highly irrelevant, but ..

.. once, at a party full of mathematicians, a friend was trying to formulate this one lemma. [1] he drew a shape and said ..

.. "ok, so this is a triangle .."

.. but at that point i had one too many and suddenly blurred out ..

.. "no. that's just an approximation of a triangle!.."

.. at which time everyone around just just burst into hysterical laughter.

terrible, unrepentant mathematicians, we were .. :-)

[1] yeah, we were that far in. i truly suspect maths is a language, because many drunken mathmos i know still revert to their mother tongue, after one too many ..

on an unrelated note, Ctrl-F is amazing.

.. not that this is of any real importance to post about ..
..
.. but i don't know what i'd do without the "find-&-replace" command that is standard on most text-editors now. ("copy-&-paste" has been indispensable for checking long chains of estimates, too.)

down, for now.

more than eight years ago in a cold, snowy december I sat alone in a cafe, trying to make sense of what had happened.

a little later, a fellow grad student stopped by, looked at me, and remembering, asked me how it went.

"well," i said, "i didn't fail, but .." [1]

i doubt i finished the sentence. we went back and forth in polarised roles, he attempting to be cheerful, me still down.

i wouldn't feel "up" for a while.

it would take a while of forgetting, earning small separate achievements, before i could look back at it without pain and malaise.

-----
that scene from my life came to mind because right now, i have a similar mood .. only less severe.

today was my last day of class .. until August, anyway.

i don't feel like celebrating, though much of me feels so glad ..

i don't feel mournful, but it feels like I lost something .. maybe a chance to have made a great beginning. instead at best i managed a mediocre but trouble-prone one.

all I feel are regrets .. that i could have done better or more, that I put to much effort in pointless things, that i never really understood or appreciated what was really going on, under my own nose and in my own classroom ..

.. that i just had no real sense of "how it all works."

i feel wrong about many things that don't matter, and i don't know how I feel about the things that do.

all this past academic year had taught me is doubt and stress and futility.

-----
on the other hand, those were the same lessons i learned after my first year in graduate school. knowing that i'd be there a while, i worked at it and eventually it all made more sense .. not quite everything, but it got better.

part of me suspects that there is no purpose in life .. in that there is no one canonical purpose. to quote the existentialists, everyone must choose for himself.

i have not determined my purpose yet, but i believe there is one that suits me, in this academic life. it will take time .. but trusting on the pseudo-repetitiveness of life, it gives me a certain illusion of faith.

so i'm down right now. it won't be forever.

[1] it was right after my comprehensive exam, which was an oral, 1 1/2 hour friendly firing squad of questions. i distinctly remember feeling awful that i couldn't prove certain facts on the fly .. and advantageously yet unfairly, the committee never asked for them.

an unhappy compromise.

i think it accurate to say that I spent the whole day trying not to think too hard about one problem.

in retrospect, i should either have worked as hard as I could have, made some small progress .. even a wrong turn would have been one more lesson in which way not go turn again ..

.. or not worked at all on it;

i guess I never learn.

Push and pull.

So I lost a debate with my co-authors, but it doesn't bother me. I guess it shows that we work well together and that I can trust them to tell me when I'm wrong about something.

The important thing about maths is that one remains with what is correct. Often it means that one has to be wrong on occasion, and to realise why. More and more it seems important to me to fail, if only to be aware of how far I am pushing what I knew and what I really understand.

It also seems that the way American universities are structured doesn't allow for this. Sometimes I wonder how new mathematicians come out off the woodwork, and if this explains why it takes so long to get the hang of research... that is, if one ever gets the hang of it.

---

I like Europe. I didn't realise the extent to which I missed it, how the universities work.

Of course life is always more appealing as a guest.. but being in Spain reminds me of those years in Finland when I was a semi permanent resident and slowly becoming a local. I wonder often enough if I should have stayed and tried for a permanent position.. maybe teach a course or two, co-advise a student, convince my sponsoring department that I might be a good guy to keep around.

Odd. I'd be scared to death of advising a Ph.d. student here in the States, but in Finland it would be more doable.

On the bright side..

My recent posts have been rather bleak, haven't they? I guess I'm still not fully used to professorial life; sometimes I wonder if it will ever feel normal.

That said, it's Spring Break and I'm away for the week, visiting my co-authors in sunny Spain.

I feel life my old self again. Ideas are coming out: a few good ones, lots of bad ones too. There's a good chance we'll finish off the guts of one manuscript.. and now I'm thinking about how to start another one.

So maybe I was wrong before; sometimes I can get my act together, finish what I started.

How it never ends.. but how it starts.

I'm supposed to go to the airport in two days, in order to cross the ocean and to keep a promise to a few colleagues. (Being that I don't keep many of those, it's rather crucial that I do so when it counts.)

Still, I'm easily exhausted. If I could say that I am exhausted right now then I would.. but the fact is that I'm not.

I know that I can still work, still have enough energy to keep the collaboration going if I budget enough effort per day of the visit.

I liken it to surviving on 5 1/2 hours of sleep per night: after a while it feels normal but you could swear that you used to be faster and sharper and maybe you're just "getting old" ..

I also know that once I come back, then I'll spend a few days feeling exhausted and bitter at having to readjust to my old routine.. to the extent that I'll probably swear that I'll never travel mid-semester ever again.

---

I don't feel the same anymore. It used to be easy, even natural, to be excited about getting up in the mornings and wanting to do maths right away.

Yesterday I met with colleagues in the department and we talked about PDEs.. rather, they did and I was trying to decipher what the underlying mechanisms were.

I am and will always be an analyst; these guys really think in terms of physical principles and what the equations are supposed to mean. I suspect that we'll keep a truce and the compromise of that truce will be geometry.

Anyway, my point is that the whole time I was absolutely ambivalent: I simultaneously thought (a) this is pretty damned cool and (b) fvck: I have.. aw, fvckity fvck! [1] .. that many incomplete projects right now and I'm supposed to learn.. no, have learned.. these disparate things; how can I juggle this one too?

---

The fact of the matter is that I don't know how long I can keep this up. It feels like a Ponzi scheme on which I can't possibly follow through. I don't know why people put up with it, with me.

Whether or not I am exhausted, I feel exhausted. So let this be a lesson to you young researchers: even if your intentions are good, never promise more than you can deliver.

[1] at last count, i have $5 + 3(\frac{1}{4})$ collaborations and $3$ solo projects; a $\frac{1}{4}$ of a project means that there is a decent lemma or two, but no real theorems yet. As for the topics, they vary from geometric measure theory and PDEs to fractals, sub-Riemannian geometry, and minimal-like surfaces .. to even Banach space differentiability! On top of these, i suspect that one collaborator is trying to convince me that dynamics is interesting.

a picture is worth .. a few hundred backslashes!

often enough it feels like i'm wilfully banging my head against a wall. in this case, it's converting visual intuition into rigorous proof. [1]

i must have made this claim before .. but i'll say it again:

every time i have a proof by picture,
it takes 4-5 pages of $\LaTeX$ to write out the details!

[sighs]

oh well: it is the weekend and i finally have time to hack out details for research. i shouldn't complain .. but what kind of "frustrated (over)analyst" would i be, otherwise? (:


[1] for those whom are actually curious about the details, i need a suitable partition of $n$-dimensional dyadic cubes so that most of the measure lies either in subsets (a) that are convex polyhedra or (b) whose translates, under suitable unions, form convex polyhedra.

in the trenches .. or so it feels.

i should probably leave the office soon, if only because ..

there are students *everywhere* in the department.

i hear many young voices from the few office doors that remain open.

the math help room is full of people.

young men and women have taken over the couches in the middle, watching a tutor intently as she's explaining demοrgan's laws on a nearby whiteboard.

needless to say, 'tis the season of midterms .. and as time goes on, fewer office doors will be open. probabilistically, it's only a matter of time before someone stops by my door and asks me a maths question ..

that said, i should probably get out of here before i have to say "NO" a lot to many slightly desperate faces.

in which it is not easy to be an adult.

this morning, after finalising my calculus lecture for the day, i stopped by a local cafe and started working on a proof of a statement that i had jotted down as a claim, months ago.

it was frustratingly fun. i almost had the proof .. when i realised that, soon enough, i would have to reach campus and give my lectures.

then i started speculating:

what if i .. just didn't show up?
what's the worst that could happen?

.. but then i sighed and realised that, deep down inside, i respect responsible people that can be counted to show up when they need to show up, and that i want to think of myself as such a person. that said, there is only one way to get what you want ..

.. and that is to put in the effort, to work hard, in order to attain that goal.

i've told my students that before, and that achieving their goals is conceptually simple but emotionally nontrivial. those things said, that means that i have to do the same ..

life would be so much easier if one could pick and choose one's convictions, at moment and whim. it is far harder to be consistent.

it isn't easy. it takes a commitment and somehow we educators do it .. but like anything worthwhile, it shouldn't be easy .. and for me, it isn't.

---

on a mostly unrelated note, i really enjoy visits to that cafe. the coffee is incredible.

so, if anyone asks ..

like all other working mathematicians out there, i am often asked ..

.."so what do you do all day?"

lately i've felt like answering:

"i've been trying to build impossible geometric objects, in order to show that certain mass distributions [1] cannot possibly exist."

as you may guess, my recent obsession has to do with finishing a proof by contradiction .. which i suspect is a means of inference that most people are uncomfortable with.

if my experience in teaching basis analysis has any weight here, i think that even mathematics majors at university have trouble with this method of proof.
..
..
.. thinking about it, that kind of answer isn't terribly helpful .. that is, to me. more often than not, conversations of this kind only on go downhill after that question; either (a) i say something too complicated and the other person, not understanding, feels dumb, or (b) i make it sound too easy and the other person wonders why i bother working on that kind of problem.

more likely, the other person would probably be wondering what would drive a person to think all day about things that might not exist ..?

often i just can't win with this kind of thing.



[1] this is my colloquial expression for what's known as a measure; i think i borrowed (read: plagiarised) the term from falcοner's book, in fact. before settling on this, i tried to use the term "prοbaβility distributιon" but this usually misled my audience that my work is related to statistics of some kind ..

on writing: when you can no longer trust yourself ..?

// from sunday, 28 july 2013 @12:19 EEST:

currently i'm editing this one manuscript for the .. who knows: 27^th? 41^st?.. $n$^th time and it's getting to the point where it's hard to spot errors, however significant or small. i blame this on the general principle that the more exposure i have to this thing, the more familiar and not-out-of-the-ordinary it seems. (in other words, i've lived with this thing long enough that maybe, unconsciously, i believe it to be true.)

so i've decided on a different tack, which hardly seems efficient. i don't know any other way, though [1].

---

each time i think about proofreading the manuscript again, (1) i pick a random lemma, (2) i take out a few blank pages and try to prove it on my own, and (3) becoming aware of what is tricky about it, i focus on those parts in the writeup ..

.. and inevitably find gaps. they're getting smaller and less significant, though, so maybe it's some measure of progress?

at any rate, i had in mind (perhaps too optimistically) to send the manuscript to a big shot in the field today; let's see if i can actually keep to my word!

epilogue (29 july 2013): i didn't keep my word.
on the other hand, i found another gap and patched it.


[1] i've been given the advice before to read every line and check if it is true. in principle it's the best way to guarantee that a manuscript is as correct and consistent as possible, but i always fall short (and by a big margin): i guess i'm just that impatient .. \-:

a template .. of a slightly unusual kind.

disclaimer: as usual, this has nothing to do with actual maths.

recently, every work email i write begins with:
".. thanks for writing, and apologies for the late reply .."

i don't know why, but it always takes me a week to reply to anything ..

(deceptive) cadence ..♫

you know, there is something very soothing about coding in $\LaTeX$ .. provided that you already know what you're putting into code, that is:

it's like being in the zone, letting the fingers go on autopilot. (i guess i mean "flow" in the sense of psychology.)

---

on a related note, maybe i was judging too quickly or harshly earlier.

so far, this and last afternoon have been rather productive. on the other hand, my typing on a computer doesn't necessarily imply that i am getting any work done.

from experience, $\LaTeX$ is as aesthetically pleasing as it is deceptive!


♫ the title was stolen from an NΡR classical music blog of the same name, which i recommend. (-:

"it is easy to be logical; it is almost impossible to be logical to the bitter end" ..▲

today i drew a paper calendar of the next four weeks,
filled in various plans and obligations, both professional and personal,
and came to a single conclusion;

if everything is to work out,
then this week has to be mathematically unproductive. )-:



^▲ this quote is taken from A. Camus's the myth of sisyphus, an excellent book.

à la pοincaré: the 4-hour day.

tuesday, 9 july 2013 @ 11:44 EEST:

my new plan: i'll concentrate on being as productive as i can, but specifically during the hours that i know that i am usually productive (even if it means that i am working far fewer hours than i usually do).

this includes first thing in the morning ..

today was already productive:
i constructed a whole class of counter-examples!

.. and probably late afternoon into early evening, just before i usually go running or join friends for climbing, actually.

odd: why would the "bookend" times be the most productive?

maybe i should also keep a "journal" of what i did during those hours, and how long it took? this is in reaction to how ineffective my to-do lists are: they are always overloaded and i can never check everything off, which eventually gets depressing.

the tricky thing is how to be productive in the hours in between. one possibility is that if i'm going to waste time, then i may as well enjoy myself, like reading novels or blogging or taking photos of the city, but another possibility is to fill it with drudgery, such as writing a review for this article that is 4 months late .. etc.

on the other hand, maybe a few hours of real work is enough; i mean if it was good enough for poincare .. [0]

---

wednesday, 10 july 2013 @ 08:38 EEST:

ups and downs again:

two days ago i knew what worked .. or at least, i thought i did;

yesterday i was convinced that a colleague's "conjecture" [1] is false and even had a rough proof in mind,

but just now i found a gap in my argument,
so i'll spend today working on a patch.

despite having been privately wrong [2] this has been a pretty exciting week, mathematically speaking. the uncertainty of it all is .. not intoxicating, but like a high. not knowing what exactly is true is all the more motivation to figuring out what it could be .. especially if it keeps on switching, due to increased effort.

so work is fun again and i can obsess about it with new abandon.



[0] to be fair, i wonder what poincare would consider "work." my guess is that the man had high standards, so a lot of things he wouldn't consider work, i would!

[1] i like to reserve the word 'conjecture' for those unproven claims that are particularly nontrivial .. and no, i don't have a definition of nontrivial, but just a sufficient condition: if, by telling someone related to your field of the basic notions, by stating the problem, and by showing why it is hard or what it would imply, that that someone become interested, then it's nontrivial.

[2] 'privately wrong' is doing something stupid in the privacy of your own workspace. 'publicly wrong' is having many people know about it. i've been both, and the former is very, very much preferable to the latter.

off the cuff: snippets before the weekend.

// snippets from thursday, 4 july 2013

i'm trying to unlock a door, figure out blueprints for objects that, in their full generality and obscurity, requires believing in statements like the axiοm of choice and their implications [1]. for the right skeleton i've recast someone else's conjecture for bones and soft cartiliage.

i have examples. i know that these things exist, at least in crude forms, but how sophisticated must the designs really be?

---

i don't know if unlock or build is the right word, mathematically speaking. i don't know what the right word could be.

all i know is that i'm stumped at the mathematics, and all i can do now is discuss the frustration of those mathematics.

[1] apparently "axiom of choice" is also the name of a band.

backlog.

i think i must be the world's worst research collaborator. despite good intentions, i never seem to get back to my co-authors in any reasonable time-frame.

[sighs]

also, forget that bit about a lack of hurry;
i'm starting to think that i have too many projects.

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.

#1300: chalkboard post.

from a few days ago:

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