Mathematically Perceptive

Sophiaolender's picture
After reading Darwin’s ideas and Dennett’s responses to Darwin’s ideas, I became increasingly interested in their views on mathematics. As a potential math major, I am already a bit more in tune than others may be to the way math is applied to the situations in the books, and I am beginning to look at math in a different light. I believe a large point of this class is to provide a stepping-stone in allowing our minds to be able to perceive our world in multiple ways. Every student in this class views the world in our own way, based on our past experiences and on our personalities. We are a group of individuals and because of that, our perceptions are individual and unique to ourselves only. This idea makes me wonder what the world looks like from one of my classmate’s eyes.
For this paper, I want to focus on mathematics and how they alter the way I understand the world, and even how a broader perception of the world might look if we perceived only through the understandings of math. I do not know if this is possible to conceive, but the idea interests me enough to make me want to try, or to at least the ponder the idea to a fuller extent.
Math seems to be the fundamental basis of perfection in our world. As I have realized from reading Darwin’s Origin of Species, math really does not exist. We invented math and I wonder if it was in order to have this basis of perfection – a non-reality in which everything makes sense, in which one answer is always correct and things always work out the way they are supposed to. The simple truth is, reality is incapable of reaching the unnatural perfection of mathematics. Only in math can I create a perfect circle. There are no means of doing this in the natural world.
Dennett continuously relates his anecdotes to the unnatural perfection of mathematical ideas, graphs, and equations. It seems to me that he understands that we, perhaps, strive for math’s flawlessness, but always fall a bit short. It confuses me both why and how humans invented this idea that does not exist. How did we even perceive it? I understand people creating numbers and learning to count, realizing that one plus one is two, but when did we create the concepts of imaginary numbers and proving ideas based on step-by-step mathematical equations. Do animals understand mathematics? Is this another concept that sets us apart from our less civilized counterparts? Maybe they are wiser (if possible) for it – they are not challenged by the just out of grasp perfection that we want to believe exists, but does not.
We know that our brains are capable of interpreting the world in many ways, so what if we looked at the world utilizing the eyes of math – the eyes of an idea that believes in an unnatural perfection? Would we view the world in an optimistic or pessimistic light? How would our lives be different, and would there be any way they could be the same?
I have to believe that we would be incredibly distressed to realize that the perfection of an idea that can exist solely in our minds can never reach perfection in reality. It makes me wonder why our brains can even perceive perfection when we have never had a solid example of it.
So, I wonder, what sets me apart from others because of my background in math. My elementary school was very different from most elementary schools, because it was very individualistic and it relied mostly on the students teaching themselves. Every day during math time we got out our own books, bookmarked at the page we had left it last time. We started working and did all the odd problems in that section, checked the answers, and moved on. Many may frown on this form of teaching, as it is completely self-reliant, and there was no teacher who would check my work – if I needed help with something, I could go up to my teacher’s desk and ask, but in most cases, I would fly through the math books, teaching myself concepts. I skipped first grade because I was years ahead in my classes, and by third grade, I was working out of the sixth grade math books. It always seemed that math was the place that I could excel with little effort. It is hard to believe that my proficiency in math was not grounded in my elementary school education. It is also hard to believe that my perception of the world was not entirely affected by the teaching styles of my adolescence.
People make many assumptions when it comes to those that choose to pursue mathematics in their lives. Math majors are viewed as dorky, too logical, and very set in one mindset. I would hate to think of myself as any of these things. I guess the majority of math majors are simply people who can excel in the area because they have exceptional minds that allow answers to come fast. I do not think this of myself. I have always wondered why math was so within my grasp, and after reading Darwin’s and Dennett’s ideas, I wonder if it is the sanest way for me to chase perfection.
As a child, I was called a perfectionist by everyone that met me. I was obsessed with organizing, with perfect grammar, with general cleanliness. If, halfway through the term, I would make a mistake in a notebook, I would literally buy a new notebook and rewrite all my old notes error-free. It was an obsessive compulsion – I needed perfection. As I have grown up, I have learned to focus my need for perfection, and few would look at me today and call me a perfectionist, because I am no longer interested in attempting to prove to the world that I am perfect. I embrace my flaws and today, my perfectionism lies mostly in my stubbornness. I am controlling and need things to go my way. I am not the perfectly organized girl I once was. I have learned to accept and enjoy my mistakes because all of the mistakes I have made are the only reason I am in the place I am today. And I wouldn’t change anything that would change who I am right now.
Math leaves no room for mistakes – a tiny mistake could alter your answer by thousands. As I grew and learned that mistakes were not something to be ashamed of, but something to take pride in, I also started to drift from math being my favorite subject. I maintain my math classes because they continue to provide a foundation for the way I see the world, but I consistently question my once sure belief that math would be my future.
As this paper unfolded, I realize it was less a view of the world through the eyes of mathematics, and more a view of my life based on my understanding of mathematics. It amazes me how my own evolution in terms of maturing, and my interest in mathematics, mirror each other on my timeline. I had never realized this about myself, and while I have lost a lot of my own obsession with mathematics, I maintain a strong interest in the field, and wonder what my life would be like without a foundation in the subject. Many of the accomplishments in my life are directly related to math and without the elementary education I received, I would not have accomplished any of that. The cause and effect of the situation astounds me, and through writing this paper, I have learned more about myself. I have to disagree with the quote that says that we are not our pasts. How could this be verified? I believe I am entirely my past, and that all people are. No, I don’t think we are directly affected by our long lost ancestors. But our own past is truly all we have. What more is there to us than layers of experiences and consequences?
Math provided me a gateway into the world – it would be easy for me to continue with math and make a career out of it, but as I continue to grow up, I really question whether it is my passion. We all view the world through the eyes that we have grown into – my eyes have seen a lot of math, and I know that I am a different person because of it. I think my next step is finding a new passion, making it my focus, and seeing where that takes me. How would my view of the world change if I were to embrace something new? I can’t help but believe that rounding out the one-sidedness of my views would make me a better and more sympathetic growing young adult.


Anne Dalke's picture



You write this paper from your own particular, valuable perspective, as someone who has always been good in math, and as a potential major. You intrigue me with your questions about the “perfection” of the world of mathematics; by your wondering “where it came from,” since it doesn’t reflect the “imperfect,” randomized world of cause and effect in which we live; and by your asking whether familiarity with such an unattainable world would lead to increased pessimism or optimism.

I have a couple of smaller questions for you—what does it mean to be “too” logical?; a couple of larger ones—if we “make” the world of mathematics, doesn’t it then exist?; and then a really big one: @ the end of your paper, you say, first, that “I believe I am entirely my past, and that al people are.” But then you move immediately to imagine that you might “embrace something new.” How would such a thing be possible, in the story you’ve just told?

This paper, like your last one, uses no sources @ all; you should draw on @ least three. If you want to go exploring further in these particular dimensions, I’d highly recommend Once Upon a Number, by Temple mathematician John Paulos (who says that the gap between stories and statistics is a synecdoche for the better-known gap between literary and scientific cultures, and suggests that describing the world is a contest between the simplifiers (scientists, statisticians) and complicators (humanists, storytellers)--a.k.a. lumpers and splitters. You might look also @ Ray Jackendoff's Patterns in the Mind, a Chomskian argument that we have an inherent impulse to find the simplest way to make sense of missing information; @ George Lakoff’s book, Philosophy in the Flesh, which argues that we are programmed to see patterns: as pattern-seeking/pattern-making creatures, we make smaller sets from large amounts of information and, conversely, infer larger structures from whatever limited information is available; and @ Lisa Belkin's "Coincidence in an Age of Conspiracy," or "The Odds of That" (New York Times Magazine, August 11, 2002), which explores the unexpected connections, with no apparent causal relations, which "rattle and rivet" us, the surprising concurrences which we construct as meaningfully related. And then there’s Mary Cornish’s quirky little poem, “Numbers”….

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