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How long is the longest pathway a neural signal can take starting from a sensory neuron and ending at a motor neuron (without loops)?

[This is a purely theoretical question concerning only the synaptic connectivity of neurons, not the propagation of real signals.]

The number I am looking for must be greater than 8 because there are 6 layers in the cerebral cortex and 2 layers of motoneurons: upper motor neurons and lower motor neurons.

The question then reads:

How long is the longest pathway from a sensory neuron to layer I of the cerebral cortex?

How long is the longest pathway from layer VI of the cerebral cortex to an upper motor neuron (which may lie in the brain stem)?

How long can be "detours" inside the system of layers of the cerebral cortex?

I assume that the cortex is not strictly layered, so that a neuron in layer $i$ normally projects on a neuron in layer $i+1$ directly, but possibly also via $N$ interneurons. Theoretically, the upper bound for $N$ is just the number of neurons in the brain, but in practice will be much smaller. To get a sensible number, it may be necessary to neglect detours that are too long because they are too sporadic and/or useless. (But how to define and quantify sporadicity and usefullness in this context?)

If my question doesn't make sense in the way I ask it here: How could I improve it to make it sensible?

[Of course, I am not looking for exact numbers but only for estimates, resp. estimates of lower and upper bounds.]

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    $\begingroup$ Theoretically the number could be huge, if you include both the sensory and motor cortices, plus cerebellum, memory areas for specific activities. But much of the processing will occur in separate areas. Would you count every synapse involved? Or every neuron? Given that a neuron can have 1000's of synapses, not all of which will be involved in the specific action. It might help to think of a specific pathway/action, e.g. reflex response to pain, sight, sound. Or a non-reflex, e.g. a chosen response to a given stimulus. $\endgroup$ – Oliver Houston Aug 1 '17 at 11:16

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