perhaps .. then it is an incredibly flexible interface. for one thing, i can write anywhere on a page, and organize the information later.
i may start with a paragraph of text, but being stuck, start drawing a diagram in one corner, then realise that i should estimate something, and write out a computation in another corner, decide that, having understood what i mean to express mathematically, then i'll return to finishing the paragraph that i started earlier.
the reason why this is harder on a computer is twofold:
  • alphabetic languages are inherently linear, which means that you must impose an order on your thoughts .. at least, if you're unwilling to cut-&-paste or delete. not every thought or series of thoughts of mine is orderly, which makes typing out ideas hard.
  • the human eye is a wonder of processing power. perhaps in the near future, image processing will advance to such an extent that a computer can see and recognise images as well as a human .. but until then, if i doodle something, then my friend can see that i was thinking abot linear homotopy. a computer has no such flexibility.
at any rate, i found that most of my recent grant application was initially written in ink and longhand. for me, it was far more helpful to include an additional dimension's worth of freedom, if only to fully express myself.

[1] and, of course, believe in the church-turing hypothesis.

i say believe, because -- let's face it: you can never prove a statement like "everything computable is Turing computable." you can only disprove it, by constructing a fundamentally different architecture that is backwards compatible with standard digital software.

honestly, when i first heard the church-turing hypothesis, i was quite impressed. then again, i was quite young then and had no taste. as for now, i view it as the computer science version of a peano curve .. in the sense that a ticker-tape (i.e. a real line) can be mapped injectively to a 2-D microchip (i.e. the coordinate plane). in that sense, it's not clear to me if there is anything mathematically interesting in applied computer science. theoretical computer science, from what little i've seen, looks quite cool. any science that will take metric-space embedding problems seriously is a fine science, in my book!

[thumbs up]
well, at least it's better than intelligent design, which seems to me utterly untestable.

[2] i was visiting a colleague once, and stopped by departmental tea. like the hapless nerds that we are, we started talking about graphics via latex. one guy was complaining about this one package and i had no idea what it was, so i asked him to explain it to me (how i can download it, etc). when he asked me what i used, i told him "pstricks" and then he paled

apparently i'm a masochist, by mathematical standards and otherwise.