Adventures in the Computational Universe

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Adventures in the Computational Universe
Modelling Flocking Behaviour
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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
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Math Gets the Job Done
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John von Neumann

• 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.

John von Neumann ( 1903 1957 )
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Automaton

• Von Neumann wondered whether a machine could
  produce a machine more complex than itself

Photoshoped by 123Lezy -The Young Shepherdess by
Bouguereau, Adolphe-William, 1895
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Tyranny by the Machine

• Subsequent generations of machines would develop
  with no limit to their complexity

I, Robot (2004) with Will Smith
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Model the Universe

• Stanislaw Ulam suggested an abstract universe run
  by self-consistent 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)
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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
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Computational Irreducibility
The failure of mathematical models to provide
explicit solutions to complex phenomena
Human behaviour is computationally Irreducibile
Position and velocity can be calculated exactly
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Cellular Automata

• 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
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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.
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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.
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Wolfram Model
A hundred generations of Rule 30
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The pattern is neither regular nor completely
random. It appears to have some order, but is
never predictable.
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Mollusc Pigmentation Patterns
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Beauty of a Recursive Model
Lindenmayer modeling of plant forms from simple
branching rules in 3D space
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A Wolfram Critic

• 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.
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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

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The Developer
The Game of Life made its first public appearance
in the October 1970 issue of Scientific American,
in Martin Gardners Mathematical Games column.
Mathematician John Horton Conway
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Rules of the Game

• 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).

FREEWARE Game of Life 1.5 http//www.bitstorm.or
g/gameoflife/
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Game of Life References
ISBN 0688039758
Wikipedia Game of Life
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Purposeful Activity

• 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
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Self Organization of Flocking Behaviour

• emergent phenomena
• where a collection of individuals interact
  without central control to produce behaviour
  which is not explicitly programmed

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Examples of Decentralized Behaviour

• 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
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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/
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The Universe Computes

• 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
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As soon as the universe began, it began computing

• It is the computational character of the universe
  which allows for the evolution of complex systems
  from the fundamental laws of physics

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Quantum Mechanics is Weird

• Seth Lloyd from MIT describes himself as a
  quantum computer mechanic he designs and fixes
  quantum computers.

ISBN 1-4004-092-2
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Double-Slit Experiment

• 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 same time

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Monkeys at Typewriters

• 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.

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Monkeys at Computers

• 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

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Occams Razor

• 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

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Monkeys at Computers

• 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

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Many Worlds Interpretation

• The parallel processing character of quantum
  computation necessitates the existence of a
  multiverse.

Lee Skinner, 2005, Many Worlds
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• 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 Cats Eye Nebula