convergent computation

• formal foundation: computation = convergence to equilibrium
• traditional paradigm: computation = derivation from axioms (Turing)
• convergent paradigm: computation = convergence to stable state
• every Turing computation can be expressed as convergence (machine converges to halting state)
• but convergent systems can compute things formal derivation cannot reach
  • they operate outside the proof-theoretic domain where Gödel’s theorems apply
• a convergent computation system is a tuple (V, E, N, T, W, τ)
  • V: set of particles (content-addressed nodes)
  • E: set of directed edges (cyberlinks)
  • N: set of neurons (agents)
  • T: token assignments
  • W: edge weights
  • τ: finality threshold
• the system evolves by focus flow: attention redistributes based on connection weights modulated by stake
• the Collective Focus Theorem guarantees global convergence to unique stationary distribution
• truth is stability above threshold. intelligence is adaptive equilibrium-finding
• see natural computing for the paradigm
• see focus flow computation for the executable model
• see future of computation for the full article
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