Sunday, July 29, 2012

barely mathematical: a designer stool.

at first i was excited because i thought it was an isocahedron, but then i took a closer look and realised i was wrong.

"wooden gem stool" from edition x,
an australian concept store / gallery.

oh well: it remains an interesting object.
i wouldn't choose to own one, though.

as for why: it appears to be made of solid wood, and would likely be a pain to pack and ship, once i move house again. \-:

article post (math ed): in which i rant for a bit.

so i ran into an article titled "Is Algebra Necessary?" in the new york times, just now. the author writes, among other things:
Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers.

Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
so based from this paragraph, you'd think that this article would be a defense in favor of mathematics and a critique of the american educational system .. but there's more:
This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources ..

Wednesday, July 25, 2012

on why i am weird with $\LaTeX$.

i suspect that i am widely misunderstood. it's either that, or it's just that i unconsciously make life harder for myself.

for instance, i try to avoid discussions about $\LaTeX$, because inevitably ..

.. when they ask me if i use winedt or texshop, i tell them that my laptop runs (ubuntu) linux;

.. and when they ask what program i use, i tell them that i just use a text editor like gedit, which comes standard with many (most?) linux distros [1].

.. and when they ask me how i compile my LaTeX, i tell them that i open up a terminal and type [2]:

      > latex myfile.tex && dvipdf myfile.dvi

.. and when they ask me how i find errors, and in particular the line containing it, i tell them that the "find" command is usually Ctrl-F.
.. and eventually, exasperated, they just ask: why the hell would you do all of that? so i tell them that, one summer long ago,
i didn't live in an apartment with air conditioning, but the public library had it, so i spent a lot of time there;

i didn't own a working laptop [3], yet the same library had desktops available for the public, so i used theirs.

they didn't have any $\LaTeX$ programs, they didn't allow users to download and install software .. but on Windows, PuTTY is a single executable file and never identified as anything other than a generic download, and i had access to a server where i could run latex remotely ..
so i spent a summer at the public library, with three PuTTY windows and one Adobe window open:
  1. one for pico, a text-based text editor,
  2. one for sftp, so that i could transfer the pdf output after each compile,
  3. one, ready and waiting for when i'd send the in-line latex commands remotely.
as for the Adobe window, i needed to view the pdf somehow ..


put another way, i use gedit because it's easier than pico.

left: gedit, which is clickable; right: pico, purely text-based

honestly, it was a fine way to spend a summer.

whenever i had something to type up, i'd go to my neighborhood public library, code until my allotted time was up, and either work on the details on paper or read graphic novels for a little while. when i was eligible for another time slot, i'd continue coding.

doing so had its perks: for one thing, breaks were automatic. i also met a lot of librarians, whom i found very cool people. i was young and maths was new to me, and there was the passingly-real possibility that i could make a living from it .. (-:

[1] it's actually a pretty robust program, and probably designed with coders in mind. it even changes the color of words, depending on command type. i've heard good things about texmaker, though, but i haven't gotten around to trying it.

[2] as for why not just a pdflatex command, i have a one-word answer for you: pstricks ..

[3] i didn't have much summer funding at the time, and the laptop that i wanted cost more than one month's rent. the prospect of being wired but homeless didn't exactly appeal to me.

Monday, July 23, 2012

mildly mathematical: sometimes an X is not an X.

a colleague of mine shared this link earlier, and i think it's worth passing along. though this video is 4min long, be warned:

once you reach the main TED website,
there might be no coming back for a while,
as there are so many fine talks to hear ..

Terry Moore: Why is 'x' the unknown? (a TED talk)

Why is 'x' the symbol for an unknown? In this short and funny talk, Terry Moore gives the surprising answer.

Terry Moore is the director of the Radius Foundation, a forum for exploring and gaining insight from different worldviews.

in other news, i'm still embedded in re-writing this preprint. there's light at the end of the tunnel .. but it's still slow going.

Friday, July 20, 2012

mildly relevant: a mathematician reads the (actual) newspaper.

in light of some new developments, i'm currently embedded in the job of re-writing this preprint. as a result, i haven't had much time for idle thoughts about the mathematician's life.

to be fair, though: i did take a break today to go and watch the dark knight rises, which came out today [1].

it did the trick:
i was completely distracted me from maths for .. 2 hours, 40+ minutes [2].

so until i can put two sentences together about mathematics again, here are some sentences of others that i've stumbled upon recently ..

from "why johnny can't add without a calculator" @ slate:
Maybe one day software will be smart enough to be useful, but that day won’t be any time soon, for two reasons. The first is that education, especially of children, is as much an emotional process as an imparting of knowledge—there is no technological substitute for a teacher who cares. The second is that education is poorly structured. Technology is bad at dealing with poorly structured concepts [1]. One question leads to another leads to another, and the rigid structure of computer software has no way of dealing with this. Software is especially bad for smart kids, who are held back by its inflexibility.
despite my acceptance of listening and giving beamer-style talks at seminars and conferences, this is exactly why i'm not especially fond of them ..

from "the psychology of discounting: something doesn't add up" @ the economist:
A team of researchers, led by Akshay Rao of the University of Minnesota's Carlson School of Management, looked at consumers' attitudes to discounting. Shoppers, they found, much prefer getting something extra free to getting something cheaper. The main reason is that most people are useless at fractions..

Consumers often struggle to realise, for example, that a 50% increase in quantity is the same as a 33% discount in price. They overwhelmingly assume the former is better value.
admittedly, i don't think that hard while shopping. most of the time, i'm just glad that something that i would actually buy would be on sale.

from "scientific publishing: brought to book" @ the economist (again):
There is a widespread feeling that the journal publishers who have mediated this exchange for the past century or more are becoming an impediment to it. One of the latest converts is the British government. On July 16th it announced that, from 2013, the results of taxpayer-financed research would be available, free and online, for anyone to read and redistribute.

Britain’s government is not alone. On July 17th the European Union followed suit. It proposes making research paid for by its next scientific-spending round—which runs from 2014 to 2020, and will hand out about €80 billion, or $100 billion, in grants—similarly easy to get hold of. In America, the National Institutes of Health (NIH, the single-biggest source of civil research funds in the world) has required open-access publishing since 2008.
nice! i didn't realise that the movement is spreading that widely .. or, for that matter, that such a practice has been in the works for a while.

again, it's the sort of thing that gives me hope, in this world.

from "the trouble with online education" @ the new york times:
But can online education ever be education of the very best sort?

It’s here that the notion of students teaching teachers is illuminating. As a friend and fellow professor said to me: “You don’t just teach students, you have to learn ’em too.” It took a minute — it sounded like he was channeling Huck Finn — but I figured it out.

With every class we teach, we need to learn who the people in front of us are. We need to know where they are intellectually, who they are as people and what we can do to help them grow. Teaching, even when you have a group of a hundred students on hand, is a matter of dialogue..
reading this, i'm tempted to gainsay what i wrote in (the second part of) my earlier post .. but i won't, due to context:
free online education gives me hope, in the same way that universal suffrage and publicly-funded libraries give me hope.

these are not perfect solutions -- e.g. voting randomly at the booth does nothing -- but they give some form of access to everyone, and hence anyone who wants to better themselves.
on the other hand, the author of the article makes a good point about lecturers having an audience. thinking about it, i wish that i had thought of that ..

.. but after a quick search, it turns out that i did! [3]

[1] no comment about the film .. at least, not yet and not here. if you're that desperate for news about it, i'm sure that you're more resourceful than to rely on me for news about it!

[2] not all diversions are created equal. if i'm really embedded in a task, then i'll think about it while running .. which makes for a terrible run. the symphony doesn't help either; i tried that, back where i did my first postdoc. as for leisure reading, i never even get to opening the book cover. i guess, for me, the film experience is rather all-encompassing.

[3] i'm referring to this earlier post, specifically the paragraph after the red text.

Tuesday, July 17, 2012

mildly mathematical: ".. a new birth of freedom — and that the science of the people, by the people, for the people, shall not perish from the earth .."

i've been hearing some awesome news about education, research, and freedom:

here's the research part ..

Free access to British scientific research within two years

, science correspondent

The government is to unveil controversial plans to make publicly funded scientific research immediately available for anyone to read for free by 2014, in the most radical shakeup of academic publishing since the invention of the internet.

Under the scheme, research papers that describe work paid for by the British taxpayer will be free online for universities, companies and individuals to use for any purpose, wherever they are in the world.
.. The move reflects a groundswell of support for "open access" publishing among academics who have long protested that journal publishers make large profits by locking research behind online paywalls.
"If the taxpayer has paid for this research to happen, that work shouldn't be put behind a paywall before a British citizen can read it," Willetts said.
(cont'd here)
as for the education part, it seems like many well-known universities in the u.s. (and abroad) are taking part in the free on-line learning trend .. which is relieving to hear.

you'd think that these institutions would have the least to gain from cooperating with these new developments, unless you're willing to take the conspiracy-theorist perspective [2].
12 new universities join Coursera!
We are THRILLED to announce that 12 universities—including three international institutions—will be joining Princeton University, Stanford University, University of Michigan, and University of Pennsylvania in offering classes on Coursera.
(a link to their course catalog is here.)

at any rate, i think that the rise of online public lectures like those from ted and the99%, and others is already a good sign. call me an idealist, but if there is such an interest purely in learning, then maybe there is hope for the future and for the internet, after all ..

[1] quoted from abraham lincoln's gettysburg address in 1863, with changes put in italics; my hope is, like that battle, that this be a turning point in scientific publishing ..

[2] two thoughts:
        (A) many students will still be willing to pay a premium for a degree from prestigious universities, so those on the list are safe .. at least for another generation. it's the middle-tier universities, with comparable tuition costs as these places, that should worry about their enrollment; if one day a web-based college degree becomes a good, viable option for middle- to lower-class society, then why pay tens of thousands of dollars just for physical proximity?
        (B) a free course online is like advertising for the university; these lecturers will be delivering their courses anyway, and the amount of server space (or whatnot) is negligible. my guess is that when most high school students think of university, they think of large, boring lectures and wild campus life. the benefit to these universities is that really good lecturers can "wow" prospective students, inspire them, convince their parents to take out loans .. \-:

Monday, July 16, 2012

mildly mathematical: can a planet be disconnected?

i had thought it final, that pluto is no longer classified as a planet .. but apparently the debate isn't over.

in particular, this article proposes to generalise the 2006 definition of "planet" as formalised by the iau, which according to the wiki, is a celestial body which:
  1. is in orbit around the Sun,
  2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
  3. has "cleared the neighbourhood" around its orbit, (meaning it has become gravitationally dominant, and there are no other bodies of comparable size other than its own satellites or those otherwise under its gravitational influence).
the novelty is in weakening the second condition: really, why should planets be round .. or even connected? the difference, to me, is whether we want the notion of a "planet" to be a geometric / topological one (i.e. dependent on shape) or a measure-theoretic one (or dependent on how mass is distributed).

having professed an affinity for gmt in past posts,
i suppose it's clear where my loyalties lie, this time.
-- ✂ -- --
from "Not a Dwarf: Is Pluto a Binary Planet?" @discoverynews

".. that Pluto really has only four moons (all discovered by Hubble over the past seven years). He argued that the largest moon in the system, Charon (found in 1978), is really a planet in its own right.

Why? Because Charon is 12 percent the mass of Pluto. That may not seem like much, but our moon is only one percent the mass of Earth. Pluto's four other satellites are a very tiny fraction of the mass of the system.

The consequences are that Pluto and Charon pivot like a waltzing pair of ice skaters around a center of mass. So do the Earth and moon, but the center of mass, or barycenter, is inside Earth's radius.

However, alien astronomers watching Earth transiting the sun would note the passage of our moon as well. They might catalog Earth as a "double planet."

That was the reader's point. The four outer satellites don't really orbit Pluto; they follow strictly Keplerian orbits (the orbital period is directly related to orbit size) around the system's center of mass, which lies between Pluto and Charon. Pluto and Charon complete one pivot around each other every 6.3 days."

-- ✂ -- --

this might be mathematically meaningful, but still seems like so much posturing. on the other hand, there's more to the second condition of hydrostatic equilibrium. again, the wiki:
Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force.
i claim no real understanding of physics, but this sounds like a stability property, in that the object under scrutiny has finalised its shape. it's just that typically, this forces the object to have a round one.

so for me, the jury's still out.

to prove that pluto is not a planet, someone has to convince me that pluto and charon are meant to collide and form a single, larger body, and that their current hydrostatic equilibria is just a transition before the chaos from that collision.

Saturday, July 14, 2012

regrets: i really should have gone to this colloquium.

maybe i should quit following the internet so closely. often it makes you feel connected, in tune with events happening right now. other times, it just reminds you of what you've missed out.

take, for example, this excerpt from a title/abstract for peter jοnes's uni. helsinki maths colloquium from this past may (2013):
...The new result in topic 3 concerns Lebesgue measurable sets $E$ of small Lebesgue measure (in any dimension). The set $E$ can be decomposed into a bounded number of sets with the property that each (sub)set has a nice "tangent cone". Roughly speaking each subset has very small intersection with any Lιpschitz curve whose tangent vector (to that curve) always lies inside a fixed cone. This had been proven in dimension two by Albertι, Csörnyeι, and Preιss by using special, two dimensional combinatorial arguments.

The main technical result needed in our work is a $d$-dimensional, measure theoretic version of (a geometric form of) the Erdös-Sζekeres theorem. (The discrete form of E-S is known only in $d = 2$.) In what is perhaps a small surprise, certain ideas from random measures can be used effectively in the deterministic setting. Our result yields strong results on Lιpschitz functions: For any Lebesgue null set $E$ in $d$ dimensions, there is a Lιpshitz [sic] mapping of Euclιdean $d$-space to itself, that is nowhere differentiable on $E$. (Thus Rademacher's theorem, which states that such a map is a.e. differentιable, is sharp. Any Lebesgue null set can be in the set of non-differentιability for such a Lιpschitz function.)

[jaw drops]
why didn't i attend this colloquium?
i could have learned so much!
why didn't anyone *tell* me?


this topic of measurable differentiable structures on metric spaces is small, but right now it has the potential to advance very quickly. as a general principle, techniques towards lebesgue null sets in euclidean spaces have interesting consequences for analysis on metric spaces ..

now i'm absolutely curious:
how do random measures fit into the picture?
what does "random" mean, here? [1]

if they lead to a higher-dimensional erdös-sζekeres theorem, then what replaces the ordering for curves?
curiouser and curiouser ..

[1] if they mean this in the probabilistic sense, then wouldn't this correspond to a measure on the space of measures? or does this refer to baιre categοry, with the class of measures on $\mathbb{R}^d$ treated as a metric space under an appropriate weak topοlogy?

Thursday, July 12, 2012

code, compile, repeat.

no matter how many times i print out another version of the preprint, the same amount of red ink spills on the pages.
i see bad, inconsistent uses of notation .. probably due to having written large chunks of it, at different times.

sometimes constants are missing along a series of estimates .. which doesn't matter in the end, but it makes proofs hard to follow.
sometimes i realise that entire lemmata are unnecessary. it's the consequence of the ugly, first version of proofs i wrote, months ago.
at the time i was content that they simply "worked" .. that i even had a proof!

now the standards are higher: now that i know they are true, i want them to be readable and contain little more than clear, basic ideas glued together by rigor.

sure, it's aesthetics, but there's another point: the clearer the proof, the easier the job for the referee. in maths, the journal submission process is already so long that anything that can speed up the process is advisable.
i feel like some kind of analog compiler: being given source code in the form of LaTeX, all i seem to do is spit out errors and warnings.

i hope that this procedure halts, eventually!

odd: the preprint is 15 pages long, but there are 29 references cited and they take up a full page. i guess i'm overly optimistic, in that i believe: if i cite others appropriately, then maybe they'll do the same for me ..

Tuesday, July 10, 2012

i might read humε again, but this time, i'll stick to his mathematical works.

holy crap: the rumors of david humε's death in 1776 has been greatly exaggerated;
it turns out that he is actually alive and well!
moreover, he's given up philοsophical empiricism in favor of geοmetric grοup theory, which seems like a fine choice to me;

a few of his preprints are on the arXiv, in fact.
yeah, yeah, i know: he probably gets this a lot,
much like how guy davιd is often confused for .. well, guy davιd.

Monday, July 09, 2012

off the plane, back to work.

so july is the holiday month in finland, or rather: the vacation month.

if i remember correctly what my friends told me,
the finnish government guarantees 4 weeks of paid time off.

having chosen to go to the office today, after a long hiatus, i feel a little like the pixar character wall·e, methodically puttering around and arranging things in an abandoned world ..

.. with the hope that, over enough time and effort, a larger order appears. [1]

(images borrowed from jusco's reviews and from the random independent, respectively.)

today, in particular, felt inconsequential. i almost wrote an introduction to an upcoming preprint .. the important word being almost.

at some point, i felt like the background lacked depth, so i kept clicking links on mathscinet to references in the literature. more information has to make it better, right ..?


i should have just written something quick and dirty, printed it out, and leaving the office for the sunshine, edited it into something better. (one of these days i'll buy a printer for my own use.)

i am feeling pleased, though.

i'm back at home from the conference(s) to settle into peace and quiet. there's a long stretch of time for me to get back to my life, finish some tasks that i've been putting off ..

.. like writing mathscinet reviews,
doing my part in a few collaborations, both very overdue tasks. \-:

call it egoism, but i'm most excited to finish off this one project. the preprint is almost ready. it almost reads like one.
the more i think about it, though, the less significant the result becomes .. but ultimately that doesn't matter too much:

i just want it to take a particular shape,
have it capture something that i intend,
make clear what is really essential in these phenomena.
after traveling and seeing friends, i guess i'm glad to get back to work .. because this is the fun, creative kind of work. (-:

[1] yes, the fact that wall e is making structures out of trash is not lost on me. sometimes my results do come out of a mess and assembled from the theoretical scraps of others. i prefer to compare it to forming diamonds from coal, myself.

Friday, July 06, 2012

another conference, day 5: disappointment.

so i learned some bad news yesterday:


maybe i should have known better,
having been aware that he has done this kind of thing before;

maybe, though, there's a good reason.

there were other talks that i was looking forward to, but .. this was the one talk that i was truly, truly anticipating and among the main reasons why i chose to attend this conference.

of course, he cancels .. while the conference is in progress!

Wednesday, July 04, 2012

another conference, day 3: mostly photos.

being a conference of close to 1000 participants, i was expecting every square centimeter of the host building to be occupied .. but i was pleasantly wrong.

in particular, the fourth floor is almost always empty, even though you can hear the remaining three floors quite well (and in fact, observe the crowds from a height).

when i think about it, though, it makes sense: no coffee is served on the fourth floor! (-:
on a more serious note: despite encountering old friends and making new acquaintances here, i'm getting a little tired of people. there's not a lot of solitude made convenient to conference participants .. at least, not without heading far away from the conference venue.

then again, the whole point of a conference is to meet up and talk with colleagues, whether it's discussing research or simply sharing information or experiences about the life of working mathematicians! so i guess i've just not gotten into the conference mood yet ..

.. and knowing my luck, by the time that i will, the conference will be over .. \-:
lastly, a few photos from the book display center: among other things, apparently elsevier is trying to restore its good name.

Tuesday, July 03, 2012

another conference, day 2: breaking bad habits.

this sounds like sacrilege, but i'm considering switching from coffee to tea .. at least for conference afternoons.

the trouble is that patience wears thin, after a few talks, so coffee breaks become highly valued.  when walking out of the lecture room and immediately seeing the coffee urns and cookies .. one thing simply leads to another.

Monday, July 02, 2012

another conference, day 1: first impressions.

so i'm currently in krakow, attending the ecm (european congress of mathematicians) and i must say, the meeting is big enough to .. confusing.

fool that i was, i registered just the day before the conference .. and are among the "unregistered" badge-less few. on the other hand, i'm not 300€ poorer yet .. (-:

on the plus side, though ..
  • there's (decent) coffee everywhere and it's even served in cups and saucers.
  • at the various book stands, i got a free issue of revista, as well as a free calendar.
(more thoughts to come ..)