Neural nets require a couple of FLOPs per synapse. The processing power required is a direct function of the number of synapses. Each neuron is essentially applying a particular logical op, and counting the neurons and their inputs gives you the number of ops. I don't get why this seems so objectionable.
Sure, real neurons in the brain might be doing something a couple of orders of magnitude more complicated than the nodes in an ANN, so you could tack on another 10^2 factor to those estimates if you like. But fundamentally, counting synapses is a reasonable way to get a Fermi estimate of the brain's processing power, and Bostrom's estimates are not significantly different from those others have arrived at by similar methods.
Sure, real neurons in the brain might be doing something a couple of orders of magnitude more complicated than the nodes in an ANN, so you could tack on another 10^2 factor to those estimates if you like. But fundamentally, counting synapses is a reasonable way to get a Fermi estimate of the brain's processing power, and Bostrom's estimates are not significantly different from those others have arrived at by similar methods.