Is this a permutation, a combination or what?
Answer:
Since you didn't state how many times a neuron can synapse with another neuron there can be an infinite number of connections. And in fact some neurons synapse with hundreds if not thousands of other neurons, but there are alot of neurons that synapse with only one or very few other neurons. As a general rule if the order doesn't matter it's a permutation, if it matters it's a combination. Given a set of numbers there are always more permutations than combinations. By the way, there are 100 billion neurons in the adult brain, with 10,000 trillions of connections and the brain has a reported maximum processing speed of 100 trillion transmissions per second.
It is a combination, not permuatation, but it's just so frickin huge it is beyond belief. Suffice it to say it's a hell of a lot more than the number of atoms in the universe (about 10^40).
This just like your computer memory chip !
The way you state the problem is a bit of a simplification. As you posed the problem, any neuron can connect to any other. In this case, if there are N neurons, there are N*N possible connections. For a trillion neurons (10^12) there are one septillion (10^24) possible connections. For scale 5*10^24 is roughly the mass of the earth in kg.In reality, it is not possible for any neuron to synapse with any other. Each neuron projects to a relatively small area and synapses with only neurons in that region. Neurons have on average 10,000 synapse each, so that yields 10^5 * 10^12 = 10^17 or one hundred quadrillion synapses.
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