Interactive Computations

Use the free Wolfram *Mathematica Player* to interact with the math
behind NUMB3RS.

CHARLIE goes through a thick pile of files with LARRY -- CHARLIE Wideband Mixer-Circulator Retro-Reflector. LARRY Obviously not... CHARLIE Ternary computing. LARRY Mmm... no. Each rejected file going on a tall stack, next to a second, very small one, as AMITA and ALAN enter.

A number represented in binary is a
sum of the powers of
2 (1, 2, 4, 8, 16, ...) multiplied by 0 or 1. For example, 60 in binary notation is
111100 = 1×32 + 1×16 + 1×8 + 1×4 + 0×2 + 0×1, using six "bits".
Balanced ternary notation
multiplies each power of 3 (1, 3, 9, 27, ...) by -1, 0, or 1. In balanced ternary, 60
is 1__1__1__1__0 = 81-27+9-3+0, with __1__ indicating -1; 60 requires five "trits".
With weights 1, 3, 9, 27, and 81, the notation can be used to balance any unit amount
from 1 to 121 by putting the weights on either side of the balance pan.

CHARLIE With my NSA clearance suspended, sometimes it feels like that's all I get to do -- look. (beat) My next paper might very well be "Our Friend the Triangle." AMITA Actually, John Conway and Steven Sigur already wrote a great book on the subject.

LARRY I suspect I'm looking at a combinatorics problem. Would you mind -- AMITA Sure --

For *n* points in a unit square, find the three points that make
the triangle with minimal area. Finding the placement of *n* points that produces the largest such triangle
is known as the Heilbronn triangle problem.
The point placements shown here are the best known. Minimal triangles are colored red. All solutions
above 12 points are due to Mark Beyleveld and David Cantrell, with optimization and exact solutions found by *Mathematica*.

The SAME FEEDS that were in the War Room are visible on screens here, now -- as DON brings up the SPIDER program for Amita and Larry -- DON SPIDER is a -- AMITA -- real-time ATM tracking program... Charlie and I did work on its Distributed Neural Network -- along with half the Calsci math and computer departments...

This Demonstration shows a neural network evolving under rules similar to those for a four-neighbor
outer-totalistic cellular automaton.
You can sample a variety of evolution rules exhibiting integrate-and-fire-like behavior. Red indicates
cellular activity (a neuronal spike), while blue indicates inactivity. Color intensity encodes the value
of a binary internal state variable.

COLBY Then why risk Herman on the kidnappings in the first place? CHARLIE Because he was running his own version of a scheduling algorithm. AMITA (to others) Computers use them to weigh the duration or difficulty of different tasks against the system's resources and allocate them accordingly. DON So what does that tell us? CHARLIE The interesting thing about scheduling algorithms is that no one has come up with a perfect one. AMITA There are thousands -- the Smith Rule, the O2, the Beam Search... any programmer can design one, name it, test it... CHARLIE And just like a programmer's design... or a guitarist's signature riff, or a painter's brush stroke...

This Demonstration shows the optimal transport scheduling for two depots that are responsible for supplying
building materials to seven construction sites. Given the amount of supply available at each depot and the
demand at each site, the optimal scheduling minimizes the transport cost, assuming that the distance
between a depot and the site is the Euclidean distance.