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Introduction
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Coarse graining Alice and Dinah
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Coarse graining part I - Clustering algorithms
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Coarse graining part II - Entropy
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Markov Chains
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Mathematics of coarse grained Markov chains
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Mathematics of Coarse grained Markov Chains: The General Case
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A puzzle: origin of the slippy counter
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Where we are so far
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Cellular Automata: Introduction
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Israeli and Goldenfeld; projection and commuting diagrams
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Networks of Renormalization
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Fixing a projection: From CA’s to Ising
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Introduction to the Ising Model
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Coarse-graining the Lattice
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Inducing Quartets & Commutation Failure
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Finding Fixed Points
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Ising Model Simulations
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Poking the Creature: An Introduction to Group Theory
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Irreversible Computations, Forgetful Computers and the Krohn-Rhodes Theorem
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From Quantum Electrodynamics to Plasma Physics
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The Thermal Physics of Plasma
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How does a particle move the plasma?
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Charge Renormalization and Feedback
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Conclusion: Keeping the things that matter
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6.4 Charge Renormalization and Feedback » Quiz Solution
What is a "non-renormalizable" theory? (As we use the term here.)
A. a theory where when you coarse-grain, you get new terms that can't be neglected or fit into the original theory.
B. a theory that has a large amount of fine-grained detail that gets lost when you coarse-grain it.
C. a theory where parameters that are finite at one level of coarse-graining become infinite when you got to a finer-grained scale.
D. a theory that does not normalize.
Answer: (A). Theories of type (B) are actually what we love the best, and that fit really well in our paradigm -- recall the Markov chains, that get simpler as you coarse-grain in time. Theories of type (C) are unusual and interesting (when they appear, it's usually when you're doing physics) -- but renormalization actually again works pretty well. Yes, you have some barrier to description at fine-grained scales, but you can go to larger scales without difficulty. In this case, think about (for example) the "slippy counter" Markov Chain -- there we had a theory that we could coarse-grain, but that got really weird when we asked "what does it look like on a finer-grained scale"?