Adventures in the Computational Universe Modelling Flocking Behaviour.
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Transcript of Adventures in the Computational Universe Modelling Flocking Behaviour.
Adventures in the Computational Adventures in the Computational UniverseUniverse
Modelling Flocking Behaviour
Clockwork UniverseClockwork Universe
http://www.philgraham.net/excursion1.htm
Laplace, Leibnitz, Decartes and Kant espoused the idea that the universe was nothing more than a vast clock, composed of many interacting parts.
Math Gets the Job DoneMath Gets the Job Done
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John von NeumannJohn von Neumann Neumann was a pioneer of the Neumann was a pioneer of the
modern digital computers.modern digital computers.
He developed the computer He developed the computer not merely as a calculating not merely as a calculating machine but considered it machine but considered it foremost as a logic machine. foremost as a logic machine.
In the same way, he regarded In the same way, he regarded life as a process of logical life as a process of logical functions with no room for functions with no room for randomness.randomness.
John von Neumann ( 1903 – 1957 )
AutomatonAutomaton Von Neumann Von Neumann
wondered whether wondered whether a machine could a machine could produce a produce a machine more machine more complex than complex than itselfitself
Photoshoped by 123Lezy -The Young Shepherdess by Bouguereau, Adolphe-William, 1895
Tyranny by the MachineTyranny by the Machine
Subsequent Subsequent generations generations of machines of machines would would develop with develop with no limit to no limit to their their complexitycomplexity
I, Robot (2004) with Will Smith
Model the UniverseModel the Universe Stanislaw Ulam Stanislaw Ulam
suggested an abstract suggested an abstract universe run by self-universe run by self-consistent rulesconsistent rules
Create a model which Create a model which is complex enough to is complex enough to model the essentials model the essentials of the universe but of the universe but otherwise keep it as otherwise keep it as simple as possible.simple as possible.
Stanislaw Ulam, (1909-1986)
“ “A New Kind of Science” 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 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
Cellular AutomataCellular Automata
Consider a grid Consider a grid populated with populated with cells at various cells at various states at a given states at a given timetime
Recalculate the Recalculate the arrangement or arrangement or state of cells at state of cells at fixed steps of fixed steps of timetime
SARS Infection Model http://jasss.soc.surrey.ac.uk/7/4/2.html
Wolfram ModelWolfram 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 ModelWolfram 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 ModelWolfram 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 PatternsMollusc Pigmentation Patterns
Beauty of a Recursive ModelBeauty of a Recursive Model
Lindenmayer modeling of plant forms from simple branching rules in 3D space
A Wolfram CriticA Wolfram Critic
these automata could these automata could run for trillions run for trillions iterations, and the iterations, and the image would remain image would remain at the same limited at the same limited level of complexity level of complexity
these patterns do not these patterns do not evolve into anything evolve into anything more complex, we do more complex, we do not see any insects or not see any insects or humans or Chopin humans or Chopin preludes 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?What is the Game of Life?
This is a game with This is a game with • no winning or no winning or
losinglosing• no players no players
controlling the controlling the gamegame
• fate is fate is predetermined by predetermined by simple rulessimple rules
The DeveloperThe DeveloperThe 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 GameRules of the Game A dead cell with A dead cell with
exactly three live exactly three live neighbors becomes neighbors becomes a live cell (birth).a live cell (birth).
A live cell with two A live cell with two or three live or three live neighbors stays neighbors stays alive (survival).alive (survival).
In all other cases, a In all other cases, a cell dies or remains cell dies or remains dead (overcrowding dead (overcrowding or loneliness).or loneliness).FREEWARE Game of Life 1.5
http://www.bitstorm.org/gameoflife/
Game of Life ReferencesGame of Life References
ISBN 0688039758
Wikipedia: Game of Life
Purposeful ActivityPurposeful Activity There is no need for a There is no need for a
central controller central controller orchestrating behaviour orchestrating behaviour
Each member exchanges Each member exchanges information with its information with its neighbour and acts for neighbour and acts for some common purpose some common purpose
From simple, shortsighted, From simple, shortsighted, generally selfish actions, a generally selfish actions, a transcendent global transcendent global behaviour emergesbehaviour emerges
William Blake, 1794 Ancient of Days – God as Architect
Self Organization of Flocking BehaviourSelf Organization of Flocking Behaviour
emergent emergent phenomenaphenomena
where a collection of where a collection of individuals interact individuals interact without central without central control to produce control to produce behaviour which is behaviour which is not explicitly not explicitly programmedprogrammed
Examples of Decentralized BehaviourExamples of Decentralized Behaviour
Ant behaviour is Ant behaviour is determined by the local determined by the local interactions of many ants interactions of many ants
car traffic patterns arise car traffic patterns arise from local interactions from local interactions among individual cars among individual cars
antibodies seek out antibodies seek out bacteria in a systematic bacteria in a systematic attack without generals attack without generals
corporations are corporations are decentralizing decentralizing management structuresmanagement structures
The centralized mindset: The centralized mindset: intuition suggests that intuition suggests that when there is structure when there is structure there must be an organizer there must be an organizer Self organized ant behaviour
Flocking Behaviour RulesFlocking Behaviour Rules
Separation: steer to avoid crowding local flockmates
Craig Reynolds http://www.red3d.com/cwr/boids/
Alignment: steer towards the average heading of local flockmates
Cohesion: steer to move toward the average position of local flockmates
The Universe ComputesThe Universe Computes In the universe, every In the universe, every
particle processes dataparticle processes data
Because the universe is Because the universe is governed by the laws of governed by the laws of quantum mechanics, quantum mechanics, every elementary particle every elementary particle registers bits of registers bits of informationinformation
The universe is a quantum The universe is a quantum computer which computes computer which computes its own behaviourits own behaviour
“The Universe at a Glance"
mural for the Metanexus Institute
As soon as the universe began, it As soon as the universe began, it began computingbegan computing
It is the It is the computational computational character of the character of the universe which universe which allows for the allows for the evolution of evolution of complex complex systems from systems from the the fundamental fundamental laws of physicslaws of physics
Quantum Mechanics is WeirdQuantum Mechanics is Weird Seth Lloyd from MIT Seth Lloyd from MIT
describes himself as a describes himself as a quantum computer quantum computer mechanic; he designs and mechanic; he designs and fixes quantum computers. fixes quantum computers.
ISBN 1-4004-092-2
Double-Slit ExperimentDouble-Slit Experiment
Light as waves will create an Light as waves will create an interference pattern at the far wallinterference pattern at the far wall
A light particle reaching the double slit A light particle reaching the double slit will appear at both slits at the same timewill appear at both slits at the same time
Monkeys at TypewritersMonkeys at Typewriters We can consider a large We can consider a large
number of monkeys number of monkeys typing away randomly at typing away randomly at typewriters. typewriters.
Eventually there will be Eventually there will be some character strings some character strings that are meaningful but that are meaningful but the character that the character that follows the string will be follows the string will be a mistake. a mistake.
This will not lead to This will not lead to patterns, evolution nor patterns, evolution nor complexity.complexity.
Monkeys at ComputersMonkeys at Computers
Now imagine Now imagine monkeys typing into monkeys typing into computers. computers.
The random The random characters will characters will eventually produce eventually produce short meaningful short meaningful programs.programs.
But a short program But a short program can produce a wide can produce a wide variety of interesting variety of interesting outputsoutputs
Occam’s RazorOccam’s Razor
If there is a choice between theories If there is a choice between theories then the correct one is the simpler of then the correct one is the simpler of the two.the two.
The shorter or the more simpler The shorter or the more simpler program that generates the needed program that generates the needed complexity will be the correct one.complexity will be the correct one.
These simpler programs will produce a These simpler programs will produce a universe suspiciously similar to our ownuniverse suspiciously similar to our own
Monkeys at ComputersMonkeys at Computers
The computers are the quantum laws of The computers are the quantum laws of nature which process inputnature which process input
The monkeys are quantum fluctuations or The monkeys are quantum fluctuations or accidents within the fabric of the universeaccidents within the fabric of the universe
The quantum fluctuations are injecting new The quantum fluctuations are injecting new information for the quantum laws to information for the quantum laws to processprocess
Many Worlds InterpretationMany Worlds Interpretation
The parallel The parallel processing processing character of character of quantum quantum computation computation necessitates the necessitates the existence of a existence of a multiverse.multiverse.
Lee Skinner, 2005, Many Worlds
““The collision of two atoms can - and does The collision of two atoms can - and does – change the future of the universe.”– 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