Energy Limits to the Computational Power of the Human Brain
by Ralph C. Merkle

Xerox PARC 
3333 Coyote Hill Road 
Palo Alto, CA 94304 
merkle@xerox.com

This article will appear in Foresight Update #6

The Brain as a Computer

The view that the brain can be seen as a type of computer has gained
general acceptance in the philosophical and computer science community.
Just as we ask how many mips or megaflops an IBM PC or a Cray can perform,
we can ask how many operations the human brain can perform.  Neither the
mip nor the megaflop seems quite appropriate, though; we need something
new.  One possibility is the number of synapse operations per second.

A second possible "basic operation" is inspired by the observation that
signal propagation is a major limit.  As gates become faster, smaller, and
cheaper, simply getting a signal from one gate to another becomes a major
issue.  The brain couldn't compute if nerve impulses didn't carry
information from one synapse to the next, and propagating a nerve impulse
using the electrochemical technology of the brain requires a measurable
amount of energy.  Thus, instead of measuring synapse operations per
second, we might measure the total distance that all nerve impulses
combined can travel per second, e.g., total nerve-impulse-distance per
second.

Other Estimates

There are other ways to estimate the brain's computational power.  We might
count the number of synapses, guess their speed of operation, and determine
synapse operations per second.  There are roughly 10**15 synapses operating
at about 10 impulses/second [2], giving roughly 10**16 synapse operations
per second.

A second approach is to estimate the computational power of the retina, and
then multiply this estimate by the ratio of brain size to retinal size. The
retina is relatively well understood so we can make a reasonable estimate
of its computational power.  The output of the retina -- carried by the
optic nerve -- is primarily from retinal ganglion cells that perform
"center surround" computations (or related computations of roughly similar
complexity).  If we assume that a typical center surround computation
requires about 100 analog adds and is done about 100 times per second [3],
then computation of the axonal output of each ganglion cell requires about
10,000 analog adds per second.  There are about 1,000,000 axons in the
optic nerve [5, page 21], so the retina as a whole performs about 10**10
analog adds per second.  There are about 10**8 nerve cells in the retina
[5, page 26], and between 10**10 and 10**12 nerve cells in the brain [5,