## Monday, December 26, 2011

### mοnty hall as a meme.

earlier tonight my brother-in-law asked me about the mοnty hall problem and why his solution wasn't the correct one.  so i took one of my credit card offer envelopes and we started drawing diagrams ..

.. and just as he finally accepted the answer, my brother walks over and asks me what we're talking about .. so we tell him the problem, he thinks about it, and then we start drawing on the refrigerator ..

.. and he, too, accepts the answer eventually.

now, though, my dad is starting to look at the fridge ..
[sighs]

## Wednesday, December 21, 2011

### holidays.

my flight is delayed and there's free wifi in helsinki airport:
i suppose that certain outcomes are therefore inevitable.

thinking it through, these last few weeks haven't been very efficient;
i blame the lack of structure in my daily life:
without the constraint of teaching (and hence regularly scheduled blocks of time beyond my control) i've found my workday wide open, apart from meeting colleagues everyday for lunch.

since the start of december the seminars have not been meeting regularly, and the lectures i attended at universιty of helsinkι ended .. two weeks ago?

i can't remember anymore.
the days are now a blur.

the holidays are beginning, and my family swells: with my sisters come their boyfriend and fiancee in tow: good men, though.  they treat my sisters well, which is the important thing.

there will be a lot of people in the house, so i suppose that i won't get any work done until after new year's ..

.. on the other hand, my laptop has a 8-hour battery:
i wonder if i can write up an entire preprint during the flight home!

[thinks]

helsinki to reykjavik,
reykjavik to home ..

.. let's see, shall we? (-:

epilogue (4 jan 2012). i never got close to finishing that preprint.

the introduction was what balked me: every time i tried to motivate the result, i thought about the stronger result that i wanted to prove, and couldn't convince myself to write any further.

## Monday, December 19, 2011

### an update, 3-4 months in.

say, is anyone still reading this?
..

it's been a while, hasn't it?

somehow it's become my habit NOT to write in this blog.  not a lot's been happening, i guess: i applied to a few more jobs, written up a close-to-complete set of notes [1] on some recent results, and started getting back to a few research collaborations.

when i think about it, i do a lot of worrying and complaining here.  i suppose that's natural, for two reasons:

1.  it's year number four since i defended my dissertation, and i still don't know if i have a future in mathematics.  part of me wants to blame the economy .. but most of me acknowledges that i haven't been doing enough, my results not particularly noteworthy.

i don't know.  i'm trying, but often i don't see any progress, and not much hope. [2]

2. apart from the future and general malaise, the present day is going fairly well.  aside from the climate around here [2] my complaints are few, and i think the freedom from teaching has done me some good.

i feel like i now understand more about mathematics, and become a better researcher.  i haven't had mathematician's block [3] in a while: the ideas are still there, some are taking shape.

[1] -- i think i referred to it as a "preprint" in recent memory -- if not here, then in an actual conversation with colleagues.  in truth, it used to be a preprint, but while i was checking some details, some new ideas come up.  then i had my doubts if anything worked .. but now i think i can see why the proof should and does work.

the short version: i'm pretty sure i proved some new special cases of the Ambrοsio-Kirchheιm conjecture, and reduced the full conjecture to a different (still unsolved) special case.

[2] -- that could be the seasonal affective disorder talking.  today it became bright at around 9:30am and dark again, near 3pm.  i feel tired most of the time, except late at night.  i haven't gotten around to taking any vitamin d supplements yet .. maybe i should do so.

[3] -- it's kind of like writer's block.  instead of not being inspired to write, it would be a combination of not getting new ideas and none of the old ideas working.

## Sunday, December 11, 2011

### call me old-fashioned, but ..

sometimes i think that my work is superficially relevant to this setting of metric spaces and analysis on them.

deep down, i am just a euclidean geometer,
working with balls, lines, planes ..

.. and, of course, the occasional Lipschιtz function. (-:

## Monday, November 28, 2011

### "the horror comes in reality from the mathematical aspect of the event."

evidently, albert camus believed in a deterministic reality, and probably disliked maths.  maybe someone should have told him about quantum mechanics. \-:

as for the title, it's lifted from camus's long essay the myth of sisyphus --- specifically, from the section an absurd reasoning.

to get a sense of this book, the first sentences read:
"There is but one truly serious philosophical problem, and that is suicide.  judging whether life is or is not worth living amounts to answering the fundamental question of philosophy.  all the rest -- whether or not the world has three dimensions, whether the mind has nine or twelve categories -- comes afterwards."
evidently camus was destined to be a philosopher, not a geometer [-1]. q-:

as for the excerpt that included the title, here's the context:
"here it is barely possible to speak of the experience of others' deaths.  it is a substitute, an illusion, and it never quite convinces us.  That melancholy convention cannot be persuasive. [0]

"if time frightens us, this is because it works out the problem and the solution comes afterward.  all the pretty speeches about the soul will have their contrary [1] convincingly proved, at least for a time.  from this inert body on which a slap makes no mark, the soul has disappeared.

"this elementary and definitive aspect of the adventure constitutes the absurd feeling.  under the fatal lighting of that destiny, its uselessness becomes evident.  no code of ethics and no effort are justifiable a priori [2] in the face of the cruel mathematics that command our condition."
ah, the cruel mathematics, indeed! (-:

[-1] the more i travel, the more the term "geometer" seems rare.  i thought it was the standard name for someone who studies geometry of some kind, but acquaintances tend to refer to me as a geometrician.

[0] this entire excerpt is from part of one big paragraph: the spacing has been included for easier reading on a computer screen.

[1] i think "contrary" is meant in the sense of "all that is contrary (to a particular thing)" but since i don't have the original french version in front of me, this is mere speculation.  as a mathematician, i would still say "negation."

[2] his exact words, none of mine.

## Saturday, November 26, 2011

### today i found out that i am an author.

every so often, i run a goοgle search on myself to see if i've inadvertently done something stupid (and if so, deciding on how to erase it from existence).

this time around, something odd came up.
my thesis is available on amazοn.com;
there's even a used copy available! (-:
that said, is this happening to anyone else, out there?

it's one thing to download preprints from the arχiv and mirror them somewhere else, but .. come on: this is just my thesis ..

so if you want a copy,
then just email me and ask ..

(.. or at least until someone threatens to sue me.)

## Thursday, November 24, 2011

### for some of us, certain LaTeX symbols are un-natural.

yesterday, while writing notes to a colleague, i happened to use the LaTeΧ symbol \bigoplus \bigotimes, which i have only seen used for tensor products in algebra.

as an analyst, i became slightly ashamed of myself for a while.

to the algebraists: it's nothing personal.

think of it this way: if  you were giving a talk in your friend's seminar, and in the middle of the talk, suddenly assumed "let ε > 0" .. i wouldn't think that it would go particularly well.
(-:

## Friday, November 18, 2011

### in which some constructions are "natural" ..

perhaps all of you knew already, but today i learned that "magenta ain't a colour" in the sense that it cannot be created with a single wavelength from the visible light spectrum.

however, since the human eye processes colors in terms of opposites, so magenta appears as the complementary color to green.
initially i nodded,
thought it was a neat factoid,
and went back to wasting time on the internet ..

.. but then it occurred to me:
this is exactly the 1-point compactificatiοn of the real line [1]!
despite the abstract nature of lοcally cοmpact Hausdοrff spaces, this is a concrete example that some ideas in tοpology sit naturally in the real world ..

this is just as cool as when i learned that the video game "asteroids" is played on a torus ..

[1] yes, for the record the visible spectrum is a bounded interval, not the whole real line .. q-:

## Thursday, November 17, 2011

### on a wholly unrelated note ..

in my work notes today i'm using the symbol Ξ, or uppercase ξ, a lot.

not having much practice with this greek letter,
oftentimes it looks either like:
either way, it just feels .. ridiculous?

## Wednesday, November 16, 2011

### boredom is a luxury.

the last two months have been quiet.  apart from daily life at the office and a few regular seminars, not much happens in my life that's worth blogging about.

in other words, it's been awesome.
i can concentrate on chasing down ideas, some of them infeasible, a few of them interesting.  i can pursue a line of thought for days at a time, see where it goes.

i can latex for a full day, hack out the details in a single uninterrupted vision, identify the parts that make no sense, work through or around them.
telling you how it's really going -- that requires a level of technical detail that i'd rather not see on a blog, myself.

this is not to say that all of my ideas are working .. but that i feel productive.  i haven't felt that way in a long time.

## Friday, November 11, 2011

### after & before: part two.

i can't remember when i first drafted this, but it was probably the day before my second talk (at TKK) which was .. one and a half weeks ago already.

when i give talks about generalizations of the schοenflies problem or Sobolev extensiοn domains or ΡDEs, i get quite anxious, and with good reason. [0]

these are well-established topics with much history to them.  try as i might, i always seem to be ignorant of some significant part of the literature .. and in particular, what types of theorems or proofs are "standard." [1]

when i talk about my "geοmetric" work, however .. and by this i mean this stuff relating to (metric) derivatiοns .. then the situation changes completely.

it would be wrong to say that i am an expert on the subject, if only because there are plenty of things that i don't understand about them.  it's safe to say, however, that nobody is an expert, either!

i guess that makes me a little like socrates [2] .. (-:

it's not that i insist on knowing more than everyone else in the room; i've resigned myself to the fact that there is always someone smarter or more familiar with the literature.

rather, it's the matter that if i make a mistake, then the fallout is minor.  like everyone else, i hate it when people criticise me by my mistakes .. even if i do deserve it, sometimes.

there's another aspect about derivatiοns worth mentioning, as the topic of a talk:

if this is a subject little-known, then my role can be put to good use.  there are few references on the subject, so i can point out how the theory works.  doing so, perhaps i can convince others that the theory can be put to good use.
put one way, a beautiful theory is like a night sky: a canvas of stars that is well-arranged by Nature's Benevolence, distant but worthy of contemplation.

a useful theory, however, is more like a clutter of heavy stones in a field, perhaps meteors comedown to earth, long ago.  stone, despite being crude and ugly matter, are fodder for tools and building material.  from them we form homes and towns, societies and civilizations. [3]
i don't believe that mathematics is always beautiful.

look hard enough at the details of a theory, and it becomes hard to see any beauty in them.  sometimes i wonder if the notion of beauty is inherently retrospective .. in the intellectual sense, anyway.

[0] there was this one talk i gave about manifolds with non-negatιve Riccι curνature, some years ago.  my plan was to learn a setting in which you can actually prove the validity of a Pοincaré inequality (vs. most of the time it is taken as a hypothesis).  it wasn't until i started discussing the proof, that the audience pointed out an error to me .. which lay in the textbook i used, but the fact remains that i missed it completely .. [sighs]

[1] oddly enough, most of my non-geοmetric work is collaborative, especially the stuff relating to ΡDEs and Sobοlev spaces.  This cannot be a mere coincidence.. \-:

[2] according to legend, a man from athens traveled to see the oracle at delphi and asked: "who is the wisest man in all of athens?"  unlike the usual cryptic answers, the oracle simply answered, "socrates."

upon hearing the news, socrates became disillusioned instead of delighted, because he couldn't believe that he knew more than every other athenian.  so began a long and systematic inquiry: socrates found experts on every subject he could think of and began to debate with them, and after a while each expert admitted that he, too, knew nothing.

this put socrates into a further melancholy.  he discovered that nobody knew anything ..

.. until one day, while taking a stroll, it occurred to socrates: nobody knew anything, but he himself knew that nobody knew anything.  this meant that he indeed knew something.  since everyone else he encountered knew nothing, it meant that he was the wisest man in athens, after all ..

[3] i've been reading thoreau's walking lately ..

## Tuesday, November 08, 2011

### a little too easy (updated)

[from evening of 6 Nov 2011]

i'm getting suspicious.
last week i came up with a proof to a particular case of a conjecture,
but it was shorter than i expected it to be.

over the weekend, i thought i spotted an error,
but yesterday i checked it again, and was easily fixed.
i'm still suspicious.

if it were this easy,
then someone would have written it up by now ..

.. so it's time to take a long, hard look at it,
see where the error really is.

[updated: morning of 7 Nov 2011]

i'm LaTeXing the argument, as we speak.  there are subtleties to handle, but no big problems yet.

in fact, the biggest problem is handling my keyboard:
in regards to LaTeX, the annoying thing about european keyboard layouts is that the dollar sign ${\$}$isn't as accessible as in a US keyboard layout (for obvious reasons). in particular, to type a "${\$}$" the command is assymmetric:

it's [Alt Gr] + [4] on a finnish keyboard, as opposed to [Shift] + [4] in the US, so i have to consciously type the command with my right hand.

this wouldn't be a big deal with anything else, but i use dollar signs all the time, in order to pass to math mode.
so i've switched to the US keyboard layout .. with the problem that the labels on the keys are still in the Finnish layout.

luckily, i've been typing for enough years that i don't consciously think about the keys .. but every so often, i forget:

where's the asterisk key again?  is it [Shift] + [8] ..?

## Tuesday, November 01, 2011

### after & before: part one.

so i gave another talk today, this time in my department.  the topic was the same .. regarding differentiability in a certain class of metric spaces.

originally i wrote down some thoughts while writing the talk, but right now it seems more natural to talk about how it went.

the good news is that it was well-received:
all signs point to that, at any rate.

the bad news is that it didn't go the way that i wanted.  something didn't feel right when i was talking, and i'm almost sure that i went too fast.  there were enough clues, i think, as to pick up the basic trail of the argument ..

.. but, admittedly, i was often looking at my watch, seeing if there was still enough time.

so: i prepared too much.
it actually reminds me of a film called wonder boys [1] ..
the basic premise is that the main character, a literature prof, cannot finish the book that he's writing: the pages number in the thousands.  at one point, one of his students reads the draft without his permission, gives her critique.  the message is essentially this:

good writing is about making choices.  this thing .. it doesn't look like you made any choices.  you follow every lead, the tangent of every story of every character ..
the fault of the talk is that i made a similar mistake.  what i had in mind was (essentially) a complete discussion, but even in 2-hour finnish style seminars, there still isn't sufficient time.

put otherwise, it's not that i didn't have enough time;
rather, the talk just wasn't well-organised, the message not appropriately succinct [2].

epilogue. afterwards, a few people came and asked a few questions.

the striking thing is that, despite the metric space setting of the discussion, i was asked instead about Lie groups, as well as Riemannian manifolds ..!

sometimes i wonder whether metric spaces are really a good field of analysis in which to work.  maybe i should concentrate on more familiar settings .. if anything, i might be able to communicate with more mathematicians ..

[shrugs]

[1] interestingly enough, it's set in pittsburgh.  the story is modest, but it's told well.

[2] "i didn't have time to write you a short letter, so i wrote a long one instead .." ~ mark twain.

## 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.
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

### gluttony.

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 ..

[thinks]
.. 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.

## Wednesday, September 28, 2011

### bombast (or: i really need to finish this grant)

i wrote this earlier in the morning, more because i wanted to get it out of my thoughts and move to more realistic matters.

as you can see, the wording is a bit .. grandiose.
"The path of research is not meant simply as one of self-discovery, but one where hard-won insights are shared with others, in hopes that the body of knowledge is further extended and refined.
in that sense we researchers seek a kind of diffuse immortality -- not through selfish means, but collective ones."
for those curious: i was originally thinking of a first sentence of a paragraph, regarding "visibility" and how to disseminate forthcoming research results.

## Sunday, September 25, 2011

### realisations.

when i learned two years ago that NSF grant applications require 15-page research plans, i could swear that my heart stopped beating for a minute. that probably didn't happen, of course ..

.. but what did happen was that my thoughts turned to desperation and fear.

15 pages of ideas, no proofs;
how the hell could anyone do that?

thinking about it now, i feel silly .. because i now think the opposite: 15 pages is short. somehow, these days i always have to cut it down.

[sighs]

to be fair, "no proofs" isn't quite right. ideas of proofs are necessary to the exposition, if only for two reasons:

(1) they help explain what's going on;
(2) they indicate that you do know what you're doing, that you know how to get your projects going.

then there's a lot of 'why's:

why am i studying this problem?
why is it important or natural or relevant?
why is it hard? ..

and tying back to a previous theme,

why me? that is, what do i know that fits the problem and the subject, that affords me a better chance of success than average?

these are all hard problems, but not the technical kind that mathematicians tackle on their usual working days. in fact, it's almost opposite to how we tend to act and work.

speaking for myself, i chose an academic path precisely because the thought of "selling myself" for a job seemed unnecessary. that made the last year of my ph.d. and of my (first) postdoc to be especially traumatic ones.

well, i've changed my mind a little. grοmov has said once that you can't be a mathematician and live in the world at the same time, and maybe that's true ..

.. but i'm not grοmov. i see now the necessity, despite my love for the field and for my work, to live in the world, deal with its faults .. join the rat race.

this was actually supposed to be an optimistic post, and i still intend it to be. i think i'm getting a hang of this part of the job .. not to say that i'm good at it [1] but that things make more sense.

tonight i looked at a printout of this application and i realised what i want to say. it will take time to really refine the message and it still won't be easy to say it exactly right ..

.. but, after struggling for a week, i think i see why i've been doing what i've been doing, how it all fits together.

[1] come on. if i were actually good at this, don't you think i'd have gotten a grant by now?

## Wednesday, September 21, 2011

### #1000: lots to say, lots to do, little time to write.

it's been a while between posts, hasn't it? you'd think that by moving to a new country, i'd have more things to say and complain about ..

.. and there are. i've plenty of complaints about grant-writing, paper-writing, how the maths is going, and even how it feels to be illiterate in a post-industrial western society ..

.. and then, there's always the weather. seriously.

rather, perhaps i mean climate. everyone's been warning me about november, which is the time when the darkness comes. (at this latitude, there are far fewer hours of daylight in winter, so when it's still warm enough NOT to snow, everything looks dark and bleak .. so they say, anyway.)

that said, these very sources of complaints (except the weather) are tasks, and time-consuming ones at that. no one post ever takes too long, but for academics and non-academics alike, you know the drill:

it seems like any time you take away from a project is precious, even if you accomplish nothing in that hour. murphy's law applies, and odds are: in that very hour, you would have obtained the break-through you've been waiting for ..

.. and so i hedge my bets, suffer the usual lack of productivity, but still feel glad that i might be accomplishing something.

9 days before the application deadline;
perhaps you hear from me before then.

oddly enough, this is my 1000th post since the start of this blog. amazing: i've had that many things to bemoan, over these last few years ..! (-:

## Monday, September 12, 2011

### you can leave the states, but you can't leave the grant applications ..

it was the first day at the department at aaltο, when i suddenly felt very busy and that there were many things to do -- each of which would take a long time to do. for one thing, there were (and still are) manuscripts to finish and submit.

on the other hand, having left the united states, i've been spared the usual frustration of applying for an NSF grant ..
you can't believe how happy i am, not to have to do this until i return to the U.S. of A.

some of you have told me before that writing a grant is a good thing: if anything, it gives one focus and makes clear one's future research goals .. even if you didn't know beforehand what those goals were. (in short, it's a trek of self-discovery.)

i'll agree to that, in the same way that i believe that adversity tempers us and makes us more effective, well-rounded people. that doesn't mean that those adversities are in any way enjoyable!

so as a compromise, once the NSF decides to fund me,
then i'll stop complaining about it.

until then .. (-:
several days ago, however, i was told that applications for postdoctoral positions at the acadεmy of fιnland are due at the end of september ..

.. wait: isn't september this month?
[sighs]

to be fair, the academy accepts applications from non-finns and they have funded non-finns and even non-europeans. this is a fine thing: i imagine, for most nations, that this would be an excuse to practise nationalism.

but .. [sighs] .. it's just the timing. i really wanted a huge chunk of uninterrupted time to finish writing these metric "geometry" papers, and then switch gears to learn new topics and see what i can do in them.

instead, my september will be its usual rush. this next preprint must be finished quickly, preferably before september, if only to be used as "evidence" that my research plan (to be written) shows enough promise that i can do more ..

.. and then there is the actual application to write ..

oh well: it's still a year off from teaching, so who am i to complain?

## Friday, September 09, 2011

### a clean, well-lighted place.

i think the receptionists have developed a dislike to me.

an apartment in helsinki is harder to find than i expected, especially around september, as the city experiences a rush of students looking for housing. (also, rental prices are high and not very forgiving.)

so at the moment i'm staying at a long-term hotel for university guests. there's a free breakfast included and it's a pretty good spread ..

no, i'm not devouring all of their food,
though i am eating more bread than i really should ..

.. on the other hand, i'm drinking a lot of their coffee.
at the very least, they must think it odd that i linger over breakfast for hours with this little notepad and pen.

so yes, i'm treating them like a free cafe:

it's clean and there are windows facing the street,
it's quiet and they haven't bothered me yet,
it's a time of day when i do my best thinking ..

.. and a pot of coffee is sitting right there, from 7 to 10am.
they have had mathematicians stay with them, right?

..
on a related (technical) note, a project i'm working on has become noticeably more interesting. first of all, the main theorem remains true.

as for a side theorem, an inspection of the proof shows that it only checks a special case. unfortunately, i can no longer give a full characterization of these things called measur&alpha,ble dιfferentiable structures (that is, on dοubling metric measured spaces) .. but only a partial one.

as for why it's interesting: if anyone can prove it, then it will have to be very subtle. put another way, if your proof is too strong, then you could accidentally 'prove' that "every dοubling metric measured space supports a pοincare inequality," which is clearly false.

* .. and yes, i stole the title from an ernest hemingway story .. *

## Saturday, September 03, 2011

### the storm before the calm.

today's my third day in helsinki as a visiting postdoc, but there's quite a bit left to do before i'm officially in the finnish system, both the government and the university.

namely, i'm still missing;
• a finnish social security number (so that i can open a bank account),
• a bank account (so that i can be paid by the university),
• a (more permanent) place to live (so that i can work and therefore be paid [1]),
• also: a university computer account.
it's a non-trivial thing to obtain an apartment, at least this time of year:
apparently helsinki suffers from the fall rush of new college students, just like many cities around the world.

the system for apartment rentals is also different from what i've seen in the states, too: it's not uncommon that one submits an application for renting a particular apartment, attends a viewing day with all the other applicants, and the landlord(s) then choose a tenant.
that said, i never realised how convenient the process is, in the states. usually it's just an issue of what you can afford.

with all of these things in mind, i can't help but feel hyper-transient in an already transient situation (as mine's a 1-year position). honestly it's hard to concentrate on anything, much less maths.

today's the first day in a week that i could sit down and work on something!
as for what i'm working on ..

i think i'm going to set aside this recent argument (regarding a conjecture of cheegεr). maybe by spending some time apart from it, i can later see more clearly which ideas are crucial and what really makes the proof work.

besides, there are other papers to edit. it's been a while since i submitted a preprint, and one of them is almost ready ..

on the bright side, this looks to be a fine workplace for me.

between aalto and helsinki uni, there are plenty of postdocs and visitors, which makes for a lively crowd. i have friends and cordial colleagues here, some of which i met in previous times and places. mathematically, many of us speak the same language!

also, my post-doctoral mentor is really cool and his group's research interests sound like fun. i think i'll learn a lot about nonlinear parabοlic ΡDE from them -- who knows? maybe even contribute something myself ..

.. so as long as i can survive the winter here, i think i'm set. (-:

[1] admittedly, i might have the direction of causality wrong, there .. \-:

## Monday, August 29, 2011

### so far, so-so.

odd: i haven't found an error yet in my "proof" of this one conjecture.

could it be .. that i have a correct, complete proof?

[winces, sighs]
as much it looks correct, experience tells me that it's probably not. likely i just haven't spotted the error yet.

on a wholly unrelated note ..

i was watching "stranger than fiction" starring will ferrell, and at some point it started bugging me: dustin hoffman's character is named professor hilbert and the main character was to die from a bus crash on the kronecker line ..

.. sure enough, on imdb:

The last names of all the characters (and the bus line and publishing firm names) are the names of mathematicians, scientists, engineers, artists, etc.

## Friday, August 26, 2011

### all work and no play .. something something something ..

wednesday was day 3 of a conference, here @ MSRI, and only one talk was scheduled. for once i had actually planned a fun, whimsical day of activity.

sure, i'd do some work in the morning, but ..
• instead of dwelling in my hotel room, i'd pick a nearby cafe, try out their organic coffee blends .. and when stuck, watch the passerby through the windows;
• then i'd take the train into san francisco, find a spot for lunch, and then wander around a few museums and well-suggested parts of town;
• if luck would hold, then i'd acquire a crash pad from one of my contacts and then go outdoor climbing (bouldering) with a friend at indian rock park. otherwise, there is a 7-mile "fire trail" around the foothills that looked particularly interesting for a run;
• then there would be a gourmet food-truck event, suggested by my sister, where i could sample local fine cuisine .. then a beer or two, and who knows?
well, i never got to half of it.

i had woken up and started LaTeXing in my room a little, if only to get a good pace started before heading to the cafe. that was before i found a gap in my proof ..

.. and before i knew it:
it was noon and the cleaning woman was knocking on my door.

that cast a strange color to the rest of the day: san francisco today would be out of the question. i went to the nearest lunch place, managed a sandwich, and suddenly remembered the climbing arrangements ..

.. wait: when was i supposed to meet ..?

.. but as these matters go, everyone else was happy to delay the climbing from 3pm to .. 5-6ish. there was plenty of time for a coffee and mull over the argument, so in the end i did go to a cafe ..

.. and find a cleaner, more elegant proof. by the time i met friends to go climbing, i didn't much worry that i was moving badly and (having taken a month's hiatus) lost all strength in my grip.

i've LaTeXing up the notes, and no more surprises have appeared. it's a good feeling.

## Monday, August 22, 2011

### perhaps it is time.

[i wrote this 4-5 days ago but was sidetracked by family matters]

yesterday i was math-walking .. which is a little like sleep-walking, except instead of being asleep i was distracted by mathematical thoughts.

i've had this germ of an idea. the first version, which came to me more than a week ago, clearly doesn't work, but aspects of it had merit ..

this morning i woke up at 7am [1], and i couldn't go back to sleep because i was too excited.

the idea can be modified,
it must be able to work ..

so i thought about it, then latexed it, and things seemed to "click" together .. which is fine, but not worth celebrating yet.

[now]

i've had too many occasions when things are looking really promising, only to discover a gap in the proof of a lemma leading to the result. (it's why i try to avoid saying that "i proved something" because initially, it's never fully clear whether there is enough rigor ..)

this time around, there is a difference. i think the idea is robust enough that i'm willing to discuss it with others;

maybe, with a few more pairs of eyes looking at it, the argument can be modified, clarified, optimised .. and i'll get the right proof.

[1] which is early-ish for me. these days i wake at 7:45am or so, if only because my father, who is retired, is up and about at 10am. that affords me two hours or so of work time, without interruption.

## Wednesday, August 17, 2011

### a few links, memory tricks.

i'm no number theοrist ..
unless it pertains to hausdοrff dimension [1], and even that's a stretch!

.. but i think that today's gοogle logo is pretty cool:

as long as i'm posting links, a friend of mine sent me this article from new scιentist:
Mental αbacus does away with words
by Ferrιs Jαbr (13:56 09 August 2011)

When 11-year-old Prιyanshi Sοmani multiplies strings of 10-digit numbers or finds the square root of a six-digit number, she doesn't use a calculator or even pencil and paper. Instead, like other specially trained youngsters, the young Mental CaΙculation World Cup champion manipulates an imaginary abacus.

Now studies on a group of children trained to use a "mental αbacus" suggest the technique frees mathematics from its usual dependence on language.
i wonder how geometric this approach is. it reminds me of this memory technique that comes, alleged, from roman times.
The method of loci is also commonly called the mental walk. In basic terms, it is a method of memory enhancement which uses visualization to organize and recall information. Many memory contest champions claim to use this technique in order to recall faces, digits, and lists of words. These champions’ successes have little to do with brain structure or intelligence, but more to do with their technique of using regions of their brain that have to do with spatial learning.

...

having tried neither technique, i have no idea how effective they can be. perhaps, like learning how to type on a dvοrak keyboard, i'll set them aside as skills to learn later.

[1] i learned of the following theorem from falcοner's book, some years ago. it's about rational approximations of real numbers and the hausdοrff dimension of the corresponding subsets:

Theorem. Take $a > 0$ and a sequence $\{n_i\}_{i=1}^\infty \subset \mathbb{N}$ so that $n_{j+1} \geq n_j^j$. Let $F$ be the set of real numbers $x$ so that

$$\textrm{dist}(n_jx, \mathbb{Z}) \,\leq\, n_j^a$$

for all $j \in \mathbb{N}$. Then the Hausdοrff dimension of $F$ is at most $1/(1+a)$.

## Tuesday, August 16, 2011

### thoughts between LaTeχing commands

i'm currently Teχing up a proof, which is good ..
.. but not only does it proceed by cases,
it (unfortunately) further proceeds by subcases.

[winces] .. [sighs] ..
sometimes life is necessarily complicated.

is it in good taste to write a short warning the reader,
before the \begin{proof} command ..?

on the brighter side of things, i think i'm unambiguously closer to proving a particular conjecture .. though by no means is it a full proof.

if there's anything i learned about the job, in the last few years, it's to appreciate any measure of progress and improvement. (-:

## Thursday, August 11, 2011

i think i'm developing a dyslexic tic:
when writing out indices by hand, i keep writing '3' for 'ε' .. which ruins the estimates. up to symmetry, though, it's typographically the same
on a related note, i've decided to treat most of my stay in ny state as a 1/2-holiday. since one is supposed to relax and do things one wants to do, when on holiday ..

.. i'm going to work on another idea to attack this one conjecture.
wish me luck! (-:

## Monday, August 08, 2011

### when jargon creeps into colloquialism ..

it makes sense to think of maths as a language. it explains, for example, why students seem so able to write wholly nonsensical things on the pages of their calculus exam. [1]

on the other hand, the technical nature of mathematical jargon can be utterly confusing for the uninitiated. i mean something different from the ubiquity of "normal" (in the sense of normal subgroups, normal convergence, etc) and the loaded use of the word "trivial."

it's the smaller, subtler uses of technical words, like:

"modulo the republicans steering the debate to the right, congress will accomplish nothing this year."

"coke and pepsi are isomorphic, as far as i'm concerned."

last week for instance, i told my brother that 'if you condition on the fact that my last three relationships began when i was in a transition, then likely i'll never meet another woman again.'

when he asked me what the hell i meant by "condition," i explained to him what conditional probability is. (he subsequently thought it was a fine linguistic construct.)

tonight i told my friend that when it comes to real life, i don't feel embedded in it. when he asked me what i meant by embedded, i immediately said that sure, i feel immersed in things but that it wasn't quite a perfect fit.

after another odd look, i paused, thought a little, and told him that nowadays i feel a little less in touch with reality and society than i used to be .. which satisfied him.

[1] for instance, too often i've seen equal signs (=) treated as logical implication symbols (→). thinking about it, this is not so surprising: to most, mathematics is no more than computation, so an equals sign only confirms the logical progress of a computation.

## Wednesday, August 03, 2011

### the song remains the same (or: i found a cool preprint on the arχiv)

the more i think about it, the more it seems that the differentiabιlity property for functions seems to be a rather rigid property -- in terms of both the type of function and the geometry of the underlying (metrιc) space.

today i stumbled upon a further rigidity result on the arχiv:
Dιfferentiability, Pοrosity and Dοubling in Metrιc Measure Spaces
David Batε, Gareth Speιght [1]

We show if a metrιc measure space admits a dιfferentiable structure then pοrous sets have measure zero and hence the measure is pointwise dοubling. We then give a construction to show if we only require an approximate dιfferentiable structure the measure need no longer be pointwise dοubling.
a short-&-sweet abstract, an interesting result!

to give this result some context:
in functiοnal analysιs, one can make sense of derivatιves in terms of fréchet or g&ahat;teaux differentiabilιty. according to hearsay, radεmacher theorems in this context are quite hard ..

.. however, the dοubling condition implies that the underlying space must have a finite Hausdοrff dιmension. so in the context of measures [2], differentiabιlity (even in a generalized sense) must be a fιnite-dimensiοnal phenomenon!

[1] the names sound familiar; i think i met both of them before ..?

[2] strictly speaking, a(n outer) measure is not necessary in order to formulate a radεmacher-type property. it suffices instead to have a notion of what null sets are. according (again) to hearsay from my colleagues, there are quite a few ways to define notions of null sets in infinite-dimensional Baηach spaces ..

## Tuesday, August 02, 2011

### 20 days and 20 nights?

currently i'm in limbo. i'm starting to think that moving in with my parents was a bad idea; maybe i should have inspected aιrbnb for a cheap one-month rental somewhere nice.
every so often i remember an acquaintance of mine named renzo, who spent a summer in costa rica, doing math, enjoying tropical weather, and entertaining guests who would visit him.

i think of the possibility of living in .. say, portland, OR, for a month .. working in cafes, hiking, drinking fine coffee and beer, wasting away in various powells bookstores.
sure, it's only for 3 weeks .. but i wonder if i'll get half of what i would like to get done.

on an unrelated note: i think geometers have moved in, across from my parents' house.

## Wednesday, July 27, 2011

### in media res

in case you were wondering:
i spent the last 4 days rock-climbing, and managed to reach the summit of a rock structure several hundreds feet high [1];

this week i am packing and sorting and playing host to my visiting family
this, of course, is an excuse not to post any new thoughts on maths or the mathematician's life. so, if only to provide a somewhat mathematical flavour to this post ..
"[This] must be done in your head only. Do NOT use paper and pencil or a calculator. Try to add up the following numbers as quickly as you can. Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total?"

~from Challenge Your Assumptions to Avoid Common, Frequent Mistakes @lifehacker

apparently the most common answer is 5000 (which is wrong).

[1] i would say that i climbed, with help, to the top of a mountain .. but strictly speaking, the rock structure couldn't possibly be high enough to be a mountain, much less a hill.

## Friday, July 22, 2011

### one of those holidays again .. q-:

i almost forgot:
happy (european) rational pi day, everyone!
to clarify, i would interpret 22/7 as 22 july, but read as 227, some odd ones out there might celebrate it on 27 february.

[shrugs]

## Wednesday, July 20, 2011

### "don't let the mornings get you down .."

in the last two semesters of teaching, i developed the morning routine of working for 1-2 hours at home before heading to the university to teach.
at the time i became paranoid of the office.

not only would students show up unannounced, at random times of the day [1], but so would colleagues .. and sometimes just for small talk.

i like my colleagues .. but if i truly wanted to accomplish something,
then it was important to protect the territory of my work time.

for a while, it worked. i'd generally curse my luck as the lecture times were approaching, but i was able to stay productive.
as for now, though, the dynamic is different. i think it's because of the content of my work. in the mornings, i generally think about open problems (read: obsessions).

it was fine to do this months ago, since preparing and delivering a lecture has the benefit of taking your full attention for the allotted time. so if i started feeling depressed about not making any progress, then by the end of the workday i'd have forgotten.

however, this doesn't work the same way when you're not teaching:
lately i've been productive in the mornings, but by afternoon i'm beset by the persistent frustration of failure.

yes- nobody else knows how to solve these problems either,
but honestly, i don't care: i still want to solve them.

so despite having other work goals in the afternoon -- writing, for instance -- this malaise is hard to shake. i lose focus and do very little.
[sighs]

so i suppose it's time to change my routine .. \-:

[1] .. which is fine, in the strict sense. instead of asking for make-up quizzes or leniency in grading, usually these students came to ask questions about lecture or homework problems. the problem became a matter of scale: word spread that i would take questions outside of the scheduled times, so more and more students started showing up.

it was easier for me to avoid the office, rather than shooing them away .. which probably reveals something about my personality.
\-:

## Monday, July 18, 2011

### necessary difficulties (also: maths in the media)

it worries me when my introductions are too short. it's one thing for researchers in ΡDEs to write a paper, as everyone knows what a derιvative is.

on the other hand, it's rare that i run into anything knowing the jargon of metrιc spaces, their analysis, and/or their geometry. the asking price of writing a paper about them is therefore at least a half-dozen pages of basic definitions.

the same applies to talks, too;
it's hard to fit everything in 20 minutes .. \-:

on wholly unrelated notes, i've been running into references about mathematics in popular media.

for instance, this past weekend there was a short NΡR podcast about fibοnacci, his book Liber Abaci, and computation at the time ..

.. and in a more mainstream vein:
i was surprised that lιsbeth saΙander, the protagonist of the girl who played with fire, spend several pages musing about fermaτ's last theοrem ..

which makes some sense, i guess. the character is meant to be an elite cracker [1] and probably thinks discretely, not continuously. pοincaré's conjecture would probably be a bit of a stretch .. q-:

[1] depending on whom you ask, "hacker" isn't a fully unambiguous terminology.

## Thursday, July 14, 2011

### sometimes, my first instincts are mathematical.

These smaller groups are always arranged in a tree structure. Your boss is the point where your group attaches to the tree. But when you use this trick for dividing a large group into smaller ones, something strange happens that I've never heard anyone mention explicitly. In the group one level up from yours, your boss represents your entire group. A group of 10 managers is not merely a group of 10 people working together in the usual way. It's really a group of groups. Which means for a group of 10 managers to work together as if they were simply a group of 10 individuals, the group working for each manager would have to work as if they were a single person—the workers and manager would each share only one person's worth of freedom between them. [1]
.. i started wondering if this could be viewed as something like a sub-martιngale or a variant of a hardy-littlewoοd maximaΙ function.

[1] from "You Weren't Meant to Have a Boss" by PauΙ Graham

## Monday, July 11, 2011

### internet troubles (and more)

apologies for the long gaps between posts:
in the two weeks of the SMS @ Montréal, i stayed in a dormitory building that had no internet access, so all my recent posts were written at coffeehouses and the university maths building (where the lectures were held).

also: last thursday my laptop and passport were stolen, which may explain the lack of posts in the last few days.
on a related note, i learned a few things:
1. despite the hassle of it all, you must file an official police report in order to get a replacement passport;
2. if you don't make an appointment in advance at the U.S. Consulate, then you are put to the very back of the line.
on a related note, i'm glad that i brought a notebook and pens with me [1]. i think i had scrapped out 3-4 ideas before they called me to the passport window .. which was fairly productive, actually.

in particular, i have a new idea to attack the usual conjectures that i'm obsessed with. almost surely, they won't work, but i might learn something that could be useful, later on. (-:

those things said, i still like the city of Montréal. to be honest, i think it would be a fine place to live; too bad they don't seem to be hiring .. \-:

[1] due to issues of security, large bags and knapsacks are not permitted in U.S. Consulate buildings. i'm glad that i was warned of this in advance: instead of spending hours being frustrated at what i couldn't prove, i would have spent hours being frustrated and with nothing to do (and in particular, not being able to be frustrated at what i couldn't do, anyway).

## Wednesday, July 06, 2011

### sometimes maths is like food.

learning about οptimal transportatiοn is like a lunch buffet, in the sense that if you're not careful, then you will have too much and make yourself sick.
moreover, dilemmas appear even in advance of that stage of discomfort. suddenly one starts making priorities, like picking only the dishes you really like and which you can reasonably digest ..
.. so: i'm starting to prioritise these final summer school lectures.

both ambrοsio's and sτurm's talks are fascinating, from both geometric and functional viewpoints. this theory of οptimal transpοrtation is a mysterious, deep thing.

i mean, i like (metric) derivatiοns, but i wonder if it would have been wiser to have written a thesis about this stuff instead.

on a related note (to the title, i mean): of all the conferences and summer schools i've attended, this coffee has been the best. (montréal is so cool.)

## Sunday, July 03, 2011

### work vs. lectures: also, theorems/problems as machines.

one week of lectures done, one week of lectures to go.

it's hard to strike a balance. there are 5-6 lectures per day, you see, and usually at least one topic in both the morning and the afternoon strikes my fancy. so i end up attending both sessions ..

.. and then there's little/no quality time for me to think about my own work.
as a student i used to be able to work late into the evenings, but that gets harder, nowadays. i guess i'm getting lazy.

then again, when i was a student i hardly had my own agenda of research. it's always simpler, i suppose, when one has a single focus in mind.
the topics are interesting. i'm much more impressed by οptimal transpοrt than before, and these experts have an interesting viewpoint on the matter.

they treat the mοnge-kantοrovich problem as a machine.
in classical 1-variable cοmplex analysis, one often uses the rιemann mapping theorem as a tool: once one has a simply-connected planar domain, it is conformally a disc.

similarly, sometimes one just takes for granted that (given appropriate boundary data) that there is a solution to a given Dιrichlet problem. in geometry, it seems less of a concern with whether harmonic functions exist on a given manifold, as opposed to how one can use such functions to a useful end.

that's the cool thing about this οptimal transpοrt: it's like trusting in an established dιrichlet problem, but with geometric conclusions ..!

## Monday, June 27, 2011

### stranger in a strange land.

after 24 hours in montréal, i learned that i am apparently incapable of speaking french.
reading french (which sometimes amounts to guessing) and listening to french [1] is fine. i just can't think in french that quickly:

fvck:
is arriver one of those verbs with an irregular past tense?
the french word for station can't just be station, can it?
[2]?
luckily, the lectures are given in english.

on a related note, i love summer schools. i wouldn't ever want to go back to graduate school and do another ph.d., but i do miss sitting in lectures and have someone explain something difficult to me.

the older i get, the rarer that seems to happen \-: ..

.. but on a happier note:
perhaps i'll finally learn the basics of optιmal transpοrtation! (-:

[1] i could swear that the quebecois accent is slower than a parisian accent: less mumbling, too.

[2] yes, and yes .. [sighs]

## Thursday, June 23, 2011

### a quick nod to teaching [another article post]

.. still visiting my parents, so:
no technical details today, dear readers.

NFL Player Turns To Teaching During Lockout
by Amy Ta @ NPR

As the NFL tries working through its lockout, one professional football player decided to teach youth from grades one through 12. In April, Denver Broncos safety David Bruton started giving social studies and math lessons at Jane Chance Elementary School and Miamisburg High School (his alma mater) in Ohio.

Bruton says he got the idea from his high school coach and teachers. Why did they think he was teacher material? Bruton says maybe it was because he performed well during his own high school and college years, and he had what it took to be a role model. His patience and persistence also helps, he adds.

... The NFL player naturally taught social studies because he majored in Sociology at Notre Dame. But math came as a total surprise, he remarks. The last time Bruton took math courses was his first year in college. "I was definitely in the books, on my iPad looking up how to figure out quadratic equations and finding out angles," he says.

Calling teachers "the guiding source of our youth," Bruton says no one in such a position should take it lightly. He describes the challenge of constantly being on the move in classrooms, "You go around, helping them out individually, and you constantly using your brain, especially teaching stuff that you — in my position — haven't done in six years."
it reminds me of how it feels to teach a new course and the work involved in figuring out what kind of structure it should have, how might the students best understand this or that concept.
sometimes we don't know everything, but that's not the point.

instead, a good teacher can pick up the material as (s)he goes, then effectively and appropriately convey the same lessons to an audience of students, who lack the same ease of "being good at learning."

in other words, it's not a bad thing for a teacher to know how to be a good student.

also: it's nice to hear a public persona say that "it is hard to teach well."

## Wednesday, June 22, 2011

### maybe our reality isn't very real? (from an NYT blog post)

most of the time, physics makes no sense to me. the exceptions are when, for some reason, the discussion uses mathematical language:
Physicists talk about a vast landscape of physical realizations, where myriad valleys are related to different universes, each with its own set of natural laws. Which begs the question: If laws vary across the multiverse, how can we understand our own?

Is our universe typical or atypical?

Could physics be moving from a quest for the laws of nature to a quest to explain the origin of the laws of nature? Can we even make quantitative sense of this question? In an infinite multiverse, how can we come up with a probability measure to explain the likelihood that we exist?

from "landscaping the cosmic garden"
by marcellο gleιser (13.7 @ NYT)

for some reason, i find it a hilarious idea: that our universe lies in a set of measure zero, with respect to some measure of "reality."

it's not that i disbelieve it;
i just find the terminology amusing.

imagine it: we're part of some exceptional set that defies Lιttlewood's three principles ..! (-:

## Monday, June 20, 2011

### tonight: speaking to a small, yet (very) general audience.

this week i'm visiting my parents, which essentially means seven days' worth of diplomacy and subterfuge ..
• getting up in the mornings earlier than everyone else, in order to get a few maths errands done [1]
• conveniently forgetting to announce my arrival to friends from high school, if only to cut down the number of obligatory dinners and meet-ups;

if they really wanted to see me that badly,
they'd have hunted me down by now;
it's not like i'm that hard to find.

"yes, mom: i did try to look for jobs near home;
no, mom: i don't think that particular ivy league school will hire me and give me tenure ..
" \-:
at some point i should just stop treating these weeks away like any other work-week and just treat it like a holiday.

on the other hand, this year the timing's off. next week i'm supposed to head to a 2-week workshop on all sorts of cool topics, like ..

.. optimal transport,
analysis on fractals,
analysis on metric spaces, etc.

so it seems strange to suddenly slack off .. more so than usual, i mean. (-;

besides, some of my co-authors will be attending as well, which means i really should send them a complete draft soon ..

as for immediate concerns:

tonight i'm meeting my best friends from high school, for dinner. one's bringing his wife. as for the other, we're meeting his girlfriend for the first time ..

.. which means, among other things, that i should expect variants of the following two questions:

1. what do you do?
2. oh .. so what does a mathematician actually do, other than teach?

these being my best friends, i can't be glib ..
"well, i usually stare at a piece of paper for hours, maybe write something down. occasionally i stare at a wall instead, or if there's more to write, a computer screen."
.. or highly technical, either:
i don't think they know any trigonometry or basic mechanics [2] or the basics of computer programming .. so i'll even have to be careful with analogies.
[sighs]

you'd think --- after 4 years of undergard, 5 years of grad school, 3 years at a postdoc --- that i'd have become good at this, by now .. \-:

[1] at one point in my last relationship, my (ex-)girlfriend and i were living together for about a month. the fact that she couldn't wake up before 10am (some hours after i would) probably kept the peace for a while: by that time in the morning, i was ready to set aside the frustrations of work and we'd have breakfast together.

[2] the newtonian kind, not the automotive kind. q-:

## Sunday, June 19, 2011

### retreat.

perhaps it's time to stop researching derιvations.
sure, last week wasn't particularly a good one for research .. but there's something else.

a few new ideas came up in the last 8 months or so,
but their strength is limited; so is their applicability.

in particular, i still can't make any progress towards any of those open problems that i'd like to solve.

i think i've done all that i can with them. i have a new theorem or two, however, and that's good enough.
it's important to know when to stop or to retreat. for much of my first year as a postdoc, i tried the same ideas over and over, to no success.

sometimes i wish someone had just told me to stop, pointed out that my strategy was (ultimately) flawed. that's too ideal of an event to happen, though, and not fair to say.
for one thing, it's too much to expect someone to understand exactly what you're thinking, not even your thesis advisors.

besides, i'd have been too stubborn to listen to that sort of advice. even if there were some way to travel back in time, i'm not completely sure that my past self would listen to the present me.

it's not that i believe in fate. i'm just more aware of how my own mathematical brain works (or fails to work) and what kinds of mistakes i'm prone to making.
that said, i'm not giving up completely. there's still a preprint to finalise and to submit. if i get a good idea during the writing process, then sure:

i'll make a note of it,
put it somewhere that i'll remember to revisit,
and leave it alone to continue writing.

if there's one thing i've learned, in the last few years, it's the importance of "following through" --
for, in the business of mathematics, ideas are NOT good enough. rather, it's important to shape ideas into complete proofs and have them accessible in written form.

it's true that few people will likely read your paper. if you never write up your ideas, though, then it guarantees that nobody will ever listen.
i always think in retrospect that my own work is crude and obvious, probably not worth publishing. (i wonder if everyone feels that way.)

it's better, though, to have something modest but fully-formed, rather than nothing at all.

## Friday, June 17, 2011

### if time is money, then it's best to budget it.

33 states,
10 countries,
3 continents,
dozens of conferences ..

.. and i still haven't learned:
never underestimate the toll that traveling takes on you.

i have a new rule about summer traveling:

no matter how exciting traveling may sound,
never organize two trips with only 1-week interim period (or less).

it's not worth it.

last weekend i was visiting friends in d.c. all of this week, i struggled with setting up a new work routine [1] and accomplished nothing. i couldn't even pinpoint what problem i wanted to work on!

instead, i was running errands and planning out the next 3 weeks ..

1 for visiting family,
2 for a workshop in montréal ..

.. the key concern being: what can i do in that time?
my father is retired, keeping busy with projects and repairs in the house. does that mean i have uninterrupted time to work on my own, or will he pop in, every five minutes, complaining about the water piping?

maybe i should revise the preprint(s). then again, there will be a lot of emphasis on optimal transport in the workshop; should i read about that topic instead?

i'm getting older. the pessimist in me would say that i'm becoming more inflexible and brittle; the optimist would say that i've begun to appreciate consistency and order. forgetting the interpretation, those two (and i) are in accord:

[sighs]
i should have planned more carefully.

why did i ever think that summers were long and slow, with plenty of occasion to think matters over ..?

[1] from an economical viewpoint, i'm being a blockhead. i'm unemployed but still working as a mathematician in my free time (i.e. for free). on the other hand, it's fun .. in a frustrating way .. and i'll be better off if my research comes to fruition.

i have never heard of a job application being harmed by having too many papers! (-:

## Tuesday, June 14, 2011

### a gradual transformation into a mathmo, again.

"you can't be both a mathematician and live in the world." [1]

apologies to my readers, if you've been waiting in vain for posts in the last few days: i was away, visiting friends.
in case you were suddenly wondering,
yes: they're doing fine.
q-:

it's probably the longest stretch of time, this year, that i've taken off from mathematics.

the previous instance was fairly recent: sunday and monday of memorial day weekend. i spent it
• running a 5K in humid, 88oF heat,
losing to kids that were 10 years younger than me,
• rock climbing with people that were much better at it than me.
so perhaps some habits die hard; even without any maths,
some frustration out of life is inevitable ..!
as for today, it's hard to concentrate.

i'm a little rusty already, not fully embedded into the maths personality. i spent 3-4 days immersed [2] in being a person,
catching up with my friends and their lives,
meeting new people,
remembering various song lyrics.
my friends are fine people and i'm fond of them,
but by the last day, i was itching to think about maths again.

there's something soothing about tuning the world out, floating away from this feeling of self, from matters of streets and cars and food and rent and bills and smiles and expectations ..

.. and into a platonic world of ideas,
reasoning out a map of the landscape.
whenever i meet someone new, a non-mathmo or -techie, i might say -- "oh, cool: you deal with reality!" -- and get a few laughs.

i mean it honestly, though:
at this point in my life, i'd struggle with a "real" job.
from experience, it takes a few days for the transition, so i'm taking it slowly. today will consisting only of working out little lemmas, getting used to technical details.

maybe tomorrow i'll try the big picture again, tackle something hard.

[1] i think this quote is attributed to grοmov (in support of pereΙman's refusal of the fιelds medal) but i can't seem to find the article or blog that would have posted it .. [shrugs]

[2] in the sense that everything went smoothly, except when i tried to sing "cielito lindo" at this one karaoke bar .. (-;