Original Math Notes
All Seasons
Season 5
Episode 520: The Fifth Man
Voronoi pyramids of a parametrized spiral
Scene 1:
                  ALAN
          Maybe all those great minds will rub
          off on you -- just sitting here.

Charlie smiles.  Then... a thought sparks --

FLASH CHARLIE VISION
PHOTOS of EINSTEIN, HEISENBERG, SHRODINGER, CURIE, etc. (with
an overlay of NAMES and IMAGES OF THEIR ACCOMPLISHMENTS --
i.e., E = mc^2, the Uncertainty Principle, Shrodinger's Cat, etc.)
float through space and come to rest in a FAMOUS 1927 PHOTO
of them gathered and seated for a portrait, as we MATCH INTO:

Charlie -- pulling the SAME HISTORIC PHOTO from his box of stuff --

                  CHARLIE
          ...That's it, Dad.  I've been dancing 
          around the idea of neural networks.
          Maybe what I'm looking for has been
          here in front of me the whole time --
          a historical neural network.

                  AMITA
          "Great minds think alike."

Gravitational Lensing of a Point Source »

Einstein's general relativity tells us that matter and energy bend spacetime. One of the best examples of this can be seen with "gravitational lensing." Lensing occurs when the path of light from a source (or in this case a grid of point sources) travels near a massive or energetic object, called a "lens," and bends due to the mass/energy of the lens. In this Demonstration the massive object is an infinitely small point of variable mass, marked with a brown dot.
Scene 2:
                  NIKKI
          So what've you got?
            (off his blank stare)
          You haven't even started yet?

                  CHARLIE
            (thinking on his feet)
          In terms of analyzing their M.O.,
          classic game theory -- maybe a "Payoff
          Matrix" -- should do the trick.

Restricted NonCooperative Game Theory »

In conventional non-cooperative game theory, each player can see and can instantaneously select any element of its strategy set in response to the other players' strategy selections. In real settings, however, the strategies available to a player at any given time will often be a function of the strategy it selected at a prior time. For example, changing only one aspect of a strategy at a time may be possible. Sometimes these constraints on the dynamics of strategy selection may be the result of external circumstances or cognitive limitations on the part of the player; other times they may be deliberately engineered by the player itself.
Scene 59:
                  DAVID
          Even if we make a key, that still
          doesn't tell us where the box is.
          There are jewelry wholesalers all
          over the city, Charlie.

                  CHARLIE
          Path Minimization should help us there.

                  LIZ
          ...analyzing the most efficient
          routes from point A to point B.
             (off Charlie's look)
          Hey, some of this stuff sticks.

Traveling Salesman Game »

You are a traveling salesman. Your task: visit the cities (represented as dots on the gameboard) one by one by clicking them. Start anywhere you like. You will trace out a route as you proceed. You must visit every city once and then return to your starting point. The goal is to find the shortest possible route that accomplishes this. Your total distance is recorded at the bottom of the panel, along with the total distance of the best route that Mathematica can find.
Scene 60:
                  CHARLIE
          I thought Path Minimization would be
          the easy part.

                  AMITA
          What's the problem?

                  CHARLIE
          I'm using Djikstra's algorithm,
          overlaying it with CalTrans data on
          traffic flow...  It's not working.

Connecting Towns Using Kruskals Algorithm »

A government wants to construct a road network connecting many towns. Suppose each road must connect two towns and be straight. Kruskal's algorithm gives the least expensive tree of roads. Allowing nodes that are not towns leads to a different problem involving soap bubble theory.
 
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