More Math and Shakespeare

Well Professor, here's something more on math that you sparked.  Just a little thing though.  You wanted me to tie sin(x) in with Ophelia.  Here's something you can look at between her, Hamlet, and trigonometric functions.

First, here is what normal cosine and sine functions look like:

Now, what does this graph make you think of?

If you thought of both Hamlet and Ophelia going crazy, you are right!  Think of the oscillations as the frantic thinking of a person's mind as it nears certain outside influences.  Now, sin(1/x) has no real value when x=0.  We can think of that as the point where a person no longer wants to live.  So, where would Hamlet lie throughout his "to be or not to be" soliloquy?  What path does Ophelia follow?

With that under your belts, this one is just another way to view it:

So, let's imagine that the distance you go to the right represents a certain distance into the future.  For both Hamlet and Ophelia, they felt more and more constricted as time went on throughout the play.  So, for this sine-looking function, I'd say it could represent they way they both felt.  For example, let's take Ophelia.  She begins by seeing Hamlet's love for her die.  She feels pushed down.  Then her father dies.  She feels like she has lost everything.  As these, and other, events take place, she feels pushed into a corner more and more until she reaches the point of "1/x."