remembrances and promises.

off and on i've been watching episodes from this japanese tv series from the 1970s, called zatoιchi (the blind swordsman).

today i thought about one particular episode from season 1: "A Memorial Day And The Bell Of Life."

despite being blind, ichι always remembers one particular day of the year and a promise he made, long ago, to a dearly departed one. i won't spoil the rest of the episode for you.

as for why i remember,

today is also a very memorable day,
for me and for metric analysts, anyway.

two years ago, when i first heard the news, it was 3:00 or 4:00pm. the timing was terrible: i had to rush quickly to student analysis seminar and introduce the speaker.

afterwards i went to my office, closed the door, and didn't know what to do.

duties are duties: i have to go and teach now. then i have to work .. and there is a promise i made.

it's about time i finish that preprint and submitted it. the advisor had asked me to do so, in what seems like a long time ago.

learning about manifolds, teaching sequences and series.

i'm giving myself a week to learn about manifolds or rather, riccι curvature. it seems like one of those things that everyone should know but that few actually know well.

it's not that i want to become a geometer,
i just want to give a talk about analysιs on manifolds, that's all ..

.. then again, it would be nice to work on more concrete spaces. if i learn enough about them, then maybe i can prove something about them.

[shrugs]
a boy can dream, right?

---

on an unrelated note, i love teaching sequences and series. it took me a while until i figured out why: it's the closest thing to analysis that you can teach in a standard calculus course.

my students may hate the comparιson test, but i quite like it. there's nothing like estimating something when you don't have to compute it. q-:

i know that the stewarτ textbook doesn't cover the root test, because i was tempted to teach it to my students, but decided against it. are there other "standard" textbooks which do cover it?

then again, it could be that i like them too much:

i think my students are ill at ease with series and convergence tests, because every time i show them an example or two where a particular test works, i also show them a non-example where it either cannot be applied or that it gives no conclusion. [1]

you'd think that this wouldn't make much of a difference. students seemingly understand that some definite integrals are better off done with substitution, rather than by parts ..

.. but show them a series, and suddenly they freeze.

[1] i likened the ratio test to a "magic 8-ball" in that sometimes it just tells you: "reply hazy, try again .."

maybe i should woo a mistress.

at some point today i escaped my office and went to the 7th floor lounge. i then took the stairs to the second floor of the lounge ..

.. yes, it is a floor within a floor.
that's the beauty of it: nobody ever expects one ..

.. and looking around, i was finally convinced that nobody would find me there. relieved, i set down my coffee and my folders, and then i began to work in earnest.

---

as for why i wasn't home, my girlfriend is there. if i stayed home, i would have to be a boyfriend, not a mathematician.

as for why i wasn't in the office, my students keep appearing and asking for help. i may grade their exams with a cold-blooded heart, but my sangfroid disappears when they ask me, face to face, for a quick question. [1]

as for why i didn't just close the door, my new officemate is constantly asking me how one reads aloud mathematics in english, e.g.

"the ιntegral from zero to ιnfinity of one over x squarεd plus one is equal to pi over two." when i think about it, the parsing is nontrivial:

sub-e.g. why is it 'x squared' and not 'x to the two?'
or why is it 'pi over two' and not 'pi halves?'

i used to think that, becoming a postdoc, i should act "professionally" -- be in the office during normal working hours, and generally hold myself responsible and accountable.

as for the office bit, forget it: all it does is make me a stationary target. it's much more productive to be a moving target!

[1] yes, i am a softie at heart. just be thankful that i didn't write "my sangfroid thawed." q-:

suddenly civilised.

my girlfriend is visiting me for two weeks, so life now feels orderly and civilised. i suppose this means that, earlier, i was living an 'uncivilised,' but research productive lifestyle.

granted, both she and i are academics.
we have the usual 'workaholic' habit that academics do.

on the other hand, our work styles, even hours, are different:

before: i used to wake up, make coffee, and get right to math. i'd eat breakfast while drafting out work notes or reading a paper. somehow, when half asleep, it's still possible to weigh a few research ideas -- and when the coffee kicks in, so do better ideas.

now: we sit down, eat breakfast together. i drink coffee, try to make conversation, slowly wake up.

there is also the fact that we work in different disciplines.

for a mathematician, mιcrosoft word isn't terribly useful. most people i know use LaTeχ when they have something worth typing up. so as long as a computer operating system supports LaTeχ [1], any will do.

on the other hand, my girlfriend isn't a mathematician. she needs ms word. openoffice is a good start, but formatting issues persist.

so i learned yesterday afternoon, as we tried to hunt down a windows computer before a job application deadline. (my department essentially runs linux exclusively.)

also, the relationship: when you're one person, your schedule is what you want it to be. when you are two people, then suddenly scheduling matters.

i have to think about when i'll go running, or if i can go running; maybe i agreed to run errands, and suddenly it's 9pm ..

there's a word for this: compromise. those of you who have been in long-term relationships for a while, sure: feel free to laugh.

like i said, i've been living an uncivilised life for a while. (-:

for now, i think i am half as productive as i usually am. give a few more days, and perhaps i'll be back up to speed.

[1] then again, there are web-apps for this, such as monkeyteχ. others readily appear on a googlε search.

weekend obsessions.

at some point i should treat my weekends more seriously, or at least, more productively.

this morning i thought about derivatιons again, with no progress; the same obstruction always recurs. that said, i should quit this problem, stop trying naive things, until i can resolve the obstruction.

letting go of obsessions is never easy.

sequences, familiar and strange [a teaching post]

for this university, it's that time of the semester when we work towards Taylor serιes expansions. i gave my first lecture today, in this direction; sequences.

almost every calculus textbook i've read will give the Fibonacci sequence as a standard example.

apparently it's "not clear" how to write down the general term.

really- come on. i understand that textbook authors don't want to explain the formula, but don't say it as if a formula were impossible!

i get a kick out of showing them the general formula involving the goldεn ratio. it especially surprises the computer programmers in the audience, who have been indoctrinated that recursιon is holy.

the formula is simple .. just square roots and exponentials.

then again, i don't explain its origins -- maybe that one needs linear algebra. a few students, the curious ones, ask about it. if i had to guess, the other students probably chalk it up to my being over-excited about obscure abstractions (again).

this year i added a new "weird" example to the lesson: "the see-it-say-it sequence." [1]

the students seemed to receive it well, but only because:

1. i told them they don't need to know it for homework or for the exam (so that they can relax).
   
   
2. i tell them that they can use the sequence to stump their friends, drive them nuts with a good riddle. honestly, it's not the sort of pattern that's obvious to guess:
   
   1
   11
   21
   1211
   111221
   312211
   13112221
   1113213211...
   
   indeed, who doesn't like a good riddle? (-:
   

all that said, they seemed to tolerate me when i describe that it actually has good limit behavior (but not prove, of course). the same curious students get shocked, which is good.

too often a calculus student thinks that everything has been done, that there is nothing interesting and new in mathematics.

i think it does them good to see that there are always new(ish), unexpected directions. there is something new under the sun, something possible.

as related to a general theme of calculus:

if you can convince the students that they can "do" mathematics, then up to laziness, they will. this is not to say that you must build up their self-esteem, for that must be earned, but to get them to try -- do that, and that is worth something.

[1] benji: if you're reading this, thanks for telling me about this sequence.

a good start; also, cookies.

this morning i woke up earlier than usual. this afforded me 1 1/2 hours in the morning to think about my research, before heading to campus and teaching. i didn't prove anything, but i was still pleased to have tried.

subsequently my lectures were error prone. for some reason i kept missing little details like negative signs and forgetting to change sines into cosines after differentiation.

maybe calculus and research don't mix very well .. at least, if it's calculus on a euclidean space! q-:

---

also, i think my students think i'm quite weird. today, while discussing damped oscillations for springs, i may have said the following things:

"so imagine that you have a chocolate chip cookie, dangling from a spring, bouncing up and down, in a tantalizing manner .."

"damping forces are caused by setting the spring-mass apparatus into an ambient fluid. as an example, if you took that chocolate chip cookie with spring and dipped it completely into a vat of melted chocolate, then subsequently the periodic motion would slow down .."

"it may happen that there are other external forces. for example, suppose you have little elves, say in scuba gear, swimming in the vat of chocolate and constantly pushing the cookie this way and that, for maximum chocolatey effect .."

admittedly, i was thinking of E.L. Fudge cookies and commercials with the Keebler elves. my students, however, gave me the strangest looks.

later, during office hours, one student admitted that he couldn't take it anymore. after class, he immediately went, bought, and devoured a chocolate chip cookie.

".. but i have promises to keep, and miles to go .."

.. before i slip and break them.

---

i think i make too many mathematical promises to too many people. if you take my word at face value, then by the end of next week ..

1. i should have finished final edits of a preprint, chosen a journal, and submitted the preprint to it,
   
   
2. i should have written a rough draft of a new (but short) preprint,
   
   
3. i should have proven a few new lemmas/theorems,
   ready to be discussed with (separate) colleagues in the department,
   
   
4. i should have started reading this one paper and have the rough idea in mind, in preparation for a seminar talk in two weeks,
   
   
5. i should have read another paper that a colleague sent me.
   

then again, this backlog of work isn't completely dire:

1. after browsing through the outline again, it doesn't include any substantial changes. i've also narrowed down to a handful of journals; if pressed, two coin tosses can settle that decision.
   
   
2. i have some work notes already in LaTeX form, and the estimates are fleshed out. there are some technical details lacking, as well as the misery that is writing an introduction .. but it's something.
   
   
3. i've already worked out most of the details, for one theorem.
   
   
4. the talk is in two weeks, so there's still time.
   
   
5. i don't think they actually believed me when i said i would read it soon. heck, i never believe anyone, either. it's not that people are untrustworthy, but simply that people are good-intentioned yet busy. [1]
   

odds are good that i won't do everything in its entirety.

it also doesn't help that i'm taking a day off from the usual research. instead, i woke up and immediately decided to revisit some topics from to my dissertation.

as for what i learned, so far ..

the bad news: the theory of dirιchlet forms is probably not relevant, after all. it's a great theory, but like Weavεr's theory of derivatιons, the setting is quite abstract and nothing comes for "free."

it's not unlike IKEA furniture: the items are affordable, but you have to take the time and effort to build them yourself. it's one thing to have a dirichlεt form ready on your space. on the other hand, it's quite another matter to start with a space and build such an operator yourself.

the good news: i might not need the theory of dirιchlet forms, after all.

as a side note, i wish i had time to read the work of sτurm and other related authors and works. that looks like interesting, useful stuff.

anyway: back to work. the list will only grow if i don't get back to it.

---

[1] also: here's a belated thanks to those of you who read my draft about the schoenflιes result and quickly came back with comments. that's item (1), above; i'll submit it soon.

an academic litmus test.

i originally wrote this in september, but then writing the NSF grant application got in the way.

i meant to polish this somewhat, but rather than risk never publishing this, here are some unfinished thoughts.

---

maybe i should teach an undergraduate course in analysιs next term. teaching preference forms were due last friday; i applied for such a course.

i suspect that my basic analysis skills have atrophied, after years of specialization into research topics.

heck, i call myself an analysτ (sometimes), yet it's no longer clear to me what is "analysιs" from the perspective of a student's first course.

is it a lot of δ's and ε's?
i don't remember anymore.

i'm curious: what is it like, teaching those young minds who want to learn the details, not just to satisfy the requirements of their major or to scratch the surface?

there are other reasons, of course.

---

i doubt very much that i'd make a good "role model" for undergraduaτe maths students. even after all these years, i still feel like i don't know what i'm doing.

i don't think that i'm flattering myself here, with the premise of the question. i'm not asking based on any assumption of conceit.

after all- to a student, untraveled and new to mathematics, who are mathematicιans but their teachers?

on the other hand, i'm in a business where, if i want to advance my career, then i have to become this kind of 'role model' for the next generation of maths scholars. this gives little room for these kinds of doubts.

so teaching undergrad analysιs will be a kind of litmus test.

if it's an unequivocal disaster, well ..
.. then at least i'll learn whether i should stay in this business or not.

---

epilogue: the decisions are in.
they gave me an undergraduate analysis course ..!

in which tuesday is the new "monday" ...

this week i lost tuesday, my beloved day of the week. i blame the phenomenon that is called fall break.

---

when i was an undergrad, we had no such thing. we just soldiered on until thanksgiving. i first learned of this as a graduate student and summarily dismissed it as some artifact that well-to-do schools afforded their well-off undergrads.

as it happens, it's more prevalent than i thought.

this past monday was the so-called break. the day after was tuesday only in name. as mandated by the university, classes ran instead on a monday schedule. i admit, we academics are creatures of habit. i'm surprised that there wasn't a flood of confused profs showing up to empty classrooms, wondering what had happened.

(so yes: i'm complaining about having to teach two days in a row.)

as for why anyone would switch up the pattern, it's for reasons of balance. when you count the days off in the fall term,

• one monday is for american labor day,
  
• one wednesday,
  one thursday,
  one friday are all taken for american thankgiving,
  

which leaves tuesday as the only day which meets uninterruptedly. turning one tuesday into a scheduled monday means that instructors on the tuesday-thursday lecture schedule get the same amount of time off as instructors on other schedules.

i'm all for fairness, but really ..

just as three day weekends lend themselves to painful four-day weeks, the academic world runs on monday-wednesday-friday and on tuesday-thursday schedules.

couldn't they just have given us both monday and tuesday off, and add one last monday as the last day of fall classes? that still keeps parity, and the pattern is easier to follow.

---

no matter. tomorrow will be a productive morning. as for the afternoon, it will be busy yet unproductive.

the aftermath of the exam went as i expected. i have a lot of spooked students now: i met with one today, i'm meeting two tomorrow, and three are scheduled for friday.

[sighs]

from now on, i'm dividing by four ..

not a well-planned exam, since young minds are fragile.

when i taught for the first time as a graduate student, i made an error in arithmetic.

it took me 10 minutes to solve a quiz i wrote, so i figured that my students could do it in 20.

how wrong i was; half the papers had blanks in one or more parts of the last question (there were only two problems).

since then, i used a factor of three to gauge time.

now it appears that i should change that.
the average score is about 57%.

for my classes last week, the midterm i wrote took about 16-17 minutes for me to solve. it was supposed to be a 50-minute exam. i even chose variants of the practice problems that were listed in the course schedule and examples i did in class.

after grading it, i think i have to use a factor of four now.

sometimes you can tell that a student has some understanding, but panicks due to a lack of time. on many papers i see good work scratched out, and oversimplified, incorrect work takes its place.

the more i think about it, the more crucial it is to have an exam that students can do in the time allotted, and some with a few minutes to spare.

only two students in a class of 62 finished early [1], and in another class of 48, nobody finished early. if your best students need the entire exam period, then this is a bad sign ..!

there is another reason: give a student an exam that (s)he cannot finish in the time allotted. that only reinforces the suspicion that yes, i am bad at math. then, depressingly, (s)he just stops trying.

when the exam is curved, the instructor knows that as long as everyone has done comparatively badly, the majority of student grades will go unscathed.

but some students never realise this. they only consider their own performance, and in this american culture, it seems that "if you can't get the correct answer quickly, then you aren't good at what you're doing."

i don't believe in that, myself -- mistakes are a natural part of learning -- but i'm only reporting what i observe.

i haven't returned the exam yet. already, though, some students have scheduled appointments with me, in efforts to determine "what they are doing wrong."

---

there's also something unusual about our syllabus, at least to me. at this university, students learn about the definite integral and methods of integration at the end of calculus i, which is confusing to me.

subsequently, one assumes that students know how to integrate at the start of Calculus II. in two lectures, we are supposed to cover all of the usual methods of integration -- substitution, parts, trigonometry, partial fractions!

this sounds to me like a recipe for disaster. there are too many schools who do not cover integration in calc i -- michigan, for one -- and there are always transfer students.

each method, from my own habits, takes its own lecture to learn. there's barely enough time to run through the characteristic examples of each of them, in 3 lectures!

other topics of the calc ii syllabus strike me as odd:

1. methods of integration, numerical methods, improper integrals
   
2. applications to geometry (areas, volumes, arclength) and to physics
   
3. differential equations, including second-order linear homogeneous ODE ?!?
   
4. power series and the like;
   
5. three-dimensional geometry ?!?
   

this is .. a lot. moreover, the topics are less cohesive than i'd like. it's good to learn geometry, but wouldn't it be more fitting to fit it into multivariable calculus (calc iii)? [2]

this is an unfounded suspicion, but i suspect that there was some politicking, which led to this syllabus.

perhaps the school of engineering complained that their students don't know how to solve ODE early enough in their training, and demanded an accelerated program.

if this is true, then they never accounted for the fact that it actually takes time to learn anything of substance. heck, it took the great minds of newton and leibniz to invent calculus. moreover, leibniz was interested in computational engines, and wanted to make calculus accessible for applications.

put another way, engineers: if you think that calculus is easy, it's because leibniz designed its implementation that way.

take, for example, the standard problem of showing that



using only the definition of a derivative. you actually have to know how to use the binomial theorem to understand this fact!

even putting n=3 causes trouble to most students. judging from how much trouble students have with using (not proving) even the quadratic formula, be glad that leibniz had an applied mind!

all i know is: any decent calculus instructor would have known that integration is hard enough for students, and it would be folly to demand more of them otherwise, and more quickly.

in retrospect, i should have ignored the syllabus and incorporated basic methods of integration questions on the exam. i should have realised what my students would find difficult.

most of the problems, instead, used integration at one step, such as improper integrals, hydrostatic pressure and force, ODE ..

[sighs]

why do i get the feeling that the next two weeks will be full of instructional "damage control?"

[1] "early" means handing in the exam before the last 5-10 minutes. there will always be some students that will try to leave a few minutes early, if only to make it to their next class early or simply because they can't stand looking at the exam any more.

as a result, you cannot trust these flighty students to gauge how hard the exam was.

[2] having taught calc 3 here, last year, i can assure you that these geometric topics are assumed and there is no budgeted time to review them.

what i learned, while writing an NSF grant proposal.

[i started this last month, on 20 sept.
i still agree with what i wrote then.]


ALWAYS START EARLY. as someone who failed to do so, trust me: this task takes up a lot of time.

remember how difficult it was to write a research statement, when applying for postdoc jobs? remember when you had to be nontechnical and not span past 5 pages, in discussing your thesis work?

now add 10 more pages, and write more diplomatically: no full proofs, but some details so that the math makes sense. in short, you need 10 pages full of ideas -- not summaries of past work, but unfinished, new ideas.

---

i exaggerate, of course: unless your field is well-established, there is a good deal of exposition involved. i think half of what i wrote was to explain why the analysιs on metric spaces is even relevant to study, what it affords you and why it is hard.

"analysis on metric spaces is interesting in its own right" is one reason to study the area, but i hesitate to say that it's the only reason. besides, can't everyone say the same about their own field?

if time is money, then it's throwing good money after bad.

i don't know why i work in the afternoons. almost always, that time is wholly unproductive for research:

no good ideas,
more paper thrown into the recycling bin,
staring through space and into the wall.

i don't know why it's so hard just to take a break, and work later.

why didn't i just perform less creatively-demanding but useful tasks,
like grade exams or write lesson plans,
or even go to the gym or running?

i tell this to other people often, but never take my own advice:

mathematicians are not like factory workers, or employees at a company office.

we think for a living,
so we should work in a way so that we think our best.

as long as we get enough good ideas, write enough papers, give enough talks .. and show up when we have to teach or hold office hours .. why should we hold ourselves prisoner from 9am to 5pm?

admittedly, i have an answer: paranoia.

you never know if you suddenly get that one idea, the one key that unlocks the problem. if i work just a little longer, maybe i'll see it.

the problem, of course, is when i iterate this reasoning.

"just a little longer,"
repeated 5 times,
is usually equivalent to "wait, where did the afternoon go?"

[sighs]

oh well. at least i know i'll be productive in the evening ..

guilt (and expertise?) by association.

sometimes academia can be very misleading.

---

at some point, years ago, i co-wrote a paper about the p-Laplacε equation on a class of singular manifolds. [1]

if all goes well, by the end of this month i'll co-write another article -- with different co-authors -- about solutions of a non-homogenεous version of the p-Laplacε equation, in the setting of metrιc spaces [2].

to any readers in the PDE crowd, this probably sounds alarming. differentiation on metrιc spaces is a tricky business, and in this setting, we often work without an integratιon-by-parts formula.

so we're not studying PDE, per se. rather, we're studying variational problems -- which still make sense in this generality -- and using the analysιs that we would use on uniformly ellιptic PDE.

as for what is misleading: i don't really study PDE.

my colleagues do, though.

there is a cottage industry of PDE on singular/metric spaces, and every so often, i get consulted about matters of analysis or geometry on metric spacεs. i ask enough questions --

does harnacκ imply hölder continuity, or vice versa?
wait, what are the "standard" conditions on the functιonal again?

-- and eventually, i suggest something. so far, i haven't been exposed as a fraud yet.

as for how i became a metrιc space "expert," the reason is much the same:

as a student, i worked with many colleagues who were experts. the advisor, in fact, played a large role in shaping the field.

so when new colleagues meet me, learn who i am, they assume i'm one of these metrιc guys. they ask me metrιc questions ..

.. and i still haven't been outed as a fraud. [3]

like i said, academia can be pretty misleading.

---

[1] for those not in the know, on euclidean spaces the p-Laplacε equation is:

where p > 1.

[2] to the experts out there, yes: we are assuming the usual hypotheses.

[3] this is not modesty. i know experts in this area. give me 5-10 more years, and i'll get back to you about expertise.

examinations and aftershocks.

since yesterday afternoon, every time i've check my email, another student has written me, requesting to meet and to discuss the course. tomorrow i have 3 appointments with students.

ye gods;

had i known it would be this much trouble,
i would have written an easier exam .. \-:

---

thinking it through, the average student has an advantage:

before the exam, they have to study,
but afterwards, they are free (at least until the next exam).

before the exam, my students flood my office hours,
i have to think it through -- what i want the exam to be,

afterwards, students still flood my office hours, even make appointments. there is damage control for another week ..!

sometimes getting older just isn't worth it.

the trauma of examinatιons.

today is midterm #1 for my students. i get up early, just so i can have copies of the exam ready, with time to spare.

i wait for the bus.
it arrives ..
full of people, like sardines.

it doesn't bother stopping. i don't blame the driver, but ..

[sighs]

lost time: 10 min.

---

doors in my department are strange, because they have two locks: one for metal keys and another 5-button combination lock.

i never use the combo lock, so i don't know the combination. last night, apparently, my new officemate decided to use it. so this morning i was locked out of my office.

lost time: 15 min.

---

i teach two sections of calculu∫ ii, which makes a total of 120 students. [1] and 120 copies of exams to make.

the photocopier works,
the collator works,

but the stapler attached to the collator stops working after 20 copies or so. it's mildly interesting: at some point i learned how much an exam should weigh, because i had to staple 100 of them by hand ..

lost time: 20 min.

---

i made it to the classroom just in time ..

.. and people wonder why i'm paranoid. in retrospect, i should have just stayed late at the office, last night, and made the copies before midnight.


as for the exam, if my students had any love for me before, it's gone now. i guess it was a hard exam, despite being a collection of practice problems and lecture examples.


[1] maybe they'll give me an undergraduaτe analysιs class, next term. that's only fair: i've been a good little mathematician this year ..

in which i lost track of "time."

i think my students believe that i hate the english.
this is inaccurate.

however, i hate using english units when working out basic mechanics problems.

earlier today i was working out an example about hydrostatιc pressure and forcε.

for a full minute i was stuck, wondering how to account for the gravitational constant and "where the seconds went." suffice to say, british pounds (lbs) carry a lot of information in them ..

.. ye gods. how do english measure mass?
in units of lbs × sec²/ ft?!? [1]

that said,

1. any "physics" on their upcoming midterm will be in metric units.
   
   
2. if i could go back in time, i would have hid in the tree and threw the apple at newτon's head, as hard as i could.
   
   well .. maybe not as hard as possible ..
   .. and sure, it's not really newτon's fault.
   
   in fact, force is measured in newτons N = kg × m / sec².

[sighs]

it wouldn't be this frustrating, had it not been a review session for an exam. students are jittery, and it doesn't do to cause uncertainty amongst their ranks, at a time this close to their ordeal.

---

speaking of which, i should write one .. and get back to research .. and article-writing .. and so on.

[1] about lbs and ft: the only notable matter about them that comes to mind is this: there's a scene from the shιning where jack nιcholson laments to the ghost about .. well, child abuse, and in terms of foot-pounds.

it only makes the whole discussion all the more ridiculous. come on: foot-pounds?!?

a day, back in the life.

in terms of research, i may have to learn patience again-- discipline, too.

all day yesterday i worked on a problem,
off and on, but more off than on.

i blame it on the fact that yesterday was saturday, the first one after weeks of grant-writing. it's hard to focus.

i also blame the grant-writing process.

in a short span of time i came up with a host of research ideas. if successful, it would take me a few years to enact all of them.

realistically i know that i cannot accomplish them all at once, but that doesn't mean that i don't want to.

anyway, yesterday was full of breaks and distractions.

---

in the morning i re-read the outline of a strategy that i wrote the day before. then i recalled a lemma that i remembered from a book. not having the book on hand, though, i proved it just to be sure.

then i jotted down an idea -- maybe i could write it as a variational problem -- and after working out a few lines, i dismissed it as out of hand.

then i checked my email, read the news from several websites, and went on flickr to look for new desktop wallpapers.

after a while i felt unproductive and lazy enough to return to my workbook.

forget highfalutin ideas; just work out an easy special case. do something.

so i did.
no, that's too easy. what about ..?

and so it went, on and on. more cases followed, coalesced into something good and general, and then ..

wait. i wanted a single function out of this, didn't i? then why is this a vector field ..?!?

dejected, i went and read more news online,
then went lurking at a few online maths communities,
answered a question about compacτness [1],
felt better, made lunch, then took a nap.

sometimes a nap is a good excuse to wake up and make a fresh cup of coffee. by then i felt good enough to return to the workbook.

i had meant to flip immediately to the next blank page, but the pages were hard to separate with only one hand [2]. the first page of that day's worknotes appeared and something caught my eye ..

i'm an idiot. why didn't i do this first?
anyone would have done this first. it's obvious ..

.. and yes, it works.

two steps of the strategy are now complete, but a few steps remain. those would have to wait until i learn more about this one theory that i've learned from hearsay [3] and when i reach the maths library again, on campus.

closing the notebook, i saw that it would get dark soon. where did i leave those running shoes again? ..

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[1] it didn't sound like a homework problem and therefore warranted an answer. even if it were someone's homework, i gave a metrιc toρological answer to a hιlbert space problem: illuminating but mostly useless.

[2] the other was holding a cup of coffee.

[3] for experts out there, i mean abstract dirιchlet forms. admittedly, i'd never thought i'd actually use them, but they seem exactly the right fit.

i kid you not: "calculu∫, the musical."

this department gets stranger and stranger.

---

i can accept the notion of an integratιon bee.

heck, i even participated once .. 7 years ago?
i nearly won, too, but i was off by a constant .. [sighs]

but this is going extreme: from my departmental webpage,

October 8, 2009 - 8:00pm
CALCULU∫: THE MUSICAL!
Tickets are free and available in 301 Thackeray Hall
G23 Graduate School of Public Health

oh well.
at least it isn't "Calculu∫: a Tragedy in 5 Acts .." \-:

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in other news, i found out that advancεd calculu∫ isn't just a course, but a music album and once, a radio show on a pιttsburgh fm station.