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After a few conversations with Phillip about the whole cat-recognition problem thing, I’ve decided to do a bit of reading in a book I bought a few weeks ago, as well as some light research on Wikipedia on computer vision.  Well, it didn’t take long for me to hit upon a few helpful articles:

SIFT (Scale-invariant feature transform) Algorithm

Difference of Gaussians

Object Recognition

The only problem is that when we are considering a live, breathing cat, we probably wouldn’t see much of any clean linear transformations in the space we’re working with (imagine a cat who curls up in a ball from a standing position.)  But there’s still a lot more reading I have to do about this stuff before I can say any more about it…

This is mostly for my own knowledge, and probably not for hardcore scientific applications.  Why am I asking this question in the first place, then?  Because I’m trying to figure out whether it’s worthwhile in maybe building a super cheap (and hopefully low power) Beowulf cluster to run at home in order to learn more about the nuances of such a configuration.  I’ve been reading an ebook on the motivations behind building such a beast in the first place, and though of course it helps enormously in running scientific data through the cluster, I’m largely untrained when it comes to any sort of science.

So… what the hell can I do with a (hobbyist) Beowulf cluster?

I suppose I should write something about this topic.

These five years have been pretty awesome; I’ve learned a lot about many different subjects and developed a lot of appreciation for topics that I’ve never thought I’d be interested in.  For instance, I’ve learned to appreciate literature in different ways than I’ve ever imagined, from learning about the ties between “Frankenstein” and the movie “Blade Runner,” to learning about (I think) the differences between an act (or duty?) and a wish, both with the novel “War and Peace” and with the lineup of films by Stanley Kubrick (I’ll have to thank Willis Konick for that, he was probably one of my most favorite professors that I’ve had the pleasure of taking two classes from.)

My conception of what math was all about was thoroughly smashed apart by the time I got to my sophomore year as well.  And after that happened, my interest in it only increased.  I hadn’t done all too well, but my interest has been fairly steady, and I think I wouldn’t have been acquainted with the subject all too well if I hadn’t forced myself to go through the classes.

I also thought that I wasn’t all too interested in philosophy when I started taking it at the UW, though the logic and set theory classes sucked me in.  (When I started taking classes in philosophy, I had Leroy Searle’s “Method, Imagination and Inquiry” in mind the entire time; I felt like I was left disappointed when I saw that most classes weren’t about some sort of historical narrative when it came to stringing together the different philosophical positions in each class.)

But other than academic stuff, I’ve also learned a lot about myself and about the world around me.  I’ve probably changed the most as a person during these past five years and broke apart many misconceptions I’ve had about the world… sorta.  Well, I feel that I’m at least in a better spot when it comes to critically looking at my own position and other’s positions and maybe coming to some sort of conclusion.  But overall, I’ve at least started experiencing the world in a much bigger way than I’ve ever had before.  I’ve met a lot of great people with friendships coming and going and had quite a few memorable experiences that I wouldn’t trade with anything.

Overall, I’ve become a hell of a lot more curious about the world and I’ve started to temper myself into becoming a better person.  I think that’s what’s college is about: it’s training us to become more curious about the world and develop ourselves into better citizens.  I don’t think it’s necessarily about getting ourselves into a career path, since all of us start on the bottom once we leave college; we learn to be curious, which opens us up for more learning.

Anyway, it’s been a great five years, and I’m glad to be through with the whole damn thing.  Maybe graduate school will be in the horizon sometime soon…

Breakout, the game

So, I’ve been trying to figure out how to code the game “Breakout” from scratch as an exercise in game development.  One of the things that I’ve been trying to flesh out is how to model the behavior of the ball as it hits the different parts of the paddle.  For one, the ball should change it’s angle so that it travels more to the left (if it hits the left side of the paddle) or more to the right (if it hits the right side).  Second, if it hits the “dead zone” in the center, then the angle should be preserved (so the “dead zone” will be a few pixels wide, so that the player doesn’t have to be super precise when he wants the ball to travel with the same direction.)  Third, if we are representing the ball’s motion with a vector, then the “x-axis” vector (I put “x-axis” in quotes for a reason, which will be explained in a little bit) should not change, while the “y-axis” vector will be flipped in direction (so if the ball was traveling down and left, then the ball will still travel left, but will now be traveling up instead.)

Using a bit of geometry and trig, we want the y-axis vector to be multiplied by -1 so that the orientation is flipped (analogous to reflecting the ball’s motion vector over the y-axis, and drawing the arrow away from the origin, rather than toward the origin):

Simple reflection

But what should the ball’s behavior be when it hits the paddle to the left or to the right of the dead zone?  We want the y-axis vector to flip AND reduce in magnitude, plus we want the x-axis vector to proportionally increase in magnitude:

Hitting the paddle's edge

So I figured that we could do this fairly easily if we imagined drawing a “collision plane” and it’s corresponding normal vector, so that instead of reflecting over an absolute y-axis, we reflect over the plane’s normal vector:

Collision plane reflection

The math is probably messier than keeping everything in terms of the xy-plane (I haven’t worked it out quite yet), but it would generalize nicely when we consider all possible collisions along the paddle.

So, here’s what I imagine how some of the collision planes would look like when we are considering the possible ways that the ball could hit the paddle:

Hey look, collision planes

So the corners of the paddle would have a collision plane tilted about 45 degrees in relation to the xy-plane, and the angle it makes with the xy-plane scales down toward 0 degrees when we move closer toward the dead zone.

However, I think there’s still a few problems with this model.  For one, I need to play the game a bit more in order to get the behavior right. :p  Second, there could be problems with the ball bouncing totally parallel to the line that it travels on, even if the ball’s motion vector is going toward the edge of the paddle (I don’t know if this is really a problem, though.)

I think next time, I’ll try to talk about how to go about modeling more of the possible collisions and modeling some of the game logic.

I have a bit of a conundrum; maybe some of you guys who are involved in teaching could convince me otherwise.

I love teaching stuff to other people in whatever capacity that I can muster.  Seeing people finally understand a concept that I’ve been trying to teach in many different angles is simply fucking awesome.

However, I’ve been reading a few articles, websites, and watched a lot of videos on the realities of K-12 education in the United States (especially on mathematics education, something which I was thinking about going into), and to me, the entire system seems to be a huge monster of mediocrity, disallowing anyone (teachers, textbook editors, students) from presenting any sort of ingenuity.

I remember learning from those god awful textbooks that the first link describes.  When was it ever interesting for someone to write multiple steps in order to solve a math problem involving an ice cream man?  I suppose the textbook editors / writers are trying to show us how “useful” and “fun” math can be, but all they are doing is constraining us to a set of banal examples which only restricts our world view on how applicable math can be.

But you might think about this and say, “well, kids really would be lost if you lay the heavy math on them!  How can X, Y, or Z be useful if it can’t be translated into a problem that kids can understand?”  I’m inclined to think that if we do not give any intellectual charity to these kids, then they will either become frustrated or will become constrained within the bounds that we’ve set up for them.  For instance, I remember matrices being introduced in one of my high school math classes just because the curriculum demanded that the kids needed to learn the largest amount of concepts as possible.  However, the usage of matrices never amounted to anything more than simply learning how to actually add and multiply them together; how surprised I was to learn several years later that there was a lot of “deep” results to be had with matrices that could have been “dumbed down” a little bit for high school consumption.  For instance, any linear transformation can be represented as a matrix.  Rotations are linear transformations (thus, it can be represented as a matrix).  Multiplying two rotations together is another rotation.  These things, as intuitive and easy as they sound, have far reaching consequences, both in the theory and in applications (if you had a student in a high school class who was interested in math and in computer games, just tell them that all of the fancy 3D graphics rendering has to do with matrices).

In a lot of ways, I think school textbooks should be written by a few key authors with no constraints whatsoever, just like in college.  College textbooks written by a few people end up having less errors, anyway.

The problem doesn’t end here, however.  The textbook market is simply a part of a larger problem in our education system.  The strict adherence to a district wide curriculum is also troublesome, though I know that some of the better teachers often drift away from such a constraint while staying within the standard.  Imagine if literature classes were taught out of a heavily edited anthology, so that it contains none of the more “colorful” authors and none of the politically incorrect works from famous authors!  We would, again, be constrained in safety from such works, so that our minds would not be polluted with such subversive thoughts!  Imagine if we had to teach creationism as science (it’s not, for the mere fact that it is not falsifiable; it belongs in a philosophy course, not in science.)

In any case, I really would love to teach, but I fear that the public school system would hold me to the fire if I didn’t comply with the culture of mediocrity that they’ve bred in the United States.

Maybe you guys can give some insight in this?

So, I’ve been thinking about what I should possibly do after I graduate.  I’m hoping that I can get a full time entry level / junior level position in IT, but the job market is looking real terrible right now.  I was also thinking about graduate school, maybe in something like statistics.  But how everything will line up, I don’t know. . .

One possible choice is to work a little bit in IT for a year, apply to graduate school, and get a masters degree in, say, statistics.  Another possible choice is to simply go right into IT and just stay there until I turn blue in the face.  It’s just the graduate school part that’s a little distressing for me; my grades simply suck and I don’t know if any department around here in Seattle would want to take me in.  My set theory professor suggested that I talk to the statistics department here, but the only problem is that I don’t have demonstrable probability and statistics skills (I’ve never bothered to take MATH 394 / 395 at all, and I’m starting to realize how much of a mistake that was.)  An acquaintance suggested that I check out the engineering disciplines, as they apparently are in want of people with a decent math background with no prior engineering experience required.

I think, maybe, it was a good thing that I didn’t apply to grad school yet.  I could use a break in order to sort everything out in my head. . .

Twenty credits.  Here they are:

PHIL 472: Axiomatic Set Theory
PHIL 460: Philosophy of Science
PHIL 120: Intro. to Logic
AAS 308: Basic Tagalog

 I can’t wait for 472 myself; I’ve been clamoring for math for a while, and though this isn’t in the math department, it will have to do for now.

This is going to be my final quarter in college as well.

As much as I want to start working, I also want to keep going in college… but I think this is just me being a bit sentimental about a period of time which I won’t be able to live through again.

My college career was filled with a lot of uncertainties and doubts, as well as a lot of slacking after working hard for a year or two.  I learned a few extremely good lessons, things which ultimately turned my life from being asocial to being much more social, and then I learned more things which subdued my demeanor quite a bit.  But overall, I’ve learned a lot about myself over these past five years (and I’ve learned a lot, of course, from my classes), and I wouldn’t give up these five years for anything.  I’m sure everyone who has been through college would say the same thing about the whole experience.

The truth of the matter is, I totally lost myself almost two years ago or so.  Before that, I was an extremely nerdy kid who spent all of his time on homework and didn’t know any better about how to socialize.  I eventually learned how to socialize, went into my first relationship, then I’ve started to downspiral following the breakup.  I honestly think that that was my watershed moment, where I honestly started to give some thought about who I was, what I was doing, and what was actually important in life.  I was already trying to change myself before getting into my first relationship, but after getting hit with what seemed like a ton of bricks at the time, I was wondering if this sort of change was actually something that was mostly genuine.  And I think, now, all of this changing, thinking about my life, etc. has culminated into me getting back into what I used to do: doing crap with computers.  I’ve also learned to welcome back my old self and cherish it.  This is probably why I’m clamoring to get out of college: because I know, now, exactly what I love doing.

But I also have some lingering regrets, which, when combined with my sentiments about these past five years, shows a somewhat better picture as to why I want to stay in college.  For instance, I failed A LOT of math classes because I both didn’t have the intellectual drive to actually put in the hours of work required for the classes, and I also wasn’t in the right place in my life at that time.  If I had time and money, I would absolutely love to stay in college and retake those classes now that I have a little bit more clarity in my life.  I also regret the worst quality about me, which is my laziness; I loved the subjects, but I had no tenacity when it came down to actually doing the work.  And that, I think, was also what killed me in my college career.

In any case, I’m going to miss college.  I’ve learned a lot in my courses, finally found a solid starting point for the rest of my life, and I’ve made a lot of good friends as well.

Two and a half more months until I’m out of this joint!

To put it bluntly, there is way too much unwarranted use of science, mathematics, etc. in philosophy in order to establish or attack philosophical positions.  ”Determinism vs. indeterminism” is one such problem child debate: this debate is almost analogous to a religious argument, with a good dose of unwarranted use of math.  Another example is my philosophy professor saying that there are less even numbers than there are natural numbers: he stated that it is intuitively clear that there are less even numbers than natural numbers, therefore, it ought to be clear that if we stretch it to the entire infinite sets of natural numbers and even numbers, the same relation of cardinality holds.  AND NO, IT DOESN’T!  Argh!  I’m not even going to try to entertain the idea on how to justify that the two sets are exactly the same size, because it is almost all too clear to most, if not, all practicing mathematicians, and at the very least, it’s clear to almost all math students.

I was reading a thread on indeterminism and mathematics, and while I am pretty dumb at physics, the discourse on the forum pretty much shows me that Norton’s proof of indeterminism fails for the mere fact that he is, (1) doing the math wrong, (2) getting high school physical intuition totally wrong.

Determinism is highly problematic as well: it’s extremely convenient, philosophically, to whittle the world down to simple causal chains between one state of the world and the next state of the world.  It’s foolish to say such a thing in face of evidence.  And it’s even more foolish to claim that we are missing a variable or two in order to collapse a probabilistic system to a deterministic system!

Meh.  Maybe I’ll get a more level headed post in here sometime in the near future.

So, for next quarter, I have to take Intro to Logic, a 400 level course, a philosophy elective, and Tagalog.  Okay, cool, so I saw that there was an Axiomatic Set Theory course offered next quarter, a Philosophy of Kant course, and I just found out that there is a Philosophy of Math course as well.  Cool, those ALL sound super interesting, except that the first two courses are at the same exact time on the same exact days, while taking Phil. of Math would conflict with both Logic and Tagalog (yes, out of all of the three or four sections of Logic, NONE of them work with Phil. of Math and Tagalog).

This happened this quarter as well, though I forgot exactly which courses I was thinking of taking.  I ended up in Epistemology and Intro. to Metaphysics eventually, and I can’t say I enjoy either of them as much as I thought I would.

At least the math department knew that people would want to take, say, Fundamentals of Analysis, Algebra, Topology, maybe some sort of special topics course, etc. all in the same quarter, so they actually schedule them at different times on different days from each other.  Philosophy, on the other hand, is a fucking mess.

So, after reading a friend’s blog, I got to thinking about what sort of stuff I should probably set for myself in the short term, which hopefully will turn into long term habits.

One of these things is appropriately budgeting my money.  Okay, so I’m still in college, and I don’t have to pay my loans (yet), so the highest priority expenditures have yet to incorporate anything more than simply rent, utilities, and groceries.  Fair enough.  I don’t spend all too much on groceries, maybe ten dollars per week at the most, and my rent is real cheap as well (though it is doubling in a little over a week from now since I’m moving soon with Sara), so my income minus these highest priority expenditures equals a fairly high disposable income.  However, my current “luxurious expenditures” are pretty damn high.  For instance, I buy coffee at least twice a day (only a double shot espresso, which is about $2.00 per cup), but I also buy chips (~$1.25), an energy drink (~$2.50), and a cookie (~$1.50).  Yeah, I buy chips and cookies every day because I’m way too lazy to prepare my own food ahead of time.

So that equals about $10 per day.  I spend almost nothing during the weekend, so in the seven days in a week, that’s already $50 per week.  That, and I buy a pack of cigarettes once every three days, so that’s about an extra $10-$15 per week.  $60-$65 total.  Shit.

So here is my plan: if I absolutely need to keep myself awake, I’ll make coffee in my house and put it into my Thermos before I head out.  While I’m doing that, I should prepare breakfast and pack whatever is left over for the entire day.  I should buy groceries instead of eating crap from deli’s and coffee shops.

I’ll need to get myself to stop smoking as well, though I REALLY REALLY need a compelling reason in order to get myself to stop.  So far, I haven’t stumbled upon such a compelling reason, so that’s something I’d have to work on as well.

More time needs to be allocated to sitting down and reading my assigned readings, as well.  I’m finding out more and more that the current dogma of philosophy is real hard to swallow, but well, fuck, I need to actually get decent grades for the final two quarters of my college career.

Anyway, that’s about it. :O