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 Goedel's theorems apply — escaping the Goedel prison
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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