Why is a Music Major taking Calculus III?

It is a good question, and I’ve been asked it quite a bit this semester. The answer I usually give is that the requirements worked out for my degree such that I have to take Calculus III. This is true, but my experiences this semester in this class has led me to something else.

The class started out rocky. The actual professor wasn’t there for the first 3 or 4 weeks of class, and during that time, we had 4 seperate teachers come in to cover basic Vector Calculus. I struggled for the first time in a math class. It had been 2 years since I took Calculus II, and I had heard that Calculus III is supposed to be the hardest undergraduate class someone can take. So I was very anxious about this venture. But now, with two weeks left in the semester, I couldn’t be happier with my choice. I have fallen in love with mathematics once again.

When you really understand an equation, there is something almost spiritual that happens. Others have described it as ‘reading the mind of god,’ but I don’t like that language. It doesn’t seem descriptive enough. It’s finding out something about reality completely with your mind, something that you know is true! You are literally discovering an ultimate truth with every step of the theorem.

Call me crazy but my two favorite math class periods in high school we when they actually showed the proof to two important concepts: the irrationality of square-root of two, and the derivation of the quadratic equation (x equals negative plus or minus the square root of b-squared minus four A C, all over 2 A.). It was one things to just be told these things, but for me, the more important question was, ‘How did we know them?’

This leads to something else, something that has drawn my interest lately, especially after reading ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences.’ I am a music major – how does this all fit together? Music may be the universal human language, but mathematics is the language of the Cosmos.

Marco Polo’s Dilemna

From a blog entry about psychiatry:

“When Marco Polo saw the exotic one horned quadruped, his frame of reference required that it could be none other than a unicorn, even though it did not conform exactly to his prior conception of it. Marco Polo made his observation fit his existing paradigm of zoology. While superficially (and in retrospect) this may seem silly and arbitrary, it is in fact the opposite, Marco Polo believed the only thing he could believe—because the alternative was to believe he had discovered an entirely new, unheard of, creature.

While the original post dealt with psychiatry directly, I think there is a wider lesson to be learned here. Our assumptions about knowledge and authority can lead us down the wrong path.

What does the Prisoner’s Dilemna Teach us about Morality?

The Prisoner’s Dilemma is a classic non-zero-sum game in game theory. I know that can sound a little intimidating, but I’ll lay it out in it’s simplest terms, because it really is quite simple to grasp, and quite valuable to understand.

As a former Objectivist, I really understand the power of selfishness and what it entails. Everyone is basically selfish – in fact, it’s impossible to be completely altruistic. However, that explanation depends on very rigid definitions of both altruism and selfishness, and those definitions are rarely used outside of Objectivism. The main point is that most people, most of the time, will look to maximize their own gain, and I think that most people will agree with that. Objectivism states that this can be a very valuable tool for the betterment of everyone, and there is a lot of evidence that backs that up. The problem is that it never takes into account non-zero-sum games, such as the Prisoner’s Dilemma.

To illustrate what I mean by a non-zero-sum game, let me explain the Prisoner’s Dillemma. Imagine two people who committed a crime together. When they are arrested, they are seperated into two different rooms, and the prosecuter comes in to talk with each of them. The situation is explained to them. If they betray the other person and turn states evidence, they will get away scot free. If they stay silent, while the state can’t convict them for the original criminal act, they can easily get a conviction for a smaller act committed later. The options each person is facing are these:

1. Stay silent, get convicted for the smaller offence, serve 5 years in prison.

2. Turn states evidence, betray their partner and serve no prison time.

It seems pretty obvious that option (2) is the best option. However, there is a twist. The other person is also getting the same deal, so the situation is more complicated. The possibilities are now this:

A. Both stay silent, both serve 5 years in prison.

B. One talks while the other stays silent, and so one goes free while the other spends 10 years in prison.

C. Both talk, where they both serve 10 years. In other words, if they both turn states evidence, there is no need for a deal, so they both go to prison.

Now the Dilemma should be clear. If they both take option (2) from above, they will both serve 10 years prison time. However, if one stays silent, they risk the other turning states evidence and getting off free while they serve 10 years prison.

What would you do?

Given that situation and the options given to each, I’m going to define option (1) as altruistic in nature, and option (2) as selfish in nature. If both people act purely selfishly, as our tendencies are, they both lose greatly. If only of them acts altruistically, they risk being screwed into something pretty bad. The best option now becomes for them to both act altruistically, seeking cooperation instead of self-preservation.

That deserves quite a bit of meditation. As in the Tragedy of the Commons, the best option for both the group and the individual over the long run is more altruistic behaviour than purely selfish behaviour. However, where as the tragedy of the commons can be addressed through private ownership to a point, the Prisoner’s Dilemma is more about interaction, which can be more difficult to really grasp, and I think relevent to morality. Where-in Objectivism holds selfishness as the highest moral principle, it does not necessarily reflect reality. Obviously, altruistic behaviour can lead to an even greater gain, depending on the situation. Those situations are non-zero-sum games.

Given that gaining and keeping resources is good for the individual, we can now derive a moral principal. In a non-zero-sum game, it is morally best for an individual to act altruistically, and immorral to act selfishly.

Okay, you might be wondering why I’m taking the time to write something so blazingly obvious to anyone. As an atheist, I’ve been accused as being a moral relativist, or even worse, completely lacking in morals. This is obvious to the accuser because morality can only come from god. I have now answered those accusations. I have demonstrated the creation of a moral principal using only reason, and without invoking the supernatural. What’s more, it can be applied equally to everyone, and it’s reasoning is available to everyone. It is not dependent on revelations to the elite, or an ancient and contradictory book. It something you can learn, here and now.

This is not something new. It’s not something I did completely on my own. This has been explained over and over again, and as I mentioned, there is a whole field dedicated to the study of such situations. Richard Dawkin’s has done a documentary on the subject called ‘Nice Guys Finish First,’ which explains the subject much better than I can hope for.

Love and Compatibility

About two weeks ago, I had a discussion about love with my friend Tara about love, and it’s launched me into considering it a bit more lately.  Then today in my blogroll, I saw this article pop up from Psychology today, which threw a wrench into my thoughts to say the least.  If you don’t want to click on the link, it’s entitled “The Truth About Compatibility.”

The main point of the article is that we tend to give compatibility too high of a place in our priorities for finding love.  Here are a few quotes that I found especially enlightening:

“There is no such thing as a compatible couple. All couples disagree about the same things: money, sex, kids, time. So, it’s really about how you manage your differences. If there is chemistry, then the whole courtship is about convincing yourself and others that you are compatible. But, really, you create compatibility. And then, eventually, maybe in 25 years, you will become soul mates.” —Diane Sollee, founder and director, Coalition for Marriage, Family and Couples Education

“People might agonize and think, Do we have the same likes and dislikes? But people are not aware of how powerful self-fulfilling prophecies are. We have expectations in a relationship, and we tend to make them come true. The most satisfied couples are those with overly rosy views of each other.” —Lisa Diamond, assistant professor of psychology and gender studies, University of Utah.

These are both very interesting takes, and put that way, I can’t help but think that they are probably right.  I mean, what are the chances that someone will agree with you on everything, and yet not share most of your faults as well?  What’s more is the question, do you really want someone 100% compatible?  When I really examine the question, I realize that having 100% compatibility would be undesirable.

A relationship should be a non-zero sum situation.  Each side should be able to augment the other.  As one person from the article put it:

“People assume compatibility as a baseline requirement, then want more. “I want him to fit in with my family and do all the things I love to do—and he should be sexy, and he should take me out to cool places.” I think you can have an even more fulfilling relationship if you respect each other’s worlds, and learn a little bit from each other. I always think of the phrase, “You’ve met your match.” You really do want someone who challenges and spars with you.” —Nancy Slotnick, dating coach, founder of cablight.com

Challenge is the right word.  Sparing can conjur negative images, but I think it’s apt too.   You become better at something by overcoming.  I think a ‘Significant Someone’ would be there to help you along, press you, and face hurdles with you.  Compatibility no doubt plays an important part, especially in the early stages, and perhaps in a different emphasis that what we usually give it.  Over-all, though, perhaps there are more important things.

Love is truly complicated.