Energy Limits to the Computational Power of the Human Brain
\nby Ralph C. Merkle<\/p>\n
Xerox PARC
\n3333 Coyote Hill Road
\nPalo Alto, CA 94304
\nmerkle@xerox.com<\/p>\n
This article will appear in Foresight Update #6<\/p>\n
The Brain as a Computer<\/p>\n
The view that the brain can be seen as a type of computer has gained
\ngeneral acceptance in the philosophical and computer science community.
\nJust as we ask how many mips or megaflops an IBM PC or a Cray can perform,
\nwe can ask how many operations the human brain can perform. Neither the
\nmip nor the megaflop seems quite appropriate, though; we need something
\nnew. One possibility is the number of synapse operations per second.<\/p>\n
A second possible “basic operation” is inspired by the observation that
\nsignal propagation is a major limit. As gates become faster, smaller, and
\ncheaper, simply getting a signal from one gate to another becomes a major
\nissue. The brain couldn’t compute if nerve impulses didn’t carry
\ninformation from one synapse to the next, and propagating a nerve impulse
\nusing the electrochemical technology of the brain requires a measurable
\namount of energy. Thus, instead of measuring synapse operations per
\nsecond, we might measure the total distance that all nerve impulses
\ncombined can travel per second, e.g., total nerve-impulse-distance per
\nsecond.<\/p>\n
Other Estimates<\/p>\n
There are other ways to estimate the brain’s computational power. We might
\ncount the number of synapses, guess their speed of operation, and determine
\nsynapse operations per second. There are roughly 10**15 synapses operating
\nat about 10 impulses\/second [2], giving roughly 10**16 synapse operations
\nper second.<\/p>\n
A second approach is to estimate the computational power of the retina, and
\nthen multiply this estimate by the ratio of brain size to retinal size. The
\nretina is relatively well understood so we can make a reasonable estimate
\nof its computational power. The output of the retina — carried by the
\noptic nerve — is primarily from retinal ganglion cells that perform
\n“center surround” computations (or related computations of roughly similar
\ncomplexity). If we assume that a typical center surround computation
\nrequires about 100 analog adds and is done about 100 times per second [3],
\nthen computation of the axonal output of each ganglion cell requires about
\n10,000 analog adds per second. There are about 1,000,000 axons in the
\noptic nerve [5, page 21], so the retina as a whole performs about 10**10
\nanalog adds per second. There are about 10**8 nerve cells in the retina
\n[5, page 26], and between 10**10 and 10**12 nerve cells in the brain [5, \ufffd\u008f34\ufffd\ufffd\ufffd\u008f3\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd
\n\u0160page 7], so the brain is roughly 100 to 10,000 times larger than the
\nretina. By this logic, the brain should be able to do about 10**12 to
\n10**14 operations per second (in good agreement with the estimate of
\nMoravec, who considers this approach in more detail [4, page 57 and 163]).<\/p>\n
The Brain Uses Energy<\/p>\n
A third approach is to measure the total energy used by the brain each
\nsecond, and then determine the energy used for each “basic operation.”
\nDividing the former by the latter gives the maximum number of basic
\noperations per second. We need two pieces of information: the total energy
\nconsumed by the brain each second, and the energy used by a “basic operation.”
\nThe total energy consumption of the brain is about 25 watts [2]. Inasmuch
\nas a significant fraction of this energy will not be used for “useful
\ncomputation,” we can reasonably round this to 10 watts.<\/p>\n
Nerve Impulses Use Energy<\/p>\n
Nerve impulses are carried by either myelinated or un-myelinated axons.
\nMyelinated axons are wrapped in a fatty insulating myelin sheath,
\ninterrupted at intervals of about 1 millimeter to expose the axon. These
\ninterruptions are called “nodes of Ranvier.” Propagation of a nerve
\nimpulse in a myelinated axon is from one node of Ranvier to the next —
\njumping over the insulated portion.<\/p>\n
A nerve cell has a “resting potential” — the outside of the nerve cell is
\n0 volts (by definition), while the inside is about -60 millivolts. There
\nis more Na+ outside a nerve cell than inside, and this chemical
\nconcentration gradient effectively adds about 50 extra millivolts to the
\nvoltage acting on the Na+ ions, for a total of about 110 millivolts [1,
\npage 15]. When a nerve impulse passes by, the internal voltage briefly
\nrises above 0 volts because of an inrush of Na+ ions.<\/p>\n
The Energy of a Nerve Impulse<\/p>\n
Nerve cell membranes have a capacitance of 1 microfarad per square
\ncentimeter, so the capacitance of a relatively small 30 square micron node
\nof Ranvier is 3 x 10**-13 farads (assuming small nodes tends to
\noverestimate the computational power of the brain). The internodal region
\nis about 1,000 microns in length, 500 times longer than the 2 micron node,
\nbut because of the myelin sheath its capacitance is about 250 times lower
\nper square micron [5, page 180; 7, page 126] or only twice that of the
\nnode. The total capacitance of a single node and internodal gap is thus
\nabout 9 x 10**-13 farads. The total energy in joules held by such a
\ncapacitor at 0.11 volts is 1\/2 V**2 x C, or 1\/2 x 0.11**2 x 9 x 10**-13, or
\n5 x 10**-15 joules. This capacitor is discharged and then recharged
\nwhenever a nerve impulse passes, dissipating 5 x 10**-15 joules. A 10 watt
\nbrain can therefore do at most 2 x 10**15 such “Ranvier ops” per second.
\nBoth larger myelinated fibers and unmyelinated fibers dissipate more
\nenergy. Various other factors not considered here increase the total
\nenergy per nerve impulse [8], causing us to somewhat overestimate the
\nnumber of “Ranvier ops” the brain can perform. It still provides a useful
\nupper bound and is unlikely to be in error by more than an order of
\nmagnitude.
\n \ufffd\u008f3k\ufffd\ufffd\ufffd\u008f3\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd
\n\u0160To translate “Ranvier ops” (1-millimeter jumps) into synapse opons we
\nmust know the average distance between synapses, which is not normally
\ngiven in neuroscience texts. We can estimate it: a human can recognize an
\nimage in about 100 milliseconds, which can take at most 100 one-millisecond
\nsynapse delays. A single signal probably travels 100 millimeters in that
\ntime (from the eye to the back of the brain, and then some). If it passes
\n100 synapses in 100 millimeters then it passes one synapse every millimeter
\n— which means one “synapse operation” is about one “Ranvier operation.”<\/p>\n
Discussion<\/p>\n
Both “synapse ops” and “Ranvier ops” are quite low-level. The higher level
\n“analog addition ops” seem intuitively more powerful, so it is perhaps not
\nsurprising that the brain can perform fewer of them.<\/p>\n
While the software remains a major challenge, we will soon be able to build
\nhardware powerful enough to perform more such operations per second than
\ncan the human brain. There is already a massively parallel multi-processor
\nbeing built at IBM Yorktown with a raw computational power of 10**12
\nfloating point operations per second: the TF-1. It should be working in
\n1991 [6]. When we can build a desktop computer able to deliver 10**25 gate
\noperations per second and more (as we will surely be able to do with a
\nmature nanotechnology) and when we can write software to take advantage of
\nthat hardware (as we will also eventually be able to do), a single computer
\nwith abilities equivalent to a billion to a trillion human beings will be a
\nreality. If a problem might today be solved by freeing all humanity from
\nall mundane cares and concerns, and focusing all their combined
\nintellectual energies upon it, then that problem can be solved in the
\nfuture by a personal computer. No field will be left unchanged by this
\nstaggering increase in our abilities. <\/p>\n
Conclusion<\/p>\n
The total computational power of the brain is limited by several factors,
\nincluding the ability to propagate nerve impulses from one place in the
\nbrain to another. Propagating a nerve impulse a distance of 1 millimeter
\nrequires about 5 x 10**-15 joules. Because the total energy dissipated by
\nthe brain is about 10 watts, this means nerve impulses can collectively
\ntravel at most 2 x 10**15 millimeters per second. By estimating the
\ndistance between synapses we can in turn estimate how many synapse
\noperations per second the brain can do. This estimate is only slightly
\nsmaller than one based on multiplying the estimated number of synapses by
\nthe average firing rate, and two orders of magnitude greater than one based
\non functional estimates of retinal computational power. It seems
\nreasonable to conclude that the human brain has a “raw” computational power
\nbetween 10**13 and 10**16 “operations” per second.<\/p>\n
References<\/p>\n
1. Ionic Channels of Excitable Membranes, by Bertil Hille, Sinauer, 1984.
\n2. Principles of Neural Science, by Eric R. Kandel and James H. Schwartz,
\n2nd edition, Elsevier, 1985.
\n3. Tom Binford, private communication.
\n4. Mind Children, by Hans Moravec, Harvard University Press, 1988.
\n5. From Neuron to Brain, second edition, by Stephen W. Kuffler, John G. \ufffd\u00ef\ufffd7\ufffd\ufffd\ufffd\u008f3\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd
\n\u0160Nichols, and A. Robert Martin, Sinauer, 1984.
\n6. “The switching network of the TF-1 Parallel Supercomputer” by Monty M.
\nDenneau, Peter H. Hochschild, and Gideon Shichman, Supercomputing, winter
\n1988 pages 7-10.
\n7. Myelin, by Pierre Morell, Plenum Press, 1977.
\n8. “The production and absorption of heat associated with electrical
\nactivity in nerve and electric organ” by J. M. Ritchie and R. D. Keynes,
\nQuarterly Review of Biophysics 18, 4 (1985), pp. 451-476.<\/p>\n
Acknowledgements
\nThe author would like to thank Richard Aldritch, Tom Binford, Eric Drexler,
\nHans Moravec, and Irwin Sobel for their comments and their patience in
\nanswering questions.<\/p>\n
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