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Gabriel’s Horn

By Mark | March 27, 2008

Or: How to fit an infinite surface area into a finite space, and how that relates to my student debt

Gabriel’s Horn, a/k/a Torricelli’s Trumpet
Gabriel's Horn, the mathematical version


There is a three-dimensional mathematical figure known as Gabriel’s Horn which has an infinite surface area and a finite volume. You create it by graphing y=x^(-1) where x >or = to one, then spinning that 2-D graph around the x-axis. Put into layman’s terms, that is like a banana with an infinitely large peel but that doesn’t contain any more “banana-stuff” inside. Imagine that: an infinity contained within a finite volume, an unlimited amount held by a limited object.

This the perfect analogy for my student loans.

Here I am, a finite individual in a finite space with a finite income and a finite attention span, and somehow I am expected to pay off a debt that growing, presumably exponentially, every day. I say “presumably exponentially” because I didn’t look at the terms of my promissory note that closely. The interest rate may be geometric, for all I know. The main point is that a whelk has a better chance in a supernova than I have against the financial volcano that is Sallie Mae.

Being debt-free is like this.
Unicorn

I have so much debt that I cannot realistically picture the day that it will be paid off; I can imagine that day, but not in any way that resembles the real world. When I imagine having zero debt, I also imagine other fantastical things that I’d like but will probably never have, like a unicorn. Or a teleportation pad in my house. Or an angst-free childhood. I’ve often heard that “you can’t put a value on an education.” This is true: a precise value is impossible to pin down because interest accrues. To put a value on an education, you have to add the e^(rt) term.

The reason I’m writing about this is that, for the first time in my life, I no longer see the “paying back the debt” phase of my life as occurring some time in the future, but as happening right now. I wouldn’t trade the college or graduate experiences that I have been lucky enough to get for the world, but, dang, it turned out to be a lot of money. How I feel about my education right now is broadly equivalent to how I feel after a night of hard, hard drinking. It feels awful, and yet I oddly don’t regret the decisions that have gotten me to this point. Also, I’m probably going to throw up.

Topics: Science / Evolution, Humor, Education | Trackback | Comments RSS

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