Original Math Notes
All Seasons
Episode 417: Pay to Play--Interactive Computations--Explore the Math
Episode 417: Pay to Play
Mathematical transformation from NUMB3RS to the treble clef
Scene 2:
INT. EPPES HOUSE - LIVING ROOM/FOYER - NIGHT
ALAN, CHARLIE and AMITA.  Amita has her keys and purse,
looking a little stressed for some reason.

                  AMITA
          What do you think?  This time of
          night, I can probably just take the
          110 to the 105, right?  Shouldn't
          be too much traffic...

                  CHARLIE
          If you want, we can run a quick
          aggregated speed density function,
          or we could do a mesoscopic traffic
          simulation...

                  ALAN
          Give the abacus a break, for once.
          The Dodgers are in Houston.  Rush
          hour's long over.  The 110 to the
          105 should be just fine.

Mesoscopic scale

The term "mesoscopic" refers to the length scale at which bulk (i.e., average) properties of a phenomenon can be considered without the need to describe the behavior of individual constituent atomic (i.e., indivisible) particles. Charlie's usage thus refers to a study of traffic patterns in which the overall flow of cars is modeled without needing to include characteristics or properties of individual cars making up that flow. (Of course, it may not be much of a reassurance to Los Angeles drivers to know that traffic is flowing well at mesoscopic scales when it is not flowing well at the scale of their own automobiles.)

Charlie could mention he's got some traffic programs he could run, used for example in Episode 303, "Traffic." Charlie could also propose using mutual information to model each route as a separate vehicle, substituting real-time traffic data and setting the airport to be the crossing point (for example, see the research paper "Enhancing Border Security: Mutual Information Analysis to Identify Suspect Vehicles" by Siddharth Kaza, Yuan Wang, and Hsinchun Chen).

The abacus

Abacus

The abacus is a mechanical counting device consisting of a series of parallel rods on a frame that hold beads. Each bead represents a counting unit and each rod represents a place value. The primary purpose of the abacus is not to perform actual computations, but to provide a quick means of storing numbers during a calculation. Abaci were used by the Japanese and Chinese, as well as the Romans.

In his book "Surely You're Joking, Mr. Feynman," the late Nobel-Prize-winning physicist Richard Feynman discusses his ability to perform computations more quickly in his head than a talented operator could achieve using an abacus using a variety of mathematical properties, shortcuts, and cleverness.

Scene 20:
EXT. L.A. RIVER - VIDEO SET - DAY

Mathematics in music

                  CHARLIE
          Larry, that's hip hop.  It's not
          all about what you say, it's how
          you say it, right, Kilo?

                  KILO
          Look at the Professor droppin'
          knowledge.  Maybe you oughtta come
          through our lab one day and lay
          down some friendship math rhymes...

There have been a number of prominent songs involving mathematics and mathematicians. Some mathematicians themselves are even talented performers. One prominent example is the great Tom Lehrer, who not only produced insightful and irreverent political satire but also wrote and performed such mathematical ditties as "New Math" (lampooning the 1960s movement that promoted the teaching of set theory and base arithmetic very early in math education: "It's so simple, so very simple, that only a child can do it") and "Lobachevsky" (taking the great Russian mathematician and codiscoverer of non-Euclidean geometry as a fictitious example of writing mathematics papers by plagiarizing others: "Plagiarize. Let no one else's work evade your eyes. Remember why the Good Lord made your eyes, so don't shade your eyes, but plagiarize, plagiarize, plagiarize. But be sure always to call it 'research'").

MathWorld contains a listing of mathematical references in music, ranging from Gilbert and Sullivan's famous "The Major General's Song" (which mentions, among other things, differential calculus), to Rhett Miller's curious mention of long division in his 2006 song "Singular Girl," to the cult Schoolhouse Rock favorite "My Hero, Zero," which extols the virtues of the number zero (performed by the Lemonheads).

An amusing (at least to mathematicians) and clever song, "Finite Simple Group (of Order 2)," has been written and performed by the Northwestern University mathematics department a capella group "The Klein Four Group" (whose name itself is a mathematical pun referring to the Klein four-group, also known as the vierergruppe). This song employs numerous, not-so-subtly-veiled mathematical puns and is predicated on the fact that the cyclic group on two elements is both finite and simple (in a group theoretic sense), and hence is commonly known to mathematicians as "the finite simple group of order two."

References

Feynman, R. P. and Leighton, R. "A Different Set of Tools." In "Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character. New York: W. W. Norton, pp. 69-72, 1997.

Kaza, S.; Wang, Y.; Chen, H. "Enhancing Border Security: Mutual Information Analysis to Identify Suspect Vehicles." Decision Support Systems 43, 199-210, 2007.

The Klein Four Group. "Finite Simple Group (of Order Two)." http://www.youtube.com/watch?v=UTby_e4-Rhg

Wikipedia. New Math

 
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