Transcript Slide 1

Adventures in the Computational
Universe
Modelling Flocking Behaviour
Clockwork Universe
Laplace, Leibnitz,
Decartes and Kant
espoused the idea that
the universe was
nothing more than a
vast clock, composed
of many interacting
parts.
http://www.philgraham.net/excursion1.htm
Math Gets the Job Done
p  mv
H   j   U  PV   j N j
F  ma
G   j   U  PV  TS   j N j
m1m2
FG  GN 2
r
dS  dQ
T2  T1
T1T2
E  
1 E j
 B 

c t c
B  0
1 B
 E 
0
c t
John von Neumann
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John von Neumann ( 1903 – 1957 )
Neumann was a pioneer of the
modern digital computers.
He developed the computer
not merely as a calculating
machine but considered it
foremost as a logic machine.
In the same way, he regarded
life as a process of logical
functions with no room for
randomness.
Automaton
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Photoshoped by 123Lezy The Young Shepherdess by
Bouguereau, AdolpheWilliam, 1895
Von Neumann
wondered whether
a machine could
produce a
machine more
complex than
itself
Tyranny by the Machine
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I, Robot (2004) with Will Smith
Subsequent
generations
of machines
would
develop with
no limit to
their
complexity
Model the Universe
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Stanislaw Ulam
suggested an abstract
universe run by selfconsistent rules
Create a model which
is complex enough to
model the essentials
of the universe but
otherwise keep it as
simple as possible.
Stanislaw Ulam, (1909-1986)
“A New Kind of Science”
"I have come to view it as one of the
more important single discoveries in
the whole history of theoretical
science." Stephen Wolfram, p2.
Stephen Wolfram
ISBN 1-57955-008-8
Computational Irreducibility
The failure of mathematical models to provide explicit solutions
to complex phenomena
Position and velocity
can be calculated
exactly
Human behaviour is
computationally Irreducibile
Cellular Automata
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Consider a grid
populated with
cells at various
states at a given
time
Recalculate the
arrangement or
state of cells at
fixed steps of
time
SARS Infection Model
http://jasss.soc.surrey.ac.uk/7/4/2.html
Wolfram Model
Rule 1
Rule 2
Most of the rules are degenerate, meaning they create
repetitive patterns of no interest.
However there are a few rules which produce surprisingly
complex patterns that do not repeat themselves.
Wolfram Model
we can view the state of the model at any time in the future as
long as we step through all the previous states.
Wolfram Model
A hundred generations of Rule 30
The pattern is neither regular nor completely random.
It appears to have some order, but is never predictable.
Mollusc Pigmentation Patterns
Beauty of a Recursive Model
Lindenmayer modeling of plant forms from
simple branching rules in 3D space
A Wolfram Critic
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these automata could
run for trillions
iterations, and the
image would remain
at the same limited
level of complexity
these patterns do not
evolve into anything
more complex, we do
not see any insects or
humans or Chopin
preludes
Ray Kurzweil,
Boston Globe, Sept. 25, 2005
Ray Kurzweil takes hundreds
of nutritional supplement pills
every day in order to
reprogram his biochemistry.
What is the Game of Life?
This is a game with
• no winning or
losing
• no players
controlling the
game
• fate is
predetermined by
simple rules
The Developer
The Game of Life made its first
public appearance in the October
1970 issue of Scientific American,
in Martin Gardner’s “Mathematical
Games” column.
Mathematician
John Horton Conway
Rules of the Game
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FREEWARE Game of Life 1.5
http://www.bitstorm.org/gameoflife/
A dead cell with
exactly three live
neighbors
becomes a live cell
(birth).
A live cell with two
or three live
neighbors stays
alive (survival).
In all other cases,
a cell dies or
remains dead
(overcrowding or
loneliness).
Game of Life References
ISBN 0688039758
Wikipedia: Game of Life
Purposeful Activity
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There is no need for a
central controller
orchestrating behaviour
Each member exchanges
information with its
neighbour and acts for
some common purpose
From simple, shortsighted,
generally selfish actions, a
transcendent global
behaviour emerges
William Blake, 1794
Ancient of Days – God as Architect
Self Organization of Flocking Behaviour
emergent
phenomena
 where a collection
of individuals
interact without
central control to
produce behaviour
which is not
explicitly
programmed
Examples of Decentralized Behaviour
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Ant behaviour is
determined by the local
interactions of many ants
car traffic patterns arise
from local interactions
among individual cars
antibodies seek out
bacteria in a systematic
attack without generals
corporations are
decentralizing
management structures
The centralized mindset:
intuition suggests that
when there is structure
there must be an organizer
Self organized ant behaviour
Flocking Behaviour Rules
Separation:
steer to avoid
crowding local
flockmates
Alignment:
steer towards
the average
heading of local
flockmates
Cohesion:
steer to move
toward the
average position
of local
flockmates
Craig Reynolds http://www.red3d.com/cwr/boids/
The Universe Computes
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In the universe, every
particle processes
data
Because the universe
is governed by the
laws of quantum
mechanics, every
elementary particle
registers bits of
information
The universe is a
quantum computer
which computes its
own behaviour
“The Universe at a Glance"
mural for the Metanexus Institute
As soon as the universe began, it
began computing
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It is the
computational
character of
the universe
which allows
for the
evolution of
complex
systems from
the
fundamental
laws of physics
Quantum Mechanics is Weird
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Seth Lloyd from MIT
describes himself as a
quantum computer
mechanic; he designs
and fixes quantum
computers.
ISBN 1-4004-092-2
Double-Slit Experiment
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Light as waves will create an
interference pattern at the far wall
A light particle reaching the double
slit will appear at both slits at the
Monkeys at Typewriters
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We can consider a
large number of
monkeys typing away
randomly at
typewriters.
Eventually there will be
some character strings
that are meaningful but
the character that
follows the string will
be a mistake.
This will not lead to
patterns, evolution nor
complexity.
Monkeys at Computers
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Now imagine
monkeys typing into
computers.
The random
characters will
eventually produce
short meaningful
programs.
But a short program
can produce a wide
variety of
interesting outputs
Occam’s Razor
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If there is a choice between theories
then the correct one is the simpler of
the two.
The shorter or the more simpler
program that generates the needed
complexity will be the correct one.
These simpler programs will produce
a universe suspiciously similar to our
own
Monkeys at Computers
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The computers are the quantum laws of
nature which process input
The monkeys are quantum fluctuations or
accidents within the fabric of the universe
The quantum fluctuations are injecting
new information for the quantum laws to
process
Many Worlds Interpretation
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The parallel
processing
character of
quantum
computation
necessitates the
existence of a
multiverse.
Lee Skinner, 2005, Many Worlds
“The collision of two atoms can - and
does – change the future of the
universe.”
At the astronomical scale atoms do collide and
provide us with wonders of the universe as in
this supernova remnant the Cat’s Eye Nebula