Original Math Notes
All Seasons
Episode 417: Pay to Play---Explore the Math
Original Math Notes
Episode 417: Pay to Play
Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
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.


An abacus computes numbers by sliding beads on rods. In this Demonstration, click a bead to move it. The upper disks add 5. Thus each row can store the digits between 0 and 9.
Scene 6:
Hunter's iPod is hooked to Charlie's laptop, the display also
seen on one of the LCD's.  Data code spills down as it did in
Don's Suburban.  Charlie types as Don and DAVID look on --

          The encryption code is somewhat
          elementary... There.

Hill Cipher Encryption and Decryption

In a Hill cipher encryption, the plaintext message is broken up into blocks of length n according to the m × n matrix chosen. Each block of plaintext letters is then converted into a vector of numbers and is dotted with the matrix. The results are then converted back to letters and the ciphertext message is produced.
Scene 6:
AUDIENCE VISION - starting very tight on only a few letters,
then WIDENING to include several words.

                  CHARLIE (cont'd)
          It's made up of individual letters
          and words, but comparing letters
          and words would be meaningless...
WIDER now to include sentences and paragraphs.

                  CHARLIE (cont'd)
          To detect plagiarism, you'd need to
          look at larger strings: sentences,
          paragraphs, entire pages...
Pages of the book begin to turn, more and more rapidly. A
SECOND BOOK appears alongside, pages turning in unison.

                  CHARLIE (cont'd)
          A String Metric allows you to
          compare the two systems... and
          expose the plagiarist.
The page-turning suddenly stops, several passages in each
book HIGHLIGHTED.  Identical.

Brute-Force String Matching

Brute-force string matching compares a given pattern with all substrings of a given text. Those comparisons between substring and pattern proceed character by character unless a mismatch is found. Whenever a mismatch is found, the remaining character comparisons for that substring are dropped and the next substring can be selected immediately.
Scene 11:
Don and Colby at Don's desk, Charlie appears with the iPod.

          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.

Same but Different

The aesthetic success of all music lies in the constant unfolding of novelty versus familiarity. Is the next moment refreshingly surprising, but not too unexpected? A common compositional device that guarantees such success is to play an existing theme backwards (retrograde) or upside down (inversion).
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