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\title{Explanation by Metaphor: \\ What I Learned in \\ Introduction to Critical Feminist Studies}

\author{Amanda Hittson}

\date{\today}

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In thinking about trying to convey what I learned in this class to the class I found myself hung up on what method I would use to convey what I learned. Should I draw a picture? Or write a speech? Or write an essay? Since the grasp I have on what I learned in this class seems to me to be so tenuous I rejected all of these. I decided I would try to convey what I learned through a more tenuous means: a metaphor. In particular, I wanted to construct a metaphor that would explain how this class has made me think about the world. I start with a sketch of what I think I learned in the class to motivate my metaphor. I learned that communication of experiences is reductive in meaning. If I have an experience, say when I walked to class I tripped and fell in a mud puddle, and then try to explain the experience to you by communicating, say through sentences in the English language, my experience. Then I could say I fell in a mud puddle. Then you, the class try to get at what I mean, you try to understand what I experienced. So you might remember a time when you fell in a mud puddle and conclude that what I experienced was similar. But you might have never tripped into a puddle before and so you might imagine it. However, experience is a vague word. In tripping I might have felt fear for my safety, I might have felt anxiety that I would drop this sheet of paper and render it unreadable... I might have thought various things, I might have smelled a variety of smells or tasted a variety of tastes or \ldots My point is that in trying to convey to you through, say languague, I must pick out what I consider to be the important parts of the experience, for example the fact that the mud reminded me of how far from home I am because where I come from there isn't much mud because it doesn't rain much and as a child I always wanted to play in the mud, but here it rains so often and is very muddy and so what I want to convey to you is my feeling of alien-ness in tripping on the east coast. However, it could be that some person can't move beyond the fact that one time she tripped in the mud on a trip to the mall with her friends who completely humiliated her for the remainder of the trip and so all she gains from my story is that I must have felt humiliated. So my starting metaphor tries to describe the interaction between the at least two-step process of communication and experience. Another thought I gained from this class is that a person's identity isn't constant and may or may not fit into the language categories at any time. So my metaphor tries to take this into account as well. Since my main training is in mathematics and I find it easiest to think of mathematical metaphors, but probably most of the people in this class haven't had any math beyond calculus, I decided to try to make my metaphor in the simplest language of calculus that I could come up with. If communication, say sentences, are represented by some subset of $\R k$, with $k>0$, then to convey how information is lost in communication, I will say that the world and all experiences in the world, for each time $t$ is some subset of $\R n$ with $n>k$. So in order to communicate, what each person tries to do is represent life with language. In the words of my metaphor, each person $A$ at time $t$ tries to find a function $f_{A,t}: \R n \to \R k$. Then if person $A$ is trying to convey an experience $E$ to person $B$, person $A$ says to person $B$, $f_{A,t}(E)$. Then person $B$ tries to recover the experience from these sentences, probably by looking at $f_{B,now}^{-1}(E)$. What further complicates this is the changing of people over time. At each point in time person $A$ is (potentially) a changed person then at time $t' \neq t$. So if you think of a person, what you really have is a function $g: \R{} \to \R n$ where $g(t)$ is the set of experiences that define a person at time $t$ and most likely depend on $t < t'$. Before this class I thought that $g$ was continuous and locally mostly constant. After having taken this class I have no idea if $g$ is continuous or not and think that $g$ is probably mostly not constant. Also, the way that I fit education into this metaphor is that teachers try to teach students standard ways of defining $f: \R n \to \R k$; they try to erase language's dependence on $A$ and on $t$. This class in particular attempted to examine why this might be problematic. \noindent \underline{Note}: I have written this up in \LaTeX, a program that most mathematicians use to write math papers. In an effort to be open with the class I am posting not only the pdf-version of this paper that one would normally turn in, but also the code written to produce this picture.

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