Prodigal.

So in a few days I have to return to real life.. that means finally grading these exams, prepping another exam for another class, getting back to a scholarly journal, to colleagues in my department about a potential project and journal club, and so on.

Why do I feel alone in my endeavors? Why do I think I'm so ineffective and inefficient?

I feel refreshed.. but the sort of relief that will quickly deplete itself in a week's time and stress. My one track mind is a disadvantage in this modern society, where one had to stick to a multi-tasking schedule of barely controlled confusion..

On what to prep.

In my previous travels to attend conferences or visit colleagues,I used to bring printouts of preprints (most of them by others, not me) as well as a few books and a laptop.

Experience has shown me, however, that most of this stuff is never used.

These days I bring a netbook, the preprints stay in PDF form [1], and there's room for both my running shoes and climbing shoes.

[1] .. and the books are digital, too.. though legal copies are harder to come by.

Push and pull.

So I lost a debate with my co-authors, but it doesn't bother me. I guess it shows that we work well together and that I can trust them to tell me when I'm wrong about something.

The important thing about maths is that one remains with what is correct. Often it means that one has to be wrong on occasion, and to realise why. More and more it seems important to me to fail, if only to be aware of how far I am pushing what I knew and what I really understand.

It also seems that the way American universities are structured doesn't allow for this. Sometimes I wonder how new mathematicians come out off the woodwork, and if this explains why it takes so long to get the hang of research... that is, if one ever gets the hang of it.

---

I like Europe. I didn't realise the extent to which I missed it, how the universities work.

Of course life is always more appealing as a guest.. but being in Spain reminds me of those years in Finland when I was a semi permanent resident and slowly becoming a local. I wonder often enough if I should have stayed and tried for a permanent position.. maybe teach a course or two, co-advise a student, convince my sponsoring department that I might be a good guy to keep around.

Odd. I'd be scared to death of advising a Ph.d. student here in the States, but in Finland it would be more doable.

On the bright side..

My recent posts have been rather bleak, haven't they? I guess I'm still not fully used to professorial life; sometimes I wonder if it will ever feel normal.

That said, it's Spring Break and I'm away for the week, visiting my co-authors in sunny Spain.

I feel life my old self again. Ideas are coming out: a few good ones, lots of bad ones too. There's a good chance we'll finish off the guts of one manuscript.. and now I'm thinking about how to start another one.

So maybe I was wrong before; sometimes I can get my act together, finish what I started.

How it never ends.. but how it starts.

I'm supposed to go to the airport in two days, in order to cross the ocean and to keep a promise to a few colleagues. (Being that I don't keep many of those, it's rather crucial that I do so when it counts.)

Still, I'm easily exhausted. If I could say that I am exhausted right now then I would.. but the fact is that I'm not.

I know that I can still work, still have enough energy to keep the collaboration going if I budget enough effort per day of the visit.

I liken it to surviving on 5 1/2 hours of sleep per night: after a while it feels normal but you could swear that you used to be faster and sharper and maybe you're just "getting old" ..

I also know that once I come back, then I'll spend a few days feeling exhausted and bitter at having to readjust to my old routine.. to the extent that I'll probably swear that I'll never travel mid-semester ever again.

---

I don't feel the same anymore. It used to be easy, even natural, to be excited about getting up in the mornings and wanting to do maths right away.

Yesterday I met with colleagues in the department and we talked about PDEs.. rather, they did and I was trying to decipher what the underlying mechanisms were.

I am and will always be an analyst; these guys really think in terms of physical principles and what the equations are supposed to mean. I suspect that we'll keep a truce and the compromise of that truce will be geometry.

Anyway, my point is that the whole time I was absolutely ambivalent: I simultaneously thought (a) this is pretty damned cool and (b) fvck: I have.. aw, fvckity fvck! [1] .. that many incomplete projects right now and I'm supposed to learn.. no, have learned.. these disparate things; how can I juggle this one too?

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The fact of the matter is that I don't know how long I can keep this up. It feels like a Ponzi scheme on which I can't possibly follow through. I don't know why people put up with it, with me.

Whether or not I am exhausted, I feel exhausted. So let this be a lesson to you young researchers: even if your intentions are good, never promise more than you can deliver.

[1] at last count, i have $5 + 3(\frac{1}{4})$ collaborations and $3$ solo projects; a $\frac{1}{4}$ of a project means that there is a decent lemma or two, but no real theorems yet. As for the topics, they vary from geometric measure theory and PDEs to fractals, sub-Riemannian geometry, and minimal-like surfaces .. to even Banach space differentiability! On top of these, i suspect that one collaborator is trying to convince me that dynamics is interesting.

transformation.

If I could do anything right now then I'd..

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taken from tours4fun

..first take a week off to go hiking, maybe rock climbing. Maybe Zion, where I'd carry a rope and harness, my own water and in doing so, suffer the weight of existence. I'd do nothing but cross sand and boulders, shoot photos, and make campfires and sit in front of them, starting into the randomness of their flames and sparks.

I'd hunt the hidden moon by day, feel stones at my feet, be guided by the wind at my back and the mountains that frame the land-scape. I'd imagine myself made blind by an oppressive sun, finding a path of least resistance, some kind of order amidst the entropy that is desert.

---

Then dried by desert heat, seeking life and creation .. I'd spend a month doing nothing but writing.

There are too many manuscripts to revise, ideas to shape ..good ideas to initially obscure and when the shortcomings are clear, to revise into clear, intuitive shape.

In leaving Finland there were too many things left incomplete, plenty of angry impatient collaborators.. or at least, should be angry and lack any more patience.

I would become strange for a while, shaped by self-imposed solitude, transforming into something less than human.. if only to create maths that I hope will transcend my mortality.

---

if i could .. [sighs]

the curse of time.

i don't know what exactly i mean by the title;
at best, i can only explain it by example.

---

a month ago I was absolutely delighted to convert one of my old proofs .. which initially relied on weak star cοmpactness .. into a purely geometric argument.

at the time i thought this was the coolest thing ever .. and i still think it was worth the effort .. but it's been a month and now i have to stop myself from saying ..

wait: shouldn't it be obvious..?

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as another example: whenever i wrote an exam for one of my courses, i'd take it myself and multiply the elapsed time by 4; if the product was less than the length of the exam period, then the exam was too hard for the course.

now i'm considering changing it to a factor of 5.

either students today are slower or i'm getting faster .. and i'm almost sure that i'm not getting any faster.

whatchamacallit (or: i'm tired)

i don't know what to call it.. maybe a research bender, a maths hackathon, an intense weekend of work?

all i know is that this morning i woke up from 5 hours of fitful sleep, felt like old, wrung-out towel, made coffee, and sat down and proved a lemma that bothered me all of yesterday.

i sighed after i was done. it was only 9am, and there was a day of work waiting for me .. my day job, you could say.

---

based on years of experience, i'm not one of those mathematicians who can work all the time and still wake up excited every morning. i wish i was.

maybe i should take weekends off. lately i just feel tired all the time.

a picture is worth .. a few hundred backslashes!

often enough it feels like i'm wilfully banging my head against a wall. in this case, it's converting visual intuition into rigorous proof. [1]

i must have made this claim before .. but i'll say it again:

every time i have a proof by picture,
it takes 4-5 pages of $\LaTeX$ to write out the details!

[sighs]

oh well: it is the weekend and i finally have time to hack out details for research. i shouldn't complain .. but what kind of "frustrated (over)analyst" would i be, otherwise? (:


[1] for those whom are actually curious about the details, i need a suitable partition of $n$-dimensional dyadic cubes so that most of the measure lies either in subsets (a) that are convex polyhedra or (b) whose translates, under suitable unions, form convex polyhedra.