Category Archives: Mathematics

Considering Learning

At times, when I play witness to something beautiful, I simply want to spend time knowing the individual components of it. The wicked truth of the matter is that this can not be done without divorcing the intimately entwined parts. Shortly after snapping this photo montage on the microscope I took a razor blade and sliced through the ovary, gaining new perspective on the prismatic fibers of  that which is unknown to me. I am not the first to come this way, nor will I be the last. Any one have any pointers on histology technique?

I’ve been thinking a little about this; the taking apart and how it might work in learning. In my intro to statistics class, the assignments take no more than an hour for me to complete.The professor is wary about discussing theory in class, but his mechanical introductions are (overly) patient and methodical. The value of the course is in gaining confidence and growing vocabulary for clearly reporting data.  The confidence from standing firm in an answer as you are quadruple challenged feels good, but shallow. The unfortunate side to this method is that there is no exploration into why we are doing what we do. It would be as if mathematics were truly discrete and all the rules already written. If we stopped to ask; if we were challenged to make our own formulas; we may be humbled in new ways.

On the opposite side, in Organic Chemistry and Biology, I skipped the expected prerequisites for the courses that I have been taking for the past year so that I could graduate with a study Depth that approximates “Biochemistry”…one gets easily side tracked at this school. Infiltrating the class as a writer has been challenging, but I’m a chameleon, so it’s worked out more or less to the extent I’ve expected. I don’t know a lot of things that other people do who have had let’s say 1-50 years of experience on me, but I’m mixing into the average. It takes me a long time to do my work, and often I have no driving force to really do it. This is because I need to make up for vast knowledge gaps which are not readily apparent. Here, when I am challenged, I am often quite happy to yield to opposing suggestions. I am still, after many months, afraid to speak up because I might reveal how unprepared I truly am. Here is an xkcd comic for the occasion.

How Mathematics Became Beautiful

This is a window to one year ago and beyond.

I was in a class, which I shall affectionately call “Algebra to Alcohol” because that spring coincided with my roommate and I stocking the fridge with 24 packs of beer.

There was a lot of cognitive science involved in this course. A lot of “Why is our culture math-phobic” being asked. Most students in the class were in the “Mathematics is amazing” camp and couldn’t see the other side of the fence. I was the lone student voicing a differentiated state of mind. I still remember the tears falling down my cheeks as the protist blob of a math teacher I had in 8th grade scolded me, branding me the laziest girl she knew. I probably took algebra 3 out of 4 years in high school each time being uniquely told that I was lazy and stupid for not catching on…and yes it was boring and repetitive. My first college adviser (who held all say in registration) one upped it all, and just plain didn’t allow me to sign up for any mathematics, because it would be “too difficult” for me. Besides, everyone I knew told me that I was damn good at writing, and that’s what I needed to be focusing on.

I was having issues with sleep, as well as issues caring about the work I did. I desperately wanted to understand what it meant when someone talked of the beauty in mathematics, but I could not. “Fake it ’till you make it,” my professor advised.

Due to seminar readings, I met a proof that changed my mind about math: Euclid’s proof of infinite prime numbers. I couldn’t wrap my mind around it. Three people in seminar patiently spent 20 minutes explaining it to me, we played with it. Things started clicking. As the class regrouped my mind assumed a low hum. Ideas from readings about linguistics collided with the primes. Patterns snapped and popped, and I started scribbling furiously into my notebook, ignoring everything else around me. The class ended. I made it home that night, but I could not say how.

The next day, I asked my professor, “If they believe prime numbers occur randomly, how do they have prime number generators?” “Look it up,” he said. “Start with the sieve of Eratosthenes.” The next week he threw the sieve into a programming workshop with a mischievous grin. Over the next few days I witnessed myself buying color coded pens, writing every prime number down well past 1,987 and calculating the difference between them along with a few other variables. It was suddenly no longer foreign to get out of a bath, pen down some calculations and then wake up a few hours later slightly confused, my face in a puddle of numbers. I did a decent amount of research on primes and started building a rudimentary program to aid me in calculating my thoughts, but all too quickly, the quarter ended.

My first ever (organic) chemistry course kicked in. The ball was rolling, and I was going to fall off if I didn’t drop everything else.

I haven’t forgotten how that project made me feel, and I would still love to throw hours at it, but I have a lot of excuses and obstacles. I’ve begun learning statistics, which are important to number theory, scientific experimentation, & informed decisions.

Statistics is a small step to understanding infinity.