To give you some perspective on these issues, let's compare a biological computer like an adult human brain (see upper left image) with the Blue Waters parallel computer (see upper right image) which, when it becomes available for academic research in 2011 at the National Center for Supercomputing Applications in Illinois, will be one of the world's most powerful computers. It is difficult to compare brains with digital silicon-based computers since they work on such different principles (and because we actually don't know yet all the principles of how brains process information). But a rough estimate based on the number of digital electrical pulses (action potentials) that the approximately 1011 neurons in a human brain send to one another per second via approximately 1014 contacts (synapses) suggests that an adult human brain carries out about one thousand trillion (1015) logical operations per second, which is known as a petaflop of computational ability. The Blue Water supercomputer will also have a raw hardware capability of about one petaflop. (So you are living during an interesting time in history when digital computers are just starting to attain the raw computational capability of an adult human brain).
Although a human brain and and the Blue Waters computer are roughly comparable in computational power, they differ enormously in terms of their thermodynamic properties. The Blue Waters computer will occupy approximately 2,000 square meters of floor space, will consume about 15,000,000 watts, will require an intricate cooling system (hidden under the floor) to dissipate the resulting heat, and will be utterly non-portable. A human brain is about the size of your two fists, consumes about 15 watts (even when you are solving a hard physics problem), and is completely practical to carry around since it has a mass of about 1.5 kg. (It is also worth pointing out that brains, unlike computers, self-assemble themselves and are also able to program themselves.)
So brains are much more impressive than the current best
supercomputers in terms of computational capability per unit
volume per unit power. But as physicists, we are obliged to
ask an additional question: although brains are impressive
compared to computers, are they impressive in some absolute
physical sense? That is, has evolution led to brains that
are close to optimal in that no other physical system that
operates at room temperature and that consumes 15 watts
can achieve a petaflop of computation or more? The answer is
not known and is being studied by a variety of physicists,
engineers, computer scientists, and biologists.