Sunday, June 23, 2013

on the lack of hurry lately.

from: saturday, 22 june 2013

all i did today was make coffee, read a little, and sort out photos from yesterday. i didn't do any maths.

today is midsummer's day (or juhannus) and yesterday was midsummer's eve. both are official holidays in finland and arguably the most important ones. celebrating it has the same, easy feeling as thanksgiving in the u.s.: you don't have to believe in anything, other than the fact that the longest day of the year is upon us, and one observes it during the closest weekend to it.



i used to work through holidays or, at the very least, try to do so as much as possible .. where "possible" depended on whose company i kept. living in finland these last two years, though, has tempered that desperate feeling.

i'd like to think that i'm a tireless, relentless researcher, but that's hardly true. for instance, i found out that there's only so much time in a single day that i can spend thinking, reading, attacking a certain line of thought.
the truly productive hours are preciously few, in fact: usually two hours in the morning and two in the late afternoon or early evening. maybe the former is fueled by an early surge of coffee and dopamine, the latter by the mere suggestion that the end of the day's work is near and sh-t, i'd better get something done! [1].

it is hard to ignore the regular workday, even if one isn't beholden to it. during the academic year the department is often quite empty by 4pm, if only because that's when kids get off from school and the faculty, most of whom are parents, are off to pick them up!
in contrast, i remember teaching 2+2 during my first postdoc, going home exhausted, and just being too mentally drained to get any real thinking done. [2] i was always struggling to find long blocks of time in order to get something done, only to regularly come up with nothing of consequence.

it got to the point where i really wondered if i was really right for this job, that maybe i wasn't meant to be a mathematician. heck, i still don't know if i'm right for this job. i mean, it's working well enough .. but often i fear for the next dry spell of inspiration. even during holidays now, it's hard to let go completely and just forget.

at any rate, i now know that there's an opposite to the spectrum: sometimes i feel like i have too much time and it's wasted: i can neither use it for research gain, and it's probably not enough to warrant taking on a partial load of teaching duties ..





[1] there are exceptions, of course. if i'm in the middle of a draft of a paper, then the hours fly by and i have to take care, set the work aside, and do something else before going to bed at night .. if only to guarantee that i'll sleep well enough to work efficiently the next day.

there's a difference, i suppose, between the initial understanding and development of the problem and, upon success, the technical implementation of its solution.


[2] it took me a while to get used to the routine of lecturing and developing plans for enough of the standard courses, before i could "shut off" that part of my brain during my non-teaching hours. sometimes i suspect that i'm just highly inefficient at scheduling and multi-tasking.)

Wednesday, June 19, 2013

some "comic" relief.

as you can imagine, i'm not feeling very productive today. (-:


[ via phdcοmics ]

on a related note, i haven't really been following ρhdcomics much, anymore. it's getting to the point where they become painful reminders of how hard graduate school was.

hard is a relative term, of course. maybe it really was hard .. it felt like that to me, anyway .. and certainly postdoc life here in finland feels far easier, or if anything, freer.

mathbio!

now this is the kind of mathematical biology that i like to see .. the kind with geοmetric measνre theοry in it!

// as indicated by the link below, this preprint is a few weeks oldl
i stumbled upon it on 5 june 2013.
Beside the obvious geοmetric intrinsic interest such a minimization under isοperimetric and geηus constraint could have, a motivation to study this problem comes from the mοdelization of the free energy of elastic lipid bilayer membranes in cell biοlogy. Indeed the Willmοre functiοnal is closely related to the Helfrιch functional which describes the free energy of a closed lipid bιlayer $$ F_\text{Helfrich} \;=\; \int_\text{lipid bilayer} \left( \frac{k_c}{2}(2H+c_0)^2 + \bar{k}K+ \lambda \right) + p \cdot V $$ where $k_c$ and $\bar{k}$ denote bending rιgidities, $c_0$ stands for the spontaneous curνature, $\lambda$ is the surface tensiοn, $K$ and $H$ denote as usual the Gauss curνature and the mean curνature, respectively, $p$ denotes the οsmotic pressure and $V$ denotes the enclosed volume. The shapes of such membranes at equilibrium are then given by the corresponding Euler-Lagraηge equation. If $c_0 = \lambda = p = 0$ the Willmοre functiοnal captures the leading terms in Helfrich's functional (up to a topolοgical constant). Whereas if these physical constants do not vanish, $\lambda$ and $p$ can be seen as Lagrange multipliers for area and volume constraints. Thus, thanks to the invariance under rescaling of both the Willmοre functiοnal and the isοperimetric ratio, we exactly face the problem of minimizing the Willmοre functiοnal under an isοperimetric constraint.

In the context of vesιcles, imposing a fixed area and a fixed volume has perfect biological meaning: on one hand, it is observed that at experimental time scales the lipid bilayers exchange only few molecules with the ambient and the possible contribution to the elastic energy due to displacements within the membrane is negligible. Thus, the area of the vesιcle can be treated as a fixed one. On the other hand, a change in volume would be the result of a transfer of liquid into or out of the vesicle. But this would significantly change the οsmotic pressure and thus would lead to an energy change of much bigger scale than the scale of bending energy.

At first glimpse one may think that biologically relevant vesicles should always be of spherical shape. But in fact also higher geηus membranes are observed: for tοroidal shapes see [43] and [60], for geηus two surfaces see [37], and for higher geηuses see [38]. Further details can be found also in [34]..
from "Embεdded surfaces of arbitrary geηus minimizing the Willmοre energy under isοperimetric cοnstraint" by L. G. A. Κeller, A. Mondinο, and T. Rivιere @ cvgmt.

Monday, June 17, 2013

MoAR: a bit about politick, other bits too (*slightly updated*)

i'm starting to think that these roundups are a little .. artificial; maybe 'unfulfilling' is a better word. honestly, most of these posts have nothing to do with maths and are hardly instructive.

also, sometimes it's a struggle to find enough interesting articles to share, every week. other times there are too many to choose, and to list them all would contribute little more than social media websites like /. or reddit .. and less effectively, at that.

i used to post articles that were interesting to me upon finding them, and sometimes added commentary of some depth. maybe i'll switch back to that, especially as two of the shared links below are already in that format. (if you have a constructively critical opinion on the matter, then let me know in the comments.)

at any rate, this is what i found this week:


well, it's not the fields medal ..

.. but i suppose it's nice to get recognition for your work, even if it's from your local congressperson!
"The congressman concluded by congratulating Philip T. Grεssman and Robert M. Straιn of Penn State’s Department of Mathematics for solving the equation. Another odd thing about McNerneγ’s speech on the House floor? The “new advancement in mathematics” is about three years old."

~ from Math invades the U.S. House @rawstory


a rebuttal: what's wrong with boring?

the following excerpt sounds inspiring ..
I’m not talking about the kind of travel that neatly fills those allotted twelve days of annual vacation. No, that kind of travel is frenzied, restricting the majority of life to an unnatural cycle of constant want of more. I’m talking about the kind of rugged, unplanned long-term travel where you give up owning most things, leave behind a stable home, learn to live simply on a budget, and really see the world for months on end. The kind of travel that was possible after graduation, when you strapped on your backpack and jumped into the unknown world, flowing carefree wherever the wind blew.

~ from "Why you should quit your job and travel now @ medium:
.. but i have a different opinion.

i've been telling my colleagues that i am looking forward to a boring summer;
this means, in particular, no unnecessary traveling for work [1].

boring is an under-rated word. it belies qualities like safe and predictable, of course, which are qualities much maligned in this modern age that favors innovation and novelty.

my opinion is different, if only because it is personal. i already strive for plenty of innovation in my work. i don't need anymore creeping into the rest of my life. every day of research is a cumulative attempt of seeking new explanations of phenomena that i just don't understand.

to give you an idea of my time frame:
every few months, i make a small discovery or two ..
.. but nothing that really clears everything up.

i've been thinking about the same fundamental problems for about .. 5-6, maybe 7 years, and i still don't have a full answer. i wish i did [2].
to put it bluntly, i spend most of my time confused at ideas.
there's no easy way out of this, either.

my field of expertise is so tiny (read: insignificant) that probably only a dozen or two people in this world are probably familiar with the same ideas. plus, they don't always reply to their emails. the down-side is that, on average, there's nobody else around that can explain things to me, which means that i have to "think my way out" by myself and grope in the proverbial dark, alone.

so though i'm not exactly a creature of habit, i do appreciate the familiarity in my daily life. traveling for work is just that much more unfamiliarity: on top of being confused at infinite-dimensional Banach spaces, the last things i want are to remember where my hotel or hostel is, what the words for coffee and lunch are in the native language, and so on.

i'm no apologist for why life is boring. if you want to live a life of adventure and innovation, then go ahead: i'll just stick to my lonely, esoteric, academic journey, thank you very much, and enjoy predictably fine espresso, at the pleasant cafes on the street corners that i know relatively well.


the stuff nightmares are made of.

i remember a few fellow ph.d. students from china and other chinese students during my first postdoc. as the summer went on, everyone else left to see their families and take vacations. they, on the other hand, might take a road trip through the u.s. or just stay around.

when i asked them why they didn't go back and visit their families, they said that there might be visa problems, coming back: they might have to wait a few months before their paperwork was in order .. or in rare cases, they wouldn't be let back at all.

i never knew how likely the latter possibility would happen .. but it's a painful thing to hear that problems can come from the u.s. side:
"Οmar F. Zaιdan, a Jordanian citizen, was denied re-entry to the US on the eve of his PhD defense at Johns Hopkins University. It has been over a year and a half, and he has not yet been allowed to return."

~ from a publicly-available letter @jhu.edu


quantifying the liberal arts?

admittedly, i would have thought that a lack of comfort with ambiguity would actually make for better thinking, because one would be more motivated to look for the right answer.

on the other hand, if it's a problem worth solving, then it's probably hard enough that you will spend days, weeks .. even years .. working out out, which is a lot of time suffering in uncertainty.

there's also the contribution offered by creativity too, i suppose;
new ideas rarely come from overly rigid thinking.
"Afterwards, each participant filled out a survey measuring their emotional need for certainty and stability. They expressed their agreement or disagreement with such statements as “I don’t like situations that are uncertain” and “I dislike questions that can be answered in many different ways.”
..
Those who read a short story had significantly lower scores on that test than those who read an essay. Specifically, they expressed less need for order and more comfort with ambiguity. This effect was particularly pronounced among those who reported being frequent readers of either fiction or non-fiction."


~ from Study: Reading novels makes us better thinkers @salon


utility vs. fairness, sort of.

i was reading this article and right away i sided with this passage (contrary to the author's position):
"You always talk about the value of hard work.
But what about somebody in a coal mine — wouldn’t
you say he works as hard as you? Why should you
get paid so much more than that guy?"


~ from "Are coders worth it?" @aeonmagazine
somehow reading this article outraged me in a way that i cannot explain, which suggests that my reaction is purely emotional. conceptually it makes sense to me that, in a market economy, value and utility don't necessarily go hand in hand. however, i cannot help but feel a certain way about what looks fair:

i'm not one to talk, though:

i'm a university researcher whose work isn't readily applicable to society for the foreseeable future (i.e. useless). if i had to measure my utility to the economy, in the here and now, then the main contribution would actually come from my teaching instead of my research.

a lot of times i remind myself of a kind of hippocratic oath, that at least i'm not doing too much harm. i'm not directly making rich people richer, nor contributing to the further inequity suffered by disenfranchised minorities.

one could argue that i am causing harm in terms of opportunity cost: the fact that the nation of finland is paying me to work on 'useless stuff' means that less funding goes to biologists who might cure cancer, sociologists who could study how to eradicate poverty, or engineers who could find new ways to harness renewable energy or clean up the environment [1]. since i took the money, that does put a little bit of responsibility upon me to do my job well .. even if other jobs could produce more immediate societal benefit.

another passage from the article now becomes relevant:
"I do most of that work with a tool called Ruby on Rails. Ruby on Rails does for web developers what a toilet-installing robot would do for plumbers. (Web development is more like plumbing than any of us, perched in front of two slick monitors, would care to admit.) It makes tasks that used to take months take hours. And the important thing to understand is that I am merely a user of this thing. I didn’t make it. I just read the instruction manual. In fact, I’m especially coveted in the job market because I read the instruction manual particularly carefully. Because I’m assiduous and patient with instruction manuals in general. But that’s all there is to it."
the phrase "i just read the instruction manual" is especially poignant to me.

sometimes i feel the same way: if you read the same research articles and textbooks that i read, thought about the same problems for just as long as i have, then you'd probably have reached the same conclusions (and subsequently, the same modest success).

to a certain extent, RTFM really is key in life. if i've learned anything as an academic researcher, it's that we read preciously few articles carefully (if at all). the key, i suppose, is to choose those few very carefully, and do a good job on reading those selected few.


[1] i should emphasize the "for work" part of that stipulation. probably i'll take a week or two off, here and there. already some friends and i are planning a camping trip sometime in july.

[2] on the other hand, part of me wonders what would happen if i were able to solve those problems, all at once. i wouldn't know exactly what to work on next. i think i'd actually become slightly depressed at losing a long-standing adversary, to be honest.

[3] when it comes to environmentalism, i have to admit that my reasons are particularly self-serving. you see, i like to hike the outdoors (despite my dislike of travel) and human-wrought desolation just pisses me off. i don't care if most humans on this world will not get the chances that i do to explore this world. i still want mine.

Wednesday, June 12, 2013

head in the clouds, stuck in the stars.

earlier in the year i had thought that this summer would be very productive. i'd set aside long blocks of time in order to get things done .. but being at the start of a 7+ week stretch, free of traveling, all i seem to do is procrastinate and occasionally daydream.

i did try and work today. in particular i tried to get rid of some stars (or asterisks) in one of my manuscripts, but realised that it would be harder than i thought. (so, as before, i am still stuck at three.)

i don't think i can do better. maybe i should just submit the damned thing.

Monday, June 10, 2013

MoAR: no news, just snapshots (UPDATED)

i've read enough about NSΛ wiretapping and whistleblowing this week, and so might you. instead, what i thought i'd do is share what news i could find in photographs ..



#1: an oddity, just for fun. i wouldn't call this a "perfect sphere" .. but roughly, it does look like a ball:


[ courtesy of ichwan nοor @thisiscolossal ]

#2: something more mathematically designed. this next one is an ingenious combination of self-similar-like fractals, but with a more human element in mind:


[ a work by de la mano and herrero @thisiscolossal ]

#3: the applied kinds of maths. as for something more quantitative ..


[ courtesy of 60' of chaos @businessweek ]

also: The geography of Tweets: This image uses all of the geo-tagged Tweets since 2009 — billions of them. (Every dot is a Tweet, and the color is the Tweet count.)


[ courtesy of twitter @yahoo:flickr ]

.. and, if you will, one of those new fangled moving images:
"As the speaker is cycled through various frequencies the sand naturally gravitates to the area where the least amount of vibration occurs causing fascinating geometric patterns to emerge. There’s actually a mathematical law that determines how each shape will form, the higher the frequency the more complex the pattern."

from brusspup @thisiscolossal

#4: some rather old maths homework: Two math-notebook pages recently authenticated as belonging to Abraham Lincoln suggest the 16th president, who was known to downplay his formal education, may have spent more time in school than usually thought.


[ courtesy of physorg ]

#5: okay, maybe a little bit of news.. but i'll restrict them to headlines and one-sentence excerpts. those headlines that are self-explanatory or sound inherently interesting (see below) won't even have an excerpt at all.

from "Coursera Jumps the Shark" @higheredstrategy:
Yesterday, Coursera did a weird strategy about-face by announcing that, rather than competing with public colleges, it’s going to start competing with Blackboard instead.
"Spain builds submarine 70 tons too heavy after putting a decimal in the wrong place" @canada.com.

from "The Real Reason Cities Are Centers of Innovation" @theatlantic:
As they grow in population, all kinds of positive outcomes like patents and GDP and innovation (and negative ones like STDs and crime) grow at an exponential factor of 1.1 to 1.3.
from "the limits of physics" @aeonmag:
Are the waves physically real, or are they just mathematical representations of probability distributions?
"Atomic Bombs Help Solve Brain Mystery" @ scinow.

"'Cheating' Can Be An Effective Learning Strategy" @npr:13.7.

"Fear of Death Makes People Into Believers (of Science)" @scimag.

from "What can genes do?" @aeommag:
the reason is that the causation involved is so complex and deeply probabilistic that it is, in effect, unpredictable even if we were to try to enumerate all the contributing factors.
from "Technical Notes on the NSA's Prism Program" @lahiri.me:
Link prediction is a well-studied research problem where, given a graph, the goal is to predict links that are "missing" in some sense.


.. okay, fine: i couldn't resist mentioning the wiretapping thing, if only once; this bit of news just unnerves me ..

Saturday, June 08, 2013

#1300: chalkboard post.

from a few days ago:


(in other news, this is my 1300th post on this blog; time flies, doesn't it?)

Wednesday, June 05, 2013

a(n unappreciated) surprise.

on a completely mathematically-unrelated subject, i was told today by a colleague that his girlfriend thought i was 23 years old [1].

upon hearing this, i spat out: "WHAT" ..?
then he pointed out: "you should be flattered" ..!

to be fair, he does have a point; then again, so do i:
what came first to mind was how agonising life was at 23;

it was early in my ph.d.,
i probably hadn't passed all my qualifying exams yet,
and definitely hadn't started working with the advisor yet.

in general i wasn't sure of anything or whether this was the right path to take.
heck, i still don't know.

the only reason i'm so relaxed about it now is that my imagination's gotten worse, and the subsequent worst-case scenarios have stopped looking so gloomy! (-:



[1] as for some background, he's probably about 24-25 years old (though i've actually never asked him) and i surmise that his girlfriend is the same age. when i met her over dinner, there was also a masters' student joining us too, so guessing beyond the age of 30 would be a little out of context.

Monday, June 03, 2013

uncorrupted.

in light of that recent, small bit of good news, i'm now re-reading an old manuscript of mine from .. well, i'd rather not say .. and getting it type-set for publication.

the discussion is technical, but it's really clear; then again, maybe i'm too used to these kind of details by now. they are all carefully present in the write-up, though. not to make too much of it, but the discussion almost has a nice flow to it.

that said, i think i'm a lot looser with my writing now and perhaps less careful .. which is a bad thing. i guess we all pick up bad habits as we get older. 7-:

// added: 6 june 2013 @ 15:09 EEST

ye gods: under the journal's formatting guidelines, the manuscript is 38 pages long!

years ago i thought it would be "cheating" to split it up into two papers. my original intention was to (A) solve a special case of a conjecture, and so doing (B) build up the basics of a theory, which might actually be useful someday. at the time, however, i doubted that each piece could stand on its own ..

.. but now i'm not so sure. the proof of that special case takes 10 pages on its own, so it would have been fine to write a short note and cite it in the other part; that way, the theory-building part of the paper would be justified (but only that it would not be in the same writeup).

[sighs]

oh well; it's too late now. after five years of waiting, i just don't care anymore about what might have beens ..

MoAR: assorted bits.

maths follows art.

i've heard the claim before that for some phenomena, physicists "knew" them long before mathematicians did.

that choice of wording has always bothered me, because it suggests that (experimental) physicists are somehow "smarter" than mathematicians .. as if the disciplines can really be compared. it's a difference in methodology, or for that matter, epistemology:

scientific conclusions are only as accurate as the data you can physically observe and measure within the scope of the problem. on the other hand, if a mathematician proves that something is true then (s)he is simultaneously asserting that a countless number of pathologies are impossible.

at any rate .. with respect to the same abuse of language, sometimes artists are "smarter" than mathematicians:
" The same is true in visual arts. Vincent van Gogh’s later paintings had all sorts of swirling, churning patterns in the sky — clouds and stars that he painted as if they were whirlpools of air and light. And, it turns out, that’s what they were! In 2006, physicists compared van Gogh’s patterns of turbulence with the mathematical formula for turbulence in liquids. The paintings date to the 1880s. The mathematical formula dates to the 1930s. Yet van Gogh’s turbulence in the sky provided an almost identical match for turbulence in liquid.

Art sometimes precedes scientific analysis, and the relationship can go the other way too: Scientists can use art to understand math.

Even the seemingly random splashes of paint that Jackson Pollock dripped onto his canvases show that he had an intuitive sense of patterns in nature. In the 1990s, an Australian physicist, Richard Taylor, found that the paintings followed the mathematics of fractal geometry — a series of identical patterns at different scales, like nesting Russian dolls. The paintings date from the 1940s and 1950s. Fractal geometry dates from the 1970s. That same physicist discovered that he could even tell the difference between a genuine Pollock and a forgery by examining the work for fractal patterns.
"

~ from "How an Entirely New, Autistic Way of Thinking Powers Silicon Valley" @wired
the last paragraph gives me pause: to what extent is this phenomenon unique, really? the only way to check this if most drip paintings do not obey a self-similar pattern; otherwise pollock wouldn't really be unique in this sense, would he?


so i'm not alone in my confirmation bias.

this reminds me of something from a previous roundup, but better stated and not just about the job search.
" Survivorship bias also flash-freezes your brain into a state of ignorance from which you believe success is more common than it truly is and therefore you leap to the conclusion that it also must be easier to obtain. You develop a completely inaccurate assessment of reality thanks to a prejudice that grants the tiny number of survivors the privilege of representing the much larger group to which they originally belonged."

~ from "Survivorship Bias" @youarenotsosmart.com


(this excerpt is a lot more interesting, once you learn the title of the article.)

i like this article, if only because it hints at why we mathematicians study things that "don't really exist" .. at least in everyday physical reality.
" What these theories do share is a certain level of rigor. Rather than being arbitrary, they involve precisely defined conditions that collectively give rise to interesting properties. While a theory in the theoretical physics sense isn't “true” in that it doesn’t describe the real world, it is “true” in that two researchers will agree on the theory’s properties. This allows interested parties to build off each other’s work. "

~ from "Earning a PhD by studying a theory that we know is wrong" @arstechnica


lastly, some cool links!

first, some time-dependent distortion and translation on a space that is close to a sphere:


secondly, the geometric consequence of a harmonic series:

" With no wind, a lot of time, and a ridiculous amount of patience, it’s possible to make a tower like the one [below].


(Vertical axis not to scale).

The overhang for 52 cards is approximately 2.269 times the width of one card. Not bad.
"

~ from "How far can you overhang blocks?" @datagenetics