Monday, November 28, 2011

"the horror comes in reality from the mathematical aspect of the event."

evidently, albert camus believed in a deterministic reality, and probably disliked maths.  maybe someone should have told him about quantum mechanics. \-:

as for the title, it's lifted from camus's long essay the myth of sisyphus --- specifically, from the section an absurd reasoning.

to get a sense of this book, the first sentences read:
"There is but one truly serious philosophical problem, and that is suicide.  judging whether life is or is not worth living amounts to answering the fundamental question of philosophy.  all the rest -- whether or not the world has three dimensions, whether the mind has nine or twelve categories -- comes afterwards."
evidently camus was destined to be a philosopher, not a geometer [-1]. q-:

as for the excerpt that included the title, here's the context:
"here it is barely possible to speak of the experience of others' deaths.  it is a substitute, an illusion, and it never quite convinces us.  That melancholy convention cannot be persuasive. [0]

"if time frightens us, this is because it works out the problem and the solution comes afterward.  all the pretty speeches about the soul will have their contrary [1] convincingly proved, at least for a time.  from this inert body on which a slap makes no mark, the soul has disappeared.

"this elementary and definitive aspect of the adventure constitutes the absurd feeling.  under the fatal lighting of that destiny, its uselessness becomes evident.  no code of ethics and no effort are justifiable a priori [2] in the face of the cruel mathematics that command our condition."
ah, the cruel mathematics, indeed! (-:

[-1] the more i travel, the more the term "geometer" seems rare.  i thought it was the standard name for someone who studies geometry of some kind, but acquaintances tend to refer to me as a geometrician.

[0] this entire excerpt is from part of one big paragraph: the spacing has been included for easier reading on a computer screen.

[1] i think "contrary" is meant in the sense of "all that is contrary (to a particular thing)" but since i don't have the original french version in front of me, this is mere speculation.  as a mathematician, i would still say "negation."

[2] his exact words, none of mine.

Saturday, November 26, 2011

today i found out that i am an author.

every so often, i run a goοgle search on myself to see if i've inadvertently done something stupid (and if so, deciding on how to erase it from existence).

this time around, something odd came up.
my thesis is available on amazο;
there's even a used copy available! (-:
that said, is this happening to anyone else, out there?

 it's one thing to download preprints from the arχiv and mirror them somewhere else, but .. come on: this is just my thesis ..

so if you want a copy,
then just email me and ask ..

(.. or at least until someone threatens to sue me.)

Thursday, November 24, 2011

for some of us, certain LaTeX symbols are un-natural.

yesterday, while writing notes to a colleague, i happened to use the LaTeΧ symbol \bigoplus \bigotimes, which i have only seen used for tensor products in algebra.

 as an analyst, i became slightly ashamed of myself for a while.

to the algebraists: it's nothing personal.

think of it this way: if  you were giving a talk in your friend's seminar, and in the middle of the talk, suddenly assumed "let ε > 0" .. i wouldn't think that it would go particularly well. 

Friday, November 18, 2011

in which some constructions are "natural" ..

perhaps all of you knew already, but today i learned that "magenta ain't a colour" in the sense that it cannot be created with a single wavelength from the visible light spectrum.

however, since the human eye processes colors in terms of opposites, so magenta appears as the complementary color to green.
initially i nodded,
thought it was a neat factoid,
and went back to wasting time on the internet ..

.. but then it occurred to me: 
this is exactly the 1-point compactificatiοn of the real line [1]!
despite the abstract nature of lοcally cοmpact Hausdοrff spaces, this is a concrete example that some ideas in tοpology sit naturally in the real world ..

this is just as cool as when i learned that the video game "asteroids" is played on a torus ..

[1] yes, for the record the visible spectrum is a bounded interval, not the whole real line .. q-:

Thursday, November 17, 2011

on a wholly unrelated note ..

in my work notes today i'm using the symbol Ξ, or uppercase ξ, a lot.

not having much practice with this greek letter,
oftentimes it looks either like:
either way, it just feels .. ridiculous?

Wednesday, November 16, 2011

boredom is a luxury.

the last two months have been quiet.  apart from daily life at the office and a few regular seminars, not much happens in my life that's worth blogging about.

in other words, it's been awesome.
i can concentrate on chasing down ideas, some of them infeasible, a few of them interesting.  i can pursue a line of thought for days at a time, see where it goes.

i can latex for a full day, hack out the details in a single uninterrupted vision, identify the parts that make no sense, work through or around them.
telling you how it's really going -- that requires a level of technical detail that i'd rather not see on a blog, myself.

this is not to say that all of my ideas are working .. but that i feel productive.  i haven't felt that way in a long time.

Friday, November 11, 2011

after & before: part two.

i can't remember when i first drafted this, but it was probably the day before my second talk (at TKK) which was .. one and a half weeks ago already.

i'm uneasy about most topics.

when i give talks about generalizations of the schοenflies problem or Sobolev extensiοn domains or ΡDEs, i get quite anxious, and with good reason. [0]

these are well-established topics with much history to them.  try as i might, i always seem to be ignorant of some significant part of the literature .. and in particular, what types of theorems or proofs are "standard." [1]

when i talk about my "geοmetric" work, however .. and by this i mean this stuff relating to (metric) derivatiοns .. then the situation changes completely.

it would be wrong to say that i am an expert on the subject, if only because there are plenty of things that i don't understand about them.  it's safe to say, however, that nobody is an expert, either!

i guess that makes me a little like socrates [2] .. (-:

it's not that i insist on knowing more than everyone else in the room; i've resigned myself to the fact that there is always someone smarter or more familiar with the literature.

rather, it's the matter that if i make a mistake, then the fallout is minor.  like everyone else, i hate it when people criticise me by my mistakes .. even if i do deserve it, sometimes.

there's another aspect about derivatiοns worth mentioning, as the topic of a talk:

if this is a subject little-known, then my role can be put to good use.  there are few references on the subject, so i can point out how the theory works.  doing so, perhaps i can convince others that the theory can be put to good use.
put one way, a beautiful theory is like a night sky: a canvas of stars that is well-arranged by Nature's Benevolence, distant but worthy of contemplation.

a useful theory, however, is more like a clutter of heavy stones in a field, perhaps meteors comedown to earth, long ago.  stone, despite being crude and ugly matter, are fodder for tools and building material.  from them we form homes and towns, societies and civilizations. [3]
i don't believe that mathematics is always beautiful.

look hard enough at the details of a theory, and it becomes hard to see any beauty in them.  sometimes i wonder if the notion of beauty is inherently retrospective .. in the intellectual sense, anyway.

[0] there was this one talk i gave about manifolds with non-negatιve Riccι curνature, some years ago.  my plan was to learn a setting in which you can actually prove the validity of a Pοincaré inequality (vs. most of the time it is taken as a hypothesis).  it wasn't until i started discussing the proof, that the audience pointed out an error to me .. which lay in the textbook i used, but the fact remains that i missed it completely .. [sighs]

[1] oddly enough, most of my non-geοmetric work is collaborative, especially the stuff relating to ΡDEs and Sobοlev spaces.  This cannot be a mere coincidence.. \-:

[2] according to legend, a man from athens traveled to see the oracle at delphi and asked: "who is the wisest man in all of athens?"  unlike the usual cryptic answers, the oracle simply answered, "socrates."

upon hearing the news, socrates became disillusioned instead of delighted, because he couldn't believe that he knew more than every other athenian.  so began a long and systematic inquiry: socrates found experts on every subject he could think of and began to debate with them, and after a while each expert admitted that he, too, knew nothing.

this put socrates into a further melancholy.  he discovered that nobody knew anything ..

.. until one day, while taking a stroll, it occurred to socrates: nobody knew anything, but he himself knew that nobody knew anything.  this meant that he indeed knew something.  since everyone else he encountered knew nothing, it meant that he was the wisest man in athens, after all ..

[3] i've been reading thoreau's walking lately ..

Tuesday, November 08, 2011

a little too easy (updated)

[from evening of 6 Nov 2011]

i'm getting suspicious.
last week i came up with a proof to a particular case of a conjecture,
but it was shorter than i expected it to be.

over the weekend, i thought i spotted an error,
but yesterday i checked it again, and was easily fixed.
i'm still suspicious.

if it were this easy,
then someone would have written it up by now ..

.. so it's time to take a long, hard look at it,
see where the error really is.

[updated: morning of 7 Nov 2011]

i'm LaTeXing the argument, as we speak.  there are subtleties to handle, but no big problems yet.

in fact, the biggest problem is handling my keyboard:
in regards to LaTeX, the annoying thing about european keyboard layouts is that the dollar sign ${\$}$ isn't as accessible as in a US keyboard layout (for obvious reasons).

in particular, to type a "${\$}$" the command is assymmetric:

it's [Alt Gr] + [4] on a finnish keyboard, as opposed to [Shift] + [4] in the US, so i have to consciously type the command with my right hand.

this wouldn't be a big deal with anything else, but i use dollar signs all the time, in order to pass to math mode.
so i've switched to the US keyboard layout .. with the problem that the labels on the keys are still in the Finnish layout.

luckily, i've been typing for enough years that i don't consciously think about the keys .. but every so often, i forget:

where's the asterisk key again?  is it [Shift] + [8] ..?

Tuesday, November 01, 2011

after & before: part one.

so i gave another talk today, this time in my department.  the topic was the same .. regarding differentiability in a certain class of metric spaces.

originally i wrote down some thoughts while writing the talk, but right now it seems more natural to talk about how it went.

the good news is that it was well-received:
all signs point to that, at any rate.

the bad news is that it didn't go the way that i wanted.  something didn't feel right when i was talking, and i'm almost sure that i went too fast.  there were enough clues, i think, as to pick up the basic trail of the argument ..

.. but, admittedly, i was often looking at my watch, seeing if there was still enough time.

so: i prepared too much.
it actually reminds me of a film called wonder boys [1] ..
[link to imdb entry]
the basic premise is that the main character, a literature prof, cannot finish the book that he's writing: the pages number in the thousands.  at one point, one of his students reads the draft without his permission, gives her critique.  the message is essentially this:

good writing is about making choices.  this thing .. it doesn't look like you made any choices.  you follow every lead, the tangent of every story of every character ..
the fault of the talk is that i made a similar mistake.  what i had in mind was (essentially) a complete discussion, but even in 2-hour finnish style seminars, there still isn't sufficient time.

put otherwise, it's not that i didn't have enough time;
rather, the talk just wasn't well-organised, the message not appropriately succinct [2].

epilogue. afterwards, a few people came and asked a few questions.

the striking thing is that, despite the metric space setting of the discussion, i was asked instead about Lie groups, as well as Riemannian manifolds ..!

sometimes i wonder whether metric spaces are really a good field of analysis in which to work.  maybe i should concentrate on more familiar settings .. if anything, i might be able to communicate with more mathematicians ..


[1] interestingly enough, it's set in pittsburgh.  the story is modest, but it's told well.

[2] "i didn't have time to write you a short letter, so i wrote a long one instead .." ~ mark twain.