Original Math Notes
All Seasons
Episode 417: Pay to Play--Interactive Computations--Explore the Math
Episode 417: Pay to Play
Animation of the mathematical transformation from NUMB3RS to the treble clef
Mathematical transformation from NUMB3RS to the treble clef
Scene 2:
ALAN, CHARLIE and AMITA.  Amita has her keys and purse,
looking a little stressed for some reason.

          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...

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

          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


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 11:


Don and Colby at Don's desk, Charlie appears with the iPod.

          The program's meant to analyze

             (reacts, dryly)
          Seems like we might've seen that
          one coming...

          The mechanism's inspired.
          Brilliant, actually. It can
          process a song, then predict the
          expected level of success.

          You're saying it can tell whether a
          song will be a hit or not?

          Exactly. Within a certain level of
          statistical probability.

          C'mon, that's impossible.
          Music's... subjective. It's a
          visceral thing. How can an
          equation know if a song is good?

          We may want to think our tastes are
          unique... but they're not.
          There are particular rhythms, key
          changes, or chord patterns that, as
          humans, we find pleasing. Just as
          there are odors we find pleasant or
          This program's sampled thousands of
          hit songs, analyzed what they have
          in common... From there it can
          make a fairly accurate statistical
          guess as to what will be a hit and
          what won't.

          Kind of takes all the art out of
          it, doesn't it?

          But it's not art. It's business.

          So Hunter's carrying this thing
          around... to engineer his songs to
          be hits..?

          Maybe, but from what I can tell, he
          hadn't analyzed his own tracks yet.
          The data folders are set up, for
          his album and for 2BY4's as well...
          But the analysis was never run...

          Then we need to run it.

          The albums haven't been released
          yet. We can't get at the tracks.

          We can with a subpoena.


Scene 20:

Mathematics in music

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


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)."

Wikipedia. New Math

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