Monday, December 15, 2008

Research vs Homework

i don't know how these two things differ in other fields, but it seems there's a key difference between research and homework. Sure, they both involve solving problems, generally using methods previously discovered. But homework is normally structured in a much nicer format than research. Generally homework questions come at the end of a chapter which just introduced a new theoretical framework for solving problems. So these homework problems will generally just test a student's ability to put this theoretical framework into action (even if its the theoretical action of a proof). Sometimes these problems will ask you to go back a few chapters and use other theoretical work as well, but thats the most they ask.

Research is a different beast in itself. The research problems are generally just concepts that somebody notices or thinks up, so something that can seem obvious may be really hard to prove (see Goldbach Conjecture). Further, there's no general recipe for all the type of things you'll need in research. And if it happens that you need something that you haven't yet learned, then I guess you've got some studying to do.

I'm thinking about this right now because I just finished working on a research problem that was pretty annoying. When I first heard the problem proposed, I knew very little about integer programming or linear programming. I had related the problem to the Maximum Independent Set (MIS) problem and felt pretty annoyed that because the MIS problem is NP-Complete (lets just say really hard), I wouldn't be able to get further. Back then, I simply wrote computer programs to try to enumerate all the feasible solutions - but stopped when I was able to prove that the programs would take a long LONG time to finish. I was able to solve some smaller instances of the problem by hand and left the larger instances alone.

Well this weekend, I went back to the larger instances. Initially I started with some of those same thoughts, and the lazy programmer in me just wanted to write a nested for loop and call it a day. But again, being able to see how long that program would take to run, I kept doing things to increase the running time of the program and was able to finish up that larger case.

The key improvement I made this weekend was formulating the problem as an integer program and solving the LP relaxation (with a little bit of branch and bound). This seems like such an obvious way to approach the problem to my mind today, but I received so much resistance from my co-authors when I initially proposed this as a way of tackling this problem that I just gave in. But after they were unable to move past a few different enumeration techniques, this idea came back into my head with positive results.

I'm trying to wrap my head around this whole "research" concept. I know that I fell in love with it in undergrad, but each problem seems to possess its own uniqueness. I remember when I was taking proof based math classes, I would systematically attack homework problems:
- What am I trying to prove?
- What are the key terms in the assumption?
- What are the key terms in the conclusion?
- Are there any theorems that relate these key terms?

Normally by the time I've gotten to the fourth question, I can get to a proof. Its not so simple in research. First of all, I don't generally know what I'm trying to prove, except that its unproven. Sometimes, its helpful to make a claim like "I'm trying to prove a matrix is totally unimodular", but if I'm unable then it doesn't mean that the matirxis NOT totally unimodular, it means that I haven't proven that it is totally unimodular.

Second, I'm normally asking a question that can be formulated in many different ways. So the idea of key terms depends a whole lot on which format I choose to work with. Sometimes it doesn't matter, but other times after the research has been completed I'll see why I couldn't have come to the same result with a different format. But things are always easier after the fact.

And third, unlike homework where we're working out of a standard text book, research is just building on whats already been done. There may be a theorem that was discovered last month (and hence not in any text book) that helps me to proceed with a given format. But I won't know this by simply looking at a text book. So another part of it is looking back and forth at research journals and publications. Or as was the case with this weekend, I may need to look at other areas. This may provide me with a different way of looking at the problem that makes the question being asked more concrete.

But I do think that the way I learned to break down homework problems can be an effective way of doing research, but its a much more iterative process (hence the "re" in research).

Saturday, December 6, 2008

Blinded by Love

I was blinnnnnnd
dead by love
of the friendship we had built.
I had never
thought of you in that way
I had never
until that day
that we became more than friends.
It seemed so right
it seemed just like
it was meant to be
til that day when we
talked about dating seriously
I don't know why we disagreed
maybe it was something about me
or maybe you never liked me
but that breakup really hurt me.

I was blinnnnnd
dead by love
or was it love
or was it just us
was it just us
laying there in the bed
til the condom slipped off
and I lost my head
wondering if we should wed
til the condom slipped off
and you came and said
that your friend
missed a month.

I was blind
dead by love
by images of you and me
living happily
that made me
lose sight
of reality
my immagination ran away with me
you played my heart
had me write you
even after you had told me
it wasn't meant to be
I blamed me
wanted to do things differently
to go back in time
and make you love me.

Monday, December 1, 2008

Me and Math

I've just gotta say that I love math. I really don't hear that enough in my everyday life. It seems like many people around me, even in academia, see math as merely a means to an end, or as high school hurdle that they once stumbled over and thankfully never have to use again. Well, this is not a blog to convince anybody else to like math. Its just an expression of how much I like math.

I feel like I was introduced to math kinda by mistake. What I mean by 'math' here is the math I took after set theory. See, prior to this stuff, I pretty much hated math. I especially hated that we weren't allowed to use programming calculators on tests. See, I had somewhat of an affair with computer programming back in high school. This affair lasted until about my sophomore or junior year of college.

I always thought that math was stupid. My theory was who wants to sit and add up numbers all day? What would be the point of just using formulas that have already been discovered? I especially grew irritated when I would learn something like the Law of Sines, Law of Cosines, how to invert a matrix, or how to use row reduction to solve a system of equations. I would learn these things first by programming things into a calculator. Then I was told I couldn't use these programs on tests, which only frustrated my relationship with math. What's the point of using 20th century teaching methods to teach math to a 21st century classroom?

I remember entering college with a major in computer science. I was a pretty good programmer and this was the middle of the dot com era, when everybody was making money on the Internet. It just so happened that a computer science major at my undergrad consists of so many math classes that all I needed to have a math minor were a few classes - among these classes was set theory.

Set theory was a class that changed my life.

This class was like philosophy and debate for mathematicians, complete with paradoxes and all. But this was more structured than my debate classes in high school. In high school, we had topics like "Capital Punishment is Justified" and had to argue either the affirmative or the negative. The person who won was the person who made the better arguments or spoke more eloquently - not the one who spoke the truth (because truth here is ambiguous).

In math, its all about the truth! We assume only the basic necessities (which are agreed upon) and prove EVERYTHING else. There's no room for ambiguity and no room for errors. That's just beautiful to me.

I remember when I first proved the irrationality sqrt(2). All through middle school, I can remember being told that certain numbers are irrational, but never really understood what that meant or why it was true. When I first saw that proof, it was just an amazing sight. And the most beautiful thing is that each step followed logically from the one before it, and step one was just a statement of the assumption. There was no citing a survey, or claim that "correlation implies causation".

It was just pure beauty. And what made it more beautiful was its simplicity.

I don't often get to talk with people who share this same love of math, but when I do get such an occurrence I sit and smile.

Today, I'm smiling!

Sunday, November 30, 2008

Let them be artists!!!!

I was just in a discussion about the new show on Comedy Central, "Chocolate News". This seems like an ongoing discussion I'm having with my friends, with me being on different sides at different times.

Basically, the criticism of "Chocolate News" is that it reinforces too many Black stereotypes, and isn't thought provoking enough. I have raised these same criticisms of commercial hip hop today. I bring this up because I do understand this criticism and I feel it has its place. But I feel that its being used too often to generalize too many things.

There are claims that "Chocolate News" is not thought provoking and only reinforces stereotypes. I watched the episode from last Wednesday (11/26) and found it pretty interesting.

There was a skit about Nickelodian hiring a Black guy to do a TV Show. These are some of the questions posed that I'm sure are going on in many of our heads about many of these networks, including:
- why don't they have any Black shows?
- why do the few Black shows that they do have always seem to fail?

That's not to say that the show isn't above criticism, but just because a show has a skit with a Black person with gold teeth it doesn't mean the show can't be thought provoking. I feel like some are so quick to run away from certain labels (stereotypes) of our community that we do everything possible to avoid that label. So what's left - particularly in Black America - is that those of us who are ignoring these labels are unable to understand those of us who have these labels. I know there's a stereotype that Blacks LOVE fried chicken, but there do actually exist Blacks who like fried chicken. So to label any skit that shows an example of this as a reinforcement of stereotypes places a great limit on an artist's creative ability. The same goes for many other stereotypes that it seems like the moment we see one, we're turning into the police and calling an artist names.

These limited views of what's good versus bad reminds me more of how people like C. Delores Tucker and Tipper Gore attacked Hip Hop because it spoke of violence and contained graphic language, ignoring the actual content of the songs. Thats what I feel like is being done with "Chocolate News". I really wonder how many people who are criticizing the show are actually watching it, versus just seeing the commercials and saying "that's not right". What it really reminds me of more is an artist being called 'a sellout' or 'an uncle tom' for sharing his artistic vision.

I know that the show is not above criticism, and I have seen skits that I have been heavily critical of. But I don't like to throw around these trigger words like 'stereotype' without a more precise description of why they believe this.

Wednesday, November 19, 2008

My Weight Loss

I was just reading ThummyB's blog about healthy eating and was inspired to write about my own experiences.

As a result of several men in my family getting sick at about the same time, as well as my Aunt's recent death, I'd been thinking about making some changes in my own life. All through college I had been about 210, and when I got to grad school I went up to about 220. Well, it just so happened that the week that two of my uncles had strokes I was at about 230 (all while my liscense said I weigh 185). Add to that that my father has diabetes and its not too hard to imagine that I was concerned about my weight.

And its not that I hadn't tried weight loss before. I tried some things similar to the Atkins diet, I tried a high fiber diet, I tried working out more....I tried a lot of things. But after about a week or so of each, I wasn't getting results and so my impatient self would go back to my old eating habits.

It wasn't until I started dating a vegetarian that the idea came to me to actually start eating more vegetables. I also had the privilege of going with my dad to see his nutritionist, who recommended that we both eat more vegetables.

But this was an age old thing that grandma had been telling me for ages. This couldn't be the answer.

Well, I was a bit more serious about eating healthy and definitely focused on this. I wasn't even thinking about weight loss, except that I probably wouldn't lose any weight without working out, and since I'm too lazy to work out regularly I decided not to focus on weight loss.

But what I started doing was steaming my vegetables. I give much props to Steamfresh vegetables for coming out with a product I could just stick in the microwave and 5 minutes and 30 seconds later, I'd have a meal.

Now if you ask my friends, they'll say I went crazy with broccoli. I was loving the taste of it, with a little salt sprinkled on. I was literally eating steamed broccoli for breakfast, lunch, and dinner, and snacks in between. For drinks I was drinking diet soda (Orange and Sprite Zero). This went on for about two months, after which I noticed that I had gotten down to about 200.

After those first two months, I relaxed a little and began to eat meat occasionally and experimented with other veggies (like carrots, mushrooms, and spinach). Some nights I would even buy a bag of frozen mixed vegetables and make a stir fry. I still wasn't going to fast food places. And I was rarely eating out at all. I also started drinking tea (with Splenda which tastes like sugar but has no calories) more often.

But the biggest breakthrough (other than the Steamfresh veggies) was the invention of the steam bags. THEY WERE GREAT! Because now, I wasn't limited to the set of veggies that Steamfresh had available. I could choose anything I wanted and just steam it. Plus, instead of baking my chicken (which normally takes about an hour), I could just steam it (for less than 20 minutes). The same goes for fish. I really became a steam-a-holic. I was steaming any and everything that was steamable. I even realized that Boca Burgers (which I buy from Costco) were microwavable.

In addition to these things helping me to lose weight, this dramatically cut down my time in the kitchen. No longer was I spending time cooking and cleaning, but instead I just throw the bags away when I'm done and I'm DONE. That there is a blessing (cause again, I'm a lazy dude).

Overall, I lost 70 pounds (from 230 to 160). And the best part about it is that because I lost it without working out, I didn't have to change my eating habits to stay at 160. I'm not gonna act like I don't occasionally relax a few times and go up to 165 or 170, but the nicest thing is that once I go back to my 'normal' eating of veggies and chicken and fish and Boca Burgers, I get back down to 160. Thats about the weight I've been since January of this year, and I'm no longer too worried about gaining all that weight back. I just try to stay on top of my weight and know how much I weigh on a daily basis.

Thursday, July 24, 2008

That Problem

I'm that problem right in front of you trying to appeal to your context clues, so I make up some names and I tell you a story hoping I entertain you enough
that you don't ignore me and pass along to my friends down the way thinking they've got something better to say.

Now I see the look on your face and I know I'm why you hate this place I've seen it before and though nothing is said I know exactly whats going through your head. Sometimes its "why me, sometimes its "if only ...", sometimes its "it would be so great if I could just relate". I can see that from just looking at you but can you tell that I'm thinking that too?

Some say they feel bad and give me an excuse. Some say their parents said they shouldn't do it. But there's a word goin round that just hurts my ears some people are sayin the only reason I'm here is to make you feel shame like I'm the one to blame. They say to ignore me is what you should do and to do it quickly before I get to you. They say that "only a few can help me" and those that can will do so eventually. So they say "pass on by" and not to even try when in life or in class you're met with that problem in math.

Wednesday, July 23, 2008

My Thoughts

My thoughts are dramatic been locked away in the attick for years and only brought to life through fears of death, but on they last breath they decided to take a stand against envy and jealousy, against greed and conspiracy, against all the corruption I see. Honestly, these thoughts are a new breed that breeds on themselves see its impossible to keep em locked on shelves. Now I've got people tellin me what they mean - tryin to imply that I'm mean, sayin they know better than me. I'm the center of conspiracy theories. I've got people comin to get me. They tryin to silence me. They tryin to keep me quiet, scared I might start a riot, cause I can explain the game they use to keep people tame, and I use words that you can relate to, so you wont walk away all confused. I've got thoughts that'll take you to class while we on the court make you miss that layup, turn around like "what the fuck?". Some say I've mastered the mysterious. Some say its just sadness and mischievous. Enemies wish I just sat back eatin Cheerios, But I've got a brain to pick
while they pickin they nose.
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