If we could harness the undecidability of the spectral gap to implement infinite real weights for Hava Siegelmann's analog recurrent neural network model, then I suppose we could in theory achieve hypercomputation. This would have many incredible consequences. We wouldn't be able to develop an algorithm to reproduce consciousness, but perhaps by trying all possibilities (perhaps guided by intuition, as Goertzel suggests) we might then actually stumble upon a conscious being. Maybe our brains are analog recurrent neural networks that exploit this undecidability of the spectral gap...
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