Neuron Cascade and Indeterminacy

A gloss of the neural indeterminacy explanation from an essay I’m working on. I’ve skipped all the pattern handling, simplifying the discussion to a single input neuron.

A typical cortical neuron has ten thousand inputs, seventy percent are excitatory and thirty percent are inhibitory. If the sum of the voltages is greater than or equal to the threshold of the neuron, the neuron fires completely. That firing is called all-or-none.  If the threshold is exceeded by a lot, it still fires the same. If a different combination of inputs meets or exceeds the threshold, the neuron fires exactly the same as in the first case.

This is a base indeterminacy, at the neural level. Different inputs can result in the same output. I call this aspect of the neural threshold, the Almost Gate.

The human cortex has on the order of 10 billion neurons. Only about 0.1% of this 10 billion are connected to either sensory or to motor cells. The overwhelming bulk of cortical neurons communicate only with other cortical neurons. A general, functional flow is

  • from sensory input
  • development of features (it takes at least seven steps for vision)
  • association with information from other senses
  • delivery of abstracted categories to the pre-frontal lobes for executive action
  • shuttling of categories in and out of working storage
  • decision on action plan
  • delivery of action down to the motor centers

Purely considering the numbers (10 billion total/50 million input = 200), an estimate of 50 steps from input to action is an extremely conservative guess of the number of steps from sensation to action.

Each of those transmission steps have a loss of specificity at each threshold. Let’s consider the probability cascade with two different cases of fidelity due to the Almost Gate. First, let’s consider an almost exact match (99% of all inputs are the same) is required to trigger the neuron. In the second case, we relax the threshold match to 95%.

Jacob's Ladder. William Blake. Details become less certain with every step
Details become less certain with every step
  • 99%. After 50 steps, two different input streams, each which triggered the first receiving neuron, have a 60% chance of resulting in the same action
    • Alternatively, after 50 steps, two people with the same input, will have a match at the output 60% of the time.
  • 95%. After 50 steps, two different input streams, each which triggered the first receiving neuron, have a 8% chance of resulting in the same action
    • Alternatively, after 50 steps, two people with the same input, will only have a match 8% of the time.

Angels walking up Jacob’s Ladder. William Blake. Public domain. Wikipedia.

zScience

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