Energy Limits to the Computational Power of the Human Brain

by Ralph C. Merkle

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, 34 3 Špage 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 10**12 to 10**14 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 V**2 x C, or 1/2 x 0.11**2 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 10**15 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 op 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 10**12 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 10**25 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 10**15 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 10**13 and 10**16 "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.