If anybody knows me at all, they know that I have strange sleeping habits and strange car habits. My car is generally a mess, and the reason for that is I basically live in my car. I've actually been pretty good at not living in my car the past few months, but all that was crushed away after last night, where I began my bad habits of sleeping in my car again. Well, I did it once since January, so I figure that's pretty good considering what I used to do.
Let me back up a bit here. First, back in high school, when gas prices were like 79 cents per gallon of reg. unleaded, I would drive my car for hours in a loop around Enid. I would take Willow east bound, then South on Van Buren, East on Garriot, and North on Oakwood. Rinse and Repeat. Really, it was a way for me to think and argue things in my head. I would yell at myself for doing and thinking stupid things, I would savor moments of triumphs with huge grins...I think I even cried once or twice during my depression years (which may be another entry altogether). The point being, if there was a favorite place for me to be in during those years, it would be alone in my car.
So I'm quite accustomed to being in my car for long periods of time. Hell, I even drove back in forth from Enid to Norman almost twice a week for a whole semester. [good times] And when I would get tired of driving, I'd sleep in my car. Yes, I realize that it's really really safe to be doing that...but hey, at least I slept when I knew I wasn't safe to drive at that point.
I would sleep in Wal-Mart parking lots, parking lots outside of a plaza mall with a starbucks in it...I even got to the point where I was sleeping in my car in the dormitory parking lot with my bed only a 2 minute walk away. I figured, "Hey, I have an 8:00am class that I should go to, so if I sleep in a bed, I'll sleep through the class. I'll sleep in my car so I can make the class...yay!"
Yes, my logic for the sleeping in a parking lot and driving all the time is probably flawed at some point, but it all seemed like really good ideas at the moment. And driving lets me have true time for myself to think, which I'll probably be needing to do more of in the months to come.
Thursday, October 29, 2009
Wednesday, October 28, 2009
The Cauchy Sequence
So, I've finally decided on a title for this thing. I used this math concept as the backbone of my medical school personal statement (which I thought was kinda creative....but that's just me).
A sequence
x_1, x_2, x_3...
of real numbers is called Cauchy, if for every positive real number ε, there is a positive integer N such that for all natural numbers m,n > N
|x_m - x_n| < ε.
[on a personal note, I used this definition in the rough draft...apparently my English professor thought it was a little overly-ambitious and told me to change it...and I thought I was just being smart...]
So basically the idea is that as we continue along a sequence of numbers...say, for instance 1/x from 1 to infinity...that set of numbers is considered Cauchy that as we continue along the sequence, the numbers converge on a single number. In this case we would have 1/1, 1/2, 1/3,..., 1/1000,..., 1/10000000000,...
This set of numbers is naturally converging to 0.
It's sad that I have to use such an explanation of this concept to get the idea across, but my argumentation is that, although I live a very "divergent" lifestyle (I have no clue what I want to be, no goals, I want to do basically everything I can), I realize that everything I do in my life is converging to some pretty specific goals:
1. Be a good person
2. Help people out
3. Try to be happy and non-regretting in the way that I live my life
As for where my life is headed, being in medical school, I thought that I would eventually be a physician somewhere doing something medical (whether it makes me happy or not). The good thing about life is that although it is a sequence of events that will eventually converge to something, we have the opportunity to be able to change the value it can converge to...and that is, in my opinion, a pretty optimistic way to look at life (a very rare thing for me...teehee).
So here is where it truly begins. The beginning of this "blog," this "sequence." Let's see if this converges to anything...
A sequence
x_1, x_2, x_3...
of real numbers is called Cauchy, if for every positive real number ε, there is a positive integer N such that for all natural numbers m,n > N
|x_m - x_n| < ε.
[on a personal note, I used this definition in the rough draft...apparently my English professor thought it was a little overly-ambitious and told me to change it...and I thought I was just being smart...]
So basically the idea is that as we continue along a sequence of numbers...say, for instance 1/x from 1 to infinity...that set of numbers is considered Cauchy that as we continue along the sequence, the numbers converge on a single number. In this case we would have 1/1, 1/2, 1/3,..., 1/1000,..., 1/10000000000,...
This set of numbers is naturally converging to 0.
It's sad that I have to use such an explanation of this concept to get the idea across, but my argumentation is that, although I live a very "divergent" lifestyle (I have no clue what I want to be, no goals, I want to do basically everything I can), I realize that everything I do in my life is converging to some pretty specific goals:
1. Be a good person
2. Help people out
3. Try to be happy and non-regretting in the way that I live my life
As for where my life is headed, being in medical school, I thought that I would eventually be a physician somewhere doing something medical (whether it makes me happy or not). The good thing about life is that although it is a sequence of events that will eventually converge to something, we have the opportunity to be able to change the value it can converge to...and that is, in my opinion, a pretty optimistic way to look at life (a very rare thing for me...teehee).
So here is where it truly begins. The beginning of this "blog," this "sequence." Let's see if this converges to anything...
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