paper-folding (cool!)

i'm stuck; for some reason i can't get this kind of folding right ..

[ reposted from wheatpond.com ]

The Mιura-orι is a method for folding up a sheet such that it can be opened or closed in one smooth motion. A Mιura sheet has only one degree of freedom, and can be thought of as having only two states: fully open, or fully closed. Since reversing one fold in the sheet (that is, making a “mountain” into a “valley”) requires reversing all of the adjacent folds as well, the Mιura sheet feels as though it has a memory, and is very resistant to deformation.

not quite your everyday occurrence, but ..

two unusual things happened to me, today:

1. someone walked into my office, took a copy of federεr from the bookshelf, turned precisely to one page, and told me about an open problem that i could solve.  (he was friendly about it, though.)


2. i wrote to a fιelds medalist, which shook me to my nerves.
   
   i kept re-reading the text of the email, making sure that nothing could possibly be taken as an offense or annoyance.
   
   here's hoping that it works out ..

the good from the bad (also: time off)

to borrow from an old joke:
we mathematicians need pen and paper, but we also need wastebaskets.

to quote from the Wired.com article: "how do we identify good ideas?" (via lifehacker):

"How can we sort our genius from our rubbish? The bookshelves groan with how-to guides for bolstering the powers of the imagination. But how can we become better at self-criticism? How can we get excel at the rejection process?"

jοnah lehrεr has a lot to say about the human brain.  every time i read him, i learn something interesting.  for example, here is something that might be (initially) non-intuitive:

"After writing down as many ideas as they could think of, both groups were asked to choose which of their ideas were the most creative. Although there was no difference in idea generation, giving the unconscious a few minutes now proved to be a big advantage, as those who had been distracted were much better at identifying their best ideas.  (An independent panel of experts scored all of the ideas.)" 

of course, it would help to know what "best" means, here.  (this is discussed a little further in the article.)

---

it could just be my confirmation bias, but this would explain why i often struggle with an idea .. and after leaving it alone for a while, it suddenly becomes clear(er) why the idea will or won't work.  it only becomes more pronounced if, say, i "sleep on it." [1]

at any rate, it's nice to know --- though i'm being lazy about following something up --- that it could have some good side effects.  reading lehrεr today also affords me a scientific justification of ... well, why i should take a vacation.

i mean, if it's really going to make the mathematics better, then sure ..? (-:

"Taking a break is important. But make sure you do something that makes you happy, as positive moods make us even better at diagnosing the value of our creative work. After a few relaxing days of vacation, you'll suddenly know which new ideas deserve more time and which need to be abandoned."

every time i think i'm very busy, i run into a colleague that is even busier .. so experience tells me that it's not going that badly. [2]

still, i've been feeling tired lately.

i'm also traveling again on friday, with the goal of giving that aforementioned talk #5 for week 5.  though i'll be very happy to see old friends and make new ones, experience also tells me that the jet lag is going to cost me.

*sighs*

there is some lag time between that conference, a research visit, a wedding to attend, and coming back.  for once, i've settled on a plan of taking thursday (next, next week) off, as well as the following monday.

that monday happens to include a 6-hour layover in london, u.k.  as long as my bags are checked anyway, it means that i can wander the city freely for an afternoon ..

.. it's not like it would be easy to work anyway, so i might as well have a spot of fun!


[1] this is probably one of the main reasons why i've changed my mind about mornings.  it took me a while to realise that i really am more productive when i have a fresh start.

[2] i have a similar rule with whether or not i am getting old.  everyone ages, of course, but i know too many people older than me who .. upon hearing my saying that "i'm getting old" .. will not hesitate to give me a thorough tongue-lashing.

the troubles of time zones, even when not traveling.

a friend of mine once suggested to me that jet lag is the difference in time that your soul takes to catch up with your body.

in retrospect, it reminds me of the storyline from eastern standard tribe, by cοry dοctorοw.

---

one oddity about eastern european time is that the end of the "usual" workday here is approximately the start of the workday on eastern standard time.

as a consequence, my american colleagues usually don't email me until i'm heading out of the office for dinner (or a road run).  instead, i get most of my messages at night.

the same thing happens for facebook updates .. which, i suppose, is a good thing: fewer distractions, right?

then there are ways to exploit the time difference.  if you are unlucky enough to ..

1. be on the job market,
2. live in europe,
3. prefer to return eventually to the united states,
4. and have a lot of work to do,

.. then typically you might find yourself completing a full day of work, and then doing your applications at night.

as you may imagine: productive or otherwise, this gets very old .. very quickly.

it's not that i specifically choose this routine myself.  it's just that the last-minute procrastination, so inherent in my nature, causes this to happen automatically.

well, at least this last round of applying and hiring is ending.  i feel like taking off for a holiday ..

---

in other news, the preprint i've been working on is still short:

at one point it grew to 15 pages, even creeping onto the first few lines of page 16 .. but now it's back to 13 pages.

13 (thirteen!) tight-knit pages, man.

i'm set:
i might submit it tomorrow!

to my credit, i wasn't wrong.

remember when i said that "by the end, i'll have given 3 talks in 3 weeks?"

well, that's still true [1];
it's just that the plan has changed.

by the end of this week and next, i'll have given 5 talks in 5 weeks ..

*sighs*

it's my own fault, really: a problem with saying no, my sense of do-goodery [2] .. that sort of thing.  more precisely,

this week's talk is a continuation of last week's, after the seminar organiser suspected that i had more to say and suggested that i could take my time with the topic.

next week's talk is actually an expositional one.  it's meant to give the background for other speakers, who otherwise have only 20-25 minutes each for their talks.

[1] sometimes i tell people that i have a sister, which is true.  it is also true, however, that i have more than one sister. (-:

[2] .. and yes, "do-goodery" is an actual word.

a snapshot from last week.

last week, i spoke with a university dean, and he fired off the standard question that one hears in interviews:

"so, describe your research to me."

i gulped.

so i told him about embeddings of metric spaces,
gave a toy example of computer networks,
and hinted that additional geometrical constraints give a "litmus test" to check embeddability.

then a few seconds of silence followed.

him: so .. you study non-euclidean geometry?
me: highly non-euclidean geometry!

well, at least he smiled.

dr. strange-talk (or how i stopped worrying and love my audience)

i've been giving a lot of talks lately.

after tomorrow, it will have been three talks in three weeks [1];
on top of that, each talk is newly written [2].

it's getting a little tiring [3] ..
.. and yes, i promise to stop with the footnotes now .. for a while, at least. q-:

---

if i've learned anything about giving talks in the last few weeks and months, it's that there is a trade-off at work:

1. you can either be clear and never get through all you wanted to say;
2. you can plow on, say what you want to say, lose more than half the audience, and probably go overtime.

(this isn't even accounting for questions from the audience, in the middle of the talk.  for some reason, this happens to me all the time.)

anyway, i've opted for option #1.  the operative word here, though, is all.  at this point, i think i'm already doing well if the audience actually remembers something from my talk.

let's face it:

metric spaces make a pretty abstract setting.  most people know this area as a playground for topologists and occasionally, gromov.  other than that, it's a bit mysterious.

like any other field of mathematics, it gets very technical very quickly.  if the audience is full of specialists, then sure: i can say what i want to say.

being a newish field, though, i've been reminded and re-reminded that apart from my immediate colleagues, nobody has ever heard of this stuff ..

*sighs*

there's also the context to consider:

at a conference or workshop, it's safe to assume that your audience is tired from the rigors of travel and stress.  besides, they're probably preoccupied with their own talks .. so half of them are probably not listening.

a quarter of them are probably confused by one of your first four definitions .. and if you're using slides, then they will be lost for the remainder of your talk. [4]

i think i'm being generous, here.

every one of these aspects is familiar to me.  i may be a rather unique (read: strange) person, but i like to think that some of my experience and bias is kin to others'.

---

this sounds like i'm giving up, but i'm not.  it's just that my expectations have changed.

i liken it to having taught undergrads for a while, planning for the possibility that some students will be curious about the subject, but being aware that most of them just want to get through the class.

it's not their fault: they want to do something else in life, and prefer to be curious about other things.

to think otherwise sounds like complaining about why the entire audience doesn't specialise in your field.

the only difference between you and your students is that you happen to have a ph.d. and suffered your share of misery for your achievement.

they, of course, have not: among other reasons, it's usually because they're younger than you.

that said, i know that tomorrow is my talk, that i will not get through half of what i wanted to discuss, but that doesn't matter.

i'm going to have fun.

i'll try to say why i think this stuff is cool,
give an idea of why it's hard,
and an idea of why the proof should work.

anyway, i still have a few pages to write .. so: back to it!








[1] a more precise count would be 2 weeks and 2 days, but my point persists.

[2] somehow it doesn't seem fair to use slides, if i am given two hours to talk.  what's the hurry?  as i told a colleague recently, i can think as fast as a chalkboard, but not as fast as a computer.

[3] to clarify, i mean "tiring" and not "tiresome" .. though audience members might agree with both.  you'll have to ask them. (-;

[4] odds are that few, if any, of us have thought about repeating a slide later on, just to remind the audience of an important technical point.  this is rarely a problem with chalkboards, of course ..


chalkboards: 1, slides: 0  .. ho ho!

sometimes being a little antisocial is helpful ..

this morning i worked at an idea for a while, until 9am.

when i thought about heading to the office, continuing with other bits of work, i got up to fetch my knapsack .. but then paused.

we have many visitors, this week;
there's lunch and then a seminar [1],
probably afterwards, a few discussions ..

.. so i sat down again, looked once more at my diagram ..

maybe 10am instead?

.. and continued to work at my kitchen table, with these funny "projections" on Lebesgue null sets.

---

i like my colleagues, i enjoy talking with them, but time often runs away if i don't keep a close watch on it ..

.. and in general, projects don't naturally fit themselves into my schedule.

like anyone else's work, my projects need attention and creativity .. and according to zenhabits, creativity needs solitude: to paraphrase,

“In order to be open to creativity, one must have the capacity for contructive use of solitude. One must overcome the fear of being alone.” 

~Rollo May.

at any rate, solitude may not be necessary for me, but it is sufficient.  so to my friends, i enjoy your company ..

.. but i'll see you, sometime.  there's work to do. q-:


[1] as a general rule, seminars in finland are 2 hours long (2 x 45 min).  suffice it to say that it's something of a time investment.

dilemma.

i've just been given a paper to review for Math Reviews, which was accepted into an Elsevier journal ..

.. so, in light of recent boycotts, i now have a dilemma.

*sighs*

any advice, guys?

not the usual kind of interview question, but ..

today someone complimented me on my suit and asked me if i did my own ironing .. which was flattering, but .. startling.

.. but yes, i ended up deciding on wearing a suit to day one of the interview.. but i stopped short of wearing a tie.  having never given a talk while wearing a tie, i thought it best not to have anything resembling a noose around my neck, especially if i encounter a firing squad of "this isn't clear" kinds of questions ..

.. which happened anyway.

somehow i planned for 23 slides (not counting pauses) in 50 minutes, with some slides intended to be quick ones to clarify the notation.  probably i got through 14-15 .. which is good enough:

i told a robust enough story,
explained a few definitions by way of concrete examples,
and advertised my results.

somehow i picked up this rule about jobs talks: you should never end early, which seems contrary to the advice that as long as you don't go overtime, then you are fine.

*shrugs*

oh well.  at least i didn't dress too badly for the occasion .. (-: