Wednesday, October 31, 2012

mildly interesting: i don't see a singularity .. but still cool.

over at abstractstrategygames they've posted about a so-called singularly chess, where the pieces and rules are the same as usual (western) chess but the boards are non-linearly tiled ..

.. almost like a polar coordinate system;
as a result, pieces move in unconventional ways:

for more examples, visit the abstractstrategygames website (here).

Tuesday, October 30, 2012

i remember.

on a more sombre note, i just realised:
five years ago, the advisor passed away at the age of 47.
the thing is .. more years have now passed than the number of years that i've known him.  it's a very odd feeling, but maybe not:
the people that influence us most and the good mark they leave on our lives .. these are things that cannot really be quantified and should not be, either.

i've known some people all my life and others for just a few days or hours, and the time i've spent with each of them is hardly proportionate to their place in my life and thoughts.
so what are the rules of arithmatick, the measurement of time, in regards to people?

i still remember.  i still think of him,
less often than i did before ..

.. but i still do.

mildly relevant: for collaboration purposes?


from mathιm

it would be more convenient, though, if they allowed rendering through LaTeX .. (-;.

Monday, October 29, 2012

memories: when i was a (mathematical) gun-for-hire ..

the season of job applications is in full swing, isn't it? [0]

in point of fact, last month i helped a colleague with a research statement [1], and a week ago my old officemate sent me his "research statement for non-experts" .. which seems apt, since his work is as far removed from mathematical analysis as i can think of.

every time i see a job ad that's not on mathjοbs or the usual channels, i pass it to a colleague who's on the market and seems to fit the bill.

there were some thoughts that i wanted to write about last year, but i was always too busy with this application, writing another talk, or chasing another research idea ..
.. more on the latter case, below.

maybe this year i can make up for that lost time .. and in the process, those of you on the market can have a welcome distraction from your own endeavours in the job market.

2010-11 was, in general, a bad year for me.

Saturday, October 27, 2012

as an aside: rigorous conversation!

sometimes i think that i over-think casual conversation;

for instance, sometimes i forget and think about about how to respond to my friend's "how are you?" when (s)he simply meant hello. [1]

that said, yesterday i met an acquaintance, who is defending his Ph.D. today.  i paused for a second, after hearing the news, and then said:
"it could be that you believe in a completely deterministic universe;
but if not, then good luck!"

to his credit, he smiled briefly.
to be fair, one of my friends from school doesn't believe in luck .. so i never quite know how to wish her well in her endeavors ..

[1] it's not unlike looking at your watch when asked, "do you have the time?"
it is, after all, a yes/no question
.. 7-:

Thursday, October 25, 2012

from the arXiv: third derivatives could be useful ..

admittedly, i have always dismissed derivatives of orders 3 and higher.

maybe it's because my background in physics is poor, and i never rightly learned good mechanical interpretations of third-order derivatives.  (i still don't know how to think of them, honestly.)

at any rate, this title/abstract from the arXiv is suggestive.  maybe third derivatives are worth something, after all!

The Taylοr Expansiοn of the Expοnential Map and Geometric Applications

In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in ${\bf R}^n$ up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in ${\bf R}^3$. Also we compute, by using the Taylor expansion, the directions of high contact with hyperspheres of a surface immersed in ${\bf R}^4$ and the asymptotic directions of a surface immersed in ${\bf R}^5$.

from the arXiv: a title/abstract, short and sweet.

i really admire works with straightforward, easy-to-understand problems.
from the arXiv:

Answer to a question of Kolmogοrov

A. N. Kolmogοrov asked the following question. Let $E\subseteq \mathbb{R}^{2}$ be a measurable set with $\lambda^{2}(E) < \infty$, where $\lambda^2$ denotes the two-dimensional Lebesgue measure. Does there exist for every $\varepsilon > 0$ a contraction $f\colon E\to \mathbb{R}^2$ such that $\lambda^{2}(f(E)) \geq \lambda^{2}(E)-\varepsilon$ and $f(E)$ is a polygon? We answer this question in the negative by constructing a bounded, simply connected open counterexample.

Tuesday, October 23, 2012

mildly interesting: speaking of genius and innovation ..

~ from "how to spot a genius" @scientificamerican:
.. but progress is faster if you are born with the right skills. Personality also plays a role. If you are very open to new experiences and if you have psychopathic traits (yes, as in those shared by serial killers) such as being aggressive and emotionally tough, you are more likely to be considered a genius ..

when i think of aggressiveness [1] and emotional toughness, psychopathy doesn't immediately come to mind.  actually, i think first of successful athletes .. both men and women, actually.

i also wonder if there is a difference between the "geniuses" that are easily spotted, as opposed to the perfectly well-adjusted geniuses that are happy not to be in the spotlight ..? then again, in ακαδημια, it could be the self-promoters that ulitmately win out ..7-:

[1] "aggression" doesn't seem like the right nominative.  i reserve it only when discussing politics, just like how i try to use the word "normalcy" only when referring to the harding administration of the american post-wwi era.

man, with an office: disorientated.

as a change of pace today,
i'm looking at ΡDEs,
specifically, nοn-linear parabοlic ones ..

.. and to clarify, on euclιdean spaces.
the non-linearity seems hard enough in that setting already, so there's no need to make life harder and study metrιc spaces (yet)!

- - o - -

i suppose that this reflects how my life seems to be going lately:

jet-lagged, uncertain and confused,
constantly on the move.

maybe i can get away with staying put until mid-november.  (here's hoping!)

Sunday, October 21, 2012

man without an office: disparate bits.

// originally written: thursday, 18 october 2012

i'm currently visiting family;
there was also a marriage ceremony involved, and it went very nicely.

at first i was worried that i wouldn't have time to work, but then i underestimated how often my siblings are on the internet .. whether it be their laptops, phones, or tablets ..

.. so as long as my $\LaTeX$ing looks like web-surfing and i say something both interesting and seemingly-sounding from internet news, then it's all good! (-:

// added: friday, 19 october 2012

i have a bad case of jet lag.

this morning i woke at 4am .. which has its perks: so far i've had 2-3 uninterrupted hours to work before anyone is awake!

// added: later, on friday

so apparently my sister (a postdoc in biology) had already taken a teaching orientation last year .. and therefore she needn't do the scheduled one for this afternoon ..

.. which, in turn, means that
  1. we now have more time to hang out;
  2. i lost those 2-3 hours that i was planning to edit this one write-up .. 7-:
it's like expecting a rainy day:
having made plans to stay in, read, and say .. bake some fresh bread and slowly simmer a pot of soup .. all the while, allowing your mind to wander in and out, grasping aspects of a problem here and there ..

.. all of a sudden it becomes sunny and fine and everyone now want to head out to the beach, play football, and be wild.
this is of course very good .. but it's not quite hot soup and a cozy blanket, you know?

// added: even later, on friday

so while wandering aimlessly through town, we stopped by a used bookstore .. and i stumbled onto a copy of jacques hadamard's the psychology of invention in the mathematical field!

interesting: according to the wiki ..
In sharp contrast to authors who identify language and cognition, he describes his own mathematical thinking as largely wordless, often accompanied by mental images that represent the entire solution to a problem.
at any rate, i love this part of the country ..!

Friday, October 19, 2012

mildly interesting: time as a spatial dimension (photographically)

these are spacetime photos, as found off an article @slate:

in the words of the author:
"The abstract-seeming images here are not the result of some wacky Photoshopping. Jay Mark Johnson’s photos are actually incredibly precise. The reason they look like this is because he uses a slit camera that emphasizes time over space.
This unique look is possible because the fixed-position slit camera registers only a vertical sliver of a scene. Whatever passes that slit by gets registered in a narrow line. Over a period of time, which Johnson can control, it registers line after line. The final result is a bunch of these lines all pushed together. (In this sense, you could say each photograph is actually a composite of hundreds of very skinny images.)
it therefore makes sense that a periodic motion, like that of ocean waves, would appear the same as a typical photograph:


Thursday, October 18, 2012

on survival and risk, academically speaking.

// originally written: 16 october 2012

one of the risks in staying in this business ..
.. not that i ever had a backup plan or anything ..

.. is that one grows older, more young people arrive into the game, and by default one's status becomes a more senior one (even if not formally so).  like it or not, we become role models of a kind .. especially in university environments, where one encounters a lot of students.

i wonder how often others meet us, and we are immediately viewed as "old."

this very phenomenon played a decisive part in my decision to extend this postdoc position for another year .. not the "old" part, i mean.  (i'm fine with that.)  rather, the seniority and responsibility seemed very real to me.

i still don't know if it feels right to be Professor Geminus yet instead of just Janus, but i can't put it off forever.  we all need to grow up, i suppose .. or at least enough of us, if only to make sure that the world keeps turning.

--- o ---

i don't think i make a very good role model. [1]  it's not just the circumstances of my last talk, either, though that was a rare exception.  there's more to it.

some mornings, as the coffee slowly wakes me up, the thought occurs to me:
i can't believe it: despite all the bad strokes of luck,
all the stupid mistakes i've made .. i'm still in the game
i dwell on this a while, honestly stunned.  (then, of course, i set aside such thoughts and get to work .. but you get my point.)

maybe i've met too many talented and well-organised mathematicians, which probably warps my sense of what "average" means in this business [2].  at any rate, many of my colleagues have successfully applied for research grants, make excellent mentors, give fine presentations, and work on many different sub-fields.

in contrast, to this day i still don't feel like i know what i'm doing.

Wednesday, October 17, 2012

mildly relevant progress: knowledge can stay free, for the people.

as found this arstechnica ..

Court rules book scanning is fair use, suggesting Google Books victory

Judge rules for Google's library partners in lawsuit brought by Authors Guild.

Now a judge has ruled that the libraries who have provided Google with their books to scan are protected by copyright's fair use doctrine. While the decision doesn't guarantee that Google will win—that's still to be decided in a separate lawsuit—the reasoning of this week's decision bodes well for Google's case.

Most of the books Google scans for its book program come from libraries. After Google scans each book, it provides a digital image and a text version of the book to the library that owns the original. The libraries then contribute the digital files to a repository called the Hathitrust Digital Library, which uses them for three purposes: preservation, a full-text search engine, and electronic access for disabled patrons who cannot read the print copies of the books.

Monday, October 15, 2012

mildly relevant: live free or .. well ..

~ from "a plan to open up science journals" @bostonglobe
Hrvatin and his college roommate, Robert McGrath, think they can solve the problem by incorporating an iTunes model of ­single sales. Reducing the cost of individual articles — with some restrictions to protect the publishing business — will help scientists keep up with research and help libraries hold down costs, say the pair, who have named their product ReadCube Access.
i wonder at the wisdom of this. already there are a lot of pirated mathematics books in djvu and pdf out there. it wouldn't be that hard to develop a decentralised network to cache illegal copies of pirated research articles ..

.. and yes, it sounds ridiculous: who would pirate a research article?
i asked myself the same thing about textbooks once.

Saturday, October 13, 2012

mildly relevant: an unexpected formation, some unsolicited advice.

~ from "topοlogy: the secret ingredient in the latest theory of everything" @techreview
For example, certain quantum particles cannot form pairs but do form triplets called Efimov states. That's curious--surely the bonds that allow three particles to bond together should also allow two to become linked?

Actually, no and topοlogy explains why. The reason is that the mathematical connection between these quantum particles takes the form of a Borrοmean ring: three circles intertwined in such a way that cutting one releases the other two. Only three rings can be connected in this way, not two. Voila!
~ from "you and your research" by richard hamming ('86) @paulgraham:
One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to. Courage is one of the things that Shannon had supremely. You have only to think of his major theorem. He wants to create a method of coding, but he doesn't know what to do so he makes a random code. Then he is stuck. And then he asks the impossible question, ``What would the average random code do?'' He then proves that the average code is arbitrarily good, and that therefore there must be at least one good code. Who but a man of infinite courage could have dared to think those thoughts? That is the characteristic of great scientists; they have courage. They will go forward under incredible circumstances; they think and continue to think.

.. There's another trait on the side which I want to talk about; that trait is ambiguity. It took me a while to discover its importance. Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance. But most great scientists are well aware of why their theories are true and they are also well aware of some slight misfits which don't quite fit and they don't forget it. Darwin writes in his autobiography that he found it necessary to write down every piece of evidence which appeared to contradict his beliefs because otherwise they would disappear from his mind.
~ from "why does it take so long to learn mathematics" @tonysmathsblog
I don't think I'm a better mathematician than I was 35 years ago. In terms of solving exam questions, I would not perform as I did when I was twenty. Even with practice, I am sure I could not get back to that level, and not only because I no longer value that kind of cleverness enough to put the effort in. I now have a much better general understanding of mathematics and how it all fits together, but I no longer have the ability to master detail that I once did.

Perhaps I am misremembering my difficulties as a student: perhaps I didn't find it as difficult as I now remember it.  Certainly I had little understanding of how an area of mathematics fitted together: my learning at University consisted of reading strings of definitions and theorems, with little idea where it was all going, making sure I understood each result before going on to the next one, until, perhaps, in the last lecture of the course the lecturer would say something like "and so we have now classified all Lie algebras" and I would suddenly find out what the point of it all had been.  I now feel that I would have been a much more effective mathematician if I had read more superficially, skipping proofs until I understood the context, but since got good marks as an undergraduate I had no incentive to adopt what I now feel would have been a much better strategy.

Friday, October 12, 2012

showtime, before-&-after: slow to heal, some damage done.

// originally written: wednesday
// while tired/slightly irritable

ye gods, i (still) feel exhausted. i wish i could give my friday talk today, just to get it over with.

having another talk to think about seems to diminish my capacities. i know many people who take on such commitments as if they were appointments to the dentist; like those cases, there's little to no stress. one just brushes a little better than usual, maybe try out flossing, and make it to the office on time.

i've never been able to do that. i don't know why.

this reminds me of my days from school, where i used to run track-&-field. the tournaments where i was scheduled to run two events were always stressful ones:
when the events were too close together, then i'd inevitably run one of them badly. if i pushed hard on the first one, then i would feel dead during the second; if i wanted to do really well in the second event, then i'd have to throw the first race.

i don't know if other kids had the same problem. then again, i never seemed to heal or recover particularly quickly.

when the events were spread apart, say one in the morning and one in the afternoon, then it would just be a long, drawn-out affair. is it better to stay limber between events, or just "shut down" completely and then do a new, second warmup for the second event?

the time in between just seemed lost to me .. though that didn't bother too many of my teammates. again, i don't know why.
it must really be a matter of biology .. or maybe psychology. personality?

// originally written: thursday,
// while slightly less tired.

the same problems are recurring:

there's too much background,
the discussion is rather technical ..

i don't know how i'll say anything intelligible tomorrow,
and i mightn't get to the really cool geometry part at all ..!


on the bright side, there's no dearth of things to talk about. /-:

// written: friday (today),
// while noticeably more tired.

ye gods: i felt awful during today's talk.

Thursday, October 11, 2012

points in spacetime: fluids, anyone?

i'm considering attending a conference with the word "fluids" in the title ..

.. which, at first, looks like a bad sign;
i'm no applied mathematician!
on the other hand, i recognise quite a few of the invited speakers' names as well as the organisers, and even know a few of them personally.

but back to the first hand [1]: do i really want to travel more than i need to .. especially with all the trips coming up, this fall and spring?
decisions, decisions ..\-:

[1] there's no idiomatically natural way of saying this, is there? (-;

mildly relevant: by far, the coolest thing i've heard in a while.

~ from "the non-euclidean geometry of whales" @ numberplay:
If whales had invented geometry, the geometry they would have invented would be hyperbolic.

Suppose, for a moment, that you are a whale. Light is not very useful in the deep ocean, because the water is dark. So you mostly communicate and experience the world through sound. The shortest distance between two points in your world would be the path taken by sound waves. To you, this would be the analogue of a straight line.

Now here’s the catch. Sound does not travel at a constant speed in the ocean. Below a certain depth, roughly 2,000 feet (600 meters), it travels at a speed that is proportional to the depth below the surface. So the path that sound waves travel is not straight, but curved. A sound wave will get from whale A to whale B quicker if it goes downward, to exploit the greater sound speed at depth, and then comes back up. Thus, to a whale, what humans call a “circle” is actually a “line” (the shortest distance between two points).

(courtesy of NYT's numberplay)

Tuesday, October 09, 2012

mildly relevant (and amusing): maths and poetry.

~ from letters of note, in reply to alfred, lord tennysοn's poem, the vision of sin.

In your otherwise beautiful poem "The Vision of Sin" there is a verse which reads – "Every moment dies a man, Every moment one is born." It must be manifest that if this were true, the population of the world would be at a standstill. In truth, the rate of birth is slightly in excess of that of death.

I would suggest that in the next edition of your poem you have it read – "Every moment dies a man, Every moment 1 1/16 is born."

The actual figure is so long I cannot get it onto a line, but I believe the figure 1 1/16 will be sufficiently accurate for poetry.

I am, Sir, yours, etc.,
CharΙes Babbagε
// added later

to be fair, it might still be true. i'm reading "every moment dies a man" to mean that for each moment, there is a man who dies, but there's no claim that exactly one man dies that moment.

however, it would be incorrect if there were moments when no man dies.

(at any rate, don't mind me: i didn't sleep well last night, was tired after a giving a seminar talk, and unwisely decided to tackle a lemma for a new problem to work on .. all of which have drained my energy and good sense for the evening.)

Monday, October 08, 2012

talk neuroses: more matter, with less art.

.. since brevity is the soul of wit ..

i'm still thinking through the first talk that i'll give this week. i'm weighing how to say what i want to say without writing technical details at top speed for 2 x 45min.
in case it isn't already clear, this is the first time i'll be giving this particular talk. it makes situation slightly loaded, i guess.

until recently i've been obsessed with writing up the associated preprint, which is almost done. (i might even submit it this week.)
the abstract i wrote is rather vague, though, which means that there's no need to keep my word and i can essentially talk about what i want. as for the title, i guess i have to stick to certain subjects, like GMT and metric geometry ..

.. which is slightly scary.
.. but this above all, to thine own self be true,
and it must follow, as the night the day, thou canst not be false to any man ..

i still feel like i don't know any GMT, which in most cases is fine. speaking with a colleague last week, though, she seemed rather interested in the talk .. which means that she might attend and bring her colleagues who do study GMT along ..!

so now i have to know some GMT .. and explain why my non-standard version of a standard construction makes sense in this one setting.

there is one more thing, though, that worries me.

Saturday, October 06, 2012

budgeting topics for a talk is like packing a weirdly-partitioned backpack with ill-fitting objects.

// initially posted on sat, 6 oct 2012

so i have $C = 16$ pages to write (by hand) for next week.  if you think of $C$ as a quantitative constant, then it depends on the following parameters:
$C = 4C'$, where $4$ is the average rate of pages* per hour i can discuss,
$C'=2C_{\rm talk}$, with $C'$ the number of talks i'm giving next week, and
$C_{\rm talk} = 2^{**}$ is the length of a typical talk in a finnish seminar.
the good thing is that i already have both punchlines in mind, so each talk outline essentially writes itself.  i don't think i can fit in all that i want to say, though, which for me is normal.

in my talks, i always run out of time. /sighs/

the constraints are the usual ones for presentations ..
various components of the talks depend on each other, of course.  if i don't add this one part to the exposition, then later on, another part won't make sense at all ..

meanwhile, the point of the main result is that it has this nice application, as advertised by the title .. but to explain it would probably take a precious 11/2 pages ..!

i hate making choices, deciding what is important.  i always have this fear that i'm making the wrong choice.

// added later, the same day.

when i think about it, these are just talks. i don't know why i'm so wound up about them. i've given dozens of them over the years; sure, there have been some bad ones, but there were plenty of good ones, too.

maybe in having no teaching duties this year (and hence, no recent feeling for what is "reasonable" in a lecture) i've gone to over-thinking a lot of it, dwelling on things that i wouldn't usually dwell on.

not more than a year ago, i wrote twice as many pages per week for the lectures i was giving .. and i rarely worried about any of it.

* = this iaccounts for "simple" pages, which are handwritten analogues of slide #1 or #2 (i.e. basic definitions)
** = 1 lecture hour = 45 minutes

Wednesday, October 03, 2012

as an aside ..

i should stop telling people that my work is tangentially related to ΡDEs. it only causes them to ask more questions and if i happen to know how to solve this or that.
this has happened to me at airports,
indoor climbing walls,
and even saunas.

being that my colleagues would be more qualified to handle such questions, maybe i should keep their business cards [1] on hand, so that i can dispatch such inquiries directly to them ..! (-:

[1] .. not that they would actually have business cards, but you get the idea.

Tuesday, October 02, 2012

mildly relevant: growth rates, as mentioned by pauΙ graham.

~from "startup = growth" by pauΙ graham
The phase whose growth defines the startup is the second one, the ascent. Its length and slope determine how big the company will be.

The slope is the company's growth rate. If there's one number every founder should always know, it's the company's growth rate. That's the measure of a startup. If you don't know that number, you don't even know if you're doing well or badly.

When I first meet founders and ask what their growth rate is, sometimes they tell me "we get about a hundred new customers a month." That's not a rate. What matters is not the abolute number of new customers, but the ratio of new customers to existing ones. If you're really getting a constant number of new customers every month, you're in trouble, because that means your growth rate is decreasing.
yes, a basic notion, but one not immediately obvious to the unambitious. a constant growth rate implies an exponential growth, which is more than many people expect out of their endeavors.

in general, i like how graham is willing to quantify his conclusions. a rough computation, for example, explains why what we observe about startups seems different from why they should exist:
If you judge by the median startup, the whole concept of a startup seems like a fraud. You have to invent a bubble to explain why founders want to start them or investors want to fund them. But it's a mistake to use the median in a domain with so much variation. If you look at the average outcome rather than the median, you can understand why investors like them, and why, if they aren't median people, it's a rational choice for founders to start them.

i also noticed this observation of graham's, though meant for startups, might also be relevant for us mathematicians to revisit:
You'll generally do best to follow that constraint wherever it leads rather than being influenced by some initial vision, just as a scientist is better off following the truth wherever it leads rather than being influenced by what he wishes were the case. When Richard Feynman said that the imagination of nature was greater than the imagination of man, he meant that if you just keep following the truth you'll discover cooler things than you could ever have made up.
What you're looking for initially is not so much a great idea as an idea that could evolve into a great one. The danger is that promising ideas are not merely blurry versions of great ones. They're often different in kind, because the early adopters you evolve the idea upon have different needs from the rest of the market. For example, the idea that evolves into Facebook isn't merely a subset of Facebook; the idea that evolves into Facebook is a site for Harvard undergrads.
on a related note, my prejudice of startups is generally that of hyper-capitalists, fueled by powerful greed, and willing to use science and technology to do so (i.e. the dark side of the force).

the feeling i've been getting though, from the quants and startup acquaintances i've met, is that these just happen to be hard-working, quantitatively-minded people who are making usable products efficiently. they could have easily have been scientists or engineers, but working in this kind of business offers better rewards with the same interesting (and fulfilling) kind of work ..

.. or, as graham writes:
Starting a startup is thus very much like deciding to be research scientist: you're not committing to solve any specific problem; you don't know for sure which problems are soluble; but you're committing to try to discover something no one knew before. A startup founder is in effect an economic research scientist.

Monday, October 01, 2012

in medias res: when things are getting serious ..

in $\LaTeX$ writeups, sometimes i like to put
Let $\epsilon > 0$ be given.
in its own paragraph, just to signify:
no more messing around;
now we really mean business!