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.

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 ..

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#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 ..

#1300: chalkboard post.

from a few days ago:

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

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.

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?

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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

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(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

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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

a pleasant surprise.

very strange:

this morning i wrote to a journal, in as polite terms as possible, about my article submission from october 2011 and why i had received no response since then.

(yes, i know: i should have written sooner.)

they replied right away, this afternoon.

apparently they sent a reply last august, indicating that it was accepted, and have been waiting for me to submit the final version under their specific formatting guidelines!

after running a few searches with all the keywords that i could find, there was no trace of that email.

[shrugs]

oh well, it doesn't matter. it's good news .. and i finally have some closure in that part of my life.

you see, it was the only paper i was able to cut out from my ph.d. (as of now) and before that journal, it was stuck for another 18 months ..

.. in a journal that i will not name,
but to where i will never submit anything ever again.
maybe i will change my mind,
but it will be more likely that i leave mathematics,
before i'll place any trust in that journal.

pardon my vulgarity, but fvck them!
hell, i don't know if i'd even referee an article for them.

.. but it's done;
it took .. ye gods .. four years, but up to formatting it is done.

at least the referee has decided that the techniques i used, which aren't terribly standard, are reasonable. it's reassuring, because so far i haven't had much luck getting my work in this area published.

i can move on now, and build on that work. it's not an end, though, but a beginning.

counting the years.

so the offer letter came in the mail today. among other matters, it read:

Type of appointment: Tenure Track, probationary period prior to tenure ends August 31, 2020.

wow: 2020?

i can barely fathom that far ahead in the future. in my mind, i'm still a little boy and we're supposed to have flying cars by now.

on a more serious note, i still have trouble believing it. six years: i've never had such a length of time committed to any one stage of my adult life before:

it's going on 2 years for this postdoc,
the last 3 were for another postdoc,
the last 5 i spent completing a ph.d.,
the last 4 were my undergraduate years ..
..
[blinks]
[counts]

ye gods: i've spent more than a third of my life on college campuses!

MoAR: surprises, mostly non-mathematical.

so yes: this week's round-up is late. i blame it all on yesterday's airport transit and today's busy routine in hosting a(nother) visitor.

anyway, most of these aren't really maths related at all ..

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wtf?

well, i suppose that it's a form of internet addiction .. but really?

"I don't think it's very healthy" is the confession of Pavel Lepin, a 35-year-old in the Latvian city of Jelgava who has earned certificates in "about 30" MOOCs, some from Coursera, some from Udacity, and some from edX. "My friends and co-workers are already making fun of me for being a Coursera addict."

Mr. Seiter agrees that it as possible to learn as much online as in a traditional course, but that to do so usually requires doing optional readings, which most MOOCers skip."

~ from "What Professors Can Learn From 'Hard Core' MOOC Students" @the_chronicle

.. and now, from the physicists:

"Physicists have long known that quantum mechanics allows for a subtle connection between quantum particles called entanglement, in which measuring one particle can instantly set the otherwise uncertain condition, or "state," of another particle—even if it's light years away. Now, experimenters in Israel have shown that they can entangle two photons that don't even exist at the same time. "

~ from "Physicists Create Quantum Link Between Photons That Don't Exist at the Same Time" @sciencenow

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measuring intelligence .. somehow?

to some degree, the mechanism seems right .. but does it account for cultural differences?

"This surprisingly simple exercise measures the brain's unconscious ability to filter out visual movement. The study shows that individuals whose brains are better at automatically suppressing background motion perform better on standard measures of intelligence."

~ from "Motion Quotient " @rochester.edu

.. and as for more "depressing" news ..

"This paper proposes to analyse the relationships between depression and high intellectual potential through a multidisciplinary and original approach. Based on their respective experience in psychology and child psychiatry, the authors will focus their analysis on creative potential .. This case study sheds light on the paradoxical role of depression in the overinvestment in intellectual and creative spheres as well as on the impact of traumatic events on high intellectual potential."

~ from "Relationships between Depression and High Intellectual Potential" @hindawi:drt

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lastly, a breakthrough.

i would call this an amazing feat of mathematical "engineering" .. which is its own kind of genius. still, i wonder how many mathematicians are slightly disappointed at the lack of new tools that this solution provides.

"As details of his work have emerged, it has become clear that Zhang achieved his result not via a radically new approach to the problem, but by applying existing methods with great perseverance. “The big experts in the field had already tried to make this approach work,” Granville said. “He’s not a known expert, but he succeeded where all the experts had failed.” "

~ from "Unheralded Mathematician Bridges the Prime Gap" @simonsfoundation

away, again.

it's been quiet on my end. i took the week off and headed to france to go bouldering with friends [1]. i feel tired .. not necessarily in a good way, not in a bad way either, but just tired .. and certainly not from maths.

honestly, it felt like a bad time for a holiday .. especially as the last one wasn't too long ago. though it was fun, it didn't feel like an earned holiday.

at times it was hard to shut my brain off:

every morning i tried to wake earlier than everyone else and think about a problem or two over a cup of coffee, occasionally jotting down a few computations in a notepad that i brought.

come to think of it: with few exceptions,
i've been doing this every day since i moved to finland.

this routine worked for the first few days. after a while, though, the climbing became serious and everyone started getting up early for more time on the rocks.

there was also the matter of a research visitor next week .. one whom i actually invited this time but whom i've never met in person. during the last few days i was often preoccupied with how the visit would go. (as you may recall, hosting isn't one of my strong points.)

lately i feel like i've not been accomplishing much and that my recent endeavors haven't been very deep [2] .. and both without good reason. maybe it's just the flight i took home this morning, but paradoxically i'm tired yet feel like working.

there's the standard cliché that i need a vacation from my vacation. that's not what i want, though: not exactly, anyway. it would be nice to get away, go somewhere with only an empty notebook and pens, and just work without interruptions .. work and not come back until i had something complete.

i get the feeling, though, that paradoxically and simultaneously, i'd miss being at the office. it just goes to show you that, for some people, perfection doesn't really exist in life; at most, one gets a sufficiently nice balance of a "uncertainty principle" towards their quality of life.





[1] interestingly enough, one of the main pioneers of bouldering as a sport was actually a mathematician named john gill. according to the wiki, apparently he studied cοmplex dynamιcs!

[2] part of me suspects that those weeks spent at IΡAM have warped my usual research expectations. it's easy to forget that maths isn't about getting ideas .. but following through and shaping them into rigor.