[M.M.X.I.V. 182] Duck Dodgers

One of my favorite sixty-two-year-old cartoons will motivate this post.

This cartoon I am able to pull out some applicable math concepts from, and also distill a bad math joke.  These involve coordinates and calculus.  Don’t worry, this post should be accessible to everyone.  I should have shown it in class today, but thought that would be a strange first impression for my students.

So, in “Duck Dodgers and the 24.5th Century,” Duck Dodgers (Daffy Duck) gets the mission to travel to Planet X in order to obtain the shaving cream atom.  The boss shows a map of “Unknown,” but Daffy says that he will find it.

After putting the silly rocket in reverse, Dodgers tells his space cadet (Porky Pig) the route to get to Planet X, going on some really weird, convoluted path, and after Porky says that he knows how to get there, Dodgers is incredulous.

“Well, if we follow those planets [Planets A, B, C appear outside the window], we can’t very well miss Planet X!”

This gets into coordinates.  My non-technical definition of coordinates: A set of independent sub-descriptions which lead to a certain place/point.  These can be described graphically (e.g. on a map or a grid), algebraically (e.g. as the solution to an equation), or in words (e.g. a street address).

Street addresses are both numerical and verbal.  For example, the Technological Institute at Northwestern is at 2145 Sheridan Road.  Mapping this to numbers in the sense (East/West, North/South), I can describe it by (-600, 2145).  That is, 600 west and 2145 north.  The origin of this coordinate system (i.e. 0 EW, 0 NS), however, happens to be in Lake Michigan.  🙂

It would be nice if street addresses were always given in the order “East/West, North/South,” particularly when NO streets are numbered in a city.  In this case, it would be “Sheridan Road 2145” so that you know to go to 2145, and then can look up the east-west elsewhere.  That would never fly, I would guess…

In Lincoln, numbered streets start at 1st (duh), but the ones west of 1st are called “West nth Street.”  I always joked that, for example with Northwest 48th Street, “Why can’t it be Negative North 48th Street?”

Either way, it shows that there are easy ways to think about coordinates in terms of everyday places.  Another good example: at least in the USA, room numbers in a building often are coded such that the first digit(s) is/are the floor number, and the second digit(s) is/are the room number.  There can also be a wing coordinate coded in there.  For example, my office is M-445, which is on the 4th floor of the M-wing, room number 45.  That’s 3 independent coordinates.

The other math thing that Duck Dodgers has is the idea of integration as anti-differentiation.  Dodgers encounters Marvin the Martian, who is packing a disintegrating pistol.  Dodgers: “Little does he know that I have on my disintegration-proof vest.”

Of course, it only protected the vest, leaving a pile of dust and the vest.  Porky’s ACME Integrating Pistol restored Dodgers’ normal state, plus a constant of confusion!  Therefore, using the fact that $e^{x}$ is unaffected when a derivative is taken, IT is the disintegration-proof vest!  That must mean that Daffy Duck has a derivative (e.g. disintegration) of Dust times $e^{x}$.

The Fundamental Theorem of Calculus in action, based off "Duck Dodgers in the 24 1/2th Century."

The Fundamental Theorem of Calculus in action, based off “Duck Dodgers in the 24 1/2th Century.”

Yes, I can be so silly sometimes.  Gotta make math fun!

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Today is the one-hundred and eighty-second day of M.M.X.I.V.  That makes twenty-seven weeks.

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