Computational Mechanics: Why Model?

• Structural Complexity of Information Source

C_ = H[Pr(S)], S = {Casual states}

• Uses:

  • Environíl complexity: Amount/kind of relevant structure
  • Agentís inferential capacity: Sophistication of models?

• Theorem: E _ C_

  Conclusion: Build models vs. storing only E bits of history.
  

  • Raw sequence blocks do not allow optimal prediction,
    only E bits of mutual information in blocks.
  • Optimal prediction requires larger model: 2C_, not 2E.
  • Explicit: 1D Range-R Ising spin system: C_ =E+Rh_.

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