Original Math Notes
All Seasons
Season 5
Episode 521: Disturbed
Fourier transform of a 2-D random signal
Scene 7:
Charlie in the cosmos -- a vast star field.

          The universe creates an endless
          background of electromagnetic 
          static.  SETI, the Search for Extra- 
          terrestrial Intelligence, uses
          algorithms to sift through all this 
          random cosmic "noise"--
A vast array of radio telescopes stretching to the vanishing
point -- aimed at the heavens -- receiving emissions.  We 
HEAR the HISS, CRACKLE and STATIC of random cosmic noise. 

                  CHARLIE (cont'd)
          -- to find a signal that is complex 
          yet repetitive -- a non-natural 
          pattern created by an intelligence. 

We HEAR a faint repetitive ALIEN SIGNAL emerge from the
static (think eerie Morse Code). It grows louder.

Decoding the Arecibo Message »

In 1974 a message was beamed from the Arecibo radio telescope towards a cluster of stars 25,000 light years distant in the constellation of Hercules. It consisted of 1679 binary digits transmitted in sequence. To read the message, the binary digits must be formed into a low resolution image on a two-dimensional grid. But what sized grid should be used? Use the slider control to vary the number of columns in the grid and "decode" the Arecibo message.
Scene 7-2:
                  CHARLIE (cont'd)
          I adapted the signal detection 
          algorithms to analyze the patterns--

Charlie moves to his laptop and puts his data up on the big
screen: a colorful circular and linear Spatio-Temporal
Visualization GRAPH (very eye-popping and complex).

                  CHARLIE (cont'd)
          --and got this Spatio-Temporal 
          visualization model.  The sequence
          is half lunar, indicative of a
          recurring emotional need buffered
          by planning and surveillance. 

Lunar Calendar Maker »

The Moon goes through a cycle of phases approximately every 29.5 days. The Moon orbits the Earth about every 27.3 days, but the same relative positions of the Moon, Earth, and Sun occur less often. The reason for the discrepancy is that while the Moon orbits the Earth, the Earth is also moving in its orbit around the Sun.
Scene 12:
David on the move through the office -- he's now the acting
supervisor. Charlie follows.

          The pattern isn't perfect. There
          are -- micro-clusters.  And they
          are, currently, anomalous.  But the
          overall pattern is extraordinarily
          regular, indicative--

          How many murders make up a "microcluster?"

          Two.  Mostly.  Sometimes three.

          That's very micro.

          But these are outliers.  The macro
          pattern is persistent and
          statistically valid.

David stops, meets Charlie's eyes.

Cluster Analysis for 2-D Points »

Cluster analysis groups data elements according to a similarity function. In this case, the similarity function is simply the Euclidean distance function, which allows us to group them into clusters automatically based on how close they are. Drag the points around or vary their number to see how they are grouped into clusters.
Scene 14:
          But the time pattern -- the
          knowledge of victims' routines.
          Very similar.  And then this-

Gene flips to a POLICE PHOTO, CLOSE ON HANDS tied with ROPE.

                  GENE (cont'd)
          Constrictor knot.  Simple, secure.
          Difficult to untie once tight.
          Same knot was used in five of the
          cases you're looking into.
          Whoa. Freaky.

Knots »

See some of the variety of known knots in various families.
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