blank stares (at myself)

it feels like a long time since i've done any math. moving and other errands have taken all my recent attention. when i sit down and try to think about mathematics, my mind goes blank.

so i've decided that i should read more mathematics and specifically, new stuff. i need to expose myself to new ideas, that is, new input. if a mathematician is indeed a machine which converts coffee into theorems, then i say that coffee is only the fuel.

sometimes we machines need a tune-up or an upgrade. perhaps a new idea is like an oil change!

---

as for what i will read, i haven't committed to anything yet.

the most obvious choices are topics relevant to my thesis, but lately i've felt ambivalent about that stuff:

1. either my work seems boring and the ideas not worth pursuing, even those ideas which are related to other areas,
   
2. the related ideas are too hard (for the moment) and the problems technical and intractable.
   

so it's tempting to learn something completely new, though that is always problematic. put one way, once you learn how to walk, you're loathe to bother spending time crawling just so that you can learn to walk in another manner ..

.. but perhaps i'll get over that hurdle of laziness.

at any rate, the moving isn't done yet. i still have many affairs to sort, and no time available to be a mathematician. there's a lot of complaining time left before i have my chance to do something about it ..

sneaking out, reading maths.

1. i should really be cleaning out my last belongings from my office.
   
   
2. i should be LaTeXing, so that i can have a complete (first) draft of an article, in case friends are willing to read and to critique it.
   
   
3. i should be reading certain papers and thinking about certain problems, because .. well, i promised some colleagues that i would.
   

however, i have only done one of the above things lately. i must say: dust collects in the office.

as for things that are not pending, yesterday afternoon i sat down and read some work of @l6erti et al. this concerns a notion of "di$tributi0nal jac06ian" as given by a magical formula:

the idea is that one can compute formally the jac06ian of a map between euclidean spaces to be an exact differential form, when the map is sufficiently smooth. then one runs with the idea and works with the theory of di$tributi0ns, in order for things to make sense.

---

i want to say more about this -- nothing expert, of course, because this is not my area -- but why i think this stuff is cool. among my reasons are how it relates to some other ideas that colleagues of mine (in n0nlinear el@$ticity and the ca1culu$ of v@riati0ns) have been kicking around, and how this relates to ge0metric mea$sure theory and n0rmal curr3nts.

anyways, i'll leave it at that. there are three types of things that i should be doing instead of blogging and reading "new" mathematics, after all!

0utline of a manu$cript (i.e. what little i did today)

i did very little math today. over a bagel and a cup of coffee, i read over a 22+ page manu$cript and decided that i haven't been exactly fair with my thesis work. i guess you could say that it's not exactly trivial.

though i've done my best to write in a smooth, natural manner, the mathematics jumps all over the place:

in one section i bring up standard results from functi0nal ana1ysis, such as weak-$tar c0mpactness;

in another section i summon up several nontrivial facts about re¢tifiable sets in 9e0metric me@$ure theory (on euclidean spaces);

in the third section i wage guerilla warfare with null sets in the plane, with gory, detailed constructions;

then there is another (yet unwritten) section about analysis on metric spaces.

you know, i already feel bad for the poor mathematician who will referee this article, when i'm done with it and submit it somewhere.

---

anyways, that's it. the only math i did today was read what i've already written. i didn't even edit any of it .. well, because i didn't have a pen with me.

however, i was mildly productive. i've cleaned out my desk, where i have spent 4 years of my life. it's ready for my successor, now. however, the 3 shelves that i've taken over still need to be sorted out:

what books to keep, what books to give away,
old notes from classes, seminar talks, conferences,
lectures from the last time i taught calculus ii,
all that malarkey.

that stuff is the most difficult of all. i get sentimental easily, and arranging those belongings will take a lot of time.

and on, it goes.

i try to write (or edit) my draft of a research article every day, though the time of day varies, as well as how long i work on it.

sometimes i face a screen full of LaTeX. other times i scrawl on pages of scratch paper, in preparation for the LaTeX days.

i might have written about this before but it's worth saying again, to those of you who are new to writing up your first paper or your dissertation: it's easy to feel as if you've accomplished nothing, despite sitting for hours in front of a screen. sometimes you have accomplished nothing, because the internet is addictive and full of diversions from work ..

.. i mean, why else would you be reading this? ..

.. but that's not the whole story. when you are working out maths for the first time, before you begin to write them, there are plenty of ways to measure your progress, such as how much paper you've recycled or how much chalk dust you've accumulated on your clothes.

with LaTeX and writeups, you don't see as much accumulation, and therefore it may feel like wasted time. often you are doing work and weighing many thoughts together. it's just that there may be no physical reminders that you have done so.

myself, i keep versions of writeups and occasionally i print out the newest version. it may kill trees, but being a pessimistic sort of mathematician, it reminds me that i have accomplished something, that i may be lazy but not a complete oaf.

---

i guess i'm writing this because i need to remind myself of these matters, when writing. lately i feel like i've been getting nowhere, that my thesis is pointless and serves no purpose, and that i don't know anything and will never make it as a mathematician.

i'm not going to deny or affirm those fears today. as for the writing, it goes. it serves a purpose. that's enough for me, now.

wow: an excerpt from an article.

excerpt from "the V0lterra Chronicles," a book review by 1rwin W. $andber9 (Notices AMS):

"while a faculty member at Pisa, V0lterra served as an external examiner at a technical institute in Sicily where a student, upset by his failure to pass an exam proctored by V0lterra, fired a pistol at him. fortunately, the student's marksmanship was no better than his performance on the exam: he missed."

are we mathematicians such violent people?

we are known for ted kaczynski as well as evariste galois, after all. even descartes was a soldier, for quite a while.

read, then write?

in more personal (read: mundane) news, i think i'm almost done with one section of my first draft of a research article. what remains are references, including one which serves the following possible purpose:

if i read it and if it says what another author claims it says, then i can write a remark in my own article. it would address somewhat the sharpness of one of my theorems.

translation: i'm not being (completely) lazy. it would mean that one can't push the result to a stronger version, because there are counter-examples.

i've tried reading this paper before and i couldn't quite get it. admittedly i was pressed for time -- making thesis deadlines and the like -- so maybe it's not so bad.

to really understand it, though, i'll have to step out of my element a bit, and entertain things like principle bundles over the Grassmannιan manifοld, which that author discusses in one of the last sections.

for some reason, i thought i'd never encounter vector bundles again. maybe i've grown too accustomed to being a so-called "geometric measure theorist" .. which i'm not.

..
actually, i don't know what i am .. except soon-to-be employed (and probably overworked). maybe some kind of analyst, some kind of metric geometer.

[shrugs]

maybe it's good for me to read it. i haven't been reading anything lately, and i feel like i have no fodder for new research thoughts. if i read, you see, then at least i can learn something and draw some conclusions; maybe that will amount to something.

if i've learned anything over the last year, it's this: it's amazingly useful to know how someone else's proof works. their theorems might not be readily applicable, but their methods might.

maybe i'll read it, if only because i should read, and read now. if what everyone tells me is true, then i'll never have enough time to sit down and read maths papers carefully.

anyways, it's half-past one. i should return to writing and preparing for writing.

"for some real mathematics, see \cite{website}"

despite keeping a blog about mathematics, i don't often read the math blogs of others. however, i couldn't help but notice a few links from @rs m@thematica about some mathematical matter which is now available online.

1. in their most recent post they've announced the contents of the c1ay m@thematics in$titute library, which includes some of the following monographs and proceedings:

R!cci Flow and the P0incaré C0njecture, by M0rgan and Ti@n,
$urveys in Nonc0mmut@tive 9e0metry, by Higs0n and ρ.

odd. i think on separate occasions, i've heard a talk by M0rgan, one by Ti@n, and one by ρ.

2. in another post, they also refer to a scholarly archive called intute, but i haven't browsed through the mathematics section properly, yet.

self-criticism.

now that the final version is about 6 weeks old, i think i'm allowed to say this:

      much of my thesis is mathematically pointless and unnecessary.

i could say that the whole thing is pointless, but that's either a modestly hollow exaggeration or a philosophical understatement. [1]

this is what i mean: i can point to many a lemma, each of which serves no purpose. i wrote it because i had a proof for it. such lemmas don't imply any bigger, more interesting results. they're just there, and i know why:

      i was afraid that my thesis would be too short.

looking back, i was a fool. that thesis is 145 pages long [2]; do you really believe that all of it could be wonderful and golden and informative and useful?

i suppose there were other reasons: those results don't imply anything now, but i might need them later. it's bad taste to cite a thesis and not a published research article, but if i absolutely needed them, then at least i could find them there.

in fact, those results are clues. again, they serve no purpose now, but i might forget them. if i ever go back to that tome (read: thesis) then maybe i will remember why:

      i was this close to answering one particular conjecture.

maybe i'll come up with something later, fill the gap, and nail it down for good. then again, maybe not .. but just in case ..


so for now, i'll retract my last accusation;
maybe i'm not a fool yet.

only time will tell.


[1] this is going to haunt me for a while: try searching for "mathematics is useless" under google search. hit#1 is, unfortunately, me. to find the same page on yahoo search, you need the full title of that blog post.

[2] of those, 7 pages contain no actual maths. they include the title page, dedication, acknowledgements, table of contents, and the bibliography.

technical difficulties; still blogging.

yesterday, my laptop wouldn't start. it would ask for my unlock password, then some cursor would appear on the upper-left corner of the screen, and windows xp wouldn't start.

.. and yes, i am one of those non-Mac powerbook owners;

i find that there's a lot more freeware and open-source software for windows than for macs because, simply put, there's a greater need for it.

today, my laptop would start ..

.. but only if i turned on the power button after removing-&-reinserting the laptop battery and keeping the power cord unattached.

i don't understand it either, but it works: prospero starts and windows starts loading.

however, i can't access any wireless network.

the icons for my wireless internet software all suggest that everything's fine, and there is plenty of wifi around. i tried the current and old versions of firefox, and even internet explorer.

nothing: no webpage loads.

i guess i'll troubleshoot it later; there's writing to do. interestingly enough, the afternoon has been very productive.

hmm..
maybe i shouldn't troubleshoot it. q:

leaving home, going home.

the apartment hunt is done, and i've signed a lease. i can go home to ann arbor now -- for the short time left that it is "home" -- and be a mathematician again.

the summer is disappearing quickly, and as usual: there are many things left to do, probably too many.

moving plans, and paranoia.

i have been doing very little math recently. the closest i've come to mathematical thinking has been writing; i wrote briefly on saturday morning, but since then it's been nothing.

i tell myself that looking for apartments is a worthy task, and of course it is: without an apartment for the fall, how can i start my postdoc -- teach, and conduct research?

while on the bus yesterday, i tried to think of the last good mathematical idea i had. i couldn't. [1] i quickly thought about ideas and premises which make no sense -- these which i suspect, as drawn from the work of others -- so when i sit down and have my books and papers and mathscinet, perhaps i can think it through.

it's easy to develop an inferiority complex in maths.

[1] well, there is this one mediocre idea, but i don't think it will work out. in fact, it's more of a research thought or a question. the only good aspect of it may be its geometry and concreteness. moreover, it's not for me.

say, m@rsha11: if you're reading this,
i'll tell it to you sometime.

celebrating 4th of July with a brand-name, laziness, and a little LaTeX

sometimes starbucks is rather convenient. for one thing, brewed coffee refills are $.50 + tax, which is kept hush-hush, of course.

also, there is no FREE internet. t-mobile is a partner of starbucks, so if you want to pay a fee analogous to that in an airport, then you can have the web for a little while.

then again, it's amazing how much you can get done, when you DON'T have the web at your fingertips. hence, the convenience: i was able to work reasonably efficiently, for an hour or two.

---

today is an american holiday, so i'm not enacting my "1pm to 4pm" rule. still, in LaTeX i've changed a few paragraphs here and there, added a few lemmas to the LaTeX, but none of it is serious work.

soon i will have to be serious, if i really want to finish this paper and to publish it. i suppose that i still have some growing up to do.

the physical dangers of m@th 9rad student life.

you'd think that being a mathematician or rather, a m@th 9rad student, is a pretty safe job. myself, i've been in numerous scrapes and accidents ..

.. but when i think of all the math 9rads at U of M that i know who have suffered broken bones here,

• one recently broke his femur bone while playing ultimate frisbee on a grassy field --
  
  
• one broke his right humerus bone (the one between the shoulder and the elbow) while trying to dunk a basketball on an outdoor court --
  
  
• one broke a bone in her forearm (either the radius or the ulna) during a game of ultimate frisbee, when she struck another woman in the head while throwing --
  
  (interestingly enough, the other woman only suffered a minor concussion.)
  
  
• one broke his right humerus in an arm-wrestling contest against another math grad --
  

and then there are the usual finger dislocations and broken ankles from basketball, fractures from car accidents, and dislocated shoulder sockets from weight-lifting.

i guess we are an accident prone bunch. oh well: at least our health insurance covers visits to the emergency room.

h@rdy - 1.

these days i am following g.h. h@rdy's example again.

if i remember the story correctly, he was purported to work only 4 hours in the summer. the rest of the time he devoted to leisurely pursuits like watching cricket or playing tennis. apparently h@rdy was a rabid cricket fan, so his choices were made out of love or obsession.

remembering that, i wonder: what were littlew00d's work habits?

in the past three days i have followed this rule:

i will write for three hours, each day -- specifically from 1pm to 4pm.

if it goes well and i choose to write more, then i will write more, but i will only enforce three hours of mathematical writing.

in the mornings -- if i wake up that early -- then i am free to brainstorm about new research and work out some ideas. however, if i wake at 12:30pm, then it is straight to writing!

so this gives me a sporting chance: if i want to think about new math, then i must wake up to do so. otherwise i must reserve some willpower for those hours after writing, and work on research then.