Energy Limits to the Computational Power of the Human Brain
by 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.
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 1015 synapses operating at
about 10 impulses/second [2], 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 [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 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 basic operation.
The total energy consumption of the brain is about 25 watts [2]. 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 [8], 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.
Discussion
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 [6]. 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.
Conclusion
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.
References
* 1. Ionic Channels of Excitable Membranes, by Bertil Hille, Sinauer,
1984.
* 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.
Acknowledgements
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.