Energy Limits to the Computational Power of the Human Brain
Ralph C. Merkle
This article first appeared in
Foresight Update No. 6, August 1989.
A related article
on the memory capacity of the human brain
is also available on the web.
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.
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 1015
synapses operating at about 10 impulses/second , giving roughly
1016 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 , 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 1010 analog adds per
second. There are about 108 nerve cells in the retina [5, page 26],
and between 1010 and 1012 nerve cells in the
brain [5, page 7], so the
brain is roughly 100 to 10,000 times larger than the retina. By this
logic, the brain should be able to do about 1012
to 1014 operations
per second (in good agreement with the estimate of Moravec, who
considers this approach in more detail [4, page 57 and 163]).
The Brain Uses Energy
A third approach is to measure the total energy used by the brain each
second, and then determine the energy used for each basic operation.
Dividing the former by the latter gives the maximum number of basic
operations per second. We need two pieces of information: the total
energy consumed by the brain each second, and the energy used by a
The total energy consumption of the brain is about 25 watts .
Inasmuch as a significant fraction of this energy will not be used for
useful computation, we can reasonably round this to 10 watts.
Nerve Impulses Use Energy
Nerve impulses are carried by either myelinated or un-myelinated
axons. Myelinated axons are wrapped in a fatty insulating myelin
sheath, interrupted at intervals of about 1 millimeter to expose the
axon. These interruptions are called nodes of Ranvier. Propagation
of a nerve impulse in a myelinated axon is from one node of Ranvier to
the next, jumping over the insulated portion.
A nerve cell has a resting potential--the outside of the nerve cell is
0 volts (by definition), while the inside is about -60 millivolts.
There is more Na+ outside a nerve cell than inside,
and this chemical
concentration gradient effectively adds about 50 extra millivolts to
the voltage acting on the Na+ ions, for a total of about 110
millivolts [1, page 15]. When a nerve impulse passes by, the internal
voltage briefly rises above 0
volts because of an inrush of Na+ ions.
The Energy of a Nerve Impulse
Nerve cell membranes have a capacitance of 1 microfarad per square
centimeter, so the capacitance of a relatively small 30 square micron
node of Ranvier is 3 x 10-13 farads (assuming small nodes tends to
overestimate the computational power of the brain). The internodal
region is about 1,000 microns in length, 500 times longer than the 2
micron node, but because of the myelin sheath its capacitance is about
250 times lower per square micron [5, page 180; 7, page 126] or only
twice that of the node. The total capacitance of a single node and
internodal gap is thus about 9 x 10-13 farads. The total energy in
joules held by such a capacitor at 0.11 volts is 1/2 V2 x C, or 1/2 x
0.112 x 9 x 10-13, or 5 x 10-15 joules. This capacitor is
discharged and then recharged whenever a nerve impulse passes,
dissipating 5 x 10-15 joules. A 10 watt brain can therefore do at
most 2 x 1015 such Ranvier ops per second. Both larger myelinated
fibers and unmyelinated fibers dissipate more energy. Various other
factors not considered here increase the total energy per nerve
impulse , causing us to somewhat overestimate the number of Ranvier
ops the brain can perform. It still provides a useful upper bound and
is unlikely to be in error by more than an order of magnitude.
To translate Ranvier ops (1-millimeter jumps) into synapse operations
we must know the average distance between synapses, which is not
normally given in neuroscience texts. We can estimate it: a human can
recognize an image in about 100 milliseconds, which can take at most
100 one-millisecond synapse delays. A single signal probably travels
100 millimeters in that time (from the eye to the back of the brain,
and then some). If it passes 100 synapses in 100 millimeters then it
passes one synapse every millimeter--which means one synapse operation
is about one Ranvier operation.
Both synapse ops and Ranvier ops are quite low-level. The higher
level analog addition ops seem intuitively more powerful, so it is
perhaps not surprising that the brain can perform fewer of them.
While the software remains a major challenge, we will soon be able to
build hardware powerful enough to perform more such operations per
second than can the human brain. There is already a massively
parallel multi-processor being built at IBM Yorktown with a raw
computational power of 1012 floating point operations per second: the
TF-1. It should be working in 1991 . When we can build a desktop
computer able to deliver 1025 gate operations per second and more (as
we will surely be able to do with a mature nanotechnology) and when we
can write software to take advantage of that hardware (as we will also
eventually be able to do), a single computer with abilities equivalent
to a billion to a trillion human beings will be a reality. If a
problem might today be solved by freeing all humanity from all mundane
cares and concerns, and focusing all their combined intellectual
energies upon it, then that problem can be solved in the future by a
personal computer. No field will be left unchanged by this staggering
increase in our abilities.
The total computational power of the brain is limited by several
factors, including the ability to propagate nerve impulses from one
place in the brain to another. Propagating a nerve impulse a distance
of 1 millimeter requires about 5 x 10-15 joules. Because the total
energy dissipated by the brain is about 10 watts, this means nerve
impulses can collectively travel at most 2 x 1015 millimeters per
second. By estimating the distance between synapses we can in turn
estimate how many synapse operations per second the brain can do.
This estimate is only slightly smaller than one based on multiplying
the estimated number of synapses by the average firing rate, and two
orders of magnitude greater than one based on functional estimates of
retinal computational power. It seems reasonable to conclude that the
human brain has a raw computational power between 1013
and 1016 operations per second.
- 1. Ionic Channels of Excitable Membranes, by Bertil Hille, Sinauer,
- 2. Principles of Neural Science, by Eric R. Kandel and James H.
Schwartz, 2nd edition, Elsevier, 1985.
- 3. Tom Binford, private communication.
- 4. Mind Children, by Hans Moravec, Harvard University Press, 1988.
- 5. From Neuron to Brain, second edition, by Stephen W. Kuffler, John
G. Nichols, and A. Robert Martin, Sinauer, 1984.
- 6. The switching network of the TF-1 Parallel Supercomputer by Monty
M. Denneau, Peter H. Hochschild, and Gideon Shichman, Supercomputing,
winter 1988 pages 7-10.
- 7. Myelin, by Pierre Morell, Plenum Press, 1977.
- 8. The production and absorption of heat associated with electrical
activity in nerve and electric organ by J. M. Ritchie and R. D.
Keynes, Quarterly Review of Biophysics 18, 4 (1985), pp. 451-476.
The author would like to thank Richard Aldritch, Tom Binford, Eric
Drexler, Hans Moravec, and Irwin Sobel for their comments and their
patience in answering questions.