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

1 22G N

p mv

F ma

m mF G

r

2 1

1 2

j j j

j j j

H U PV N

G U PV TS N

T TdS dQ

TT

1

0

10

E

E jB

c t cB

BE

c t

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