188 lines
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Plaintext
188 lines
10 KiB
Plaintext
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Energy Limits to the Computational Power of the Human Brain
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by Ralph C. Merkle
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Xerox PARC
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3333 Coyote Hill Road
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Palo Alto, CA 94304
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merkle@xerox.com
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This article will appear in Foresight Update #6
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The Brain as a Computer
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The view that the brain can be seen as a type of computer has gained
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general acceptance in the philosophical and computer science community.
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Just as we ask how many mips or megaflops an IBM PC or a Cray can perform,
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we can ask how many operations the human brain can perform. Neither the
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mip nor the megaflop seems quite appropriate, though; we need something
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new. One possibility is the number of synapse operations per second.
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A second possible "basic operation" is inspired by the observation that
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signal propagation is a major limit. As gates become faster, smaller, and
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cheaper, simply getting a signal from one gate to another becomes a major
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issue. The brain couldn't compute if nerve impulses didn't carry
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information from one synapse to the next, and propagating a nerve impulse
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using the electrochemical technology of the brain requires a measurable
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amount of energy. Thus, instead of measuring synapse operations per
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second, we might measure the total distance that all nerve impulses
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combined can travel per second, e.g., total nerve-impulse-distance per
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second.
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Other Estimates
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There are other ways to estimate the brain's computational power. We might
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count the number of synapses, guess their speed of operation, and determine
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synapse operations per second. There are roughly 10**15 synapses operating
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at about 10 impulses/second [2], giving roughly 10**16 synapse operations
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per second.
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A second approach is to estimate the computational power of the retina, and
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then multiply this estimate by the ratio of brain size to retinal size. The
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retina is relatively well understood so we can make a reasonable estimate
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of its computational power. The output of the retina -- carried by the
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optic nerve -- is primarily from retinal ganglion cells that perform
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"center surround" computations (or related computations of roughly similar
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complexity). If we assume that a typical center surround computation
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requires about 100 analog adds and is done about 100 times per second [3],
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then computation of the axonal output of each ganglion cell requires about
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10,000 analog adds per second. There are about 1,000,000 axons in the
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optic nerve [5, page 21], so the retina as a whole performs about 10**10
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analog adds per second. There are about 10**8 nerve cells in the retina
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[5, page 26], and between 10**10 and 10**12 nerve cells in the brain [5, <0B>34 <00>3
<0A>page 7], so the brain is roughly 100 to 10,000 times larger than the
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retina. By this logic, the brain should be able to do about 10**12 to
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10**14 operations per second (in good agreement with the estimate of
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Moravec, who considers this approach in more detail [4, page 57 and 163]).
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The Brain Uses Energy
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A third approach is to measure the total energy used by the brain each
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second, and then determine the energy used for each "basic operation."
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Dividing the former by the latter gives the maximum number of basic
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operations per second. We need two pieces of information: the total energy
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consumed by the brain each second, and the energy used by a "basic operation."
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The total energy consumption of the brain is about 25 watts [2]. Inasmuch
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as a significant fraction of this energy will not be used for "useful
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computation," we can reasonably round this to 10 watts.
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Nerve Impulses Use Energy
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Nerve impulses are carried by either myelinated or un-myelinated axons.
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Myelinated axons are wrapped in a fatty insulating myelin sheath,
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interrupted at intervals of about 1 millimeter to expose the axon. These
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interruptions are called "nodes of Ranvier." Propagation of a nerve
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impulse in a myelinated axon is from one node of Ranvier to the next --
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jumping over the insulated portion.
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A nerve cell has a "resting potential" -- the outside of the nerve cell is
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0 volts (by definition), while the inside is about -60 millivolts. There
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is more Na+ outside a nerve cell than inside, and this chemical
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concentration gradient effectively adds about 50 extra millivolts to the
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voltage acting on the Na+ ions, for a total of about 110 millivolts [1,
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page 15]. When a nerve impulse passes by, the internal voltage briefly
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rises above 0 volts because of an inrush of Na+ ions.
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The Energy of a Nerve Impulse
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Nerve cell membranes have a capacitance of 1 microfarad per square
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centimeter, so the capacitance of a relatively small 30 square micron node
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of Ranvier is 3 x 10**-13 farads (assuming small nodes tends to
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overestimate the computational power of the brain). The internodal region
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is about 1,000 microns in length, 500 times longer than the 2 micron node,
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but because of the myelin sheath its capacitance is about 250 times lower
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per square micron [5, page 180; 7, page 126] or only twice that of the
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node. The total capacitance of a single node and internodal gap is thus
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about 9 x 10**-13 farads. The total energy in joules held by such a
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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
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5 x 10**-15 joules. This capacitor is discharged and then recharged
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whenever a nerve impulse passes, dissipating 5 x 10**-15 joules. A 10 watt
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brain can therefore do at most 2 x 10**15 such "Ranvier ops" per second.
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Both larger myelinated fibers and unmyelinated fibers dissipate more
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energy. Various other factors not considered here increase the total
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energy per nerve impulse [8], causing us to somewhat overestimate the
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number of "Ranvier ops" the brain can perform. It still provides a useful
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upper bound and is unlikely to be in error by more than an order of
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magnitude.
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<0B>3k <00>3
<0A>To translate "Ranvier ops" (1-millimeter jumps) into synapse opons we
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must know the average distance between synapses, which is not normally
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given in neuroscience texts. We can estimate it: a human can recognize an
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image in about 100 milliseconds, which can take at most 100 one-millisecond
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synapse delays. A single signal probably travels 100 millimeters in that
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time (from the eye to the back of the brain, and then some). If it passes
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100 synapses in 100 millimeters then it passes one synapse every millimeter
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-- which means one "synapse operation" is about one "Ranvier operation."
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Discussion
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Both "synapse ops" and "Ranvier ops" are quite low-level. The higher level
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"analog addition ops" seem intuitively more powerful, so it is perhaps not
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surprising that the brain can perform fewer of them.
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While the software remains a major challenge, we will soon be able to build
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hardware powerful enough to perform more such operations per second than
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can the human brain. There is already a massively parallel multi-processor
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being built at IBM Yorktown with a raw computational power of 10**12
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floating point operations per second: the TF-1. It should be working in
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1991 [6]. When we can build a desktop computer able to deliver 10**25 gate
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operations per second and more (as we will surely be able to do with a
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mature nanotechnology) and when we can write software to take advantage of
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that hardware (as we will also eventually be able to do), a single computer
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with abilities equivalent to a billion to a trillion human beings will be a
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reality. If a problem might today be solved by freeing all humanity from
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all mundane cares and concerns, and focusing all their combined
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intellectual energies upon it, then that problem can be solved in the
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future by a personal computer. No field will be left unchanged by this
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staggering increase in our abilities.
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Conclusion
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The total computational power of the brain is limited by several factors,
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including the ability to propagate nerve impulses from one place in the
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brain to another. Propagating a nerve impulse a distance of 1 millimeter
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requires about 5 x 10**-15 joules. Because the total energy dissipated by
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the brain is about 10 watts, this means nerve impulses can collectively
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travel at most 2 x 10**15 millimeters per second. By estimating the
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distance between synapses we can in turn estimate how many synapse
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operations per second the brain can do. This estimate is only slightly
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smaller than one based on multiplying the estimated number of synapses by
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the average firing rate, and two orders of magnitude greater than one based
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on functional estimates of retinal computational power. It seems
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reasonable to conclude that the human brain has a "raw" computational power
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between 10**13 and 10**16 "operations" per second.
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References
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1. Ionic Channels of Excitable Membranes, by Bertil Hille, Sinauer, 1984.
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2. Principles of Neural Science, by Eric R. Kandel and James H. Schwartz,
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2nd edition, Elsevier, 1985.
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3. Tom Binford, private communication.
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4. Mind Children, by Hans Moravec, Harvard University Press, 1988.
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5. From Neuron to Brain, second edition, by Stephen W. Kuffler, John G. <0B> 7 <00>3
<0A>Nichols, and A. Robert Martin, Sinauer, 1984.
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6. "The switching network of the TF-1 Parallel Supercomputer" by Monty M.
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Denneau, Peter H. Hochschild, and Gideon Shichman, Supercomputing, winter
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1988 pages 7-10.
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7. Myelin, by Pierre Morell, Plenum Press, 1977.
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8. "The production and absorption of heat associated with electrical
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activity in nerve and electric organ" by J. M. Ritchie and R. D. Keynes,
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Quarterly Review of Biophysics 18, 4 (1985), pp. 451-476.
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Acknowledgements
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The author would like to thank Richard Aldritch, Tom Binford, Eric Drexler,
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Hans Moravec, and Irwin Sobel for their comments and their patience in
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answering questions.
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X-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-X
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Another file downloaded from: The NIRVANAnet(tm) Seven
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& the Temple of the Screaming Electron Taipan Enigma 510/935-5845
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Burn This Flag Zardoz 408/363-9766
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realitycheck Poindexter Fortran 510/527-1662
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Lies Unlimited Mick Freen 801/278-2699
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The New Dork Sublime Biffnix 415/864-DORK
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The Shrine Rif Raf 206/794-6674
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Planet Mirth Simon Jester 510/786-6560
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"Raw Data for Raw Nerves"
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X-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-X
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