Interactive Computations
Use the free Wolfram Mathematica Player to interact with the math behind NUMB3RS.
```POV -- CHARLIE, sandwiched between TWO BEDS OF NAILS -- a
SLAB OF CONCRETE on top of the upper bed.

LARRY, protective glasses on, has a sledgehammer over his

DON (CONT'D)
Okay....

CHARLIE
This isn't what it looks like.

EDGERTON
That's a relief... since it looks
perforate you.

LARRY
Actually, Professor Eppes is
protected by the most impenetrable
armor of all -- physics.

CHARLIE
My weight is distributed among the
spikes at a very comfortable 1.7
pounds each, with the kinetic
energy of the hammer --

LARRY
-- I believe, Charles, that the
drama of demonstration will be more
instructive.

CHARLIE
Right...

Larry brings down the sledgehammer...

DON
Whoa! Larry --

... SHATTERING the concrete. Charlie is still for a beat.

DON (CONT'D)
Charlie -- ?

Charlie grins -- enjoying the rush.

CHARLIE
Fine... I'm fine.

They remove the concrete, and help Charlie off the spikes.
```

# Bed of Nails

A bed of nails can actually be comfortable, if there are enough nails. A person's weight is divided by the number of nails under them. Here, Mr. Slab weighs 200 pounds, so the default bed is actually extremely painful.
```ENTER CHARLIE VISION --
The map becoming a scattered, fragmented pastiche of images
that will explain themselves later on:
-- a BIPLANE flying through the air
-- a MOUSE scampering across a field
-- a CURVING GRAPH LINE

CHARLIE
Didn't you forget to mark one --
(points to a spot in Wyoming)
-- here?

Edgerton looks at the map, double checks the reports --

EDGERTON
No... we don't have sightings
anywhere in Wyoming.

Charlie is a little surprised --

CHARLIE
Oh... okay...

DON
Why'd you think there was?

CHARLIE
Actually --
(beat)
-- I looked at the map and... just
thought there should be a point
there.

Larry looks at the map.

LARRY
Did you see some sort of pattern,
perhaps a Markovian path --
```

# Finite State Discrete Time Markov Chains

Consider a system that is always in one of n states, numbered 1 through n. Every time a clock ticks, the system updates itself according to an n×n matrix of transition probabilities, the (i,j)th entry of which gives the probability that the system moves from state i to state j at any clock tick. A Markov chain is a system like this, in which the next state depends only on the current state and not on previous states.
```ALAN and LARRY playing chess.

LARRY
Relocation is considered a highstress
event, but in my experience
it's been nothing less than
exhilarating.
(beat)
When I sold my house... it was a
Promethean shrug, the chains of
earthly concerns falling from my
shoulders.
```

# Explaining Real Estate Price Bubbles

Bubbles form in investment real estate, leading to the questions: Where is the top? When will prices no longer rise? An answer to both of these questions is: when the money runs out. In real estate investment there are two sources of funds: the buyer's investment (down payment) and the lender's capital (the loan amount). The lender operates as a sort of governor, investing less as prices rise, thereby refusing to finance the speculative part of the bubble (that part unsupported by commensurate increases in net rent).
```
CHARLIE
This is the Green River robbery.
The missing point on a curve I
didn't realize I was looking at.
(beat)
It's a complex variation of
something called a pursuit curve...
created when one point chases
another across a graph. You see...

BACK TO AUDIENCE VISION --
of our WWI dogfight --

CHARLIE (CONT'D)
-- if a fighter pilot flies
straight at the point where he sees
an enemy plane --

-- the biplane turns, but the the Red Baron flies straight --
seeing nothing but empty air --

CHARLIE (CONT'D)
-- by the time he gets there, the
plane will be gone.

-- turning and finding the biplane again -- this time
matching its maneuvers, banking when the biplane banks,
dipping when the biplane dips --

CHARLIE (CONT'D)
Just to maintain his following
distance, the chasing pilot has to
matching the movements of his
quarry.

-- then, when the biplane turns -- the Red Baron turns deeper
-- cutting into its path --

CHARLIE (CONT'D)
If he wants to catch the plane, he
has to anticipate its movement --
plane --

-- and firing its machine gun, which hits the biplane
broadside; it goes down in a plume of smoke...

BACK TO SCENE
CHARLIE (CONT'D)
(to Edgerton)
You've been locked in a pursuit
curve with the killers; constantly