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Adventures in the Computational Universe

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Laplace, Leibnitz, Decartes and Kant espoused the idea that the universe was ... anything more complex, we do not see any insects or humans or Chopin preludes ... – PowerPoint PPT presentation

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Title: Adventures in the Computational Universe


1
Adventures in the Computational Universe
Modelling Flocking Behaviour
2
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
3
Math Gets the Job Done
4
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 )
5
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
6
Tyranny by the Machine
  • Subsequent generations of machines would develop
    with no limit to their complexity


I, Robot (2004) with Will Smith
7
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)
8
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
9
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
10
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
11
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.
12
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.
13
Wolfram Model
A hundred generations of Rule 30
14
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15
The pattern is neither regular nor completely
random. It appears to have some order, but is
never predictable.
16
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17
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18
Mollusc Pigmentation Patterns
19
Beauty of a Recursive Model
Lindenmayer modeling of plant forms from simple
branching rules in 3D space
20
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.
21
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

22
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
23
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/
24
Game of Life References
ISBN 0688039758
Wikipedia Game of Life
25
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
26
Self Organization of Flocking Behaviour
  • emergent phenomena
  • where a collection of individuals interact
    without central control to produce behaviour
    which is not explicitly programmed

27
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
28
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/
29
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
30
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

31
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
32
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

33
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.

34
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

35
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

36
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

37
Many Worlds Interpretation
  • The parallel processing character of quantum
    computation necessitates the existence of a
    multiverse.

Lee Skinner, 2005, Many Worlds
38
  • 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
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