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Hyper-Computing
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and this is where the machine’s greater power comes from. Of course such a thing might easily fit inside our skulls, and the physics within our brains are certainly capable of using real analogue values.

The biggest stumbling block for Siegelmann’s idea is the information that gives her machines their power is fine-grained and easily destroyed by noise in the environment. This is not just from the sort of electrical noise we hear when our cell phones interfere with the radio, but the precision required by her machines is so exacting that anything might interfere with them. For example, gravitational waves caused by the motions of nearby stars would disturb calculations at only the fiftieth decimal place. Since it is these digits that constitute the difference between an ARNN and a regular Turing machine, most people conclude ARNNs can’t work. There is one effect stemming from the quantum world which might come to the rescue. The potential to do something in the quantum world is sufficient to modify the behavior of a system even if the system does not actually do that specific thing. This is called a counterfactual process. The possibility an ARNN might perform infinite precision calculations may be enough to give the machine the edge, even though in practice it is disturbed by noise. This is speculation upon speculation, but interesting nevertheless.

[DIAGRAM LABELS]
Dendrites
Microtubule
Neurofibrils
Neurotransmitter
Receptor
Synapse
Synaptic vesicles
Synapse (Axoaxonic)
Synaptic cleft
Axonal terminal
Rough ER (Nissl body)
Polyribosomes
Ribosomes
Golgi apparatus
Node of Ranvier
Myelin Sheath (Schwann cell)
Axon hillock
Nucleus
Nucleolus
Membrane
Microtubule
Mitochondrion
Smooth ER
Synapse (Axodendritic)
Dendrites
Microfilament
Microtubule
Axon
[END DIAGRAM LABELS]

Neurons and Microtubules

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