not good .. not very good at all.

i've been hitting a wall lately. too often i sit at my desk at the apartment or the office, and my mind becomes a blank. i can't summon any motivation and i'm not getting any work done.

it's not because of summertime .. not directly, that is. it doesn't help to have the entire day wide open, and it seems to demonstrate that i am a contrarian:

• when classes are in session, i complain about not having large enough blocks of time to complete a single, long thought.
  
  
• now when i have no classes to attend or teach, the sheer length of the day is crippling, and my mind wanders too easily. i become incapable of completing those single, long thoughts.
  

the grass is always greener, i suppose. i wonder how other people manage to be so productive, all the time.

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yesterday i convinced myself to work a little, by making a bargain with myself:

if i buy a small coffee, then i will work either until the coffee runs out or until i finish the thought at hand.

it worked, but i'm hardly proud of that decision and i don't think it will work in the long run. there are too many possibilities for legal substance abuse (i have enough problems with coffee already) and it builds an unnecessary correlation between work and beverage.

what happens if i need to work and there is no coffee, for instance?

when i look into the future, all i see are things that could go wrong .. very wrong.

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the thesis work is turning computational (read: frustrating) and my tendencies towards obsessions and compulsions come through.

• i write something down and i don't like it because it's messy and doesn't follow well;
  
  
• i write that same something in a cleaner form, but then it's wrong or incomplete or i forgot to add a key point between this part and that;
  
  
• i realise that i'm wasting paper, and mentally snarling, i tell myself that i should think more clearly before i put anything on paper;
  
  
• an hour passes and i realise this is painfully unproductive; i can't keep everything in mind all at once, so i angrily reach for a page of paper ..
  

.. and then the cycle turns viciously, once again.

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it's not going well .. not very well at all; there's not much progress, if any, and the near future looks like more of the same.

i wonder what i'd have told my younger self, if i encountered him today. would i have anything good to say?

fair's fair (the um library racket)

today my conscience is clearer; i've finally returned a few books that i've been hoarding for ages from the shapiro science library @ um. i'm not proud to admit that i've kept one of the books [1] for over a year's time .. possibly since winter of my second year!

amongst members of the math dept, it's close to some sort of racketeering: a grad student or faculty member can borrow a book and renew it indefinitely, so dozens of mathematically useful books are eternally "checked out."

sure, there's always the option of recalling a book, but most of us are too spineless to exercise that right. my own excuse is that books are expensive to buy, and if the borrower needs the book, i'd rather not disturb their use; i can always make due.

as a result, one often sees these email forwards from the math adminstrative staff, where someone just wants to borrow a particular book for a day or a few hours, in order to look something up or parse through a proof.

i know: it's ridiculous, and one can't help but wonder at the state of affairs, when a mathematics library has been fully "staked out."

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[1] for those curious: the book is measure theory and fine properties of functions by l. craig evans and ron gariepy.

a fine book: they don't hesitate to discuss the details, and i've found the contents rather useful in my own work and study. one day i might splurge to buy my own copy .. but not today or soon.

the five-second version ..

most grad students understand that very few people in this world actually care about their research. so as a survival skill, we often learn to summarize our years' work into "the 10-minute version."

i think i can both (1) reduce the time to five seconds (no, seriously!) and (2) make it sound alarmingly comprehensible and elementary; the second condition isn't so alarming, come to think of it. as all mathematicians know, upon solving a problem, it immediately becomes obvious.

anyways,

the 5-second version: i study second derivatives.

distracted.

there are certain tasks which require pre-planning: computer programming is one of them, as well as LaTeXing. but now i will add going to the mathematics library [1] as one of those tasks.

having just come back from that wonderful archive, my intent was to borrow Reshetnyak's Space Mappings of Bounded Distorsion, but walking through the shelves to look for it, i paused a few times and grabbed a few other texts, including:

• Optimal Transportation and Applications by Ambrosio, Buttazzo, Cafarelli, Villani, and Brenier.
  
  
• the Plateau Problem, Part I: Historical Survey by Fomenko.
  

such selections aren't so bad .. i might learn something (professionally) useful from reading them.

in contrast, visiting the um askwith media library and borrowing the first two seasons of "Samurai Jack" [2] on DVD can't possibly be anything but pure distraction and diverson.

oh well. a boy's gotta cut loose, sometimes. q:

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[1] technically, the one @ um is called the shapiro science library, but as you readers know, none of that science stuff is as interesting as mathematics, anyway.

[2] found on the cartoon network, samurai jack is a wonderful animated show. it's amazing what you can do if you're an animated character named jack and in possession of a katana sword. (;

excerpt from an article.

from an article found on the economist website.

The main symptom of this, prominently displayed on the billboard, is a deification of mathematics. Google constantly leaves numerical puns and riddles for those who care to look in the right places. When it filed the regulatory documents for its stockmarket listing in 2004, it said that it planned to raise $2,718,281,828, which is $e billion to the nearest dollar. A year later, it filed again to sell another batch of shares—precisely 14,159,265, which represents the first eight digits after the decimal in the number pi (3.14159265).

for some reason i couldn't stop laughing when i read: "$e billion." (:

100 pages: on eu1er's formula.

speak of the devil.

a week or so ago i had read a thread from the livejournal mathematics community about "how terrible it is to use the notation &cet;is(θ) and not the complex exponential exp(iθ)" because "everybody who's anybody knows eu1er's formula."

in my opinion, there were too many condescending posts from practioners of the "obvious" school of thought: of course you should use the complex exponential notation to describe cosθ + i sinθ.

this hypocrisy arises from a community which is allegedly open and all-encompassing, to high school kids to professional mathematicians. if they wanted to use the term "obvious" they should have posted on their homepage that the prerequisites are sufficient completion of integral calculus and basic complex variables.

bunch of whelps and tossers.

---

anyways, aside from that rant, the topic at hand is actually relevant. these community members who make eu1er's formula "obvious" (which it is, but only when given the right background) should note that someone has written an entire book about that very formula:

Dr. Eu1er's Fabulous Formula : Cures Many Mathematical Ills [link to amazon.com page]

i didn't read 100 pages of this book, if only because i ran out of time and meant to catch a bus, but here are a few suggestions:

1. if you have some notion of abstract mathematics, skip the first three chapters or so. they are basic and at best, serve as motivation and a warm-up for the mathematical uninitiated.
   
   
2. judging only from the table of contents, this seems like a book which tries to attempt some depth. there is some discussion of f0urier analysis and applications to signal processing, and there is even one section concerning the planar is0perimetri¢ inequa1ity!
   
   any book which discusses the 2-dimensional is0perimetri¢ inequa1ity can't be that bad! q:
   

this is likely a good read, and has something even for the mathematician. one or two things i found interesting: apparently the author observes the media hype and supposes that mathematics has become "sexy."

though i disagree (the public is firmly convinced that mathematicians are nerds, and at best, crazy, as noted by the films "a beautiful mind" and "proof") they do make one good point: an educated person is free from the responsibility of having some notion of mathematics.

it varies by what you deem 'snobby,' but in many circles one deems a person uncultured and philistine if they are not sufficiently up-to-date with the literature and history and sociology of the day.

it is an opinion i share that we should return to shaming people who admit to being bad at mathematics and being proud of it. this should not be something to be proud of, especially in a world which is becoming more mathematical every moment. biology is turning mathematical, and economics has always had that attribute. even marketing in business is turning to data mining and basic probability to improve their customer base.

the public needs an easy transition if we wish for mathematics to become more commonplace, and as a result books such as dr. eu1er's fabolous formula .. serve a reasonable purpose. then again, even this book asks for prerequisites; the author asks that the reader know some calculus and a little complex variables.

it's nice to know that i'm not the only one who deems eu1er's formula something of beauty, as well as something of depth. let the livej0urna1 children have their arrogance; it's because of them and their future selves that many proofs are shoddy things and why the movement for computer-verified proofs have been given such steam.

if mathematicians only did their jobs, the world might actually run a little smoother.

a few wishes.

i wish i could summon up the will to continue working, even though it's likely unwise to do so.

the latest progress in my thesis work [1] feels like its in tatters. the weekly meeting is tomorrow .. well, provided that the advisor happens to be in the office.

i never expected that working in two dimensions would be this .. frustrating and trouble-prone. i've examined a handful of various methods of boundary extensions to homeomorphisms, but none seem right for the role. each has some defect which ruins any progress.

it's funny: in potential theory, the minimum order of discussion is often second-order. even in the crowded world of elliptic theory, the simplest papers discuss variations on the laplacian and the dirichlet problem.

however, the quasiworld is a first-order world. in particular, the beltrami equation is a first-order equation (albeit with measurable function data) yet surprisingly interesting.

trying to find middle ground is arduous work. it's either that or i'm simply not clever enough to see what simple framework lies hidden from plain sight.

argh ..........

i wish i were more clever.

my first thought was: if i were more clever, i could get work done more quickly, and being more efficient, i wouldn't have to spend so much time working and obtaining nothing for my troubles.

my second thought was: even if i were more clever, i'd probably "push the envelope" and work more. so doing, i would exhaust the use of that additional cleverness, which means that i'd wish i were even more clever.

my third thought finishes the induction: maybe it would be pointless to be more clever, after all. at best, it would be a temporary burst of efficiency and then more of the same.

my fourth thought was: i still wish i were more clever.

my fifth thought is: i wish i realised sooner that "more clever" is grammatically wrong. as it happens, the correct form is "cleverer."

i wish i had this job. the description is from the harmonicanalysis group at yahoo.

Date: Mon May 1, 2006 1:14pm(PDT)
Subject: post-doc at the university of vermont

The Department of Mathematics at the University of Vermont has an opening for one post-doctoral position in analysis for the academic year 2006-2007. The salary for the year is $47,000 (my chairman says it's "about $47,000") and the teaching load is 2 courses/semester. This position might be extendable to 2 years, but that will depend on funding.

I apologize for the late notice on this. We only learned about it very recently ourselves.

despite the bitter of winter in the u.s. northeast, imagine living in burlington and being paid to do maths. having visited that town twice, i'm envious of who gets the job. (:

[1] technically, this is a tangential aside from the thesis problem. in some sense, i haven't been working on the actual problem since .. late last fall.

are we mathematicians or social butterflies?

this past saturday i missed a valedictory cocktail party (for a friend who leaves the department). tonight is also an excursion, if only because another friend pass his/her/its orals today.

more social events arrive: this is all text from various emails. with a little luck, i've omitted enough so that persons remain anonymous.

friday afternoon jaunt: This Friday come help (omit) celebrate the completion of his oral exams by going to Dominic's [1] with us (around 4 or 5pm, most of yall will see (omit) before I do...)

friday night (potluck) dinner party: The despedida is for (omit) who's leaving for (omit). Other people are leaving whom I'll also miss!! You can come, say the send-off is for you as well, eat my food and in so doing, cheer me up. / So 7:30pm this Friday, Filipino food and further festivity at (omit)

saturday night party: The last QR exam is on May 6th, so I figure that I ought to have a party at my house (omit) then. I don't have many more certain details than that. If the weather looks good, I'll probably plan on starting the party around dinner time, and grilling food in my back yard.

i suppose we humans have this fixation with beginnings and endings, and so compelled, we can only celebrate them.

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[1] for those not in the know: dominic's is a fine, outdoor place where one can sip sangria from jar glasses until ten pm or so. by resorting to stereotypes, i've convinced myself that this collection of paradoxes in one place is the outcome of its proximity to the law quad.