Brain limits
Energy Limits to the Computational Power of the Human Brain
by<br>Ralph C. Merkle
This article first appeared in<br>Foresight Update No. 6, August 1989.
A related article<br>on the memory capacity of the human brain<br>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<br>general acceptance in the philosophical and computer science<br>community. Just as we ask how many mips or megaflops an IBM PC or a<br>Cray can perform, we can ask how many operations the human brain can<br>perform. Neither the mip nor the megaflop seems quite appropriate,<br>though; we need something new. One possibility is the number of<br>synapse operations per second.
A second possible basic operation is inspired by the observation that<br>signal propagation is a major limit. As gates become faster, smaller,<br>and cheaper, simply getting a signal from one gate to another becomes<br>a major issue. The brain couldn't compute if nerve impulses didn't<br>carry information from one synapse to the next, and propagating a<br>nerve impulse using the electrochemical technology of the brain<br>requires a measurable amount of energy. Thus, instead of measuring<br>synapse operations per second, we might measure the total distance<br>that all nerve impulses combined can travel per second, e.g., total<br>nerve-impulse-distance per second.
Other Estimates
There are other ways to estimate the brain's computational power. We<br>might count the number of synapses, guess their speed of operation,<br>and determine synapse operations per second. There are roughly 1015<br>synapses operating at about 10 impulses/second [2], giving roughly<br>1016 synapse operations per second.
A second approach is to estimate the computational power of the<br>retina, and then multiply this estimate by the ratio of brain size to<br>retinal size. The retina is relatively well understood so we can make<br>a reasonable estimate of its computational power. The output of the<br>retina--carried by the optic nerve--is primarily from retinal ganglion<br>cells that perform center surround computations (or related<br>computations of roughly similar complexity). If we assume that a<br>typical center surround computation requires about 100 analog adds and<br>is done about 100 times per second [3], then computation of the axonal<br>output of each ganglion cell requires about 10,000 analog adds per<br>second. There are about 1,000,000 axons in the optic nerve [5, page<br>21], so the retina as a whole performs about 1010 analog adds per<br>second. There are about 108 nerve cells in the retina [5, page 26],<br>and between 1010 and 1012 nerve cells in the<br>brain [5, page 7], so the<br>brain is roughly 100 to 10,000 times larger than the retina. By this<br>logic, the brain should be able to do about 1012<br>to 1014 operations<br>per second (in good agreement with the estimate of Moravec, who<br>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<br>second, and then determine the energy used for each basic operation.<br>Dividing the former by the latter gives the maximum number of basic<br>operations per second. We need two pieces of information: the total<br>energy consumed by the brain each second, and the energy used by a<br>basic operation.
The total energy consumption of the brain is about 25 watts [2].<br>Inasmuch as a significant fraction of this energy will not be used for<br>useful computation, we can reasonably round this to 10 watts.
Nerve Impulses Use Energy
Nerve impulses are carried by either myelinated or un-myelinated<br>axons. Myelinated axons are wrapped in a fatty insulating myelin<br>sheath, interrupted at intervals of about 1 millimeter to expose the<br>axon. These interruptions are called nodes of Ranvier. Propagation<br>of a nerve impulse in a myelinated axon is from one node of Ranvier to<br>the next, jumping over the insulated portion.
A nerve cell has a resting potential--the outside of the nerve cell is<br>0 volts (by definition), while the inside is about -60 millivolts.<br>There is more Na+ outside a nerve cell than inside,<br>and this chemical<br>concentration gradient effectively adds about 50 extra millivolts to<br>the voltage acting on the Na+ ions, for a total of about 110<br>millivolts [1, page 15]. When a nerve impulse passes by, the internal<br>voltage briefly rises above 0<br>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<br>centimeter, so the capacitance of a relatively small 30 square micron<br>node of Ranvier is 3 x 10-13 farads (assuming small nodes tends to<br>overestimate the computational power of the brain). The internodal<br>region is about 1,000 microns in length, 500 times longer than the 2<br>micron node, but because of the myelin sheath its capacitance is about<br>250 times lower per square micron [5, page 180; 7, page 126] or only<br>twice that of the node. The total capacitance of a single node and<br>internodal gap is thus about 9 x 10-13 farads. The...