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

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

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

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

Cellular Automata as Model Large array of cells with synchronous update in parallel. Large array of cells with synchronous update in parallel. The parallelism resembled some features in physical world, such as space and time relation. 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. 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. 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. Give an initial condition with simple rules, the universe start evolving.

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

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

Cohesive Relation Cohesion Cohesion –Concept for irreducibility –Creates stability to prevent object from fluctuate or change in its form Cohesive objects are moving through Cohesive objects are moving through –Space and Time CA also exhibit this cohesive relation 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) Organisms are cohesive. (e.g. Birds with Broken Wing) –structural connection –functional connection

Cohesive Broken Wing Behavior Killdeer Thick Knee

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

Computational Irreducibility – Random Sequence of π … … [Wolfram, p 137]

Computational Irreducibility – In CA Code Class I Code Class II

Computational Irreducibility – In CA Code Class III Code Class IV

Butterfly Growth Cycle in Biological Process EggsLarva or Caterpillar

Butterfly Growth Cycle in Biological Process cont. Pupa or CocoonAdult Monarch Butterfly Emerged

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

Entropy Increase cont. When entropy is exhibited in a system, reducing its computation is nearly impossible. When entropy is exhibited in a system, reducing its computation is nearly impossible. Second Law of Thermodynamics 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 Amount of irreducible information increase –It becomes computationally irreducible –Probability of accurate prediction diminishes

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

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

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

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

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

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

Unpredictability – A notion of Uncertainty At micro level 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. This relation has reflective implications for such fundamental notions as causality and the determination of the future behavior of an atomic particle.

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. 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. 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.

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. 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.

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? 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? Or are we more like Cellular Automata where the new states of universe get updated and created and old one is lost?

Multiway System 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. 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. As an observer, we are able to visualize possibility of multiple histories instead of unique history.

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

Model our Universe as Multiway System 12 Our Universe Another History

Determinism and Free Will Free will means 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. 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] 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. It is also our perception that dictates complex system that lead to computationally irreducible hence unpredictable.

CA rule that doesn’t obey definite laws Code State Totalistic

Conclusions The concept of emergence consist irreducibility and unpredictability that prevents scientist from concluding certain finding. 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. 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. 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. We can analyze this emergence where irreducibility and unpredictability exit.

References 1. Klaus A. Brunner, What's Emergent in Emergent Computing? Klaus A. Brunner, What's Emergent in Emergent Computing? 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, 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, John D. Collier, Causation is the transfer of information; Causation of Law and Nature, (ed, Howard Sanky) Kluwer, John D. Collier, Causation is the transfer of information; Causation of Law and Nature, (ed, Howard Sanky) Kluwer, Werner, Heisenberg History Museum, 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 , p750, 752, 967, 1132, Stephen Wolfram, A New Kind of Science, Wolfram Media, Champaign, IL 2002, p 138, 140, p 518, p 301, p , p750, 752, 967, 1132, Outdoor Photographing. Killdeer Photo Source: 6. Outdoor Photographing. Killdeer Photo Source: – – 7. TrekEarth. Thick Knee Photo Source: 7. TrekEarth. Thick Knee Photo Source: –