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Losing my religion (or my faith is shaken)

In which the mathematician gets emo

I think it's time I come to admit this. I'm not doing as much mathematics as I should be doing, and this suddenly doesn't seem all that catastrophic. My brain is burning out, the spark is dying out, and the most horrific thing is that I can't even decide if I ever had a spark to begin with or not. Or if it's not burnout, at least it's sleeping...

I've always liked mathematics. I've always had a bit of a knack for it. I could understand and work through the concepts. I was enthralled by the subject and the deep mysteries. Once in a while, I would shine.

I was looking at the past Putnam exam questions today. In other times, I would have attempted to answer a few of them, but today, when I was looking at it, I couldn't think of how to approach any of them. Worse, I didn't even feel a tug, an itch, a desire to attempt to answer any of them.

This is bad. A mathematician that doesn't feel an urge to solve problems thrown at him is a dead mathematician (in the Erdosian sense).

Last night I was trying to puzzle out how to incorporate some boundary conditions into some shallow-water equations I was solving numerically in such a way that I could still use essentially the same numerical method and still be able to get a decent solution after leaving the computer munching on it overnight. It must have been the first time in months since I picked up a pen and started scribbling on paper. I can't even remember the last time that I actually spent hours filling pages upon pages with calculations (I call this using the swap partition, heh). It was difficult. At one point, to check some differentiations, I used Maxima. I'm getting lazy, I guess, a virtue in a coder, but a vice in a mathematician. And in the end, it was all hopelessly trivial, and the only thing I could think I could do was to recast the equations with a stupid change of variable that simplified one of the equations in the system but complicated the other two, and to iterate the boundary conditions on those two equations hopefully getting convergence. There was a minor division by zero problem there, which would arise in getting a singular matrix, but easy to work around with.

For those of you still with me, the language above doesn't matter. There may be unfamiliar words there, but believe me: it was absolutely trivial. There were no deep concepts involved, no insights, nothing. Blank. This scares me to death.

Thing is, it shouldn't be like this. It is a stereotype that applied mathematics is less creative than pure mathematics, that it simply involves using recipes to get answers. There may be some truth in this, as I have spent an inordinate amount of time in the last few months doing nothing but coding instead of creating mathematics. Sure, there's creativity in coding, but after a while it gets quite mechanical. But back to applied mathematics, there's lots in there that requires creativity on the theoretical side, proving our algorithms converge, proving our equations have solutions, proving regularity conditions. I've been reading books on the subject, on functional analysis, on Schwarz distributions, on Sobolev spaces, which is all the machinery behind the proofs, say, of existence and uniqueness of the 2d Navier-Stokes equations (the 3d case is the current holy grail in the subject, the 2d case is apparently much easier).

The whole flavour of this subject, however, fails to excite me. I thought it would with time, but it hasn't. It's just that with analysis there seems to be less tangible objects to play with. Everything is fuzzy and approximation. By this I don't mean that it's in any way not mathematics, not rigourous, merely that the the feel of the subject, of finding the bounding constants, of assimilating complicated definitions of finely varying details1, of sets of measure zero never mattering for anything... It's not as exciting as the worlds of number theory, geometry, or algebra, in their various forms.

In a way, this happened gradually. I was at my best during my undergraduate days. I remember solving my number theory undergrad assignments with relish, with spark, with ingenuity. At some point, I thought that I would be too lonely as a pure mathematician. I'm not sure when this happened. There was a time when I was happiest when I was alone, that my me-time was my best time. That changed radically in university, somehow. Now I need time with others to recharge. I can be alone, but not for very long before I start to feel extremely uncomfortable. Applied mathematics is a much more social activity than pure mathematics for two reasons: 1) you get to interact with many persons who aren't mathematicians themselves, 2) you can actually explain the eventual purpose of what you're doing to almost anyone, not just to other specialists. So these are the reasons for why I made the switch from pure to applied after I graduated from McGill University.

In which our hero sees hope for the future

Wow. I needed to get that out. I haven't quite vocalised it until now. I've been much too afraid to admit publicly that I'm not doing mathematics as much as I would like.

In other times, this would have been terrifying, especially since I was a little kid I've had grand dreams of one day discovering great mathematical truths before anyone else did. But nowadays, this doesn't seem so bad. For one, it seems that I traded the recluse of lonely mathematical discovery for the ability to share more of what I do with others. Also, the fear of not doing mathematics, should I ever distance myself from the subject more than I am now, isn't so terrible either. Languages have long been something that I keep telling myself I could do instead. Coding, if I manage to do it under my terms. I'll find other things to do. Or if not, I can always go back. It's not something that once gone, is gone forever. At McGill I met many competent PhD students who started taking up the subject again after many years of absence from anything academic. I need to relax.

And above all, I can still keep focus: I must save the world. One way or another, big or small, I'll do it. Nothing else matters all that much, at least, not for now.

I'll be ok. I've always been ok.


1 The reason why definitions in analysis seem to be so complicated and nested, (e.g. a vector space is more general than a topological vector space is slightly more general than a normed space which is slightly more general than a Banach space, these last two of which happen to be a metric space which also is a topological space but not a vector space and a Fréchet space fits in this mess somewhere, as do the various Sobolev spaces, and what am I forgetting?) is that analysts like to be able to state theorems with as few assumptions as possible. There seems to be so much work in analysis about seeing if we can drop just one more hypothesis or make one constant just a bit better, so much refinement, and the big ideas are all hidden in convoluted statements of these refinements...

It is 3 a.m. in Georgia and I am sitting on the couch, staring at the backlight of my screen in the dark, unable to sleep. I am almost always unable to sleep in my new home. The bed is the same one that has been in my bedroom since we moved here, but it's in a new room in an apartment leased to my eighteen year old sister. I stare at the walls and I wait and occasionally I sleep, but mostly I lie awake and I think.

It's been raining here, and one afternoon I put a camp chair on the patio and put my legs up on the rail, feet in the rain, and read. Water crawled down my calves, wind blew in my hair, it smelled like earth and I was content. Later, I realized what a sight I must have been. Anyone could fall in love with a picture like that. But there is no one here to see it.

We sold our home on the 28th of July. Everything we have ever owned had to be taken out of the only building we have ever owned and shipped to one of the three new residences being paid for by my family. I find myself wanting to drive by my house (it will always be my house-- I carved our initials in the trees we planted) to see what's been done to it. To see if it still looks the same. I drive back to this apartment, and wonder if I shouldn't miss the house more than I do. It was my first home. It was my only home. I never told it goodbye.

The weight of the house is nothing like the weight of school. I am moving in to a house with 2 people I don't know, with animals for which I don't know how to care, to take classes for which I'm not sure I'm prepared. And as I lay in bed and think about all this pressure, all this stress, all this turmoil, I calm down again.

I am going back to school, which I love.

I am going back to science, which moves me.

I am going back to football, which dictates most of my social interactions.

I am going back to do what I have always meant to do, and there is solace in that. There is comfort in the past, but I am going back to facing the future.

That helps me sleep at night.

Day four of Lost Gems of Yesteryear sees us add 5 writeups to the quest master list. The number of new authors is tricky to pin down, seeing as one nominee is Toaster, noded by a diverse group of users under the everyone account.

I expect we have most of the entries now, so if the submisions taper off you don't have to worry about seeing a day log from me every single day of August. I do hope to put up some interim stats before too much longer, maybe once per week of the quest.

Please do read and vote ... that part of the quest continues all month. I hope to hear some nominees on H's podcast ... I'm sure he'd love to have some of you read some of these writeups for us.

Writeups nominated on or about 4 August 2007:


Brawl's choice: The Great Figure

One of my choices is The Great Figure by Lometa.

When I was young, my father was a fireman at an industrial park in small-town Ontario, Canada. I never got to see him actually ply his trade at a call, but we did get to hang around the fire hall a bit. Sometimes the firemen on duty would dress us kids in boots and a coat, and then for a good laugh put us into Scott air packs and leave us immobilized by the combined weight and bulk of the getup. But we also got to see and climb on the gleaming fire engines. We got to 'help' roll up hose and otherwise get underfoot in the fire hall.

Like may young boys, I wanted to be a fireman. When your dad is a fireman, the itch strikes you that much harder. It was heroic, it was physical, but most of all it involved a big, noisy, shiny truck that went places at high speed. We'd play fire hall all summer as kids. We mostly rode around on our bikes, imagining the trucks and making siren sounds. Getting there was all the fun.

In real life, it turned out that a fireman's life was not for me. Instead I spend my working days in a little yellow box of an office, with no windows, no special uniform, and no heroism. Deep down, I still want to be a fireman, to race to battle with a fiery beast and to save homes and cats and such. I always watch fire trucks rush by with a bit of wistfulness. Once I saw a pumper truck catch some air cresting a hill in San Francisco, racing to a call on the streets of San Francisco. The only thing cooler than a fire truck is a flying fire truck!

Anyway, reading The Great Figure when it was posted caused me to look for Demuth's "I Saw the Figure 5 in Gold". When I saw the painting, I knew that someday I would want a print. I'm no judge of art. I cannot speak to technique or composition. It doesn't even make me think of a great emergency vehicle flashing by, particularly. But it's big and strong and bold. My wife got me a print last Christmas. We had it framed and it hangs over the mantle. You might be able to see it this month on my home node, if e2's image service cooperates.

Lometa is perhaps one of the site's best known and best loved authors. Her writeups are not only erudite and educational, but crisply laid out and elegantly formatted. Lometa manages to bend e2's limited text options to her will, mixing indentation and decoration to pleasing effect. I knew I wanted a Lometa for the quest. I picked this one for its personal appeal rather than to call it out as her 'best'. Frankly, almost all of her work is 'best'. A new writeup from Lometa is always a gift, and I hope she returns from her recent hiatus ready to share more with us.

A day or two ago, I remembered that I'd wanted to submit a choice for Lord Brawl's Lost Gems of Yesteryear quest and hadn't done so yet. It's a nice opportunity to bring a favorite writeup back to the fore, and so I went traipsing through the bookmarks on my homenode. It was a hard but enjoyable decision, and I settled on Why the Willow Weeps by our Halspal.

Now, Halspal is known to many of us around here. He used to be our Senior Editor, and he's been a noder apparently since God was a boy. Halspal seems to elicit all sorts of emotions from various people ... but love 'im or hate 'im, you can't deny his way with words. I regard him as an online friend and think he's one of our best storytellers.

I don't remember when I first read Why the Willow Weeps, but I can sure remember how I felt after reading it. See, like many I've lost a few dear family members to cancer, including my grandfather, who fought lung cancer with all the grit an old Kentuckian can muster (and that's a lot of grit). Halspal's piece brought all those memories back up, and no matter how many times I read Willow, I still get that old mist in my eyes. It may not be a true story (I don't know), but I sure want it to be true. Give it, and the other fine works included in the Quest, a try. They'll make you proud to be part of this E2 thing.



The ten Haaf Shuffle



She sat at a cocktail table. My hand shook.

I imagined the vodka-full highball bouncing off her shiny, happy forehead. A pretend red throbbing welt rose from beneath sticky strands of hair. Blood? Maybe.

I smiled. She smiled. I set the glass on the table. Sans coaster. Oh, and could she also order a classic pizza? No green peppers, add onion.

Kay. No problem. It'll be out in a second. And yeah, I'll bring an extra lime. And yeah, I'll make it a double-tall next round. Sure, I've got an extra coaster around here somewhere.

Hey Jonesy, some guy just puked in the bathroom. Oh and do you have change for a hundred?

After a few days in Israel, the stench washed away. My hair was free of cigarette smoke. My fingernails absent bar mung. My skin not gooey gross with a mixture of beer, red bull, and whiskey. I almost believed I was a jet-setting, cash-dropping, well-bred, designer-wearing, passport-touting, world-traveler.

It was my first wedding in years. But for a wedding underdog, I was now the nuptials comeback king. Champagne flowed like PBR. Hors d'oeuvres passed out like french fries. The dance floor was full. The beach was empty. The buffet was all-you-can-eat. And of the two wedding party standards--drinking like a fish and making out with complete strangers--I was destined to perform the prior.

Hey Jonesy, some guy just walked out with a beer. Oh and can I get a sandwich to go?

I actually looked like a human being. I wore a designer dress I bought on consignment. The tag said forty, I negotiated twenty. The lace ballet flats were a size too small and clearance for ten. Drop earrings? Two bucks from Wal-Mart.

I looked like a million. Okay. Maybe a quarter of a million. Okay. Maybe a hundred.

The crashing waves covered the thumping disco-rave-tech beat. I popped off my shoes, sipped my champagne, and comfortably evaluated my sister's discount for Future Ex-suitor Number Three. Suitor Number Four waited in the wings. A Hall and Oates song came to mind.

I was relieved to be alone without smiling-and-nodding to eight different languages I didn't understand spoken by fifty people I didn't know.

"Why aren't you dancing?"

I looked back to see the Dutch guy I awkwardly kissed-kissed-kissed hello at entrance. (Three in the Netherlands? Is that really necessary?) He was covered in sweat. His shirt half open, his smile ear-to-ear.

"My feet hurt," I replied

Hey Jonesy, that dude just grabbed some chick's ass. Oh and can I get another Jack on the rocks?

"But your shoes are flat," he laughed.

"Flat does not equal comfortable."

No, my Dutch friend. I am not easy prey. No, I am not lonely. And no, I don't need to be entertained while my sister performs a sexy dance with some female Mediterranean beauty for fifty drooling Hebrews. (Future Ex-Suitor Number Four was about to bite the dust, by the way. Number Two was staging a comeback.)

So, Little Dutch Boy, take your pity conversation and your wooden shoes and tulips back out on the dance floor. Please. Queue up Ex-suitor Number Six. I don't need your company. This is, in fact, the best moment of my life. And I'm happy. And the only thing making me unhappy is your thinking your speaking to me is somehow comforting.

He plopped down next to me. His hair was red. He was charming. He was an actor.

I hate actors.

Thirty minutes earlier I ripped a cigarette out of his mouth and smoked it like my plane was going down. No nicotine in five days courtesy my sister's disdain. Sixty minutes earlier? He asked what I did for a living. "I'm a cocktail waitress." Long pause. Silence. Uncomfortable ballet flat shuffle. "I want to be a writer, but..." I made the universal sign for cash. Ninety minutes? Kiss-kiss-kiss and introductions. Jochum, Alaina. Alaina, Jochum.

Hey Jonesy, some guy is passed out in puke on the back patio. Oh and can I get some darts and a Jager Bomb?

A conversation started smoothly. He liked Star Wars, Chuck Palahniuk, and the Cohen Brothers. He hated New York, but loved Amsterdam. And yes, he stared on Broadway.

"Are you famous or something?" I asked.

"In the Netherlands," he replied with a like that fucking matters disregard. His hands moved expressively. He lit my cigarette. He was smiling and humble and jovial and genuine and full of light sarcasm.

Yep. He was everything I never wanted in another person. Happy. Happy and courteous. Happy and courteous and smitten with me.

And then the discomfort flooded back in. Good-bye adjectives modifying titles of glory. I felt gauche and ugly and lonely. I could smell the cigarette smoke in my hair again. I scraped under my fingernails for dirt. He reached for my hand, but I could feel a sticky film covering it. Was that a wine stain on my dress? Was that beer running down my legs? Broken glass in my shoe?

I wanted to tell him of my complete and total failure as a writer. Five years since a publication. Five years of silence. Five years of other people's voices screaming over me. Five years of passing out red headed sluts to red headed sluts with no end in sight.

I kept my mouth shut.

Hey Jonesy, I think that guy just punched the door-guy and now his nose is bleeding all over the floor. Oh and can you change the channel to the hockey game?

He smiled sweetly. I prayed for a segue.

My sister piled into the chair across from us. Half-slurred, champagne dangling from her hand, "Djew wanna dance?"

So I danced with the Dutch acteur. Fast and slow. I shifted my hand in his but finally opted for the promdate shuffle. He looked in my eyes like there was something beautiful to be found there. But I knew better.

I looked away.

I saw my sister leaning against the host signing a familiar, extravagantly drunk language. Her lips moved in slow motion. She wanted a cab.

"I have to gather my sister," I whispered.

"She's fine." Then he looked back at the type of train wreck I man on a nightly basis.

"Okay. Go get her," he conceded.

We began the kiss-kiss-kiss goodbye ritual, but he finished by softly brushing his lips against mine. And he grabbed for my hand as I walked away. And yeah. I walked away.

Fucking actors and their fucking curtain calls. I'll give you a bow, Bucko.

Hey Jonesy, some dude just smashed his car into that lightpole across the street. Oh and can you get us another round of shots? Dealer's choice.

I walked out to her table holding a pie covered in green peppers. No onions to be found.

Yeah, I can have Dean make another pizza. Oh and I'll be right back with the vodka. Two limes this time? Sure. Double tall? Sure.

The toilet is overflowing. The ladies room needs paper towels. The band needs to set up. We're out of candles, PBR, Jack Daniels, wine glasses, bar towels, bathroom cleaner, and kitty litter. Did I remember to clock in?

Hey Jonesy, that Dutch guy wanted to take you away from all this, but he can't save you. Oh and can I buy you a shot?

Maker's Mark. Double. Thanks.

Oh and forget what I said before, Random Kind Patron.

I do belong here.

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