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
head, about to smash the concrete slab.
DON (CONT'D)
Okay....
CHARLIE
This isn't what it looks like.
EDGERTON
That's a relief... since it looks
like your friend there is about to
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.
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 --
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.
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
constantly adjust his direction --
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 --
aim his nose ahead of the lead
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
adjusting and readjusting your
search pattern to anticipate their
movement.
Given a moving prey (black path) with unit
speed
and a time-dependent position (
x(
t),
y(
t)), a predator (colored path), moving with speed
v, runs at all times in the direction of the current position of the prey. The resulting path is known as a
pusuit curve.
