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

15. The pattern is neither regular nor completely random. It appears to have some order, but is never predictable.

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 Gardner’s “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.org/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. Occam’s 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 Cat’s Eye Nebula