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]

a quick nod to teaching [another article post]

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

i did stumble upon this article, though:

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."

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 ..! (-:

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.
• dodging the sorts of questions about the future, that academics find hard to answer.
  
  "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-:

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.

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! (-:

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, 88^oF 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,

reminiscing about the past,
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 .. (-;

not yet an old dog, plenty of new tricks out there ..

some projects are coming to a close, such as this project about measurαble differentιable structures. the preprint is readable now, but will take some polish before its submission ..

.. and besides, i don't know where to submit it, yet.

that said, perhaps it's time to learn something new-ish. often it seems
like what i know is not enough to attack the problems i want to solve.

so maybe i should study some new problems,
learn some new topics.

---

in september, the research group that i'll join is strong in non-linear ΡDE (particularly parabοlic equations). maybe i'll finally commit and learn some parabolic things ..

.. or learn ΡDE properly, for that matter;

the last course i took in them was 10 years ago;
even then, i never felt like i knew that stuff well.

to me, knowing about sobοlev spaces and variatιonal problems
doesn't translate to knowing about ΡDE.

related to this, maybe i should also learn about dιrichlet forms.
they seem to come up a lot, say in the heat equatiοn, but also in
the analysιs on fractaΙs.

in fact, there's a recent preprint by iοnescu, rοgers,
and tepΙyaev (arXiv link) about derivations and Fredhοlm operators
on a certain class of self-sιmilar fractals.

it's not wholly unprecedently. they're following the approach of kιgami, where the calculus on such spaces is constructed from discrete gradients on approximating graphs, and then through some heavy lifting, one earns a limiting Dirιchlet form for one's efforts.

i'm writing about it as if i know the details, but i don't. it's on my
radar, but the whole operation is just mysterious to me ..

.. i mean, think about it: most of the time in mathematics, one studies limiting processes that correspond to structures only, on a fixed space, or perhaps to a family of spaces with already-good structures.

here, they're doing both at once: nontrivial .. and mysterious.

sub-days.

the great thing about summer is that you can opt out of teaching [1].

a month (or two? [2]) ago a colleague of mine suggested that i'd be a good fit to teach a summer course, since the department knows me and trusts me to teach well.

it would be nice to make more money
.. but teaching for 1-2 hours a day, 3-4 days per week .?

i think about all the times, last semester, when i had an idea and had no time to attack it. i've been looking forward to uninterrupted research, for a while .. have probably been blogging about it, too.

having enough time .. that's worth a pay cut, i'd say.

in short i've accepted a summer of (relative) poverty in favor of intellectual freedom. so that my decision won't be in vain, i'm trying to be more productive this summer ..

.. and so i've been trying a new routine:
work on multiple projects, every day.

it hasn't been a complete disaster, no more difficult than switching between teaching and research duties on workdays. it is strange, however, to tell myself:

stop thinking about this,
because you promised to think about something else now..!

it doesn't always work. sometimes i get a seemingly good idea. experience tells me that it probably won't work, so it's a matter of finding its breaking point .. and usually i want to know, right away.

like everyone else, i hate being wrong.

---

what seems to help "multi-tasking" is splitting the day into natural blocks, and setting aside a task for each.

in the morning i drink coffee and work on "geοmetry." (lately i've been trying to characterise measurabΙe differentiabΙe structures.)

when i can't think of any more ideas to try,
then, to clear my head, i have lunch, maybe go for a walk.
some days lunch is at 11am, other days at 3pm.

"in the afternoon" i run errands and work on joint projects. (it's been sοbolev extensiοn domains lately.)

when i'm sick of being confused or of having my ideas repeatedly fail, then i go running or rock-climbing. if i haven't complained to anyone lately about my life, then i might meet friends afterward.

it's a leisurely life. there's always tomorrow to sort out yesterday's ideas, to see where i went wrong.

in other words, why worry about working for a whole day, when you can work several sub-days in a row?


[1] .. provided that your academic year salary is enough to pay the year-round bills.

[2] another great thing about summer, or not teaching, is the freedom of forgetting what day of the week it is. if i feel like working, then so what if it's sunday? if my ideas aren't working, then why not take wednesday afternoon off?

just because i haven't taken wednesday afternoon off in a while doesn't mean that i can't .. (-;

a mathematical metaphor.

The key insight of both Peters and Collins is that we spend too much time on addition and not nearly enough on subtraction.

~ from Think Tank: Why we all need a 'To Don't' List: Two management leaders reveal a simple but powerful idea for achieving high performance – deciding what not to do.

the article author puts forward his own don't-do list. among them:

• Don't answer email during peak morning writing hours;
• Don't drink coffee in the afternoon;
• Don't go to sleep after 11pm.

i agree with the first "don't" -- the pristine time of the morning, when your brain is clear and you can entertain ideas with a fresh perspective, is too valuable to waste on email.

on the other hand, it seems silly to restrict deliberately one's workload in the later hours of the day ..

a kind of holiday.

when i woke up this morning, i had fully intended to write all day.

while making coffee, though, i started thinking about a particular problem regarding measurabιe differentiabιe structures ..

.. then i realised that one little lemma suffices to solve it ..
.. and suddenly, i couldn't let it go.

so: i'm taking the day off -- from writing, anyway. i want to work on this problem until i'm sick of it ..

wow.

from now on, this is what i will imagine when i think of a round carpet (in the sense of circle packings).

from bored-to-death.com