Friday, June 27, 2008

Airports and Math

One of the joys and curses of being a mathematician (in training, anyway) is that one has the option of practicing one's craft nearly anywhere. This leads to some amount of guilt when one has the time but not the inclination to work. What is nice, though, is that when one does have the inclination, there are no barriers, save one's mental state, to reaching out to a world of ideas. 

I spent today in airports and airplanes and had a surprisingly productive day. It was surprising in that I normally require quiet and big chunks of time, but somehow the ambient noise and the small pieces of time worked for me. Whenever I travel I carry pencil and paper, and, waiting for my first flight, I opted to push on a very old idea. I had that rare experience where everything just fell into place. I was able to show that a certain alternate normalization for energy was equivalent to my normalization. It was like bowling four strikes in a row. Everything kept lining up perfectly. It makes me fearful of picking up the next bowling ball, so to speak, because I don't want my luck to end. 

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Thursday, June 26, 2008

Ice Hockey and Airplanes

At the beginning of the summer the captain of a team I used to play with asked if I'd be interested in playing as a sub. I said sure. I haven't played with this team in years. After tonight's game I remember why I stopped playing in this league. It's full of assholes. This league is the entry league where players with no hockey experience, and minimal skating experience start. I think, this allows fantasies of one day joining the NHL. Anything that darkens that fantasy -- like, say, someone who can skate better than you -- causes anger. I got knocked around tonight and endured some childish name-calling, and it isn't like I'm even a good hockey player. In the leagues where I normally play, hockey is not nearly so much a fantasy, but an enjoyable pastime, something that precedes drinking beer. The games are so much friendlier, everyone understands that it truly doesn't matter what happens. Not sure how much I'll keep subbing in with my old team. Mostly it just pisses me off that I let things get under my skin. 

Tomorrow I travel to a sort of distant city to attend a conference and give a talk. I've given various versions of this talk five times already. What I would really like to do is get this current paper hammered out, submit it, and start working on something new. I feel like it's been a while since I've been able to sit down with pencil and paper and actually do math.

Wednesday, June 18, 2008

An Interesting Read

I try to stay away from politics since I think it's a divisive topic and I clearly have my biases. Nonetheless the quotes in this post about the December 2000 decision  to deregulate the energy futures market was a fascinating read for me. 

Monday, June 16, 2008

"long double" doesn't seem to work on PPC

Part of my numerical experiments require that I add up lots of different numbers. These numbers can take on a huge range of values. Some of the numbers can be millions of times larger than others. The software I've written uses what is known as a floating point number to represent these values. The term "floating point" comes from the fact that the decimal point is not fixed at a certain place-value in these numbers. The decimal point could come after the ones' place, the tens' place, the thousands' place, or even the one-ten-thousandths' place. This allows us to represent specific values by multiplying as in the following examples

1234 equals 1.234 x 1000 (the decimal comes after the thousands' place)

.05678 equals 5.678 x 1/100 (the decimal comes after the one-hundredths' place)

The crux is that the computer affords only a fixed number of digits after the decimal place. This introduces what is known as roundoff error. If, for example, I only have four digits after the decimal place, then the following addition,

1234 + .05678 = 1234.05678,

will be problematic because the only representation I'm allowed for the answer is 

1.2341 x 1000,

which is not the same as what is computed above. Fortunately computers provide more than four digits after the decimal place. Unfortunately it isn't a lot more, and even more unfortunately it isn't the same from one type of computer to the next. 

Last semester an undergraduate and I came up with a relatively fast algorithm for adding up lots of numbers while minimizing roundoff error. Even so, we still need to measure the error. Instead of looking up the, quite possibly incorrect, answers posted on the web. I found a cute little algorithm for determining the roundoff error more directly. You perform the following sequence of computations

1 + 1/2
1 + 1/4
1 + 1/8
1+ 1/16
.
.
.

Now, none of these calculations should ever give an answer of 1. However, because of the roundoff error, eventually you are adding something to 1 that is so small that it is below the roundoff error for the number 1, and you actually get an answer of 1. This allows you to place an estimate on the roundoff error. The result depends on the type of floating point number you use.

The types of floating point numbers are:
  • float: About seven digits after the decimal point
  • double: Roughly doubles the precision, and gives about fifteen digits after the decimal place
  • long double: Step right up! Take your chances!
I wrote a program to implement the above test for the "long double" and found that it gave garbage answers. I got home and moved the program from my iBook (a computer based on the PowerPC chip) to my Mini (a computer based on an Intel chip) and the problems vanished. I then ran the software on the AMD nodes in the cluster and everything worked. Then I ran the software on the PowerPC blades in the cluster and saw the exact same problems I saw on my iBook. 

So, Yah! I've recognized the issue, but, Boo! I hate hardware! It's a sure sign of society's unraveling that a poor schmuck such as myself should have to wander through a maze of different computer architectures in an effort to do something as basic as adding up a bunch of numbers accurately.

Google is Freaking Me Out!

Ever heard of optical tweezers? Yeah, me neither until my wife built a set in her lab. The latest round of ads on my gmail sidebar included "Building Optical Tweezers? Single Frequency blah blah blah is just what you need!" I've never e-mailed my wife about optical tweezers, I've never sent or received any e-mail about optical tweezers and there it is, in my side bar. The advertisement that should have been sent to my wife. 

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Sunday, June 15, 2008

More Odds and Ends

Some months ago my university's cluster went from a 32-bit OS to a 64-bit OS forcing an end to my numerical experiments until I recompiled. Compiling software for our cluster -- perhaps all clusters, as ours is the only one I've used -- is a big hassle compared to compiling on a laptop. There are a variety of architectures, and a variety of libraries. Getting everything right involves a certain amount of trial an error. Eventually, I went to someone in the cluster support team and asked for help. Everything works now and is running once again. This brings back that familiar itch where I feel a nearly constant need to check the cluster's job queue and see the status of my jobs. Are they running? Are they producing good data? Did anything bad happen while I was away from a computer? 

I'm writing a paper with my advisor. (purely theory, nothing to do with the numerical experiments)(I hope the numerical experiments turn into a paper as well.) I would like to have it accepted for publication before I start looking for jobs, but I'm not sure if that's going to happen. The first part of the process -- getting the mathematics correct -- is done. The second part of the process -- getting the exposition down -- is taking a lot more time than I expected. Our mode of operating is that we'll sit down together and discuss how to best to present the ideas and state the theorems. This is a slow process because, when my advisor really focuses, he produces exposition far superior to mine. My role in this process is to remind him of how exactly the mathematics goes. This is one of the few times in grad school where I can't simply put my head down and work at a problem on my own.  

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Wednesday, June 11, 2008

Getting an E-Sex Change

My gmail sidebar now contains ads that are decidedly targeted at women. Perhaps this is because half my RSS feeds are from blogs written by women. The most recent ad was from a site called something like CatchHimAndKeepHim. The front page told me that I could learn how to keep a man faithful and loving, and the seven things that women do that annoy men and kill intimacy. The prospect of acquiring this knowledge was insufficient motivation for me to proffer an e-mail address to enter the site.

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Test Post

Blogger appears to be having a bad day and this is a test post. 

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Tuesday, June 10, 2008

Odds and Ends

Tonight is the third night in a row that I've played hockey. My gear is simply not drying between games. It's developing a smell that is repugnant on an intellectual level. The smell is a blend of extremely sweet and spicy mexican. Neither of these smells are particularly bad in and of themselves. But when this mixture assaults you just after the sound of a hockey bag unzipping, and sight of soggy shoulder pads being lifted out, some part of the brain tells you, "Great Fuck! That smell should not follow the sound of a hockey bag unzipping and the sight of soggy shoulder pads being lifted out!" 

It's my hypothesis that one's own stink is more repulsive to others than it is to one's self, and I find my own stink pretty repulsive. Indeed, when I open my hockey bag, I instinctively move my head so as to avoid the smell, as if the diffusion of extremely sweet and spicy mexican is somehow constrained to certain volumes of space around the bag. It doesn't work. I have another game tomorrow night and I feel truly sorry for my teammates. 

An old girlfriend wrote me. I had not spoken with this person in nearly eight years, and then two days ago my inbox had an e-mail whose subject was my name followed by a question mark. The emotions were complicated. We didn't part on the best of terms, but after years (like five) I realized that I had a place in my heart for this person and that I truly wanted her to do well and be happy. She sounds like she is doing well, and I'm glad. Most interesting is the collision of the memories of overwhelming emotions and the inescapable fact neither of us are remotely the same as we were when we were together. 

Roger Daltrey has a song 'After the fire' and the lyric that always catches me is "After the fire, the fire still burns. The heart grows older, but never, ever learns." It sounds so romantic -- love never dies! But it does because, ultimately, the love that Daltrey is singing about isn't really love but infatuation. One of the most depressing parts of getting older is recognizing infatuation for what it is. It is such a lovely illusion, and the world seems flatter and duller without it. 

The only things in this life that I regret are the times I didn't treat people as I feel like I should have. At times this ex-girlfriend treated me quite shabbily, but that doesn't balance out the times I didn't treat her with respect. The dream I have is that everyone -- ex-girl friends, former bosses, the guy I cut off in traffic the other day -- can meet in a place where love can occur unhindered by all our needs and insecurities. Certain religious texts say that there is no end, only endless cycles, but this idea of a place where love reigns supreme really would be the end. 

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Thursday, June 5, 2008

Personalities In Academia

I've pared down the list of RSS feeds to which I subscribe, and I'm returning to news websites to get my news. I wasn't better informed scrolling through hundred of unread items every day. While there is certainly bias in how news outlets choose the front page stories, I'm willing to accept this in exchange for some ordering by importance of the stories presented to me. The result is that I can spend more time reading the blogs that Google Reader has suggested to me. A number of which are by women in science or math and are quite good. (I should add them to my blog-roll)(eesh, I don't like that term at all.) Not surprisingly, a few of the posts are about being a woman in a male dominated field. 

As a guy I'm less likely to see sexism, although a few women in my department have described encounters with men that were simply shocking. Even if there were some doubt of the veracity of these stories, the percentage of women in my department decreases as one goes up the ranks -- there are a fair number of female grad students, proportionally fewer female post-docs, and only one woman on the tenure track -- suggesting something widespread that causes women to leave math at a rate higher than men. What makes sexism so pernicious is that it isn't the only hurdle in academia. For example, a visiting professor told me of a department at a large university where the topologists and geometers were trying to drive the analysts out. (I'm an analyst, by the way.) A woman looking back on the wreckage that was once a promising career might have a hard time ascertaining the degree to which sexism was to blame. 

When compared to the software world I left, there are some striking characteristics associated with academia that, I think, make it more susceptible to sexism. First, the skills associated with software engineering are much more easily delineated and can be assessed quickly. Many of the places I've worked had a technical component to the interview process. While this isn't always the most enjoyable part of the interview process, it does allow a technically savvy interviewer to get a general sense of the interviewees skills in a matter of minutes. By comparison, if a math department were hiring a graph theorist and didn't already have a graph theorist, it would be quite difficult to understand the interviewees technical strengths. I imagine that the hiring process would be based more on the personalities of the people involved. Second, the supply of good software engineers does not meet demand, so once someone has been hired and demonstrated her or himself to be competent, managers will bend over backward to keep him or her happy, even if this person is socially different. As you might imagine, this happens from time to time in the software world. Again, assessing the competence of an employee is easier in the software world, and the employee isn't on the hook to sell her or himself. Finally, software offers avenues of advancement other than promotion e.g. learning new languages and honing one's design skills. Indeed, I've met software engineers who actively avoided promotion. The upshot of all this is that, compared to academia, software does a better job assessing people based on objective measures of skill, does a better job supporting people doing software, and provides avenues for growth without competition.

Whether these factors play a role in the lack of women in math, I can say that its my experience that women are not nearly as underrepresented in software. At all the large software places I've worked many of the top engineering positions were held by women who did great jobs. It's a little weird going to conferences and seeing so few women.   




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Monday, June 2, 2008

Hockey Tournament

I spent last weekend at a hockey tournament in Knoxville where my team, in the championship game, beat a team we had no business beating. With the exception of two people, everyone on their team was under thirty. With the exception of three people, everyone on our team was over thirty. They were all fast and had clearly played and practiced together a lot. They had a team cheer and wore matching, deliberately mismatched socks -- everyone on their team wore one solid yellow sock, and one solid black sock in keeping with the yellow and black jerseys.

Our jerseys and socks reflected who we were: rink rats who travel around with hockey bags full of old jerseys from the various teams we've played on. At the beginning of each game our captain would say, "Alright, we're going with blue tonight." Everyone would dig into their bag looking for an approximately blue jersey. The extra blue jerseys were tossed across the locker room to those who didn't have one. We always made it to the ice with at least four Nashville rec-league teams represented. Our socks truly didn't match and, in many cases, were grimy and full of holes. One of the older guys was in his fifties and wore a similarly aged helmet that looked like it would do little more than a knit cap in the event of an impact. I knew most of the guys on our team in as much as I had probably played a game with or against them at some point. The exact team with which we arrived at the tournament had never played together. 

Friday night we gelled quickly, crushing the first team we played by a margin wide enough to make me wonder if we were in the wrong league. Saturday afternoon we beat another team but by a much narrower margin -- one of the things about tournaments is that the games get harder as the tournament progresses. Saturday night we played the team that we would meet again in the championship. We tied them after a game that left us feeling more exhausted than they looked. Prior plans to stay out late at various bars and parties were scrapped as most people decided that they were going to find some dinner and crash.

Sunday morning most of us awoke to tired legs and an overall sense of fatigue. It took me several cups of coffee to begin to feel like I was fully awake. We checked out of our hotel, and more or less napped in the lobby, waiting to go to the rink for the final game. Driving over all I could think was that we really needed to turn up the energy if we were to stand a chance, but that didn't I feel like I had much energy left. In the cool locker room we pulled on damp hockey gear that hadn't had a chance to dry from the game eighteen hours earlier. I definitely did not feel pumped up. I learned later that the refs who had watched prior games of both teams thought, in spite of the previous night's tie, we didn't have a chance. 

The game started and we came out strong, controlling the puck in their end and making shot after shot. After about two minutes the other team decided that they'd had enough, and our domination came to an end. Our strengths lay in the experience of our older players who could stick handle through traffic and set up plays. We also had an exceptional goalie. Their strengths were that they were all fast, didn't fold under pressure, and were really good at finding each other on the ice. This was a problem for me. I'm not one of the stronger players on our team mostly because I'm not particularly good at stick handling. My one skill is speed. Normally, I can chase someone to the puck and, if I don't get there first, at least pressure the guy into making a bad pass or coughing up the puck. But I wasn't faster than them, and they were still making good, crisp passes to their teammates who raced back to get open. When they were in our end, they would do a good job cycling low and getting someone open in front of our net. This was how they got the first goal. We came back quickly with a goal or our own to tie it up before the end of the first half of the two period game. I sat on the bench between periods trying not to think about how tired I was, how hard we'd have to work, and how my efforts seemed neutralized by their skill and stamina. I thought that whatever happens, at least we were able to hang with these guys for the first half of the game, we hadn't embarrassed ourselves. I felt like I was playing better hockey than I had in a long time and felt proud to be on our team of beer drinkers, divorcees, sales-reps and parents.

The final period wore us down. Shifts got shorter, our team was visibly getting tired. On several occasions we stalled out on their blue line because someone was just too exhausted to hustle to get back on-sides after the puck came out. With maybe ten minutes left they scored a second goal and a whoop went up from their bench like they had won the whole thing. One of our older players offered this concise pep talk, "Get to the fucking puck! Don't fuck around!" With maybe six minutes left we caught a break and found the back of the net, tying it up at two all. As the clock ran down the other team fought with extraordinary tenacity, at times our defense began to break down but we managed to hold them at bay. 

When the buzzer sounded, I was happy we hadn't lost, but the three minute, sudden-death overtime seemed like an impossible task. No one was talking, everyone was trying to catch their breath. Our strongest center came out to start. He has formidable skills, but wasn't able to find an opening. A moment later his son, playing wing, flew in on a breakaway and didn't quite find the back of the net. The next line went and made no progresses in the face of their defense. Finally it was my turn. I went over the boards and the game wound up in our end. They were doing what they were strongest at, making clean passes through traffic and getting someone open. Then one of our defense picked off a pass. Their defense were wide and had pinched in. I curled around and blasted out of our zone optimistically hoping that our defense man with the puck could get it to me. He looked up ice, saw me, and threw the puck. It bounced just beyond the reach of their defense who were now fifteen feet behind me. I managed to get my stick out to touch the puck  slowing it down enough to get control over it near the red line. I crossed the blue line, their goalie wasn't coming out to challenge me, and this gave me a second. I saw a spot between his legs (and didn't trust my skills enough to try a higher shot.)  

I buried it between his legs in the back of the net. 

It wasn't until I blew past the net and saw the puck that I realized the game was over and that we had won. I felt an amazing an unexpected sense of elation. I didn't think I cared about hockey that much. But I did, I really cared about hockey. At that moment I cared about nothing else. My teammates were pouring over the boards coming to give me a hug, and clap me on the back. The sense of gratification was so strong and so unalloyed. I was skating back to my team with my stick clenched over my head yelling, "Yes!" at the top of my lungs over and over. It was such an impossible but natural story: I scored the overtime goal that won the incredibly difficult championship game. 

I hide my happy memories away for safe keeping so they don't wear out from overuse. Nevertheless, the memory of the precise mix of emotions I felt at that moment will eventually fade and become a fact in my history rather than something I can call up to bring me happiness. What will remain is the memory that what I felt was so strong that I couldn't hide it, and didn't want to hide it. I felt so happy, in fact, that I could do little besides yell at the top of my lungs incoherently.

Some years ago I realize that there is peace to be had in this life, but there was always a resignation associated with it. Yesterday offered the possibility that the peace might come with a sense of triumph and joy.