A New Kind of Science in a Nutshell
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Transcript of A New Kind of Science in a Nutshell
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A New Kind of Sciencein a Nutshell
David SehnalQIPL at FI MU
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Motivations
• How does anything complicated get produced in nature?
• Traditional Science – i.e. calculus, Newtonian physics, …
• What if there is a more general underlying principle?– Simple programs
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1D Cellular Automata
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Cell to be updated
Left neighbor Right neighbor
New color
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• This type behavior is very surprising
1. Started from a single black cell
2. Used simple rules
3. Got something that looks to us completely random
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Is Complexity Special or Common?
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Turing Machines
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Substitution Systems
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2D Cellular Automata
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2D Turing Machines
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3D Cellular Automata
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• Simple rules do not imply simple behavior
• It seems that complex behavior is a very common phenomenon
To sum it up…
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Systems in nature
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Snowflakes
• When a piece of a snowflake solidifies, heat is released
• This heat prohibits ice nearby
• New rule: Piece solidifies if exactly on of the neighborhood cells is solid
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More systems in nature
• Fluid flow
• Patterns on shells
• Fundamental physics
• And many others …
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Why can simple programs produce complex behavior?
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Computation
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• All cellular automata can be though of as doing computations
• One does not need to know the point of the computation beforehand
Computation
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Universality
• Some automata can simulate all others
• One only needs to specify the initial conditions
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Universality
• Once universality is reached, the behavior is maximally sophisticated (from the computational point of view)
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• What about systems such as rule 30?
• Or systems in nature?
• How sophisticated are these?
More questions
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Principle of Computational Equivalence
Essentially any time the behavior of a system looks to us complex, it will end up corresponding to a computation of exactly
equivalent sophistication.
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• Simple behavior (repetitive or nested) corresponds to simple computations
• Complex behavior corresponds to sophisticated computations
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• Rule 110 is universal
Threshold of Universality
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Where does all the complexity come from?
… from the computational sophistication of the system observed
compared to the computational sophistication of the observer.
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Thank you for your attention
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Thank you for your attention