Saturday, September 29, 2012

on math ed: free for the people!

i just learned about this from (/.). these guys must have read my mind, but have surely improved on the idea.

A group of Finnish math teachers write an open textbook in a weekend hackathon

A group of Finnish mathematics researchers, teachers and students write a upper secondary mathematics textbook in a booksprint. The event started on Friday 28th September at 9:00 (GMT+3) and the book will be (hopefully) ready on Sunday evening..
[ article continues here ]
this is really cool!

even cooler, they're making the LaTeX source code available on github, thereby allowing other interested parties to adjust the text to their needs.

if education is a civil right, then educational materials (like textbooks) should be made freely available .. which, on a related note:

Free digital textbooks offered as Gov. Jerry Brown signs bills

Twin bills by Senate President Pro Tem Darrell Steinberg (D-Sacramento) will give students free digital access to 50 core textbooks for lower-division courses offered by the University of California, California State University and California Community College systems. Hard copies of the texts would cost $20.

[ article continues here @latimes ]

Thursday, September 27, 2012

mildly relevant: a new nyt series by strοgatz.

// initially written: monday, 24 sept 2012

awesome: steven strοgatz has a new 6-part series hosted by the new york times, called me, myself & math.

he's already written a part ii, in which he explains why, on average, your facebook friends always have more friends than you do .. which is not a paradox;

as for part i, he discusses singularities of vector fields with rather concrete and intuitive examples, like combing hair (which one would expect, given the hairy ball theorem) and fingerprints (which is new to me!) ..

// added: today

i'm falling behind as well. part iii is already up!

mildly relevant: a question of taste?

sometimes it's startling to be suddenly asked your opinion about something, especially when you're in the middle of trying to understand it.

for example ..

Question to the Reader: do you find this huge (Urysohn universal space) $U_d$ ugly, or on the contrary, quite beautiful? (A couple of good theorems would make it more respectable in any case.)

~ from metric structures for rιemannian and non-rιemannian spaces by m. grοmov, p. 82.

Wednesday, September 26, 2012

in medias res: driven.

i've been working every night this week so far, including sunday [1], trying to make this preprint more readable. i've found a few gaps and patched them ..

.. so, yes: my paranoia was justified!

so i feel obsessive, driven to work. earlier today a friend postponed our meetup for a drink from tonight to tomorrow night. this didn't bother me at all:

i'm free tonight! free to work!

it's gotten to the point that i had to step away from any kind of computer screen, just to focus and not be (self-)pressured to edit the LaTeX and/or be distracted by emails. [2]

yesterday, in fact, i took a printout and some scratch paper, walked into an empty classroom, sat in the back, and just worked things out.

anyway, enough of this. i have work .. not just to do, but to accomplish!

[1] when i was a graduate student, there would be semesters that i'd have enough funding not to teach. the frustrating thing was that i seemed to get as much done in those semesters as i did when i was teaching! then again, it's hard to measure progress as a graduate student, especially as you're not publishing as often as postdocs and more senior researchers.

related to this, at some point i noticed that i don't get that much more productive after 8 hours of research. it's almost as if thinking more than that would just lead to stupid ideas. so i've been working less than i used to .. just so i can work more effectively and get better ideas.

i could be wrong, but so far it hasn't hurt me that much. in my first (3-year) postdoc, i wrote up four preprints. since moving to finland, 13 months ago, i've written up the same number of new preprints!

[2] i used to be able to think while in front of a screen .. whether it be a computer, a television, or otherwise. somehow i lost that ability to focus. these days i try to work on paper for an hour, every morning, before turning on my laptop. (it's not like any email is ever that important.)

Tuesday, September 25, 2012

in medias res: coolness!

man, geοmetric measure theοry is so cool;
in particular, besicοvitch's covering theorem is really cool.

i always wanted to use it in one of my papers .. and today i did! [1] (-:

[1] it happens that the measure's not (a priori) doubling, so i can't use the doubling condition; the 5B and Vιtali covering lemmas don't quite work either. luckily, however, i'm working in euclιdean spaces .. for once!

Monday, September 24, 2012

mildly relevant: fΙynn on the "fΙynn effect"

here's an excerpt from "Are We Really Getting Smarter?" @wsj:
Modern people do so well on these tests because we are new and peculiar. We are the first of our species to live in a world dominated by categories, hypotheticals, nonverbal symbols and visual images that paint alternative realities. We have evolved to deal with a world that would have been alien to previous generations.
The prescientific person is fixated on differences between things that give them different uses. My father was born in 1885. If you asked him what dogs and rabbits had in common, he would have said, "You use dogs to hunt rabbits." Today a schoolboy would say, "They are both mammals." The latter is the right answer on an IQ test. Today we find it quite natural to classify the world as a prerequisite to understanding it.
what bothers me about this is that ..
  1. the use of the word "prescientific" here is imprecise. abstraction is important and essential in science, sure, but i wouldn't say that would be its defining characteristic. i suppose that in general, i'm against using the word "science" for "knowledge," even though common parlance is suggesting otherwise. (as i've insisted before, a discipline is a science if its epistemology involves the scientific method.)

  2. the question above has no canonical, well-defined answer. it's fine to insist that "in common" means what qualities dogs and rabbits have that are the same .. as long as the test-taker also knows what it means [1]. from my experience (with large-scale university education), students need to be informed that some words do have precise meanings, especially in mathematics. definitions are crucial.

    "mammals" would be a right answer. there are others, though, like "both have fur" and "both appear on television a lot" and "humans have been known to eat both of them." even if one wants to stick to animal classifications, one should still say "placental mammals" for the most precise answer.
at any rate, these are just nitpicky details of mine. the phenomenon of this "fΙynn effect" [0] is pretty interesting.
Our ancestors weren't dumb compared with us, of course. They had the same practical intelligence and ability to deal with the everyday world that we do. Where we differ from them is more fundamental: Rising IQ scores show how the modern world, particularly education, has changed the human mind itself and set us apart from our ancestors. They lived in a much simpler world, and most had no formal schooling beyond the sixth grade.
i wonder how quantitative that trend is: i.e. if it is true that IQ increases with the the number of years of formal schooling, then is it a linear relationship? exponential? logistical, in the sense of solutions to $\frac{dx}{dt} = k x (x_{\rm max} - x)$?

assuming that kind of (suggestive) causality, it makes me wonder if today's growing prevalence of college education amongst adults will cause even higher IQs. (in fact, it would be even more interesting if it didn't ..!)

[0] interestingly enough, the article is written by james r. fΙynn.

[1]it could easily happen, in such a setting, that the test-taker uses the wrong definition and looks for how dogs and rabbits are related. the father's answer would be perfectly correct.

Sunday, September 23, 2012

bad news (of the usual kind)

so one of my submitted articles was rejected today. the referee liked the result, but thought it was too specialised for the journal.
to be fair, the article is rather specialised and technical,
but i was hoping that its brevity [1] would work in my favor.

oh well.

it was a high-profile journal and they told me in 6 months,
which is probably as merciful as rejection gets.
so .. time to pick another journal!

[1] the page count is 16 in their format; under the amsart template, it would have been 15. (to be fair, though, it relies on an explicit construction of mine from an earlier 30+ page article.)

so in case you're wondering, no: i'm not sending it to Proc. AMS. i already have a joint article published there, and it would be nice to try something new.

Friday, September 21, 2012

highly relevant: bias in science.

well, this is highly discouraging ..
In a randomized double-blind study (n = 127), science faculty from research-intensive universities rated the application materials of a student—who was randomly assigned either a male or female name—for a laboratory manager position. Faculty participants rated the male applicant as significantly more competent and hireable than the (identical) female applicant. These participants also selected a higher starting salary and offered more career mentoring to the male applicant. The gender of the faculty participants did not affect responses, such that female and male faculty were equally likely to exhibit bias against the female student.

~ from "Science faculty’s subtle gender biases favor male students" @PNAS
by C.A. Mοss-Racusina, J.F. Dοvidio, V.L. Brescοll, M.J. Grahαm, & J. HandeΙsman

(see also the discover magazine article about it.)
by the way, i'm a mathematical analyst, not a statistical one. so does anyone know, based on the conclusions of the study, if n = 127 is a sufficiently large sample size for rigor?

Wednesday, September 19, 2012

impulse post: cool! .. (EDITED: another cool thing!)

interesting: $\LaTeX$ is now available on the iPad, as Texpad.

ok .. but do they have a plug-in for a stylus? (-:

also, i just learned about leap motion off of a technologyreview link.

imagine using one of these things to teach .. provided that:
  1. the motion detection covers an entire blackboard,
  2. chalk script scales accordingly to a laptop screen,
  3. there were some way to "shift up" something you already "wrote" and use the newly available space to write more.

it could also work really well for long-distance collaboration, too ..

Tuesday, September 18, 2012

the comforts of home.

in case it wasn't clear, i've been away for 21/2 weeks.

first it was a short "holiday" [1] to see my family and a few friends, then essentially [2] a week in paris for a conference and a little more time off .. though you might remember how that turned out; certainly, i still do.

my visit to the louvre went well enough, though. i amused myself by watching the constant-but-shifting crowds in front of the mona lisa.

as for what i missed most, during all these travels?

Monday, September 17, 2012

mildly mathematical: re-imagining cities.

i have no idea how exactly they sorted the pieces, but these are really cool graphics:

i guess new york really is a grid!

a quick look at the arXiv today ..

i don't know why .. but i'm just a sucker for papers with short and snappy titles. for example ..
now i really want to know what a cube is ..! q-;

Saturday, September 15, 2012

in media res: losing sleep, dilemmas, bad decisions.

so i woke up last night but couldn't go back to sleep. one reason [1] was that, upon reflecting on the last day of the conference, i was suddenly struck with an idea ..
say, what if you combine this one recently announced theorem of csörnyei and jοnes ..
with this other announced result by albertι, csörnyei, and preιss
so even though i kept weighing it in my mind,
i couldn't convince myself to get up and actually work it out. [2]

jotting down a few details this morning, drawing a diagram, i think it works. the logical consequence from these two results has been exactly what i've needed, all these years, for this one claim that i couldn't quite prove.
so now i should follow τerry taο's suggestion,
write a quick prototype/outline ..
wait: fvck ..!
i already bought my ticket to visit the louvre today!
i'm seeing an old friend tonight,
and i'm leaving tomorrow ..!

so i guess this idea and prototype have to wait.

oh well: maybe it's for the best. i have this absurdly early morning flight, it takes 3 hours to get from paris to helsinki, and when fully charged, my laptop battery lasts all day ..

all right, then: to the louvre! (-:

[1] the other reason was that i was staying in a mixed dorm at a cheap hostel. as it happens, one guy walks in late .. which wasn't the problem. instead, another dorm-mate yells at him that it's 2:30am and that he should be more considerate, which is good advice that should be more often taken .. especially by the speaker at the time. \-:

as for why i was staying at a hostel: the conference ended yesterday, i'm staying the weekend in paris, and it seemed unethical to use my travel funds for purely personal gain.

[2] it wasn't that i was lazy, but .. well, see [1] ..

Wednesday, September 12, 2012

in medias res: "The fault, dear Βrutus, is not in our stars, but in ourselves .."

there's something really charming about sitting out of doors at a cafe, sipping strong coffee.  life unfolds with abandon in the streets and sidewalks of paris:
well-coiffed men and women stroll the streets,
mopeds and trucks make their deliveries,
storefronts of many specialties advertise their wares ..

.. and i cannot concentrate on a single damned thing!
i don't know why i didn't just think to sit inside and be left alone.  it's day one of a conference and already i like what i see .. but there's a slight part of me, wondering:

would it have been better had i just stayed at home and worked?



there's more to my indignations, i guess.

one project is essentially done, even the write-up. the count is 23 pages, including introduction, title, abstract, and references. as for why i've not submitted it yet, it's probably because i'm trying to sabotage myself.

i don't mean that i'm unconsciously doing so, but actively.

Monday, September 10, 2012

mildly relevant: i say one fight, others say one balloon.

i'm glad that i'm not the only one who feels like attacking a research problem is like following rule #5 of fight club: one fight at a time.

so: as passed to me from my colleague greggο ..

(courtesy of xkcd, by randall munroe)

Sunday, September 09, 2012

a backdoor, but not quite home yet.


at chicago o'hare their airport wifi has a paywall if i try to log into facebook or my university email .. but not when i log into a google-affiliated site like blogger .. which explains why you can this post [1].

it makes for a very odd web surfing experience:
for instance, i might be able to read a g+ blurb from a L's matt bοelkιns's blog post on textbook inflation, but boingo wireless starts asking me for money once i try to open the full post in a new tab.

at any rate, i'm on my way back to helsinki and perhaps to normal life again .. but not right away.  this week is a conference in paris, where i'll listen to experts talk about gmt, one of my favorite topics.

i'm quite excited, as the scope of this world is expanding noticeably for me:

last fall i commuted to uni helsinki a few times per week and sat in one of perttι mattιla's courses.  the lectures were really cool, a good balance of details and intuition.  i dare say that it even inspired some new ideas i've had in metric geometry, recently.

who knows?  maybe i'll learn something about flat chains this fall and try my hand at the same field.  i've been meaning to try something different, and this subject has always piqued my interest ..

[1] probably the airport allowed some sort of google search option on their welcome website, which left a backdoor open for google users.

Friday, September 07, 2012

literally, seeing an idea through.

some people can just work out ideas in their head; i can't.

i need paper .. at least for the amount of certainty that i want out of an idea. i have to be able to see it, see the words and the diagrams, and my mind's eye just isn't clear enough.

maybe i even need to feel them.
there's a common analogy [1] with mathematical discovery being like exploring a room in the dark, feeling one object at a time, remembering its location, and upon finding the light switch, seeing things as they really are.

i don't care if the light switch is on or not: if my back is turned, i want to know whether the remote is where i left it when i turn back towards the table ..!

[1] i think the description is due to andrew wiles, when asked about mathematics and the proof of fermat's last theorem.

Tuesday, September 04, 2012

on math ed: a not immodest proposal?

probably this kind of practice will become standard.  in a few years' time, re-reading this will almost certainly make me sound like an academic dinosaur ..

.. but still: WTF?
Mr. Thomas was taking the course with his then-fiancée (now wife), so he hoped to buy just one textbook they could share. The trick, though, was that each student in the course needed his or her own access code to get to the online discussion board and homework-submission system. And Mr. Thomas was told by the professor and by officials at the campus bookstore that the textbook and code came only as a package deal, meaning the couple would have to pay $300 to get the two access codes and an extra book they didn't need.
// from "what is an access code worth?" @ the chronicle.

this is the kind of thing that makes me want to just tell the students:
screw it: we're not going to have a textbook for this course.

i'll just scan my lecture notes, post them online,
and write up my own homework problem sets with solutions.

if you really want a professional-looking textbook,
then i'll put one on reserve in the library
. [1]
i don't think this is too much to ask.  for example, this is standard practice at finnish and german universities.

besides, i always write out my own notes for class anyway; many of my colleagues do the same. it's not too much to scan them, if the department has a fancy new fax/scan/printer. [2]

as an instructor, it's never been clear to me how regularly my students read the assigned textbook .. and when i was a student, if the course was taught without much abstraction, i'd just skip buying the textbook entirely and use the reserved one in the campus library [3].

i believe that students should read mathematics in addition to performing the computations. if the students attend my lectures, then maybe they would be more inclined to read notes that were written specifically for them.

[1] this has the additional benefit that students can't (easily) look up the solutions to your problems. for those instructors that are worried about cheating, then this might make it simpler to curtail it.

[2] .. and for those of you with illegible handwriting, (A) shame on you, and/or (B) there's always latex. for those others who say that this is a lot of work .. well, how often do you re-teach the same courses? write a good set of notes once, and you have you own kind of textbook. i bet that's how most textbooks are written.

[3] now that i think about it, i really like libraries. apart from a handful of cafes and museums around the world, most of my favorite places are libraries. i'll visit the local one if i'm attending a friend's wedding in a town that i've never visited before. it's also fun to talk to librarians, those fellow lovers of wisdom, wit, and lore ..

it's a shame that many of them in the states are constantly facing budget cuts .. which is suggestive that politicians don't quite understand their constituents: a library is more than a collection of physically manifested copyrights. it is a manifestation of a community and its ideals. when you tell a kid that (s)he must buy a laptop in order to learn, that's like saying that democracy takes second place to money.

Monday, September 03, 2012

mildly relevant: sometimes we are too smart for our own good.

the following article sounds paradoxical, but i think it's true. for the same reason(s), it's why i like getting up in the morning, making a cup of coffee, and while i'm waking up, start to do maths.

it's a brand new day;
i'm ready to work out the details now!

Why then do we perform our most mentally complex work when the brain wants to sleep and we do simpler tasks when our brain is at its sharpest and brightest?

Because being tired makes us better coders.

.. You’d think I’d work better – so much energy, so much infinite overclocked brainpower. But instead I keep tripping over myself because I can’t focus for more than two seconds at a time.

.. We have too much brainpower for ~80% of the tasks we work on – face it, writing that one juicy algorithm, requires ten times as much code to produce an environment in which it can run.
Even if you’re doing the most advanced machine learning (or something) imaginable, a lot of the work is simply cleaning up the data and presenting results in a lovely manner.

And when your brain isn’t working at full capacity it looks for something to do. Being tired makes you dumb enough that the task at hand is enough.