in which string theory is mentioned.

i feel like i jumped on the bandwagon, which is never a good feeling.

this week i found two more articles denouncing string theory with the usual complaints and talking points. the first can be found @ american scientist online and the other is in new yorker magazine book review.

after reading the first article, i decided to hop off the fence and write something about it. i wonder if the trolls will swarm by that blog post, this weekend.

[shrugs]

at any rate, i found this excerpt from the new yorker article an interesting one:

String theory came into existence by accident. In the late nineteen-sixties, a couple of young physicists thumbing through mathematics books came upon a centuries-old formula that, miraculously, seemed to fit the latest experimental data about elementary particles. At first, no one had a clue why this should be. Within a few years, however, the hidden meaning of the formula emerged: if elementary particles were thought of as tiny wriggling strings, it all made sense. What were these strings supposed to be made of? Nothing, really. As one physicist put it, they were to be thought of as “tiny one-dimensional rips in the smooth fabric of space.”

why strings?
then again, why atoms of protons and electrons?

i wonder what the mathematical formula was. centuries old?

delusions of grandeur.

this might be a happy error arising from late-night fatigue, but earlier tonight i think i proved a theorem. by this i mean i really proved something: an original theorem that nobody else has proven before, though it is a generalisation of a theorem of n. weaver.

the conjecture still stands but i'm one step closer to it, if only because the theorem serves as motivation on why the conjecture should make any sense at all.

maybe in 24 hours i'll find a flaw and become depressed again, but for now i am happy and tired and tipsy from a glass of white port, and in a moment i will retire happily to bed.

let the disappointment come tomorrow, if it comes. tonight i am in happy delusion.

mathematical celebrity sightings.

when i really think about it, the most famous people i've ever met are the physicist sir rοger penrοse and the fields medalist terencε taο.

both of these meetings were accidents and forgettable events; these were before i was a graduate student and i didn't realise at the time that these were very great men, indeed.

i suppose it also means that i've actually met a knight of the british empire. (;

while i'm at it, i might as well keep boasting.

i have heard lectures from the grand old man of analysis, elιas m. steιn, fraηk mοrgan of the double-bubble conjecture, and the mother wavelet herself, ingrιd daubechιes.

less known, i've heard talks from jeff cheegεr, dennis sullιvan, l. craιg eνans, and peter jοnes.

but the real kicker is: i've never heard a lecture from fred gehriηg before.

reflections on time and days, and frustrations.

if i had to do it all over again, i think i would teach later in the mornings or in the early afternoons. in the block scheduling for calculus classes @ um, 1 to 2:30 would be ideal, i think.

i could wake in the pre-noon and enjoy my coffee. i would think for a few hours or work things out on paper or read a few references.

ultimately i'd resolve or muddle up some thoughts from my previous endeavors (it's hard to expect progress, every day!) and by noontime or later i'd be out of ideas, which would make a perfect time to have a little lunch and prepare lessons to teach.

11:30 to 1 wouldn't be bad, either: it would be a tight fit for the morning's work, though.

i'd like to believe that i could still wake up fresh and early if it means getting a decent amount of work done. i think of how tired i am, but then i think of how i'd rather not move to a third thesis problem ..

.. and it makes an early riser out of me. (;

all in all, i think my old habits are dwindling: except in cases of sheer willpower or pure curiosity, i can't work late into the night anymore. 1 am and i cannot think deeply any longer ..

.. unless the problem has marked me and i can remember it without hesitation, but that in itself is a bad, obsessive sign .. \:

---

and as you may have guessed, a problem has indeed marked me, with acute ambivalence. i love mathematics research; i also hate it, and often at the same time.

it brings out the worst in me, because i grumble too often and to myself. i become a troll and no longer a person.

too many in east hall know me now, and i have no peace. people wave or say hello to me, and i only nod curtly at them or do nothing. i don't answer the telephone and delay emails which need no immediate response.

my officemates are not mean and unfriendly enough as teachers, because their students keep flooding into our office for homework help!

from paper recycling bins i eagerly fish out pages with blank back sides. later i return them dejectedly to the bins, with back sides all cluttered with scrawls and figures and nothing useful.

it's a sequential depression: i get an idea and try it out, see how it looks .. but it fails. then another idea comes, and i try it out .. and it looks like sh*t. why did i even think of this idea? f*cking idiotic.

more ideas rise .. then fall, and after a while i cannot bear it any longer. therein lies the hate: when i work in mathematics, i have to confront my own folly and ignorance, and to allow myself my inclination towards errors and misjudgments.

i think artlessly, and brutally. i have no guiding principles, and i stumble a lot.

above all else, the most frustrating bit is that whatever works for the problem, whatever the solution .. is easy. natural. it flows .. and you curse yourself for not seeing it sooner.

i dare say that mathematics is difficult, because ultimately it is easy, but frustratingly so.

conjectures

last week the advisor made a conjecture which seems on-target, but i wasn't sure what to think of it.

i suppose it's a natural reaction. if i knew how to think of it, i'd have proven it, and it wouldn't have been a conjecture now, would it?

today i made a conjecture which encapsulates the advisor's previous conjecture, though i wasn't thinking of it at the time.

more accurately, i made it last night over a glass of white port wine. then i realised that i was indeed drinking port and thus could not be trusted with conjectures, so i labelled the page i wrote on:

crackpot conjecture

and then happily continued with my whimsical speculations.

doing so is like giving free license to be wrong. sometimes i write "scratch paper" on a recycled page and then start messing it up with scrawls and diagrams and cross-outs. when there are enough ideas, then comes the good paper and the process of clarifying the ideas.

even to this day, i feel like i can only do mathematics, draft by draft; some habits do die hard.

the weird thing is that the conjecture still sounds plausible when i'm sober, and it would relate these metric co-tangent bundle and exterior differential notions with geometric measure theory.

the cool thing is that the advisor also thinks it's plausible.

the worrisome thing is that Weaver's notion of exterior differential may be rather rigid, and it mightn't be as interesting an object of study.

then again, it could be my paranoia: after you've killed one thesis problem (for the worse), there's always the fear that you'll do it again. who'd have thought that it would be so worrying to be right, for once?

article post: my brush with someone famous.

seed magazine (a science/techie mag) has an article on one of this year's fields medalists, and for once it's not grigori perelman. instead, they chose to highlight terence tao of ucla.

the really weird thing is that i've actually met terence tao, but at the time i didn't know who he was:

it was a little more than four years ago, i had just finished my undergrad and as luck would have it, the park city mathematics institute had flexible funding and accepted my application into their three-week summer program in park city, utah.

i arrived there in the afternoon and when wandering the hallways of the conference center, i bumped into two mathematicians hard at work with a pile of pages with scribbles in front of them. one of them, a young asian man, seemed to be explaining something to the other, a young woman.

"hard at work already, eh?" i joked. to my infinite future relief, i didn't say what i thought i saw: two grad students already prepping for the lectures by distinguished faculty.

"um, yes," the young man replied, and the two returned to work.

the next day, i found out that the young man was terry tao and the young woman his student. how did i find out?

by attending tao's lectures. brilliant man.

good news, for a change.

with all the griping and ranting and moaning i do on this blog, i feel obliged to say that today wasn't one of those days, but that did have something to do with the past few days.

---

wednesday was my talk at student analysis seminar, and it lacked luster. in retrospect i should have realised that i wouldn't end up discussing things that i truly wanted to discuss .. not nearly that much at all.

i should have talked about something else .. less dear to my heart, perhaps, and maybe something lighthearted and fun, if analysis can be like that at all. i think i took it too seriously and spent too much time consolidating sources and facts and areas of study .. to the extent that half that time was a waste, and later i was irrationally upset by my own folly.

but promises are promises, and abstracts have their deadlines, and we cannot retract all our bad decisions.

if all goes well i won't be giving another talk for a while. sometime before december i trust i'll be drafted into another analysis study seminar talk, and there is a talk i promised friends for a mid-october conference. but apart from those, i'd rather be silent for a while, and wait until i have something worth saying before i speak.

at any rate: an obligation or two now met, and over.

---

yesterday afternoon i showed the advisor some colorful pictures i drew, and he pondered my idea for a construction, said that it might work, but not to dwell on it for too long. trust me: this isn't as strange as it sounds.

the idea also seems to work, which i suppose is good .. even though it took me a month, off and on, to sort out ..

.. and considering that it is one variant of someone else's very concrete example, and that doesn't prove anything deep. it's merely a motivating example.

the real work is ahead: what do two examples teach us? is there anything interesting happening, geometrically? as my friend john mackay would say, is this fit at all for man or beast?

it's too much thought for a friday night. a small job's done, but there are many more left, and i'll start another one tomorrow.

---

i may have time to write that paper, at last .. provided i don't waste it. the time for it had to come, sooner or later, but in the midst of errands and duties, sometimes i forget how things realistically follow one another, and my hope ebbs to dull expectations from dull, glassy eyes.

i hope things brighten for a spell. i could use the time to be productive.

teaching and emails ..

i've received three emails in as many days about exam time conflicts.

could it be that the students are reading the syllabi and course policy closely, because they have a quiz on those things, tomorrow?

i should have done this years ago. q:

---

not much else to say. still waking up at 8:30, even today.

(note last night was a party until 2am, hosted by none other than kevin and hannah. i wonder how late they were up ..)

so this morning i managed to do a little work, even if it wasn't research; at least the first part of my talk (student analysis seminar) is done, and the work session felt like a summer morning's, again. quite nice.

other than that and a little teaching prep, i've done depressingly little. i must find some way to reconfigure my brain into being more productive more often, otherwise i'll either finish in five years and prove little to nothing, or finish in six years with not as little to nothing.

[sighs]

start-of-semester frustrations.

the last time i felt productive was sometime last weekend, possibly monday. i thought i had overcome some obstacle of proof and was deducing corollaries and generalisations .. in short, doing a mental victory dance.

the last time i felt like i was doing something worthwhile was on tuesday morning, between 9 and 11:30 am. but it wasn't productive per se; i realised that my proof didn't work after all, and sought to find adjustments to sort it out.

this worthy time came to a halt, since i promised to meet my first-year mentoring student for lunch .. and it was a good lunch, after all.

---

since then, it's felt like damage control.

teaching prep is a headache, with the handouts for the first day and whatnot, and i've caught the bad turn of the rotation for our student analysis reading group; tomorrow it's my turn to talk as well as my meeting with the advisor, and guess what?

my proof still doesn't work: not enough peace-&-quiet time to ponder it properly.

the first floor of east hall may as well be the first floor of shapiro undergrad library, where no work is actually done and where students gab and gab and walk around and gab with other people .. i'm beginning to like working at home, more and more.

next week is another talk to give, the consistent obligation of teaching prep, and down the road, pursuing this little thing called research and a thesis ..

.. right? remember those?

---

i've been making a few vows, lately, and here is a new one:

from mid-september to mid-october, i'm committing to nothing but teaching and research and writing. i refuse to give any more talks or volunteer for anything superfluous until late october; i've been too busy for too long and it's time to take control of matters.

love/hate the office.

east hall, home of the math dept @ um, is becoming quite populated.

in fact, ann arbor is becoming quite populated, with returning undergrads and their parents arriving in droves.

sometimes it seems like the office is a paradox of intent: it is a place to do work, yet it is one of the hardest places to accomplish any work. sometimes, i can barely hear myself think, or worse, barely able to have coherent thoughts of any depth or sophistication.

this term, i think i'll try to work at home [1] in the pre-noon hours, and when i have an idea to implement, i'll do so at the office during the afternoon. it's similar to how i treat computer programming:

never sit down to code unless you have a plan in mind.

in this case, it's never go to the office without knowing what mathematics you have in mind.

[1] note that "home" also means 'caribou coffee.'