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Aspiring:mathematician, composer, photographer, fiddler

12 Dec 2013 | categories: Teaching

Catullus of the Canopy

The last question of my differential equations exam yesterday was:

A sloth has just written to you in your capacity as Dear Abby columnist for the Rainforest Gazette. Use expertise you gained in this course—solve equations, sketch phase portraits, compute limits, whatever it takes—to put this poor sloth's mind at ease.
Dear Abby,
I am in love. Majorly. But the object of my desire is indifferent.
I’ve been trying to size up just how hopeless the situation is.
I’ve managed to find an equation which seems to perfectly predict how her desire x for me and my desire y for her evolve over time. (Positive means desirous, negative means…the sad current state of affairs with x.)
Here it is: x’=x+y, y’=–x+3y.
The problem is I have no idea how to solve it. Seriously. This equation is whack. I’ve run out of ideas and tree bark for doodling with my claws. Even the iguanas (of all creatures!) are mocking my befuddlement.
And needless to say, Euler’s method converges too slowly for sloths.
Can you help me work out if she’ll ever come round?
That is to say, will x and y end up positive in the long run?
I am, as it happens, among the most patient of creatures.
But my heart needs a glimmer of hope to cling to.
Yours in need,
  Catullus of the Canopy

My favorite answer to it—one which followed a rigorous & correct mathematical analysis—was:

Dear Catullus of the Canopy,
Like Catullus you, dear friend, are dealing with some heavy unrequited love. Rough stuff, isn’t it? “Odī et amō” as our favorite Latin poet would say. Frankly, I’ve been dealing with the same issues, so I know yours all too well. The object of MY affection will send smiles and greeting from across the quads of campus, but has the audacity to follow up with not one text, call, or offer of a date. I imagine it must be the same up in the treetops for you, and that you’re feeling as green as the moss that surrounds you, as blue as the sky stretched above your canopy.
But fear not, my fair Catullus, for there is hope! Although your lady’s affections may be negative or indifferent now, with time she will see just how sexy your three toes and slow-motion body action are. Your love will increase exponentially, too, and although you may reach your love capacity sooner than her, she WILL see the light. If I can make it through hours studying for finals in C level of MSE library, you can make the trees sing with your love. Invite her to some hipster movie date, or chat it up about your favorite Stephen King and Ray Bradbury novels (two techniques that have worked for me!) Once your relationship goes a little further, you two can even break out some of those dirtier Catullus poems (har-har).
Good luck and godspeed (figuratively, not literally you sloth),
Abby ❤

[The question, incidentally, made the most oblique of references to Buñuel’s Obscure Object of Desire (1977).]