Wednesday, January 19, 2005

A Call to Attention; Dealing with the Past and Inner Demons

As of two days ago I haven't had much time to read the Gromov article in my recently-celebrated acquisition, the Sub-Riemannian Geometry text. I still stand by what I've written last time, but I'm quickly reaching the impression that it will take a lifetime to fully understand all the nuances and connections that M. Gromov writes in those 100+ pages .. or rather, it will take me a lifetime, if I estimate rightly.

Realizing my mental faults and limitations doesn't bother me as much as it used to. In one sense it is relieving, just as you'd feel relieved at seeing the sheer number of books in a single Barnes & Noble Bookstore. The sheer amount of information unknown to you is limitless, and you can rest assured that there is far more knowledge in the world that what's between your two ears. In that way human civilization can progress merrily without my being responsible to push it forward.

Moreover there will never be a time in my life when I'd run out of things to do or to learn. From my perspective, that's quite a relief: there's no end to the fodder and fun of learning, and certainly that's one less thing to worry about.

Making sure that you learn what you want to learn and in a reasonable amount of time .. that's a separate issue. It was brought to my attention today when discussing my academic career with my funding director.


I'm supposed to be getting to know the faculty and finalizing a choice for a Ph.D. advisor. The standard suggestion is to ask a potential advisor for a reading course, and I believe that the suggestion is standard for reasons easily guessed. Yet I've done nil towards those ends.

I know these profs to a relative extent, but what do I really know? Am I really sure that my personality and tendencies of study will agree with theirs? Do I really have enough information?


I don't know why it seems so difficult to do so, but it does. Why would either of them take me on? It seems that all I've done while at Michigan is blunder about, and when I've actually accomplished something I know that I should have done so a great deal sooner. This is the pessimist in me talking, but all I see from my past year and a half are:
  • setbacks because of unpreparedness: passing my Qualifying exams took far more attempts than I deem necessary;

  • some choices badly made and priorities misset; perhaps I could have organized my time more efficiently, as to keep my responsibilities in good standing and keep.

  • an incomplete understanding of course material I should have learned properly, and shoddy coursework as a result;
I don't look like a very promising student from that account, and it's getting more and more difficult to determine how to troubleshoot my progress.

Am I doing something wrong? When learning, why do certain ideas seem to me so incomprehensible? There must be a clear approach that I'm missing, and it is increasingly frustration to figure out what that is, exactly.

Argh. No good.

I hate being non-clever, unresourceful, bad at asking questions and bad at seeking the weak points of an argument. I don't know how one acquires these rather useful habits, and rather necessary towards doing well in mathematics.

Strangely enough I remain hopeful that these matters will work out, but only if I act accordingly and promptly. It's never any dearth of love or interest for mathematics, but facing setback after setback, doubts eventually and inevitably catch up to you.

Maybe I was wrong after all, in gauging how well I'm realizing my faults and limitations .. and how to reconcile them with ends and results. It wouldn't be the first time I've erred for the worse.

1 comment:

Anonymous said...

1) Gromov's article on C-C spaces is much better in inspiring readers than in educating them. Although with me it failed on both counts. ;-)

2) Never mind "personality and tendencies of study" of your would-be advisors. Adult people can communicate and collaborate, no matter what their personalities and tendencies are (within wide limits). I personally decided on my Ph.D. advisor several months before I met him. Don't be too picky and they won't be either.

3) Cut down on the number of conferences you attend. A huge distraction with little use. Quoting a common friend, "Tell the Linkoping people that you're in Albuquerque, and the other way around. Then you can stay home and do your homework". :-)

Whoa, a whopping 3 items. This may be even too much attention.