before the meeting and after; thoughts on salvage and writing.

i wrote this most of this, last night; new text from tonight begins at the symbol '#.' an epilogue follows the symbol '##.'

i suppose it could have been too much to ask for: that is, three consecutive weeks of good research ..

two weeks ago, i made a conjecture and it might still be true. however, it is certain that it remains a conjecture tonight.

at the time, i could only sketch an argument for a rather special case, but it was too simple-minded. i would be embarrassed even to state it as a lemma, because it is too transparent; upon reading the hypothesis in the lemma, it would be obvious how the proof would go. [1]

there's no art in that: no boldness. but when i tried to generalise, there was a gap.

one week ago, i filled the gap and managed a weak version of the conjecture; it's true for a wider class of examples, but remains unknown in full generality.

it's of little interest, and more a toy than anything else. i suppose that one of its few strengths lies in its concreteness. to some degree, the weakness of transparency is gone, but as usual this proof reduces to that first special case.

i dare say, though, that the reduction is not so transparent. you might even call it clever, though it is n. weaver's cleverness and not mine.

# this past week i've been unable to concentrate. i don't know why. an idea i had this past weekend now makes no sense and i can't remember the motivation. i think i fooled myself, and it wouldn't be the first time.

i hate it when this happens. tomorrow i'll stop by the advisor's office and tell him that i have no results. the most frustating part is that i have essentially nothing to say, because it's not even worth mentioning what didn't work, because i know why and it didn't teach me anything.

the meeting will be fine; i know that.

i now know the advisor well enough that that hour and half-hour will be worthwhile, indispensible time. what bothers me is that the advisor is disturbingly clever and wise, and if i don't stop him he'll prove results which should be my task to prove. he can't help it; he became faculty @ um for many good reasons.

advising and guiding are fine things, but there is no honesty in my standing in another's shadow, because one day i will move away and i must face the sun myself.

the way is difficult and we may choose our ways, but some choices are meant to be formal.

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## perhaps i shouldn't call it a conjecture. the word "conjecture" is too grand and suggests something that is inherently worth pursuing. maybe i should have said "claim."

the meeting did go well. the advisor and i philosophised, and we pondered the direction this inquiry goes. the once-conjecture/now-claim is fine, but ultimately it was meant to follow a path of counterexamples and derive a necessary condition for the geometric function theory that i study.

if i prove it, then it is a little something. but i haven't proven it and at the moment i have no more ideas, so what stands is not theory, but a souped-up class of counterexamples based on another's existing work. even if i prove it, the result won't fully resolve the issues at hand.

there are deeper issues and more relevant connections to the existing theory of the analysis on metric spaces. in particular,

• there is the theory of upper gradients through rich geometries of curves;
  
• there is p. hajlasz's theory of sobolev spaces via lipschitz-like moduli of continuity;
  
• and there another nascent, but existing notion. as yet, there is no rich theory.
  

to paraphrase aristotle, even taxonomy is no easy feat. as mathematicians, we go further and attempt an understanding between elements of this taxonomy, and assess its relevance.

this is among the goals at hand. what does it mean, a sobolev space? let us have a metric and a measure; can we have calculus? are there many types, and are they so different?

now i am too philosophical. let me prove things before i say more.

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this post grows long, but let me say: i had a thought, a few days ago. it was an old realisation, made acute and sharp by the passage of time and an unexpected reminder. the future nears, a conference quickly nears, and the job hunt will soon come; a year's time.

that first thesis problem is dead; i've left it for dead, but there is something to salvage. i want it to mean something, that a year of my work mean something. in a little while i will give a talk about it (a so-called preliminary report), and the advisor still thinks it a good idea that i write a paper about it.

it is good to have publications, if only for a strong c.v. to date, i have only one and that is a joint work. another can only help.

still .. why is it so hard to get to writing? i've heard a saying once that a mathematical paper is never finished, but given up. to write this, i will have to give up the possibility of progress for a while; i would write what is, and not what could be or is likely to be.

i think i am too used to uncertainty, and cannot bear it. it's silly but true.

[1] and yes, when i say "obvious" i do mean obvious. however, i didn't say that it's trivial .. though i dare say it's close.