> a finite number of neurons in a finite number of configurations

Neurons and synapses change, especially synapses (the connections between neurons). Some neurons have a few connections to other neurons. Others have hundreds of thousands of connections to other neurons. These grow and change. "Estimates are between 100 trillion and 1,000 trillion neural connections" Is it finite? Depends on your definition of finite. If anything countable is finite, then it is finite but the number may be practically uncountable. Is it fixed? No.