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There's a very big difference between doing the calculations needed to simulate the human brain (or any animal brain - we can do a fairly decent job on C. elegans), and doing computations. While a basic leaky integrate & fire model is fairly simple, to accurately simulate a single neuron in real time takes a pretty fast computer. See e.g. these links for more, http://www.neuron.yale.edu/neuron/, http://bluebrain.epfl.ch/ http://www.artificialbrains.com/darpa-synapse-program.

Brains do well what computers do poorly, and vice versa. The HP12C calculator on my desk, made in the early '80s, can do many sorts of mathematical calculations faster than I can, because brains aren't really optimized for doing, for example, compound interest calculations. But my brain, or my dog's brain for that matter, can do all the 'calculations' needed to process a stream of images, recognize that they show a ball, predict its path, and catch it - while simultaneously processing visual, auditory, olfactory, and kinesthetic inputs for obstacle avoidance and threat recognition, and (in my case, anyway) perhaps thinking about how to solve complex programming problems.

Maybe I should add that there are basically three different things that a computer can do in this context:

Complex calculations, whether compound interest, weather modeling, seismic tomography or whatever. Simulating the actual behavior of a brain, or some subset of one, starting from a single neuron. Trying to replicate what a brain does through algorithms, or Artificial Intelligence.

(1) is what we mostly use computers for, and they're way better at it than human brains. (2) is a special case of (1), which we do because we don't have much of an idea how to do (3), and having a simulated brain we can alter at will might help in learning how real brains do what they do.