are the dollar signs worth it?

so i spent most of the day LaTeX'ing, which went well enough.

the best thing about writing up ready results in LaTeX is that one feels smart, that maybe all those days of banging one's head against these damned technical lemmas [1] were worth it after all.

..
.. on the other hand, there's something else I should write up, but i can't convince myself to do so:

whenever i think about the proof, I don't feel smart. instead, it just seems .. trivial.

[1] technically, the plural of lemma is "lemmata."

(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. (-:

in medias res: $\LaTeX \neq \text{math}$

the tricky thing about $\LaTeX$ (and about using computers in general) is that one can easily be deluded into believing that one is doing actual "work."

it's probably due the fact that we can compile our code and get the results right away. the typesetting, moreover, is prettier than i could ever write by hand: instantaneous gratification!

be warned, though: don't ever mistake this for real work.

i think it a warning sign to think and $\LaTeX$ at the same time. in an ideal situation, all the details are written up by hand and the computer is used merely to convert the information into a digital and more easily accessible format.

it's not that multi-tasking is inherently error-prone ..

.. though there have been enough studies to show that, statistically, this is the case ..

.. but by switching from one to the other, you easily get distracted. you can easily lose the big picture. perhaps you can still keep track of what you are doing, but it's noticeably harder to keep track of whether the changes you make are actually relevant to the task at hand.

i'll just change this, which means i have to go back and change that .. and now that i think about it, why did i introduce this definition? i'll just change it to ..

if you only knew the number of times that i meant to type up half a second, but only got to a single lemma ..!

i constantly have to remind myself: a computer is just a tool; it cannot actually think. it is we who do the thinking and the planning, it is we who are responsible for our time, and how much we spend on various tasks.

typesetting is easy, especially after a bit of practice, but don't ever mistake it for real math.

argh .. hmph!

for a while this afternoon, i kept getting compiler errors with my $\LaTeX$ and i couldn't figure out what was wrong ..

wtf? what's wrong with my \begin{itemise} command?

..
it took a lot longer to figure out than i care to admit,
and maybe i've been away from the u.s. for too long ..

.. but apparently, it's spelled itemize ..! 7-:.

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on a related note, i am aware that brackets of the form \[ and \] can be use in place of dollar signs $\$$, in order to render $\LaTeX$, and it may even be the best practice, these days ..

.. but the truth is that i can't stand them.
there: i said it! for me, it's always dollar signs!

as a result, i always work with with u.s. layout on a finnish keyboard .. which causes no end of typing troubles, as the keys say one thing but pressing them gives another.

the trouble really comes when, at some point, my fingers stop moving on their own and i have to think about which one is which ..

// added: 10:49EST, same day

i'm running out of bracket symbols: argh!

curly brackets are typically used for sets ..
square brackets are already used for equivalence classes,
i'm already using open paren's for pairs of objects,
and double square brackets represent the induced current of the associated object.

now i have to write down the quotient norm of an equivalence class of a pair of finitely-additive measures, which so far looks ugly: $\| [ (\mu,\nu)] \|$.

ugly, ugly notation .. but it's a technical lemma, so maybe the referee will forgive me ..?

the screen sucks away my soul.

earlier, staring at the $\LaTeX$ code on my computer screen, i despaired of it never being finished ..

it wasn't until i compiled it again and looked at a printout that i felt better, even when i started marking typos, errors, and fixes on it. $\LaTeX$ really is a wonderful markup language, making neat and elegant these symbols and scrawls ..

.. which still need work, of course. the lemmas and theorems are taking shape, though, and i can see more clearly a clean, rigorous end to it.

the siege: something pyrrhic, but not quite a victory.

as of now, the siege is over for good reasons,
but not particularly good ones.

i'm calling a retreat, you see .. but not a surrender.

mildly relevant: a web-based, collaborative latex editor.

interesting: writelatex is a latex version of etherpad, a collaborative writing and editing tool.

i would imaging that coupling dropbox with your favorite $\LaTeX$ program would accomplish something similar but without the option of editing the same document simultaneously.

(to me, though, the only instance where this could be really useful would be if several authors are composing the introduction of a paper together.)

mildly relevant: for collaboration purposes?

interesting:

from mathιm

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

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! (-;

impulse post: cool! .. (EDITED: another cool thing!)

interesting: $\LaTeX$ is now available on the iPad, as Texpad.

ok .. but do they have a plug-in for a stylus? (-:

---

also, i just learned about leap motion off of a technologyreview link.

imagine using one of these things to teach .. provided that:

1. the motion detection covers an entire blackboard,
2. chalk script scales accordingly to a laptop screen,
3. there were some way to "shift up" something you already "wrote" and use the newly available space to write more.

it could also work really well for long-distance collaboration, too ..

on why i am weird with $\LaTeX$.

i suspect that i am widely misunderstood. it's either that, or it's just that i unconsciously make life harder for myself.

for instance, i try to avoid discussions about $\LaTeX$, because inevitably ..

---

.. when they ask me if i use winedt or texshop, i tell them that my laptop runs (ubuntu) linux;

.. and when they ask what program i use, i tell them that i just use a text editor like gedit, which comes standard with many (most?) linux distros [1].

.. and when they ask me how i compile my LaTeX, i tell them that i open up a terminal and type [2]:

      > latex myfile.tex && dvipdf myfile.dvi

.. and when they ask me how i find errors, and in particular the line containing it, i tell them that the "find" command is usually Ctrl-F.
..
.. and eventually, exasperated, they just ask: why the hell would you do all of that? so i tell them that, one summer long ago,

i didn't live in an apartment with air conditioning, but the public library had it, so i spent a lot of time there;

i didn't own a working laptop [3], yet the same library had desktops available for the public, so i used theirs.

they didn't have any $\LaTeX$ programs, they didn't allow users to download and install software .. but on Windows, PuTTY is a single executable file and never identified as anything other than a generic download, and i had access to a server where i could run latex remotely ..

so i spent a summer at the public library, with three PuTTY windows and one Adobe window open:

1. one for pico, a text-based text editor,
2. one for sftp, so that i could transfer the pdf output after each compile,
3. one, ready and waiting for when i'd send the in-line latex commands remotely.

as for the Adobe window, i needed to view the pdf somehow ..

[shrugs]

put another way, i use gedit because it's easier than pico.

left: gedit, which is clickable; right: pico, purely text-based

---

honestly, it was a fine way to spend a summer.

whenever i had something to type up, i'd go to my neighborhood public library, code until my allotted time was up, and either work on the details on paper or read graphic novels for a little while. when i was eligible for another time slot, i'd continue coding.

doing so had its perks: for one thing, breaks were automatic. i also met a lot of librarians, whom i found very cool people. i was young and maths was new to me, and there was the passingly-real possibility that i could make a living from it .. (-:





[1] it's actually a pretty robust program, and probably designed with coders in mind. it even changes the color of words, depending on command type. i've heard good things about texmaker, though, but i haven't gotten around to trying it.

[2] as for why not just a pdflatex command, i have a one-word answer for you: pstricks ..

[3] i didn't have much summer funding at the time, and the laptop that i wanted cost more than one month's rent. the prospect of being wired but homeless didn't exactly appeal to me.

LaTeX woes: when making slides, sometimes one must use slides.

so i'm going to be on this train for the next three hours .. which, at this stage in my life, equates to talk-writing time. [1]

i thought i took care of everything:

while updating the linux version on my netbook, the internet connection in my apartment suddenly seized .. so for a few days, my laptop was kaput.

i was able to save all my data before scrapping for a complete re-install [2]. there was even time, before leaving to see friends for the holiday, to re-install LaTeX (as TeXLive).

the plan was simple:

1. on the way there, finish LaTeXing up a bad first draft of the results [3];
2. start LaTeXing up slides for a talk on tuesday.

so #1 was fine, since i didn't expect to finish the draft anyway;

as for #2, apparently installing the latest version of TeXLive doesn't necessarily mean that it also installs beamer and pstricks.

*sighs*

it just goes to show that you can't predict everything.  so now i'm downloading the packages from the free wifi on the train .. which is going slowly.

*sighs further*

in the meanwhile, i'm fleshing out the talk outline, using old-school slides.

the format is faithful enough to beamer so that the visual output is similar, and it's not like the code is that different: copying-&-pasting a few begin{slide} ... end{slide} commands never hurt anyone, right?

(i probably wouldn't have gotten to working out the diagrams, anyway.)

[1] it's amazing how computer manufacturers have been able to extend battery life on netbooks.  these days, if inclined, i can code over most of a transatlantic flight .. not that i really would .. after all, a boy has to catch up on his hollywood films on small airplane screens, right?  (-:

[2] thank you very much, ubuntu one!  (it's a shame that dropbox gets all the spotlight for offering the same service.)

[3] it's easier for me to edit a bad draft into a good one, rather than to write a good draft from scratch .. that is, as long as the draft isn't that bad.  (just as in wall climbing, sometimes i need to make mistakes before i know exactly how to do it right.)

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. (-:

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:

• an equivalence symbol (or \equiv in LaTeX)
• the chinese symbol for three.

either way, it just feels .. ridiculous?

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] ..?

on why some bibliography styles are easier on me .. even obscenely so.

this is probably an issue of the (mathematically) young [1], but the bibliography is a crucial part of many papers that i pick up and browse.

in fact, most of the time i realise that i shouldn't be reading that very paper .. but instead, the earlier papers that the author(s) cite.

as a general principle: the first paper in a topic contains the purest form of the main, recurring idea.  it may not be executed in the most efficient, general, or powerful way possible, but that's not the point:

the point is to understand how it works first,
and then to see what you can do with it ..

that said, it's very helpful for me to identify right away, in the text of the paper, which of the references contains the lemma that i just read.  it's a recurring annoyance for me to remember which paper is marked [11], and usually it means flipping/scrolling to the last page and matching up the citation number to the author/article.

it affords me more ease of thought to read [Gro96] instead and immediately remember:  

right! Gromov's gruebleen book.

on the other hand, this can cause a few .. quirks.

if you use BibTeX with the alpha style, then for single-author papers it uses the first three letters of the author's name as an identifier.

so Gromov's Metric Structures for Riemannian and Non-Riemannian spaces is [Gro96], and Cheeger's 1999 GAFA paper is [Che99].

it's an unfortunate case of typesetting, though, when i'm citing Patrice Assouad's paper, regarding embeddings of doubling spaces ..

.. so does anyone know how to fix the standard BibTeX display formatting? (-:

[1] one way to test if you're still "young" is how often you agree that a particular argument is "standard." as for myself, i still have a lot of reading .. and learning, to do.

every beginning has an ending.

from xkcd:

two thoughts:

1. that webcomic would make a really cool cookie fortune. it's even the right size!


2. some years ago, i spent hours trying to debug one particular subroutine in a programming project. in the end and to my dismay, it was because i forgot to close a set of curly brackets: {}.
   
   since then, i stuck to the habit that if i ever type an open bracket, then immediately afterwards, i'll type the corresponding closed bracket:
   

   {
   {}
   {\em}
   {\em manifold}

   i do the same thing with HTML tags:
   

   <i>
   <i></i>
   <i>manifold</i>

   trauma and paranoia shape our habits, sometimes.

i ♥ DVΙ (also: addenda).

call me old-fashioned, but despite the convenience of the ΡDF format, i still have a soft spot for DVΙ files.

it was designed with LaTeχ in mind,
the files are so much smaller (especially when compared to postscript),
compiling it is slightly faster ..

my only complaint is that DVΙs are hard to view on the web (though there must be some browser plug-in that does the job ..)

---

in other news, the clock is ticking:
back to working on the grant proposal ..



added @ 15:56: i try and cite rαdemacher's paper about .. well, radεmacher's theorem, as often as i can.

there's something cool about citing a source from 1919 .. (-:

why, sometimes, i hate beamer.

this is wishful thinking, but if i ever organise a conference, then i might insist on chalkboard talks only:

no beamer, no slides,
but you'd get a full 50 minutes.

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i've grown frustrated at seeing full paragraphs on a single slide. dr. speaker: either let me read or convince me to listen to you. i can't very well do both ..!

this is harsh, i know.

i'm thinking in particular to those researchers who have trouble with spoken english and worry about it. by writing the "talk version" of their paper on beamer slides, they would have available a clear exposition of their ideas. in fairness to them, they are being considerate.

to me, though, this kind of talk is like listening to two different people at once. it remains challenging even if they are trying to say the same things!

misplaced keys.

it's nontrivial to edit LaTeX on a Finnish keyboard.

i'm getting better, but often i have to look for the bracket symbols { }, or even the dollar signs $ [1].

working with others, i forget how many LaTeX idiosyncrasies i have; for instance, i always add spaces between equality or inequality signs.

this quickly becomes a headache when, each time you want a space, it requires a hunt for the slash and semicolon symbols \ and ; ..[2]

maybe there are advantages in this.

1. it makes me think harder before i LaTeX or edit anything ..
2. i can type 'jyväskylä' without looking up the ASCII code for ä .. (-:

[1] for the record: (Alt Gr) + (8), (Alt Gr) + (9), and (Alt Gr) + (2), respectively. the "Alt" keys aren't symmetric!

[1] which, of course, are (Alt Gr) + (+) and (Shift) + (,).