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  1. Irreducibility and Unpredictability in Nature Computer Science Department SJSU CS240 Harry Fu

  2. Overview • Introduction • Using CA as Model for Nature • Irreducibility • Unpredictability • Determinism and Free Will • Conclusions

  3. Introduction • Scientists prefer using models to describe nature. • Mathematic Formula • Physics Laws • Some formulas and laws are: • Complex • Incomprehensible • Only describe some phenomena in nature • Looking for better model to describe nature • Use illustrative pattern to describe behavior of nature will fit human perception and analysis

  4. Apply Possible Models • Use Mathematic formulas or Physics Laws. • Use Philosophy, or human intuition. • Or use a simple yet meaningful representation. • Use Cellular Automata to start our science exploration.

  5. Cellular Automata as Model • Large array of cells with synchronous update in parallel. • The parallelism resembled some features in physical world, such as space and time relation. • The evolutionary progression behavior in CA also move through space and time. • CA can be setup in 1D, 2D, or 3D that emulates fundamental features of our universe. • Give an initial condition with simple rules, the universe start evolving.

  6. Emergence in Nature • Emergence emerge in nature. • Property present in some behaviors we have seen in nature. • Irreducibility • Unpredictability • In Cellular Automata, these properties are inevitably exist. • Some characteristics can be seen in these properties.

  7. Irreducibility • Cohesive Relation. • Computational Irreducibility. • Entropy Increase. • In Second Law of Thermodynamics. • Irreducibility led to notion of unpredictability.

  8. Cohesive Relation • Cohesion • Concept for irreducibility • Creates stability to prevent object from fluctuate or change in its form • Cohesive objects are moving through • Space and Time • CA also exhibit this cohesive relation • Cells are progressively updated through space and time • In Class IV CA, information are communicated over long range • Organisms are cohesive. (e.g. Birds with Broken Wing) • structural connection • functional connection

  9. Cohesive Broken Wing Behavior Killdeer Thick Knee

  10. Computational Irreducibility • Some mathematics are merely symbolic system that represent solution that we really want to find. • Fundamental Mathematics: • 1/13 = 0.076923076923076923… (Geometric Series) • √3 = 1.7320508075688772935… (Random sequence of decimal digits) • π = 3.14159… (The exact value remains mystery)

  11. Computational Irreducibility – Random Sequence of π • 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196… [Wolfram, p 137]

  12. Computational Irreducibility – In CA Code 98111117 Class I Code 91111177 Class II

  13. Computational Irreducibility – In CA Code 91151117 Class IV Code 93111117 Class III

  14. Butterfly Growth Cycle in Biological Process Eggs Larva or Caterpillar

  15. Butterfly Growth Cycle in Biological Processcont. Pupa or Cocoon Adult Monarch Butterfly Emerged

  16. Entropy Increase • Entropy • led to notion of irreducibility • Information tend to increase in a system – Inferred by Second Law of Thermodynamics • More information • Creates disorder • Randomness seem to emerge • The patterns generated in CA • Neither die out • Nor conform to any regularity

  17. Entropy Increasecont. • When entropy is exhibited in a system, reducing its computation is nearly impossible. • Second Law of Thermodynamics • If one repeats the same measurements at different times, then the entropy deduced from the system would tend to increase over time. • Amount of irreducible information increase • It becomes computationally irreducible • Probability of accurate prediction diminishes

  18. Entropy Increase – 3 State CA Example Code 93111117 Simple Nesting Pattern Code 93111117 Random Pattern

  19. Unpredictability • Defining Randomness. • Perception of Complexity. • A notion of Uncertainty. • Can multiple histories exist in our universe?

  20. Unpredictability – Defining Randomness • Defining a true randomness • Human perception • Analysis • Most intuitively, randomness is described with behavior from a system without apparent regularity. • Reversible CA Rule 37R exhibits behavior • Order • Disorder • It does not obey Second Law of Thermodynamics • The behavior of 37R seems unpredictable. • This kind of behavior can also be seen nature

  21. Unpredictability – Defining Randomness Rule 37R Unpredictable Behavior [Wolfram, p 440]

  22. Unpredictability – Defining Randomness - Maximum Slope - Absolute Upper Limit Edge Pattern Edge Pattern Rule 30 Unpredictable Behavior and Pattern [Wolfram]

  23. Unpredictability – Perception of Complexity Code 9111177 Complex Pattern Code 9111177 One Cell Initial Condition

  24. Unpredictability – A notion of Uncertainty • At micro level • Uncertainty Principle states uncertainty relation between the position and the momentum (mass times velocity) of a subatomic particle, such as an electron. [Heisenberg] • This relation has reflective implications for such fundamental notions as causality and the determination of the future behavior of an atomic particle.

  25. Unpredictability – A notion of Uncertainty cont. • The more precisely the position of an object is determined, the less precisely the momentum is known in this instant, and vice versa. • In another word, if we try to measure some moving object in the universe, we cannot both decide precisely what speed it is moving and what position it locates.

  26. Unpredictability – A notion of Uncertainty cont. • If precise measurement of either speed or position of any matters in the universe is not possible, then the entire emergence we see in nature inevitably exist without our knowledge. This led to the notion of free will when any process and behavior emerge in nature.

  27. History created or already existed? • Are we merely exploring part of the system at certain time and position of universe where the complete space-time history is always exist? • Or are we more like Cellular Automata where the new states of universe get updated and created and old one is lost?

  28. Multiway System • Multiway System • One kind of substitution system • Use to explain the history evolution created in a system • Using Multiway System as example, we can apply simple rule that generate multiple histories with different choice of evolution. • As an observer, we are able to visualize possibility of multiple histories instead of unique history.

  29. Perspective of an Observer • We are part of • Universe • Complexity • Randomness • Our intuition told us there is one unique history. • If we can act as an observer of the system, would that make any difference? • Imagine for a moment, we are the observer of the system.

  30. Model our Universe as Multiway System Our Universe 1 2 Another History

  31. Determinism and Free Will • Free will means • There must be at least two or more possibilities when facing a given choice • No coercion and choice is not forced. • Many systems in our nature seem to generate behaviors that are random and complex. • Computational irreducibility is the origin of the apparent freedom of human. [Wolfram] • It is also our perception that dictates complex system that lead to computationally irreducible hence unpredictable.

  32. CA rule that doesn’t obey definite laws Code 1599 3 State Totalistic

  33. Conclusions • The concept of emergence consist irreducibility and unpredictability that prevents scientist from concluding certain finding. • These properties appeared in many disciplines of our science, for example mathematics, physics, or even biological process. • Cellular automaton is one of emergent computing model that help us to explore phenomena in science. • We can analyze this emergence where irreducibility and unpredictability exit.

  34. References • 1. Klaus A. Brunner, What's Emergent in Emergent Computing? 2002 • • 2. John D. Collier and Scott J. Muller The Dynamical Basis of Emergence in Natural Hierarchies, George Farre and Tarko Oksala (eds) Emergence, Complexity, Hierarchy and Organization, and Selected and Edited Papers from ECHOS III Conference, 1998. • 3. John D. Collier, Causation is the transfer of information; Causation of Law and Nature, (ed, Howard Sanky) Kluwer, 1998. • 4. Werner, Heisenberg History Museum, 1976 • • 5. Stephen Wolfram, A New Kind of Science, Wolfram Media, Champaign, IL 2002, p 138, 140, p 518, p 301, p 737-750, p750, 752, 967, 1132, 1135 • 6. Outdoor Photographing. Killdeer Photo Source: • • • 7. TrekEarth. Thick Knee Photo Source: •