Wednesday, February 27, 2013

[a short digression]

huh. in one of my proofs, i forgot to fix an $\epsilon$;
i guess the referee assumed it was given?


that reminds of the time that a ph.d. student acquaintance of mine was giving a seminar talk. before estimating a certain integral, he fixed a positive parameter $\epsilon$. by the time he finished, there was silence for a moment, and her/his advisor asked:

"wait: where did you use $\epsilon$?"

then everyone scanned the lines of estimates, but nobody could find that symbol anywhere.

"well," the student replied, "it's always good to fix an $\epsilon$, you know ..?"

.. to which the crowd laughed. (-:

Tuesday, February 26, 2013

red ink, seeing red.

i'll change my mind later when i've time to reflect on the situation.
until then, i really, really hate writing ..

.. or rather, re-writing.

Monday, February 25, 2013

MoAR: mostly about reality and about education, this week.

I. in which $x^2 - x - 1 = 0$ is really intuitive, actually.

when i think about this experiment, it completely defies my intuition about human vision.

i would have thought that of all the shapes that appear in nature, something symmetric like a square or a circle would be the most readily recognised and processed ..
" Then, in 2009, a Duke University professor demonstrated that our eyes can scan an image fastest when its shape is a golden rectangle. For instance, it’s the ideal layout of a paragraph of text, the one most conducive to reading and retention. This simple shape speeds up our ability to perceive the world, and without realizing it, we employ it wherever we can."

~ from "Why We Love Beautiful Things" @nyt
i also learned that there is such a thing as optimal fractaΙ densιty too.
" Certain patterns also have universal appeal. Natural fractals — irregular, self-similar geometry — occur virtually everywhere in nature: in coastlines and riverways, in snowflakes and leaf veins, even in our own lungs. In recent years, physicists have found that people invariably prefer a certain mathematical density of fractals — not too thick, not too sparse. The theory is that this particular pattern echoes the shapes of trees, specifically the acacia, on the African savanna, the place stored in our genetic memory from the cradle of the human race. To paraphrase one biologist, beauty is in the genes of the beholder — home is where the genome is.

LIFE magazine named Jackson Pollock “the greatest living painter in the United States” in 1949, when he was creating canvases now known to conform to the optimal fractal density (about 1.3 on a scale of 1 to 2 from void to solid). Could Pollock’s late paintings result from his lifelong effort to excavate an image buried in all of our brains?

~ from "Why We Love Beautiful Things" @nyt

II. the universe may or may not be finite, but the internet certainly is.

interesting: as a graph (and hence a metrιc space) apparently the internet has a rather small diameter.
"No one knows for sure how many individual pages are on the web, but right now, it’s estimated that there are more than 14 billion. Recently, though, Hungarian physicist Albert-László Barabási discovered something surprising about this massive number: Like actors in Hollywood connected by Kevin Bacon, from every single one of these pages you can navigate to any other in 19 clicks or less.

Interestingly, this means that no matter how large the web grows, the same interconnectedness will rule. Barabási analyzed the network looking at a variety of levels—examining anywhere from a tiny slice to the full 1 trillion documents—and found that regardless of scale, the same 19-click-or-less rule applied.

~ from "Any Two Pages on the Web Are Connected By 19 Clicks or Less" @smithsonian
i can only imagine, then, how much branching there is ..

III. MOOCs: which way now, the tide?

well, this guy said what i said better .. and in particular, more quantitatively:
"First, student attrition rates — around 90 percent for some huge online courses — appear to be a problem even in small-scale online courses when compared with traditional face-to-face classes. Second, courses delivered solely online may be fine for highly skilled, highly motivated people, but they are inappropriate for struggling students who make up a significant portion of college enrollment and who need close contact with instructors to succeed."

~ from "The Trouble with Online Education" @nyt
.. and this excerpt offers psychological reasons for the reported attrition rates:
"Every January, millions of people join gyms that they won’t go to more than a few times before other things get in the way. The problem? “Getting fit” or “losing weight” aren’t things that happen immediately. Those gym visits require a lot of effort–we lose at least an hour of our day, we wake up with new aches and pains, and we face the embarrassment of public struggle–all for what usually amounts to very small visible results. So, despite our logic telling us that being fit is a long-term win, we quit not long after we start.The same is true for learning tech (or anything else) online. Logic tells us that expanding our knowledge via that machine learning course is a long-term win, but the lack of immediate results against the weight of “all the other stuff that’s going on” oftentimes causes us to drop out before we really get started."

~ from "Fixing Online Technology Education" @kufikia

IV. as the ancients have said, "know thyself."

this excerpt gives me a small bit of hope, that our students know themselves well enough to make good decisions about their academic careers.
" They found students believe ”that the paper textbook remains the superior technology for studying and achieving academic success.” Print’s primary advantage is that it presents “fewer distractions,” the students said: “The paper textbook helps them to avoid the distractions of being on the computer or the Internet, the temptations associated with checking e-mail, Facebook, or surfing the Web for unrelated information.”"

~ from "Students to e-textbooks: no thanks" @roughtype

V: .. & now a few more thousand words ..

1. i am very glad that some surfaces are not, say, area-minimising. (-:
"This extra surface comes to use courtesy of our especially wrinkled brains. But there’s another intriguing thing about those wrinkles: they are not spread uniformly across our heads. The front of the neocortex is more wrinkly than the back. This is intriguing, because the front of the cortex handles much of the most abstract sorts of thinking. Our brains pack extra real estate there with additional folds. And if you look at mammals in general, they tend to have more wrinkles at the front than the back."

~ from "On the Possible Shapes of the Brain" @nationalgeographic
2. then there is what we can see, what we can't, but what bees can:
" By placing electrodes in the stems of petunias, the researchers showed that when a bee lands, the flower’s potential changes and remains so for several minutes. Could this be a way by which flowers tell bees another bee has recently been visiting? To their surprise, the researchers discovered that bumblebees can detect and distinguish between different floral electric fields."

~ from "Floral signs go electric" @uni.bristol
3. lastly, out of seven possible charts from the following link, here is one.

~ from "The Ph.D Bust: America's Awful Market for Young Scientists—in 7 Charts" @the_atlantic

Thursday, February 21, 2013

the siege: something pyrrhic, but not quite a victory.

as of now, the siege is over for good reasons,
but not particularly good ones.

i'm calling a retreat, you see .. but not a surrender.

Tuesday, February 19, 2013

couldn't sleep .. (or: siege, part ii: early morning ambush)

// initially written ~ 7:30

odd. i startled awake this morning at 5:45 and couldn't get back to sleep. so i got up, tired, and started working ..

.. only to have everything fitting together, as if my choices for function spaces paid off and that there was no longer any fuss about what topologies to use, what structures were available.

with two lemmas or so proven, a good chunk of details worked out, the argument looks done .. well, not quite: i still need to look up some details about duality (with respect to Bochner integrals) but everything else looks intact. it's not even 7:30 and i feel like i've done a full day's thinking. i'm tired but i've just had two cups of coffee. the sun's risen, the snow is white, and the day's just begun ..
// added later @ 8:30

this is all very suspicious, of course. i'm waiting to find an obvious error when i'm better rested. maybe i should set this down for the rest of today and look at it again tomorrow.

as for some background, yesterday i felt constantly .. not interrupted, but apart from a few hours in the morning, there never seemed any significant chunk of time to work out the details: an early lunch with colleagues at 11:30, a finnish language class in another part of town, a meet-up with a friend for a sauna night .. that ended up being closed on mondays.

waking up today, i felt impelled to work everything out. maybe it's just my unconscious put into overdrive ..?

// updated: 20 feb 2013 @ 23:04

curiouser and curiouser: i don't see an obvious error yet.

i'm even trying to break up the argument into as many lemmas as possible .. if only to make sure that each proof, being short, is easy to check for correctness.

Monday, February 18, 2013

MoAR: not many this week, but there's (i) design, (ii) psychology, and (iii) biology.

by accident i saved over an earlier draft [1] of this week's roundup ..
.. which was rather annoying, as i lost a rather long rant in rebuttal to this article about classroom technology.

so here is what i rounded up today, on short notice:

i. mathematically sounding jargon .. from design.

well, apparently i've not been paying attention to the design world!
"If you're paying attention to what's going on in the design world, you've probably noticed the ongoing debate around skeuomorphism vs flat design."

~ from "flat pixels" @sachagreif
apparently, skeuomorphism isn't a special kind of homeomorphism .. not that i can tell, anyway. (it's probably not even a coarse isometry .. or what others call a 'rough' or 'quasi-isometry.')

similarly, i don't think "flat" has much to do with geometry. as the same author describes, though ..
"Flat Style embraces visual minimalism, eschewing textures and lighting effects for simple shapes and flat colors."
.. and apparently, "flat color" is a technical term in art, too. so if one thinks of colors as as a spectrum (i.e. a nonempty compact interval of real numbers) and an image as a function from a rectangle in the coordinate plane to this interval, then would flat-coloured image would be a piecewise constant function?


that seems pretty 'flat' to me. i would prefer the term: "locally flat" ..

.. but anyway, if you were wondering: apparently the image on the left is flat (in the design sense) and the other is not.

ii. revising our assumptions (on MOOCs)

first of all: yes, this is another article about online education. while browsing it, two thoughts came to mind.

ii.1. maybe it's the mathematician in me, but i rarely mind it whenever someone points out the "obvious" to me .. provided that they do so, with style:
"What I’m saying is we have to start from the position that the tidal wave is already here. Indignation, however righteous, is beside the point. The kids who are cutting their teeth on Khan Academy videos for help with their chemistry and calculus homework will grow up correctly assuming that there will always be low-cost or free educational opportunities available to them online in virtually any field of inquiry. They will naturally migrate to the best stuff and be less and less willing to pay for crap. This will cause a lot of trauma for the educational establishment, but that’s not the problem of the next generation that wants to learn."

~ from "the Internet will not ruin college" @salon
i don't know if this is obviously true. for now, however, the availability of search, in some form, seems to be a reasonably good assumption for the future.
as for my own habits, i generally prefer text to video,
so often i browse through wikipedia, pick the wikis i want,
then follow the listed references on them.

ii.2. it's worth noting that browsing for content is something quite different from enrolling in a course, though. the next excerpt is interesting in how psychology comes into play, regarding enrollment.
"It strikes me as a profound realization of the fundamental goal of the university — any university — that a course taught by an icon at one of the most elite institutions in the world would be accessible to me for just the cost of a few clicks ... But it seemed like too big a commitment to make while on deadline, so I ended up browsing..."
so i might have to change my mind in what i wrote in a previous roundup:

i still believe that when students are participating in their online courses, then they are paying much better attention than they would in, say, a randomly selected physical-classroom lecture. that doesn't say anything, however, about how often they will exercise their attention skills.

in particular, if they treat the content like any other media -- such as music, films, or television shows -- then their experience will likely consist of sporadic but concentrated bursts of activity instead of a regular, orderly routine. the problem with digital formats and experiences is that they are largely driven by (near to) immediate gratification. it's not clear to me whether the average student is sufficiently prescient and self-aware to account for this, and subsequently exercise such a deliberate practice.

a course website is still a website. it's probably going to be opened in a web-browser, along with other browsing tabs for email, social media, etc .. and that's only the web browser, a single program that is running on the computer.

maybe the average online student will be a distracted, multitasking one.

so far the "success stories" have a self-selecting population: if you're not enrolled in a university and want to take an online course, then it's your own commitment. what happens when university-enrolled students are drafted into the same environment? can we really expect such a significant behavioral change?

it's not clear to me if this is an effective way of learning anything hard .. especially if, like mathematics, the topic is sequential. i imagine a student following the first few lectures, not visiting the website in a while, and then trying to cram all the video lectures into one big viewing (due to a deadline of some kind). like cramming for exam, this is probably not going to work.

the video format is great when you want to follow an entire procedure or narrative. on the other hand, it is rigid in the sense that it is necessarily chronological. as a result, to guarantee that you get everything you want from it, you either have to (a) sit through all of it or (b) be very good at pause/rewind/fastforward and sifting the information you need.

in contrast, you can easily skim through a wiki; text is spatially ordered, you see .. not chronologically.

i'm starting to wonder: if MOOCs are to eventually fail, then would it be due to students being all too human, carrying on the same bad habits that already lead to disaster in physical classrooms?

iii. organisms are turning into computers, whereas computers are turning into .. doctors?

interesting.  computational biology might suddenly get a lot more real.
"Synthetic biology seeks to bring concepts from electronic engineering to cell biology, treating gene functions as components in a circuit. To that end, researchers at the Massachusetts Institute of Technology (MIT) in Cambridge have devised a set of simple genetic modules that respond to inputs much like the Boolean logic gates used in computers."

~ from "How to turn living cells into computers" @nature
on a related note,
"By using a new framework that employs sequential decision-making, the previous single-decision research can be expanded into models that simulate numerous alternative treatment paths out into the future; maintain beliefs about patient health status over time even when measurements are unavailable or uncertain; and continually plan/re-plan as new information becomes available. In other words, it can "think like a doctor." ..."

~ from "Can computers save health care?.." @iu.newsroom
so by the law of syllogism, surely we can engineer our own cells to become their own doctors? (-;

[1] as you may have guessed, usually i bookmark the articles links over the course of the week .. and when bored, start adding my personal rants to self-servingly-selected excerpts.

Thursday, February 14, 2013

the siege: once a battle .. now a war of attrition!

the functional analysis "battle" from a few days ago seems to have deteriorated into a siege.

as a general rule, sieges are troublesome. they have the potential to be long and drawn out affairs, and hence wasteful for limited resources. (every night i'm exhausted from trying to work out ideas, build variants of spaces, or look up relevant theorems and tools.)

on the bright side, i'm the one doing the invading;
i think the enemy is weakening, too. (-:

// updated, 15 feb 2013 @ 10:08
things are fitting together more and more nicely.
this feels like the building of siege engines, the alchemic stirring of potions, pitch, and greek fire, the readying of catapults and trebuchets to launch.

i look at these mathematical machinations and i smile:

piecewise linear cells, hyperplanes, subspaces,
Lipschitz functions, both old and new kinds,
weaκ-star topolοgies and linear inclusions and well-defined dualities!

i can't help but imagine myself now: a cruel smile, bent on destruction.
ha! soon, i feel like crying havoc! and letting loose the dogs of war [1] .. but not yet. my plans remain unready. the time to strike is soon .. i'll have my chance soon enough ..

.. and it will be bitter, yet sweet.

// updated, 18 feb 2013 @ 10:47

the siege is in full swing, there's already trouble on the front lines;
i'm invading the fortress of a claim and cannot breach the walls.

so i'm going to need heavier artillery in the form of vector-valued functions and Bοchner integrals .. but these aren't just any vector space targets;

these are flat chain-valued functions!

[1] yes, i know: the real quote is 'let slip the dogs of war' .. but 'slip' just doesn't sound right, to modern ears ..

Tuesday, February 12, 2013

sometimes i am a nerd at heart (also: a romantic).

argh! i can't focus .. for a stupid reason;
i'm too distracted by the contest to name two of pluto's recently discovered moons!

it's even online!

so .. there are two moons to name, right?
what about naming them after star-crossed lovers like orpheus and eurydice?

(that would be really cool!)

.. so ..
.. if you don't happen to care ..
.. and since i\ve a personal agenda for happy endings in antiquity ..

.. then could you go to and vote for orpheus and eurydice? (-:

(before) the siege: battle without honor or humility.

// initially written: 11 feb 2013 @ 13:20
so today i tried to build a completely new Baηach space ..

.. in the sense that i've never seen anything like it before anywhere else, and that one would be slightly crazy even to consider building it.
it all started when i wanted a certain sequence of functions to converge ..

.. and they do! (but not in a very strong sense) ..

but then i realised that all i needed was that their images under this certain linear operator converge ..

.. so "all i had to do" [1] was weaken the mode of continuity of the operator ..
.. which probably requires weakening the topology of the source space ..
.. so i might as well build a whole new space, right?
now i'm thumbing through rudin's book as well as dunford-schwartz, volume 1 [2].

you know, this was supposed to be a nice, relaxing day of computation ..

[1] famous last words, if i've ever heard any ..

[2] upon re-reading that, my mind pronounced it similarly to "kill bill, volume 1." suddenly, this old line comes to mind:

Ο-Ren Ishιi: You didn't think it was gonna be that easy, did you?
The Brιde: You know, for a second there, yeah, I kinda did.

in all honesty, though: i find vol.2 more aethestically pleasing than vol.1 ..!

Sunday, February 10, 2013

MoAR: more bad news than good, this week.

i don't think that this week's roundup will cheer you up. 7-:

the first two stories are about have's and have-not's, the next two are about setbacks in research and publishing, and the last one's about the downside of "quantifying everything" ..

1. the world might be flat, but what if you're not part of "the world" ..?

it's easy to forget that though "everything" is available on the web, some people might still not have the access to it .. especially those who need it.

on a related note, i worry about the future of public libraries ..
"Joshua sometimes does his homework at a McDonald's restaurant — not because he is drawn by the burgers, but because the fast-food chain is one of the few places in this southern Alabama city of 4,000 where he can get online access free once the public library closes.

Cheap smartphones and tablets have put Web-ready technology into more hands than ever. But the price of Internet connectivity hasn't come down nearly as quickly. And in many rural areas, high-speed Internet through traditional phone lines simply isn't available at any price. The result is a divide between families that have broadband constantly available on their home computers and phones, and those that have to plan their days around visits to free sources of Internet access.

~ from The Web-Deprived Study at McDonald's @wsj

2. name, email .. rank?

in the first lecture of the course i'd teach, i often spent the first minute or two introducing myself .. and then indicating who i was not:
you wouldn't call a corporal a general, right?
so: i'm not "professor" geminus.

these guys, though, have a similar rule but with a few other things in mind ..
"To ensure that we remain conscious of the adjunctification of CUNY, we ask that you do not call us ‘Professor.’ We are hired as adjunct lecturers and it is important that you remember that. You deserve to be taught by properly compensated professors whose full attention is to teaching and scholarship."

~ from "We Ask That You Do Not Call Us Professor" @thebillfold
well, if it really is the truth, then maybe the students should know, one way or another.

3. it might be wrong, but is it still interesting?

everyone is wrong on occasion.  for me, "on occasion" should be replaced with "almost all the time."  my ideas are wrong at least 95% of the time, in that they don't work for the intended task.

as some small consolation to myself, i happen to believe that ..

.. if you've never been wrong before, then you've never reached your limits;
if all of your ideas are working, then you're probably not getting enough ideas.

that said, these authors have my respect. it's not easy, admitting you were wrong about something ..
"On 10 December 2012, we submitted a paper “Rota’s Universal Operators and Invariant Subspaces in Hilbert Spaces” for publication, and we spoke about it several times before the more formal announcement at the RSME meeting in Santiago de Compostela on 25 January 2013. By that time, the paper had been read and no problems found by several other mathematicians. We have heard nothing so far from the journal to which it was submitted.

We regret to inform you, however, that a gap in our proof was discovered after the announcement at Santiago. After working for the past few days to bridge the gap, so far unsuccessfully, we are today formally withdrawing our submission to the journal.
So far at least, there have been no errors found in the paper besides the erroneous assertion that the work included in the paper proved the Invariant Subspace Theorem, while in fact it did not.

~ from "[a] Statement from Cowen and Gallardo" @cafematematico
i'm neither an expert in functional analysis or in psychology. the mood of this announcement sounds positive to me, though .. which might be crucial for these two researchers.

that sounded cryptic. by that i mean:

depending on one's training and personality, it can be easier to think creatively about
something when not under constraint
. it's the difference between looking (A) for
something interesting and (B) being driven to find a very specific something.

so my hope is that these guys keep in mind that they already have some good theorems
in the bag
. if they can still prove the conjecture, then great; in the meanwhile, if something
else interesting comes up from their investigations, then it already has the publicity to
make a good upcoming line of research.


for a while, everyone always told me to be optimistic .. which, to be honest, constantly got on my nerves. i guess i've finally been fully brainwashed! (-:

4. definitions can be important.

i encountered this one definition of "genius," the other day.
"The “scientific genius” Simonton refers to is a particular type of scientist; their contributions “are not just extensions of already-established, domain-specific expertise." Instead, “the scientific genius conceives of a novel expertise.” Simonton uses words like “groundbreaking” and “overthrow” to illustrate the work of these individuals, explaining that they each contributed to science in one of two major ways: either by founding an entirely new field or by revolutionizing an already-existing discipline.

Today, according to Simonton, there just isn’t room to create new disciplines or overthrow the old ones. “It is difficult to imagine that scientists have overlooked some phenomenon worthy of its own discipline,” he writes. Furthermore, most scientific fields aren’t in the type of crisis that would enable paradigm shifts, according to Thomas Kuhn’s classic view of scientific revolutions. Simonton argues that instead of finding big new ideas, scientists currently work on the details in increasingly specialized and precise ways.

~ from is scientific genius a thing of the past @arstechnica
on the one hand, there is a point to this:

professionally, it doesn't pay to have a completely new idea that is essentially unrelated
to all previous approaches. in the case of mathematics, the problem lies in who can possibly
check the work
, because there is an opportunity cost to learn something completely new
and separate from one's expertise.

on the other hand, i know of very few persons who can accurately predict history, even for
scientific trends (which draw on quantitative approaches).

the word "open" has a clear, standard definition in topology, but as for copyrights?
"One piece of evidence on researchers’ opinions comes from the open-access journal Scientific Reports, which since July 2012 has been offering researchers a choice of three types of licence. One is CC-BY. A more restrictive version, CC-BY-NC-SA, lets others remix, tweak and build on work if they give credit to the original author, but only for non-commercial (NC) purposes, and only if they license what they produce under the same terms (SA, or 'share-alike’). A third licence, CC-BY-NC-ND, is the most restrictive, allowing others to download and share work, but not to change it in any way (ND, ‘no derivative works’), or use it commercially."

~ from "Researchers opt to limit uses of open-access publications" @nature
there is a point to this, even apart from the discussion of profits, potential greed, and capitalism.

say that i take a great snapshot of a 4th of July barbecue, with a cute little girl holding a
pinwheel and grinning gap-toothed at the camera. would i have the right to forbid others to
use the photo if i have a personal objection? maybe a white supremacist group would want
to use it for their website --- it might give their theme of "america," after all --- if i chose
the wrong license, then i have no legal recourse from their use of it.

the same could be said for bio/engineering breakthroughs that lead to military weapons.

and then, what is a good definition of "lazy" ..?

lately i've been feeling unproductive .. not quite lazy, but just not effective. i think
it has to do with my not having to teach. it frees up a lot of time in the day .. which
means, shouldn't i be doing real work at some point?

i've not reconciled that feeling yet. this doesn't prove anything, but it does assuage my guilt a bit ..
"Now we also know that if you study absolute world class, best virtuoso violin players, none of them put in more than about four or so hours of practice in a day, because that’s the cognitive limit. And this limit actually shows up in a lot of different fields where people do intense training, that you really can’t do about more than four or so hours of this type of really mental strain.

And they often break this into two sessions, of two hours and then two hours. So there’s huge limits here. I think if you’re able to do three, maybe four hours of this sort of deep work in a typical day, you’re hitting basically the mental speed limit, the amount of concentration your brain is actually able to give.

~ from "Four hours of concentration" @johnbcook, via accidentalcreative
apparently it's not just musicians. it apparently worked for poincaré, too.

5. maybe numeracy isn't a bad ability to have.

i found this article off a friend's social media feed. if you've not seen it yet, it's worth a look:
"Modernity provides too many variables, but too little data per variable. So the spurious relationships grow much, much faster than real information.

In other words: Big data may mean more information, but it also means more false information.

Just like bankers who own a free option — where they make the profits and transfer losses to others – researchers have the ability to pick whatever statistics confirm their beliefs (or show good results) … and then ditch the rest.

~ from "Beware the Big Errors of 'Big Data'" @wired

Tuesday, February 05, 2013

in medias res: alas!

// initially written: 11:44EEST, 5 feb 2013
ay me: what little faith have i, in mine own self.

i looked at a proof i wrote, a fortnight afore,
thought it bent and false;

as i strove to better it,
my eyes spied it more closely, and 'lo:
'tis verily straight and true!

alack! enough of words, these lifeless things,
numbers and figures are my works and days of hands, and
much time to toil remains.

anon ..!

// added later: 9:35EEST, 7 feb 2013


you know, i have no idea why i wrote that earlier. the edits to this manuscript must be taking their toll, and i'm losing my good sense ..


on a related note, i just received word that one of the arguments in one of my preprints can probably be substantially simplified.

this is good, in that it might save me a few pages,
but bad, in that the result might now appear completely trivial!

// added later: 17:13EEST, 7 feb 2013

fvck! never mind:
i was right .. in that i was actually wrong.

there is still a gap in the "proof" ..! 7-:

Monday, February 04, 2013

MoAR: among other things, (1) keeping it simple, (2) disadvantages of campus life, as well as (3), (4), & (5).

1. simple wikipedιa is nothing compared to this ..

i've heard of talks and articles aimed for a general audience, but this sounds quite extreme!..
"Perhaps that is why the Up-Goer Five text editor, created by geneticist Theo Sanderson, has struck such a cord with many scientists, including me and my co-blogger Anne Jefferson. Inspired by a brilliant xckd comic that took the elimination of jargon to an almost absurd degree by attempting to describe the blueprints of the Saturn V moon rocket using only a list of the most thousand commonly used English words (hence, Up Goer Five - "the only flying space car that has taken anyone to another world"), the text editor compares anything that you type into it against that same list and gently chides you when you use a word that isn't on it."

~ from Science in Ten Hundred Words: The `Up-Goer Five' challenge. @sciam (via yahoo)
as for an example of science with a restricted (1000 word) vocabulary ..
"Well, you could go to each computer, and ask it for all of its words and pictures, and look in those words for Mr Turing. But that would take years (yes, really), and you would have to look at a lot of cat pictures. So what you really need is something like the set of words at the back of the book, which would tell you which computer knew something about Mr Turing. Then you could go and ask just these computers, rather than having to ask every computer in the world."

— Alasdair Mackintosh - I work on Google web search @tenhundredwordsofscience
why do i get the feeling that the ten-hundred word version of one of my research abstracts will involve terms like:

instead of "rectifiable"

.. or for that matter ..

in place of "bi-lipschitz" ..? 7-:

2. MOOCs: the human element and the lack of schlep.

the following passage gave me some small feeling of hope:
"a student in Cairo who was taking the circuits course and was having difficulty. In the class’s online forum, where students help each other with homework, he posted that he was dropping out. In response, other students in Cairo in the same class invited him to meet at a teahouse, where they offered to help him stay in the course."

~ from "revolution hits the universities" @nyt
maybe these massive online courses (or MOOCs) are on to something, for there remains a human element in the setting of such a course. one could argue that there is more, in that the online forums provide a more immediate mode of interaction with the instructor(s) and fellow classmates, with a likelier chance of response.

for you educators out there, compare this to
how many students actually attend office hours.

thinking about it though, i want to point out that not all of the strengths of MOOCs are digital in nature .. not directly, anyway.  the first time i read the following excerpt, i could imagine the why and how of the situation, but couldn't quite figure out the what ..
"One member of the Coursera team who recently took a Coursera course on sustainability told me that it was so much more interesting than a similar course he had taken as an undergrad. The online course included students from all over the world, from different climates, incomes levels and geographies, and, as a result, “the discussions that happened in that course were so much more valuable and interesting than with people of similar geography and income level” in a typical American college."
what could make so much of a difference?

thinking about it, it must be a matter of perspective.  if a lecture is a video, then that means you can choose when to watch it.  in particular, you would probably never watch it when you're exhausted or half-asleep.  that's a clear advantage which the online student has over the campus student .. but more due to a matter of habit.

for a campus student, lectures are a normal part of life .. to the extent that it becomes a "chore" to attend them.
i do believe that most students are diligent and deem their classwork important, but that doesn't eliminate the annoyances of (A) getting up early, (B) getting dressed, (C) shivering on the way from the dorm to the lecture hall, (D) waiting out the boring 5-10 minutes until the prof shows up .. so it's a bit of a schlep.

once class begins, of course, it's a whirlwind;  (E) it's all they can do to keep up with their note-taking, and at the end, (F) there's no time for questions.

to be honest, i think most students aren't paying attention in class not because they are some kind of ADHD generation, but simply because they are half-asleep or (mentally) unprepared.  this shouldn't be taken lightly, either.
if you took a reasonable sample of students from that Coursera team member's class and put them on the same campus and in the same classroom with the same schedule, then maybe you'd get the same results.  i'm not convinced, though.

there's a lot to be said for having someone's full attention.

3. in which $0.999^{365 \times 3} \approx 0.334$.

i suppose that the subtitle (above) is already quite suggestive. for instance, i rarely if ever use the number $365$ for computations unrelated to time.

maybe i'm using a more high-end calculator than other people.
"Life expectancy for a healthy American man of my age is about 90. (That’s not to be confused with American male life expectancy at birth, only about 78.) If I’m to achieve my statistical quota of 15 more years of life, that means about 15 times 365, or 5,475, more showers. But if I were so careless that my risk of slipping in the shower each time were as high as 1 in 1,000, I’d die or become crippled about five times before reaching my life expectancy. I have to reduce my risk of shower accidents to much, much less than 1 in 5,475."

~ from That Daily Shower Can Be a Killer by jared diamond @nyt_science
so i like diamond's idea, but i think his computation is non-rigorous. after all, the statistic is $0.1\%$ for each shower. granted, i'm assuming that daily showers are independent events, but the chances of not slipping in the shower in the next three years is $$ \mathbb{P}\Big[ \bigcap_{n=1}^{365 \times 3} (\text{no fall on $n$th day}) \Big] = \prod_{n=1}^{365 \times 3} \mathbb{P}[\text{no fall on $n$th day}] = 0.999^{365 \times 3} \approx 33.4\% $$ so yes: the odds are bad, but i wouldn't say that he would surely have died five times over. on the other hand, supposing that he could live forever (provided nothing happens to him otherwise) the expected number of accident-free years would be something like .. $$ \sum_{n=1}^\infty n \times 0.999^{365n} = x \frac{d}{dx}\Big[ \frac{1}{1-x} \Big] \Big|_{x=0.999^{365}}= \frac{0.999^{365}}{(1-0.999^{365})^2} \approx 7.416 \text{ years}, $$ so .. well, twice over or so. maybe it is worth being careful [1].

4. quotations of the week.

one could say the same thing about teacher's evaluations. as for what this thing is ..
"There is no feedback loop in rating colleges,” Gates explained at a small roundtable of six bloggers and journalists held on Wednesday at the Omni Berkshire Place hotel in New York City, “The control metric shouldn’t be that kids aren’t so qualified. It should be whether colleges are doing their job to teach them. I bet there are community colleges and other colleges that do a good job in that area, but US News & World Report rankings pushes you away from that."

~ from "there is something perverse in college ratings" @forbes
as for this next excerpt, i've been known to offer the following advice about writing:

write something bad as fast as you can; if it's good, then keep it.
if it's bad, then you know what would be better, if not good,
so write that down and edit the hell out of it.

such advice presupposes, however, that you will have something good enough in the end. there are other possibilities, which are discussed further and below.

maybe it's better to say that "learning from failure" is itself learned.
"But I’ve never liked this embrace of failure. We learn as much from our successes as from our failure and I suspect we learn much more. Besides, I failed a lot in school. I didn’t test all that well and didn’t get straight As. Failure made me feel awful. And I think failure makes kids in urban public schools or on the rez feel just as bad if not much worse. Many are already close to despair in their lives. Failure is deeply meaningful to them. It has serious consequences. Get labelled a “Failure” and it can ruin your life. As a pedagogical methodology, embracing failure is the last thing these kids need. "

~ from "stop fetishising failure" @creativeintelligencebook
lastly, i wonder what erdos's kevin bacon number is. (-:
"The year was 1967. Russell was by then a very frail 95-year-old man. Besides finishing work on his three-volume autobiography, Russell was devoting much of his remaining time to the struggle for peace and nuclear disarmament. To that end, he sometimes made himself available to people he thought could help the cause ... So when he was asked to appear in a movie called Aman, about a young Indian man who has just received his medical degree in London and wants to go to Japan to help victims of the atomic bombings at Hiroshima and Nagasaki, Russell said yes."

~ from The Old Philosopher’s Improbable Appearance in a Hindi Film @openculture

5. lastly, the funny pages

i found these off david olenick's website.  these are the ones that i found slightly mathematical .. (-:

and as for this one, it's a shot by pedro correa:

what makes this one seem "mathematical" is the spraypaint on the ground: it resembles scratchwork for a computation, to me.

now i imagine a proof of the pythagorean theorem, done graffiti style ..! (-:

[1] on a related note, i keep on getting weird answers when trying to compute the expected value in terms of days. maybe i should stop assuming that people are immortal .. (-:

Saturday, February 02, 2013

feeling ridiculous ..

// originally written: tues, 29 jan 2013

it's slightly embarrassing to give a slightly strange alternative to a standard definition in the literature, only to show that under your hypotheses, the standard definition and your definition are actually equivalent.

it raises the question:
couldn't i just have used the standard definition?
logically it should be possible, right?

am i just stupid?
i'd like to get back to this, throw away the hypotheses, and construct an example where the definitions give distinct classes of objects ..

.. but i'm also in the middle of finishing a $\LaTeX$ writeup, have been distracted from it by too many meetings this and last week, and really, really want to get it done.