preparing for class, part 2: preparedness.

likely i'm deeply biased about mathematical culture and conventions, but i always thought that lectures and mini-courses belong to more senior and experienced people.

for instance, i recall now some lectures that colleagues gave in chennai, a few years ago, as well as an earlier summer school in barcelona. these were very fine lectures indeed;

in particular, i admired their self-restraint.

it was clear that the lecturers knew many things, but opted to discuss a handful of ideas with care, clarity, and motivation. there was no real grand-standing and strutting: the ideas were the stars of the show.

having been impressed by this approach, i think it best to follow the same traditions. the ideas should come first.

i already sent a title/abstract of these lectures. thinking about it, many of these ideas are very new .. new as in the last few years, so this is going to require a great deal of care. i don't have too many references to depend on, and those in the literature require ..

.. some experience to decipher, you could say. so unless i expand the topics further ..

.. which runs the risk of cramming too much into the space of a few hours [1] ..

.. then whatever i present will run the alternative risk of becoming a standard reference for these topics [2] .. especially as i'm thinking of assembling the lecture materials into some kind of a monograph ..!





[1] i've gotten a little too used to the length of finnish seminars, which is 2 x 45min. when you think about it, that harrowing week where i gave two seminar talks would contain the same content as 4 usual lectures elsewhere .. and in case you were wondering, yes: that week was spent beta-testing some preliminary lecture material for next month.

if you're surprised, then you shouldn't be. come on: do you really think i'm that un-lazy? (-;

[2] re-reading what i just wrote, it sounds arrogant and self-serving, but i don't know any other way to describe it. in an expositional article, the advisor once spent a chapter outlining one particular topic, but that was 5-6 years ago and due to brevity, it doesn't discuss how exactly one uses the theory. there are some new tools available now, too, which warrant their own exposition.

preparing for class, part 1: first day jitters (to come).

so i'm scheduled to give a few lectures this november, in spain.

originally in the invitation, i was asked to give a talk or two .. where two seemed like an important detail to consider. so i asked exactly how many talks they wanted and what topics the audience would find familiar. the organiser responded, then i wrote back, then he did ..

.. and one thing leads to another ..

.. so rather than rushing in my usual manner through highly technical details, i'll instead go through a half-expository route .. and probably promote my own (recent) results as well.

i think this to be a great honor;
that said, i'm deeply worried about it.

mildly relevant: i am a masochist .. and likely, so are you.

this headline's been floating around the web recently. in particular, the excerpts below are explicitly from an article @arstechnica:

as the authors of a new paper on math anxiety point out, most forms of higher math didn't even exist until a few centuries ago. It's very unlikely that this sort of anxiety has evolved a specialized brain structure dedicated to it. So, the researchers used a combination of math quizzes and functional MRI scans to identify the areas of the brain associated with the fear of math. It turned out to be one that was previously associated with the experience of physical pain. And it doesn't appear to be the first time that area has been borrowed for other purposes by evolution: it also helps register the discomfort of social rejection..

.. well: that will certainly increase the number of mathematics majors! 7-:

strictly speaking, either we are masochists,
or that we've just had bad teachers that weren't shy about calling us stupid ..

.. others have indicated it can be triggered by indirect forms of pain, such as social rejection. But the authors note the majority of published studies associate it with pain, and that it's possible to induce the experience of pain simply by stimulating the insula ..

okay.  fine, so we're masochists;
my parents could have told me as much!

it can also be a point of pride, i suppose: mental toughness, in face of adversity and perceived pain. actually, it has a stark romanticist ring to it .. (-;

actually, there's more:

 their conclusion is that we are actually dealing with a pain response, and one that's not triggered by doing math. "It is not that math itself hurts; rather, the anticipation of math is painful," they suggest.

to be fair, what else triggers the pain center of the brain? does physics do the same thing? literature? what about sports, where there may be actual pain involved?
..
..
..
.. now that i think about it, wouldn't the readings change if the human subject had nothing to fear from maths? after all, the study is on math anxiety, not biologically-manifested cognition of mathematics.

i must be jumping to conclusions, asking the wrong questions. the point isn't whether maths inherently triggers pain. rather, if maths triggers anxiety, then does it manifest in the form of pain?

a day in the life: impromptu talks.

i think i'm developing a reputation for responsibility, punctuality, and good cheer ..

.. which, i fear, could very well lead to disaster!

the last thing i need is one more goal to juggle and meet,
and the potential fallout from if/when i drop the ball with something important.

maybe i should start breaking a few promises and failing to show up for a meeting or two .. you know, small things to keep my colleagues on their toes?

on a related note, i've been having a lot of meetings lately .. but more on that later.

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so yesterday i addressed the department .. or at least a large chunk of it. of course, i didn't intend on this at all and had i known, i'd have most likely refused.

it all began when

mildly interesting: a look back.

sometimes i forget how history unfolds .. even within the recent history of american mathematics:

"And it's kind of interesting to see what happened to engineering. So like when I got to MIT, it was 1950s, this was an engineering school. There was a very good math department, physics department, but they were service departments. They were teaching the engineers tricks they could use. The electrical engineering department, you learned how to build a circuit. Well if you went to MIT in the 1960s, or now, it's completely different. No matter what engineering field you're in, you learn the same basic science and mathematics. And then maybe you learn a little bit about how to apply it. But that's a very different approach. And it resulted maybe from the fact that really for the first time in history, the basic sciences, like physics, had something really to tell engineers."

~ from "noam chomsky: on where a.i. went wrong" @theatlantic

wow: a lot changes in 50 years. if i had to name one of the top mathematics department in the world now, MIT would be up there ..

.. then again, maybe i'm making too much of this personal anecdote. after all, how many top maths departments were in the united states before the 60's, anyway?

a day in the life: lack of willpower, and footnoted opinions about on marginal utilities of productivity and on collaboration.

(this was originally written after sundown on sunday, 4 november 2012.)

the sentiments are pretty common in my life, so this post is probably an instance of the usual affect of academic researchers who work all the time. lately i've developed the opinion that this affect mightn't be the most effective means of working, especially if one trades in the coin that is creativity and innovation [1].

with that in mind, the short post below is about trying to hack my own personal productivity function, by way of a morning routine that exploits the temporary "reboot" effect after a good night's sleep.

despite the brevity of the post, i surprised even myself by how many side opinions i have in this business. some are about the nature of collaboration .. which i'll write more about in a future post.

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in principle i want to work, but i cannot seem to gather the willpower to do so on a sunday evening to break out the pen and pad of paper, turn to section 3 of someone else's paper, and work out details to technical lemmas.

i'd much rather it be easy. anyone would.

experience tells me, however, that if i don't put in the work, then i won't really understand any of it .. at least to the degree that i can effectively use their results.

i'm not so tired from the week before and there is nothing stopping me from doing what i described above. on the other hand, i don't feel well-rested, either. there is the risk that

• i start working,
• everything's going well,
• and suddenly it's .. 2am? fvck!

my original intention would have been, as always, to get up bright and early at 7am [2] and make use of the pure productivity of the morning, as to make some significant progress on my own solo [3] projects ..

.. because i know, from experience, that the time i spend at the office will be productive, but not nearly as much as those first morning hours.



as for those footnotes ..

a day in the life: to-do lists? to-don't!

today i tried to be responsible,
so i tried to do as many of the items on my to-do list as i could.
        i can say with definiteness that it wasn't worth it.

maybe completing to-do lists just takes practice.
maybe i didn't take enough breaks,
maybe i didn't spend enough of the morning attempting creativity,
        brainstorming for research .. and just got frustrated at the lack of progress.

at any rate, running all these little errands has left me tired and unmotivated to ever do them again.

there's a reason, i suppose, why my to-do list is never fully crossed out and why i "procrastinate" with other things, like looking things up for research notes.

i guess i'm just spoiled. 7-:

mildly interesting: factoring numbers, self-similarly.

a friend of mine sent me the link to these animated factorisation diagrams, which are captured below as stills.

primes are displayed as circles ..

whereas for each factor, like the 5's in 250 or the 2's and 3's in 216, another level of  self-similarity is added.

admittedly i kept waitingfor another power of 2 or 3, just to see more iterations of four-corner sets and sierpinski-type triangles .. (-:

mildly relevant: crowd-sourced research, and could it work for maths?

when applying for grants, most of the time i expect a panel consisting of more senior researchers, possibly even a few of my peers.

this possibility, on the other hand, changes the crowd quite a bit!

Crowdsοurcing curiοsity-driven biοmedical research

Fact: the average basic-research life scientist deals with an 80% grant rejection rate, and gets his or her first big government grant at age 42. Basic biomedical research uses advanced 21st century technology, but is still fueled by a clumsy, archaic government-grant funding model that even predates the Internet.

It’s time scientists experimented with the way we all experiment.

Today, there’s a glut of highly trained but underemployed scientists. Let’s harness their idealistic passion before they turn grey, using social networks and data sharing to create an open, interactive, dynamic model of basic life sciences research. That new foundation can serve as a platform on which others will build and improve. This is particularly vital for mental health research, so often stymied by misunderstandings and blind spots, both public and scholarly.

// more @ rockethub.

to state the obvious, the difficulty is to find a way to show a project's significance to those who have the funds.

as for who might have the funds, likely they consist of normal, upper-middle class people and due to self-selection, more likely a tech-friendly professional crowd; who else, after all, would pay attention to this kind of proposal outside of their daily life?

despite a tech-friendly crowd, though, this wouldn't be easy. i doubt it would work at all for pure mathematics, and most of you (mathematicians) probably agree already. the point, however, is to figure out why, and a few reasons come to mind.

mildly relevant: amusing jargon ..

the terminology in metrιc space geοmetry is awesome;
i'm thinking of jargon like ..

• "prοpeller" (as in prοpeller cοnjecture)
  
• "exρander" (as in exρander graph)
• "Earthmοver" (as in transpοrtation cοst distances on a space of measures)
• "Tug-οf-War" (as in stοchastic games and ΡDEs)
• "Lamplighter" (as found in rigidity of quasi-isometries and metric distorsion)
• .. even "Pοlitics!" (as used in absοlute minimisιng Lipschιtz extensiοns)