state of affairs, and conservation laws.

i'm more prone to making conjectures now, which is benign in the sense that a tumor can be benign: it does no harm, but it causes awareness and one wants to take care of it, just in case.

of course it would be better if i could prove my conjectures, because they are hardly the earth-shattering variety. as is the case in academia, these are not very motivating except to a handful of academics.

oh well. work is work. it keeps me from loitering on street corners, for instance. q:

---

meetings with the advisor have taken on a different turn: not bad, but different. strange to say, but lately it's been worthwhile to mention those ideas which i tried and which failed, due to possible obstruction from examples.

i suppose it keeps the inquiry in a relatively concrete setting .. or as concrete as theoretical mathematics goes. i still don't know where things are headed, but i've been worse and i'm making a little progress now.

progress, however, can be dangerous: one tastes a little success and is hungry for more. if one isn't careful, the hungry excitement turns to frustration and then anger, or desperation and then depression.

i call it "(the law of) conservation of emotional energy."

delusions of grandeur are dangerous.

to put it simply, i thought i had a great idea .. about three days ago. i even wrote up what seemed a proof of a theorem ..

(whose existence i had suspected for weeks)

and after writing that, i thought of a corollary and "proved" that.

but then i developed doubts. [1]

if i have a proof of this case, then why doesn't it extend to this case .. which isn't true?

it took a few hours, but i settled that doubt, too.

then, yesterday morning, i thought to write down the argument, complete with the context, what is assumed, what it implies, and what it doesn't address.

my initial motivation was to write it well and settle it for good, so that i could be more productive and spend today thinking about something new. it was then that i realised that the object of my idea is not well-defined.

for the non-mathematicians out there, this can be the kiss of death for an idea.

so i today i found myself in a "dilemma-&-chase." i've just invented the term, and it means:

the method could still work, and the proof patched. maybe it will take just a little effort, and that it's worth chasing down.

then again, maybe it won't work. so here's the dilemma: should i keep going, or stop and do something new?

at any rate, i should have trusted my gut feeling. delusions of grandeur .. of having conquered something .. are never good signs, i say.

[1] when i was headed to the gym on friday and in the early afternoon, my officemate asked me why; i told him that i proved something that's a little too good to be true, and rather than getting emotionally invested in the matter, i had to do the opposite, and run away from the problem for a while.

he nodded in understanding.

the nature of ideas, and their difficulties.

i think it is very hard to have good and original ideas, or even just good ideas. for instance, the last two ideas i had which looked any good at all -- they were already thought up and formulated by others, and in a more powerful, elegant way, too.

strangely enough, both ideas can be traced to those same 'others' and in the same paper. it's good reading and i highly recommend it:

"Structure of Null Sets in the Plane and Applications"
by Alberti, Csörnyei, and Preiss.

good and bad, i suppose: good that these nascent ideas would have been worth something, but bad because someone else was quicker and cleverer. now i have to work harder to contribute something of value, which is fine.

had i been quicker, i'd have done it to someone else.
fair's fair, either way.

---

on an unrelated note, i don't know if my student analysis seminar talk will be any good. every time i sit and choose what to discuss and how to elaborate upon it, i can't find a central, meaningful theme.

the accessible ideas which come to mind seem boring and without spirit. the really interesting ideas which come to mind are quickly complicated and their motivations take too long to explain.

it's a frustrating paradox, much like how 'you can't please everyone all of the time.'

speaking of days ..

i have heard a lot of denouncements concerning pi (π) day, which is fine. everyone should be free to have an opinion, provided it causes no danger to others. as for myself, i still think pi day is funny and will bring it up again, next year.

as for truly gauche things to say, yesterday was the 16th of March, and i told everyone that it was "sqrt(10) day," because sqrt(10) ~ 3.162277..

suffice to say that it didn't go over well, but it was funny. (:

on Pi Day.

usually xkcd comics has the monopoly on techie culture and lore, but today's strip of dinosaur comics is especially good.

for today, you see, is Pi Day: March 14th, or rather, 3.14!
ho ho!

among the jovial quips that t-rex says to dromiceiomimus,

"I get it that it's celebrating the UNIVERSAL CONSTANT PI, and that it's celebrated today because 3.14159 can be translated into March 14, 1:59. But what makes pi so special? Why don't we celebrate Euler's Number Day on... February 71st?"

writing, without actually writing.

so many things to do: i mentioned some of the mathematical ones last time. i might be growing calmer with age .. or more apathetic, perhaps .. but i'm not really worried about them.

---

thesis work has become regular work, and often it reminds me of creative writing. i have an idea of how something should go and i try working out it, much like how a plot would come to mind and i'd start a first draft.

of course, something usually gets in the way: some obstruction due to geometry, perhaps, and then i'd have to weigh if the original idea has any merit left, or if something new has come out of my inquiry. i suppose this is like editing.

in either event, the initial argument has to be reworked into something more substantial, much like how re-writing goes. it will probably run through several drafts and polishes, until i give up .. and either it becomes a final draft, or tossed into the wastebasket.

the analogy is not perfect, but i still see the resemblance.

fortune of fate.

strange.

had i decided this half-baked idea (which didn't prove what i wanted it to prove) wasn't worth mentioning, i would not have spent an hour (or so) today explaining it to the advisor ..

.. but then again, i wouldn't have learned that he thought it was a good idea, and still worth investigating.

then again, i wouldn't have another paper to read.
oh well. you can't win them all.


maybe this brain of mine is useful for something, after all.

---

there seem so many math things to do, as of late.

• continue with thesis work (i.e. find a problem and solve it)
  
  
• write up some work from a collaboration, and see if we can work out the last step,
  
  
• write a talk for next week; absently i agreed to talk at student analysis seminar, but i can't remember the title that i absently told kevin.
  
  
• revise a talk for a math grad conference @ syracuse (i.e. make it less quasi-)
  
  
• write a paper which the syracuse talk will be based on (though i remain with misgivings about such a project)
  

work, work, work. older friends of mine tell me that grad student life is to be cherished, because the years afterward will only become busier.

i can believe that, but the problem is in appreciating it. if grad student life is this hard already, how does anyone survive their postdoc and pre-tenure years?!?

problems, problems, and the meaning of a ph.d.

today i thought about two distinct problems: one in the morning and one in the afternoon.

the morning problem fated as well as i expected, sadly. it is part of a larger problem and the work we've done dates back several years. but we haven't been able to make much progress on it in the last year and a half.

the afternoon problem is newer, and pertains to the latest stage of my thesis work.

i had an idea or two from before the UM spring break, but when i tried them, they didn't work. now i have to be clever, and think of another idea to try.

i hate having to be clever, because too often i'm not, which is strange to hear out of context. for instance, when i say that in front of my family or friends from school, they'll look at me strangely.

i suppose it shows a difference of opinion.

i think that for many people, a ph.d. is something dandy which smart people get .. somehow or other.

for me, a ph.d. means someone either truly loves what they are studying, or are insatiably curious in that direction of study. cleverness or intelligence probably helps, but neither motivates .. and without motivation, there would be no point to search or study.

---

anyway, both failures combined for a dismal afternoon, but that was short-lived.

marie and saara had the good taste to have planned a little party, and that made pleasant fun for the evening: nothing like a little food, wine, and light conversation to clear the cobwebs, so to speak.

explanation & the compatibility of minds.

i'm becoming predictable. two days back in ann arbor, and my research conjectures remain the same. i've made no more progress since i left on holiday, a week ago.

i remember a quote, which is something like this:

insanity is doing the same thing each time,
yet expecting a different outcome.

i suppose i haven't yet reached insanity, but perhaps a quasi-insanity: i try one idea and it fails, but then i try a similar idea, only to reach a slightly different failure. who knows: maybe the map

{hypotheses} → {conclusions}

is continuous. q:

maybe no progress is not quite right, either.

it may not be the guts of research, but i think i've become better at explaining what i study to other mathematicians.

i've narrowed my soliloquy down to ~5 minutes, if i pare down the motivations. so accounting for questions and retorts, i suppose it would take about 15 minutes to explain it to a michigander.

just to clarify, that's NOT meant to be a slight to my friends and peers.

five or so minutes is the bare-bones explanation to a random mathematician; it doesn't account for whether that mathematician actually cares about what i'm saying or not.

in contrast, it may be more likely that my fellow analysts @ um might have some genuine interest in my work, if only because they know me personally and are motivated socially, or because we have a common intersection of research interests and they are motivated by curiosity.

you'd think that an explanation would take less time between two persons of similar background and sometimes it does .. but not all the time, necessarily.

first, the level of understanding which a curious listener expects may be substantially higher than a non-curious listener.

then there is the issue of "compatibility," in that two mathematicians may know the same things, but their methods of understanding may be completely different. so in explanations to a curious listener, one also has to account and adjust for a different set of expectations.

i liken it to de-fragmenting the hard drive on a windows machine: the more data you have in memory, the longer it takes to rearrange the data into that pleasant looking contiguous block in the end.

at any rate, my research woes continue.
i wonder if i will graduate on time.