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

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