On Mathematics

I have a very awkward relationship with math. Most of my peers love it to pieces. They constantly suggest that I learn more and more of it. There are constant cheers that Math makes universe go around and the world is so beautiful with mathematician goggles. The problem is that it is not how I view math.

My view of the subject is utilitarian. I do my own thing. I am a computer scientists. I enjoy going out and writing interesting algorithms. There is certain challenge to exploring ways of modeling processes. The nature of the computation is equally frustrating and illuminating. Sometimes I run into problems representing certain aspects of the problem. The issue is usually tied to some mathematical concept that I do not know. That is the state of mathematics and me. When I am in a jam I call up math to help me out. It is strictly a tool in my set of skills.

Recently, I have been reaching into that toolbox more often than I want to. The problem is I really do not know what math is useful and which is not. I voluntarily took up to multivariable calculus. There was this underlying assumption that I would be as a computer scientist using math that uses arbitrary numbers of variables. What I forgot was that computer science uses discrete mathematics. Calculus is the mathematics of continuous systems! So while what I had just learned was very handy for mechanical engineers and physicists, it was useless to me.

Combinatorics does not come as often as the college classes make it out to be. It just has the habit of occuring just when you do not expect it. Mostly I run into it when I am employing some Bayesian learning algorithm. Geometry and graph theory are the math fields I will run into most often. Graph theory is used essentially everywhere. It is the ultimate generalization of all data structures. Most reinforcement learning algorithms require a substantial knowledge of graphs. Neural networks is all about fancy graphs. The things are everywhere.

Geometry I run into a lot due to working on projects that interface with the world. The programs in your cellphone need to some heavy duty triangulation to figure based on the locations and distances of various cellular towers where the hell you are. Geometry is the only thing that will help in that class of problems. This includes such headaches like what area does a collection of cellular towers provide coverage for. Also this is not the geometry you are taught in grammar school. This geometry will use trigonometry, and it will employ a set of procedures so repetitive that you will memorize the C function that does it, convex hull I am looking at you.

Dealing with those fields of mathematics has been annoying but acceptable. Lately, I have been running into a lot of projects that require heavy use of number theory. Number theory is the stuff of higher mathematics classes. The is the stuff of 300 and 400 level math undergraduate math courses. Saying "number theory is a strange subfield of mathematics" is about as tautological as saying circles are round. Alice in Wonderland was written by a logician that studied number theory. I do not want to get near this thing. Mathematics has given me such sharp and powerful tools. Understanding the concepts undelying my problem requires the most twisted tools in the box.

So I downloaded some pdfs and started reading. The notation alone almost overtook me. The structures they introduce are so specific and exact. They are constrained in the exactly the ways the object I am going to work with will be. This thought is comforting since most people will not have an immediate use for this stuff. I am digging since I know I need to use it. I read through a few chapters and did some exercises for myself. Then the nightmares started.

The nightmares mostly consist of me inside of these structures, and I can not get out of them. I am not assaulted with the notation and barrages of equations. It is not that the equations themselves that scratches at my face. As they fly by I try to read them and understand what they mean. Unfortunately, due to the biological natures of dreams/nightmares I can not. The frustration hurts me physically in this nightmare. That is the most generalized I can make it. They really differ otherwise. With my luck, tonight I will be murdered by an n-element ordered set.

Peace in the Middle East

Just a few hours ago, I was discussing Israeli politics with a guy on irc, and he brought up this very interesting point. In Israel it is considered taboo to use the word peace in political discussion. He likened it to the word "fuck" in english-speaking countries. The whole conversation got me thinking about the sociolinguistic properties of words. I mean all words are from a phonological standpoint fairly equal. What is it that makes a word offending?

It clearly has to involve the semantic binding to the word. The problem I have with this is that many words can equally share that semantic binding. I do not need to use the word "fuck" . I can use many of the words that compromise its definition. The sentence "Is she fucking around?" can be easily replaced with "Is she having intercourse with other people?". One can be contrued mildly offensive, the latter not so much. They convey the same concept. They deduce down to the same linguistic content.

The more bizarre situation is the p-word in hebrew. In viewing this word, I see a very strange reason for the situation in America. In the entire history of Israel there has been no such thing as a peacetime. To mention the word peace is to be looked at as a clueless idealist. This is a terrible self-defeating outlook. Since it shows that what words we view as taboo are really manifestations of our own cultural values. Some have argued that censoring words censors thoughts, it seems really to be the other way around. Thoughts and concepts that a culture finds offensive will try to be eliminated from the record by censoring their linguistic representation. It seems like an insidious way to try to stop thought.

The effort though is silly since there will always be a way to express the idea. Since some event is going to occur that requires noting the concept. "Fuck" is a product of the culture of America. Deep under the silly "melting pot" culture that people tout as American, so the devout puritian culture that started our country. It is an old system of values. It is a very hypocritical set of values, but it there. The american way of working really hard to acheive your dream, is puritan in nature. For all the consumerism that has been associated with America there is still this puritan view. The puritan goal of get into heaven seems to have been replaced with accumulate as much wealth as possible.

There is also this derived fear of sex we got from them. All sexual behavior needs to be kept quiet and out of the public sphere. It is as if those children just magically appear. This is the climate that elevates a word like fuck to infamous levels. Hopefully soon people will realize you can't censor thoughts. Only a culture can. So, I think it might be hightime to analyze our own and make some judgements calls on these dirty words.

On Clubbing

I really wanted to get this entry out last week. Unfortunately the outside world had other plans for me. It involved a lot of broken computers and downtime. Anyway last week, I went to the liberal arts campus to spend some time with friends that live there. Since I moved to this cold desolate engineering campus, I have not spoken to a lot of the people there. It almost makes me think I made a mistake. Then I remember how well I study in the quiet, and the engineering campus does get very quiet.

The general plan was for me to come down to the campus and then go with a bunch of my friends there to a club in the city. Unfortunately I did not have proper attire for the event. So I could only merely walk my friends to the train and then walk back to campus. Now that I was on this liberal arts campus, I needed something to do. This wandering eventually brought me to my friend Brian's door. He was with his girlfriend at the time, but still was up for some philosophical conversation. The details of the talk are pretty broad, and much better explained at Brain's blog: http://defeattheskeptic.blogspot.com .

Eventually, after a fatty fast-food meal, I bid Brian a farewell and went to visit another friend of mine. I caught her at a bad time. She was actually planning on heading out. Given that I was bored and did not have anything better to do, I tagged along. To make the story easier to follow I will label by friend T for further reference. T grabbed two other girls, and another guy, joined us, as we went to a party at a local frat. This was interesting since I had never gone to a frat party before, and did not really intend to now. But all that idleness finally got the best of me and I walked through that fraternity door.

When I got in I was given a cup and lead to walk downstairs into their basement. There the music was loud but it was tolerable. The genre was not really to my liking but it was managable. T led me to a bar where she wanted me to drink. Sadly, I do not like the taste of beer, and spent the rest of night just grabbing beer and pouring it to her. It was around this time that I became aware of my own perspective on this party. What was the purpose of the different people here? Was there a more effective way to achieve their goals?

From what I observed there was the overarching goal of have fun, which on subseqent goals share. I only bring this up since I feel that to some extent that is the point of a party, and sometimes it really is that simple. The problem is most of the patrons are a bit more hedonistic in their goals. First is the people that came just to get drunk. It is pretty obvious who they are, since all they do is sit by the bar and drink with their friends. They do not move and they do not dance. They have taken the 2 dollar cover as an all-you-can drink invitation. Though there really has to be a better place to drink. A pretty investment can certainly get a more cozy and tasty beverage. Why be in that loud place, just for beer.

Second is the people that just want to dance. This one is plausible, but it certainly is never a defining reason. I give that as my official reason for showing up since I really had no other purpose to be there. The problem with this logic is that the music in this frat is identical to others and the space is very cramped. A more suitable place to dance shouldnt be too hard to find. The third reason is simply to have hook up with others and possibly have some sex.

I found this to be the most likely reason for a lot of people being there. I certainly held the thought almost continuously when I was there. Though in holding the thought I made lots of obervations. I noted that couples will go to the frat and bump into each other and make out. I also noted the same few people going from person to person looking to dance. I was inclined not to care and simply danced. As time waned on, more and more guys were entering the dance floor and more and more women were leaving it. The sexual nature of the atmosphere intensified as guys scrounged for the remaining girls. I left with T and another girl shortly afterwards.

What really amazes me is how much guys like to go after girls in this situation. Clearly unless you have your A-game on this is not a fun situation. I had not run into anyone there that wanted to banter lightly. There is a genetic addiction to sex. While that is not really a new insight I feel people missing that the whole affair is, evolutionary, a carrot on a stick.

There is no evolutionary payoff in enjoying sex or any particular moment in this whole dating process. There needs to only be the illusion of payoff. If you do action X you will feel good. No one seems to notice that what actually occurs is that you feel inclined to do action Y, and then inclined to do action Z , etc. It really is a shame, but you have to rationally think. If I felt excellent just flirting with this girl, why should I push it further? Now if I feel good, but now I have this intuition that I will feel better if put my arm around the girl's waist. Suddenly there is a feedback system that propels you through these actions.

It really is a shame that evolution does this to you, but it seems to work so you have to deal with this genetic baggage. Humans are social animals and a great deal of evolution has actually been to out compete your fellow human. So that situation where the ratio of men to women started to tip till the men needed to compete for resources was a classic evolutionary situation. That means we have been designed to handle situations like it. That means there was no natural advantage and your body was tricked. I knew my body was tricked when I walked outside and saw 10 women just standing around do nothing. Clearly our genetic predisposition can get the best of us. This is why is it so crucial to understand it.

On Failure

College is an interesting place. You come to this place to learn about life, and people. It is yet another microcosm of life where you can explore clubs and other extraculicular activities. And then there are your classes.

It would make sense that since you pick your classes they should be the most exciting part of your days. My day spent learning all these cool stuff that I did not know could be done with a computer. When I am not talking computer science classes, I am talking physics and biology learning amazing things about the universe and my own body. So it makes perfect sense that I cut classes in favor of coding a sourceforge project or just sleeping. Then midterm time came last week. I switched into frantic cramming mode. Normally this works fine since I am very careful and precise in my study habits. I target morsels of data that are more likely to appear on a multiple choice exam. This cuts down what I really need to know.

I also have this habit of racing on exams in easy classes. If I understand the material and I am in the class with another smart friend, I am obligated to finish the exam before this chap. So I raced to get the physics exam. The results came in today.

Physics: B- Bio: C

Considering the conditions those grades are much better than they could have been. That is what I call the loser response. A grade can always be worse, and it can always be better. It is only my fault that it is what I got. I spent this evening trying to decide if it was appropiate for me to blame the tests for being hard, or myself. After a trivial amount of reflection is it obvious that I was cocky. I just need to study more often. Most of the my time is spent sleeping anyway. Getting bad grades in these situations pisses me off because it is so preventable. Like lung cancer or car crashes, what makes them that much more frustrating is how preventable they are. It is probably inappropriate to compare bad grades to car crashes, but for a self-absorbed person like myself the analogy could not be more fitting.

In more depressing news, I have rejected from another 2 interships. This is of course in addition to the one I applied to, after working there the year before. I really am pathetic at this whole "getting a job" thing. It seems I am better at projecting an aura of competence than pounding it into a piece of paper. So I think I am going to work off references and places that my friends work. After all doesn't every company need a crazy Common Lisp coder!

From a meta-note, I have not placed a single comment on Cogntive Science related concepts. This is a pretty big tragedy in my opinion so I will rectify this at a future point. For now I want to propose three ideas I have been kicking around in my head.

Can a computer abstract conceptual data from an image? This includes 3-dimensional data such as texture and depth.
Is the passage of time a function of the speed of our thoughts?
Is there any learning algorithm that does not decompose to some regression problem or bayesian reasoning problem?