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C
The Role of
RAW POWER
in
INTELLIGENCE
Hans Moravec
May 12, 1976
CONTENTS
1 Introduction
2 Acknowledgement
3 Section 1: The Natural History of Intelligence
3 Product lines
5 Unifying principles
6 Harangue
7 References
10 Section 2: Measuring Processing Power
10 Low level vision
11 Entropy measurement
13 A representative computer
14 A typical nervous system
15 Thermodynamic efficiency
17 References
18 Section 3: The Growth of Processing Power
20 References
21 Section 4: Interconnecting Processors
21 Log^2 sorting net construction
23 Communication scheme organization
27 Package counts
29 Speed calculations
30 Possible refinements
31 References
32 Section 5: Programming Interconnected Processors
33 A little Lisp
35 A little Algol
37 A little operating systems
38 Disclaimer
39 Section 6: Bombast
Introduction:
This essay is an argument that an essential ingredient is
absent in many current conceptions of the road to Artificial
Intelligence.
The first section discusses natural intelligence, and notes
two major branches of the animal kingdom in which it evolved
independently, and several offshoots. The suggestion is that
intelligence need not be so difficult to construct as is sometimes
assumed.
The second part compares the information processing ability of
present computers with intelligent nervous systems, and finds a factor
of one million difference. This abyss is interpreted as a major
distorting influence in current work, and a reason for disappointing
progress.
Section three examines the development of electronics, and
concludes the state of the art can provide more power than is now
available, and that the gap could be closed in a decade.
Parts four and five introduce hardware and software aspects of
a system which is able to make use of the advancing technology.
Acknowledgement:
The following entities provided inspiration, encouragement,
suggestions, data, slave labor, proof reading services, etc.:
(in carefully randomized order) PDP-KA10, Scientific American, Marc Le
Brun, Andy Moorer, Ed Mcguire, Electronics magazine, Don Gennery, Bill
Gosper, John McCarthy, Macsyma, Mike Farmwald, Russ Taylor, Cart
Project, Les Earnest, Pierre van Nypelseer, Robert Maas, Jeff Rubin,
Bruce Baumgart, HAL-9000, Tom Binford, Clem Smith, Tom Gafford, Brian
Harvey, ...
Section 1: The Natural History of Intelligence
Product lines:
Natural evolution has produced a continuum of complexities of
behavior, from the mechanical simplicity of viruses to the magic of
mammals. In the higher animals most of the complexity resides in the
nervous system.
Evolution of the brain began in early multi-celled animals a
billion years ago with the development of cells capable of
transmitting electrochemical signals. Because neurons are more
localized than hormones they allow a greater variety of signals in a
given volume. They also provide evolution with a more uniform medium
for experiments in complexity.
The advantages of implementing behavioral complexity in neural
nets seem to have been overwhelming, since all modern animals more
than a few cells in size have them [animal].
Two major branches in the animal kingdom, vertebrates and
mollusks, contain species which can be considered intelligent. Both
stem from one of the earliest multi-celled organisms, an animal
something like a hydra made of a double layer of cells and possessing
a primitive nerve net.
Most mollusks are intellectually unimpressive sessile
shellfish, but one branch, the cephalopods, possesses high mobility,
large brains and imaging eyes, evolved independently of the
corresponding vertebrate structures. There are fascinating
differences. The optic nerve connects to the back of the retina, so
there is no blind spot. The brain is annular, forming a ring
encircling the esophagus. The circulatory system, also independently
evolved, has three blood pumps, a systemic heart pumping oxygenated
blood to the tissues and two gill hearts, each pumping venous blood to
one gill. The oxygen carrier is a green copper compound called
hemocyanin, evolved from an earlier protein that also became
hemoglobin.
These animals have some unique abilities. Shallow water
octopus and squid are covered by a million individually controlled
color changing effectors called chromatophores, whose functions are
camouflage and communication. The capabilities of this arrangement
have been demonstrated by a cuttlefish accurately imitating a
checkerboard it was placed upon, and an octopus in flight which
produced a pattern like the seaweed it was traversing, coruscating
backward along the length of its body, diverting the eye from the true
motion. Deep sea squid have photophores capable of generating large
quantities of multicolored light. Some are as complex as eyes,
containing irises and lenses [squid]. The light show is modulated by
emotions in major and subtle ways. There has been little study of
these matters, but this must provide means of social interaction.
Since they also have good vision, there is the potential for high
bandwidth communication.
Cephalopod intelligence has not been extensively investigated,
but a few controlled experiments indicate rapid learning in small
octopus [Boycott]. The Cousteau film shows an octopus' response to a
"monkey and bananas" problem. A fishbowl containing a
lobster is sealed with a cork and dropped into the water near it. The
octopus is attracted, and spends a long while alternately probing the
container in various ways and returning to its lair in iridescent
frustration. On the final iteration it exits its little hole in the
ground and unhesitatingly wraps three tentacles around the bowl, and
one about the cork, and pulls. The cork shoots to the surface and the
octopus eats. The Time-Life film contains a similar sequence, with a
screw top instead of a cork! If small octopus have almost mammalian
behavior, what might giant deep sea squid be capable of?
Birds are more closely related to humans than are cephalopods,
their common ancestor with us being a 300 million year old early
reptile. Size-limited by the dynamics of flying, some birds have
reached an intellectual level comparable to the highest mammals.
Crows and ravens are notable for frequently outwitting man.
Their intuitive number sense (ability to perceive the cardinality of a
set without counting) extends to seven, as opposed to three or four in
man. Such a sense is useful for keeping track of the number of eggs in
a nest. Experiments have shown [Stettner] that most birds are more
capable of high order "reversal" and "learning
set" learning than all mammals except the higher primates. In
mammals these abilities increase with increasing cerebral cortex
size. In birds the same functions depend on areas not present in
mammalian brains, forebrain regions called the "Wulst" and
the hyperstriatum. The cortex is small and relatively
unimportant. Clearly this is another case of independent evolution of
similar mental functions.
It is interesting to speculate whether penguins, now similar
to seals in behavior and habitat, will ever become fully aquatic, and
evolve analogously to the great whales.
The cetaceans are related to man through a small 30 million
year old primitive mammal. Some species of dolphin have body and brain
masses identical to ours, and archaeology reveals they have been this
way several times as long. They are as good as man at many kinds of
problem solving, and perhaps at language. The references contain many
anecdotes, and describe a few controlled experiments, showing that
dolphins can grasp and communicate complex ideas. Killer whales have
brains seven times human size, and their ability to formulate plans is
better than dolphins', occasionally being used to feed on them. Sperm
whales, not the largest animals, have the world's largest
brains. There may be intelligence mediated conflict with large squid,
their main food supply.
Elephants have brains about six times human size, matriarchal
tribal societies, and complex behavior. Indian domestic elephants
learn 500 commands, limited by the range of tractor-like tasks their
owners need done, and form voluntary mutual benefit relationships with
their trainers, exchanging labor for baths. They can solve problems
such as how to sneak into a plantation at night to steal bananas,
after having been belled (answer: stuff mud into the bells). And they
remember for decades. Inconvenience and cost has prevented modern
science from doing much work with them.
The apes are man's cousins. Chimps and gorillas can learn to
use tools and to communicate with human sign languages at a retarded
level. As chimps have one third, and gorillas one half, human
brainsize, similar results should be achievable with the larger
brained, but less man-like animals. Though no other species has
managed to develop cultures comparable to modern man's, it may be that
some of them can be made partners in ours, accelerating its evolution
by their unique capabilities.
Unifying principles:
A feature shared by all living organisms whose behavior is
complex enough to place them near human in intelligence is a hundred
billion neuron nervous system. Imaging vision requires a billion
neurons, while a million is associated with fast and interesting, but
stereotyped, behavior as in a bee. A thousand is adequate for slow
moving animals with minimal sensory input, such as slugs and worms. A
hundred runs most sessile animals. The portions of nervous systems for
which tentative wiring diagrams have been obtained, including much of
the brain of the large neuroned sea slug, Aplysia, the flight
controller of the locust and the early stages of some vertebrate
visual systems, reveal that the neurons are configured into efficient,
clever, assemblies. This should not be too surprising, as unnecessary
redundancy means unnecessary metabolic load, a distinct selective
disadvantage.
Evolution has stumbled on many ways of speeding up its own
progress, since species that adapt more quickly have a selective
advantage. Most of these, such as sex and individual death, have been
refinements of one of the oldest, the encoding of genetic information
in the easily mutated and modular DNA molecule. In the last few
million years the genetically evolved ability of animals, especially
mammals, to learn a significant fraction of their behavior after birth
has provided a new medium for growth of complexity. Modern man, though
probably not the most individually intelligent animal on the planet,
is the species in which this cultural evolution seems to have had the
greatest effect, making human culture the most potent force on the
earth's surface.
Cultural and technological evolution proceeds by massive
interchange of ideas and information, trial and error guided by the
ability to predict the outcome of simple situations, and other
techniques mediated by the intelligence of the participants. The
process is self reinforcing because its consequences, such as improved
communication methods and increased wealth and population, allow more
experiments and faster cross fertilization among different lines of
inquiry. Many of its techniques have not been available to biological
evolution. The effect is that present day global civilization is
developing capabilities orders of magnitude faster. Of course
biological evolution has had a massive head start.
Although cultural evolution has developed methods beyond those
of its genetic counterpart, the overall process is essentially the
same. It involves trying large numbers of possibilities, selecting the
best ones, and combining successes from different lines of
investigation. This requires time and other finite resources.
Finding the optimum assembly of particular type of component
which achieves a desired function usually requires examination of a
number of possibilities exponential in the number of components in the
solution. With fixed resources this implies a design time rising
exponentially with complexity. Alternatively the resources can be used
in stages, to design subassemblies, which are then combined into
larger units, and so on, until the desired result is achieved. This
can be much faster since the effort rises exponentially with the
incremental size of each stage and linearly with the number of stages,
with an additional small term, for overall planning, exponential in
the number of stages. The resulting construct will probably use more
of the basic component and be less efficient than an optimal design.
Biological evolution is affected by these considerations as
much as our technology. Presumably there is a way of using the physics
of the universe to construct entities functionally equivalent to human
beings, but vastly smaller and more efficient. Terrestrial evolution
has not had the time or space to develop such things. But by building
in the sequence atoms, amino acids, proteins, cells, organs, animal
(often concurrently), it produced a technological civilization out of
inanimate matter in only two billion years.
Harangue:
The existence of several examples of intelligence designed
under these constraints should give us great confidence that we can
achieve the same in short order.
The situation is analogous to the history of heavier than air
flight, where birds, bats and insects clearly demonstrated the
possibility before our culture mastered it. Flight without adequate
power to weight ratio is heartbreakingly difficult (vis. Langley's
steam powered aircraft or current attempts at man powered flight),
whereas with enough power (on good authority!) a shingle will fly.
Refinement of the aerodynamics of lift and turbulence is most
effectively tackled after some experience with suboptimal aeroplanes.
After the initial successes our culture was able to far surpass
biological flight in a few decades.
Although there are known brute force solutions to most AI
problems, current machinery makes their implementation impractical.
Instead we are forced to expend our human resources trying to find
computationally less intensive answers, even where there is no
evidence that they exist. This is honorable scientific endeavor, but,
like trying to design optimal airplanes from first principles, a slow
way to get the job done.
With more processing power, competing presently impractical
schemes could be compared by experiment, with the outcomes often
suggesting incremental or revolutionary improvements. Computationally
expensive highly optimizing compilers would permit efficient code
generation at less human cost. The expanded abilities of existing
systems such as MACSYMA, along with new experimental results, would
accelerate theoretical development. Gains made this way would improve
the very systems being used, causing more speedup. The intermediate
results would be inefficient kludges busily contributing to their own
improvement. The end result is systems as efficient and clever as any
designed by more theoretical approaches, but sooner, because more of
the labor has been done by machines.
With enough power anything will fly. The next section tries to
decide how much is needed.
B
References:
[animal]
JERISON, Harry J.,
"Paleoneurology and the Evolution of Mind",
Scientific American, Vol. 234, No. 1,
January 1976, 90-101.
BITTERMAN, M. E.,
"The Evolution of Intelligence",
Scientific American, Vol. 212, No. 1,
January 1965, 92-100.
GRIFFIN, Donald R., ed.
"Animal Engineering",
W.H. Freeman and Company,
San Francisco, June 1974.
BURIAN, Z. and Spinar, Z.V.,
"Life Before Man",
American Heritage Press, 1972.
RIOPELLE, A.J., ed.
"Animal Problem Solving",
Penguin Books, 1967.
GOODRICH, Edwin S.,
"Studies on the Structure and Development of Vertebrates",
Dover Publications Inc., New York, 1958.
BUCHSBAUM, Ralph,
"Animals without Backbones",
The University of Chicago Press, 1948.
FARAGO, Peter, and Lagnado, John,
"Life in Action"
Alfred A. Knopf, New York, 1972.
BONNER, John Tyler,
"Cells and Societies",
Princeton University Press, Princeton, 1955.
[squid]
COUSTEAU, Jacques-Yves and Diole, Philippe,
"Octopus and Squid",
Doubleday & Company, Inc., Garden City, New York, 1973.
(also a televised film of the same name)
"The Octopus",
a televised film, Time-Life films.
BOYCOTT, Brian B.,
"Learning in the Octopus",
Scientific American, Vol. 212, No. 3,
March 1965, 42-50.
LANE, Frank W.,
"The Kingdom of the Octopus",
Worlds of Science Book, Pyramid Publications Inc.
October, 1962.
[bird]
BAKKER, Robert T.,
"Dinosaur Renaissance",
Scientific American, Vol. 232, No. 4,
April 1975.
STETTNER, Laurence Jay and Matyniak, Kenneth A.
"The Brain of Birds",
Scientific American, Vol. 218, No. 6,
June 1968, 64-76.
[whale]
LILLY, John. C.,
"The Mind of the Dolphin" &
"Man and Dolphin",
Doubleday and Company, New York, 1967.
COUSTEAU, Jacques-Yves and Diole, Philippe,
"The Whale",
Doubleday & Company, Inc., Garden City, New York, 1972.
FICHTELIUS, Karl-Erik and Sjolander, Sverre,
"Smarter than Man?",
Ballantine Books, New York, 1974.
STENUIT, Robert,
"The Dolphin, Cousin to Man",
Bantam Books, New York, 1972.
"Whales and Dolphins",
A BBC produced film shown
in the NOVA television series
McINTYRE, Joan, ed.
"Mind in the Waters",
Charles Scribner's Sons, San Francisco, 1974.
[elephant]
RENSCH, Bernhard,
"The Intelligence of Elephants",
Scientific American,
February 1957, 44.
[primate]
"The First Words of Washoe",
Televised film shown in the NOVA series
LeGROS CLARK, W.E.,
"History of the Primates",
The University of Chicago Press, Chicago 1966.
PFEIFFER, John,
"The Human Brain",
Worlds of Science Books, Pyramid Publications Inc.,
New York, 1962.
Section 2: Measuring Processing Power
Low level vision:
The visual system of a few animals has been studied in some
detail, especially the layers of the optic nerve near the retina. The
neurons comprising these structures are used efficiently to compute
local operations like high pass filtering and edge, curvature,
orientation and motion detection.
Assuming the visual cortex (and possibly the optic nerve
itself) is as computationally intensive as the retina, successive
layers producing increasingly abstracted representations, we can
estimate the total capability. There are a million seperate fibers in
a cross section of the human optic nerve. At the retina each is
connected to several of 10 million light sensitive rods and cones. The
thickness of the optical cortex is a thousand times the depth occupied
by the neurons which apply a single simple operation. The eye is
capable of processing images at the rate of ten per second (flicker at
higher frequencies is detected by special operators). This means that
the human visual system evaluates 10,000 million pixel simple
operators each second.
A tightly hand coded simple operator, like high pass filtering
by subtraction of a local average, applied to a 256x256 (1/16 million)
pixel picture takes at least 10 seconds when executed on a PDP-10
(KA), not counting timesharing. A million pixel image would require
160 seconds, if storage constraints permitted it. Since the computer
can evaluate only one at a time, the effective rate is 1/160 million
pixel simple operators per second.
Thus a hand coded PDP-10 falls short of being the equal of the
human optical system by a speed factor of 1.6 million.
It may not be necessary to apply every operator to every
portion of every picture, and a general purpose computer, being more
versatile than the optic nerve, can take advantage of this. I grant
an order of magnitude for this effect, reducing the optic nerve to a
mere 100,000 PDP-10 equivalents.
The size of this factor is related to having chosen to
implement our algorithms in machine language. If we had opted to
disassemble a number of PDP-10's and reconfigure the components to do
the computation, far fewer would have been required. On the other hand
if we had run our algorithms in interpreted Lisp, 10 to 100 times as
many would be needed. The tradeoff is that the design time varies
inversely with the execution efficiency. A good Lisp program to
compute a given function is easier to produce than an efficient
machine language program, or an equivalent piece of hardware.
Compilers and automatic design programs blur the issue a little by
passing some of the effort of implementation to a machine, but the
essential character remains.
Entropy measurement:
Is there a quantitative way in which the processing power of a
system, independent of its detailed nature, can be measured? A feature
of things which compute massively is that they change state in
complicated and unexpected ways. The reason for believing that, say, a
stationary rock does little computing is its high predictability. By
this criterion the amount of computing done by a device is in the mind
of the beholder. A machine with a digital display which flashed 1, 2,
3, 4 etc., at fixed intervals would seem highly predictable to an
adult of our culture, but might be justifiably considered to be doing
an interesting, nontrivial and informative computation by a young
child. Information theory provides a measure for this idea. If a
system is in a given state and can change to one of a number of next
states, the information in the transition, which I will call the
Compute Energy (CE), is given by
__N_
\
> - p log(p )
/ i i
/----
i=1
where N is the number of next states, and p[i] is the probability that
the i'th state will be occur next. If the base of the logarithm is
two, the measure is in binary digits, bits. If we consider the system
in the long run, considering all the states it might ever eventually
be in, then this measure expresses the total potential variety of the
system.
A machine which can accomplish a given thing faster is more
powerful than a slower one. A measure for Compute Power is obtained by
dividing each term in the above sum by the expected time of the
corresponding transition. This is
__N_
\ - p log(p )
CP = > ___i______i_
/ t
/---- i
i=1
and the units are bits/second.
These measures are highly analogous to the energy and power
capacities of a battery. Some properties follow:
They are linear, i.e. the compute power and energy of a system of two
or more independent machines is the sum of the individual power and
energies;
Speeding up a machine by a factor of n increases the CP by the same
factor;
A completely predictable system has a CP and CE of zero;
A machine with a high short term CP, which can reach a moderate number
of states in a short time, can yet have a low CE, if the total number
of states attainable in the long run is not high;
If the probabilities and times of all the transitions are
equal the measures simplify to
CE = log2(N)
CP = log2(N)/t
For N distinct outcomes and equal transition times the maximum CE and
CP is obtained if all the probabilities of occurrence are 1/N, so the
above simplifications represent an upper bound in cases where the
probabilities are variable or cannot be determined.
A representative computer:
For the KA-PDP10, considering one instruction time, we have
(roughly) that in one microsecond this machine is able to execute one
of 2^5 different instructions, involving one of 2^4 accumulators and
one of 2^18 memory locations, most of these combinations resulting in
distinct next sates. This corresponds to a CP of
5 4 18
log(2 x 2 x 2 ) bits 6
--------------------- = 27 x 10 bits/sec
-6
10 sec
This is an extreme upper bound, and represents the most efficient code
possible. It cannot be maintained for very long, because many
different sequences of instructions have the same outcome. Very often,
for instance, the order in which a number of instructions is executed
does not matter. Assuming for the moment that this is always the case,
we can calculate the effect on the CP, measured over a second. The raw
power says there are
6
27 x 10
2
distinct possible states after a second, or one million instruction
times. If all permutations result in the same outcome, this must be
reduced by a factor of 1000000!. The log of a quotient is the
difference of the logs, so the adjusted CP is
6 6 6 6 6
27 x 10 - log(10 !) = 27 x 10 - 18.5 x 10 = 8.5 x 10
bits/sec.
The CP is also limited by the total compute energy. If we
ignore external devices, this is simply the total amount of memory,
about 36x2^18 = 9.4x10^6 bits. The PDP 10 could execute at its
maximum effectiveness for 9.4/8.5 = 1.1 seconds before reaching a
state which could have been arrived at more quickly another way.
Large external storage devices such as disks and tapes can
increase the compute energy indefinitely, because they are a channel
through which independently obtained energy may be injected. On the
other hand, they have only a moderate effect on the power.
A disk channel connected to our KA-10 has a data rate of
6.4x10^6 bits/sec. If run at full speed, constantly stuffing new
information into memory, it would add slightly less than that to the
power, because it uses memory cycles the processor might want. If, as
is usually the case, the disk is used for both reading and writing,
the improvement is reduced by a factor of two. Further reductions
occur if the use is intermittent. The overall impact is less than
10^6 bits/sec, about 10% of the power of the raw processor.
Combining the above results, we conclude that the processing
power of a typical major AI center computer is at most 10^7
bits/sec. Time sharing reduces this to about 10^6 b/s per
user. Programming in a moderately efficient high level language (vs.
optimal machine code), costs another factor of 10, and running under
an interpreter may result in a per user power of a mere 10,000
bits/sec, if the source code is efficient. These reductions can be
explained in the light of the CP measure by noting that the a compiler
or interpreter causes the executed code to be far more predictable
than optimal code, eg. by producing stereotyped sequences of
instructions for primitive high level constructs.
A typical nervous system:
We now consider the processing ability of animal nervous
systems, using humans as an example. Since the data is even more
scanty than what we assumed about the PDP-10, some not unassailable
assumptions need to be made. The first is that the processing power
resides in the neurons and their interconnections, and not in more
compact nucleic acid or other chemical encodings. There is no
currently widely accepted evidence for the latter, while neural
mechanisms for memory and learning are being slowly revealed. A
second is that the neurons are used reasonably efficiently, as
detailed analysis of small nervous systems and small parts of large
ones reveals (and common sense applied to evolution suggests).
Thirdly, that neurons are fairly simple, and their state can be
represented by a binary variable, "firing" or "not
firing", which can change about once per millisecond. Finally we
assume that human nervous systems contain about 40 billion neurons.
Considering the space of all possible interconnections of
these 40 billion (treating this as the search space available to
natural evolution in its unwitting attempt to produce intelligence, in
the same sense that the space of all possible programs is available to
someone trying to create intelligence in a computer), we note that
there is no particular reason why every neuron should not be able to
change state every millisecond. The number of combinations thus
reachable from a given state is 2^(40x10^9) the binary log of which is
40x10^9. This leads to a compute power of
9
40 x 10 bits 12
--------------------- = 40 x 10 bits/sec
-3
10 sec
which is about a million times the maximum power of the KA-10.
Keep in mind that much of this difference is due to the high
level of interpretation in the 10, compared to what we assumed for the
nervous system. Rewiring its gates or transistors for each new task
would greatly increase the CP, but also the programming time. If the
processor is made of 100,000 devices which can change state in 100 ns,
the potential CP available through reconfiguration is 10^5 bits/10^-7
sec = 10^12 b/s. The CE would be unaffected. If automatic design and
fabrication methods result in small quantity integrated circuit
manufacture becoming less expensive and more widely practiced, my
calculations may prove overly pessimistic.
Thermodynamic efficiency:
Thermodynamics and information theory provide us with a
minimum amount of energy per bit of information generated at a given
background temperature (the energy required to out shout the thermal
noise). This is approximately the Boltzmann constant,
-16 erg
1.38 x 10 ------------
deg molecule
for our purposes the units will be rephrased as erg/(deg bit), since
for normal matter molecules represent the limit of organization, due
to the quantum mechanical fuzziness of things. This measure allows us
to estimate the overall energy efficiency of computing engines. For
instance, we determined the computing rate of the brain, which
operates at 300 degrees K, to be 40x10^12 bits/sec. This corresponds
to a physical power of
12 bit -16 erg erg
40 x 10 --- x 300 deg x 1.38 x 10 ------- = 1.656 ---
sec deg bit sec
-7
= 1.656 x 10 watt
The brain runs on approximately 40 watts, so we conclude that
it is 10^-8 times as efficient as the physical limits allow.
Doing the same calculation for the KA10, again at 300 deg, we
see that a CP of 8.5x10^6 bit/sec is worth 3.519x10^-14 watts. Since
this machine needs 10 kilowatts the efficiency is only
10^-18. Conceivably a ten watt, but otherwise equivalent, KA10 could
be designed today, if care were taken to use the best logic for the
required speed in every assembly. The efficiency would then still be
only 10^-15.
As noted previously, there is a large cost inherent in the
organization of a general purpose computer. We might investigate the
computing efficiency of the logic gates of which it is constructed (as
was, in fact, done with the brain measure). A standard TTL gate can
change state in about 10ns, and consumes 10^-3 watt. The switching
speed corresponds to a CP of 10^8 bit/sec, or a physical power of
4.14x10^-13 watt. So the efficiency is 10^-10, only one hundred times
worse than a vertebrate neuron.
The newer semiconductor logic families are even better. C-MOS
is twice as efficient as TTL, and Integrated Injection Logic is 100
times better, putting it on a par with neurons.
Experimental superconducting Josephson junction logic operates
at 4 deg K, switches in 10^-11 sec, and uses 10^-7 watts per
gate. This implies a physical compute power of 5x10^-12 watt, and an
efficiency of 5x10^-5, 1000 times better than neurons. At room
temperature it requires a refrigerator that consumes 100 times as much
energy as the logic, to pump the waste heat uphill from 4 degrees to
300. Since the background temperature of the universe is about 4
degreees, this can probably eventually be done away with.
It is thus likely that there exist ways of interconnecting
gates made with known techniques which would result in behavior
effectively equivalent to that of human nervous systems. Using a
million I2L gates, or 10 thousand Josephson junction gates, and a
trillion bits of slower bulk storage, all running at full speed, such
assemblies would consume as little as, or less than, the power needed
to operate a brain of the conventional type.
Past performance indicates that the amount of human and
electronic compute power available is inadequate to design such an
assembly within the next few years. The problem is much reduced if
the components used are suitable large subassemblies. Statements of
good high level computer languages are the most effective such
modularizations yet discovered, and are probably the quickest route to
human equivalence, if the necessary raw processing power can be
accessed through them. This section has indicated that a million times
the power of typical existing machines is required. The next suggests
this should be available at reasonable cost in about ten years.
References:
WILLOWS, A.O.D.,
"Giant Brain Cells in Mollusks",
Scientific American, Vol. 224, No. 2,
February 1971, 69-75.
KANDEL, Eric R.,
"Nerve Cells and Behavior",
Scientific American, Vol. 223, No. 1,
July 1970, 57-70.
AGRANOFF, Bernard W.,
"Memory and Protein Synthesis",
Scientific American, Vol. 216, No. 6,
June 1967, 115-122.
KENNEDY, Donald,
"Small Systems of Nerve Cells",
Scientific American, Vol. 216, No. 5,
May 1967, 44-52.
BAKER, Peter F.,
"The Nerve Axon",
Scientific American, Vol. 214, No. 3,
March 1966, 74-82.
HUBEL, David H.,
"The Visual Cortex of the Brain",
Scientific American,
November 1963, 54-62.
WILLIAMS, Peter L., Warwick, Roger
"Functional Neuroanatomy of Man",
W.B. Saunders Company, Philadelphia, 1975.
"PDP-10 Reference Handbook",
Digital Equipment Corporation, Maynard Mass., 1971.
TRIBUS, Myron and McIrvine, Edward C.,
"Energy and Information",
Scientific American, Vol. 224, No. 3,
Setember 1971, 179-188.
GLASSTONE, Samuel, Lewis, David,
"Elements of Physical Chemistry",
D. Van Nostrand Co. Inc., New York, 1960.
MILLER, Richard T.,
"Super Switch", 284, in Science Year annual 1975,
Field Enterprises Educational Corp., 1975.
LANDAUER, Rolf,
"Fundamental Limitations in the Computational Process",
IBM Research Report, Yorktown Heights N.Y., June 1976.
Section 3: The Growth of Processing Power
The references below present, among other things, the
following data points on a price curve:
Transistor price
.0001c .01 1c $1 $100
+---+---+---+---+---+---+---+---+---+---+ Year
| |
+- O -+ 1950
| # | 1951 $100 transistor
| # | 1952 transistor hearing aid
| # | 1953
| # | 1954
+- # -+ 1955 transistor radios
| # | 1956
| O | 1957 $10 transistor
| # | 1958
| # | 1959
+- O -+ 1960 $1 transistor
| # | 1961
| # | 1962 $100,000 small computer (IBM 1620)
| # | 1963
| O | 1964
+- # -+ 1965 $0.08 transistor (IC)
| # | 1966 $1000 4 func calculator
| # | 1967 $6000 scientific calc.
| # | 1968 $10,000 small computer (PDP 8)
| # | 1969
+- O -+ 1970 $200 4 func calculator
| # | 1971
| # | 1972 1K RAMS (1 c/bit)
| # | 1973
| # | 1974 $1000 small computer (PDP 11)
+- O -+ 1975 4K RAMS (.1 c/bit)
| # | 1976 $5 4 func calc (.05 c/trans)
| | 1977
| | 1978
| | 1979
+---+---+---+---+---+---+---+---+---+---+
The numbers indicate a remarkably stable evolution. The price
per electronic function has declined by a steady factor of ten every
five years, if speed and reliability gains are included. Occasionally
there is a more precipitous drop, when a price threshold which opens a
mass market is reached. This makes for high incentives, stiff price
competition and mass production economies. It happened in the early
sixties with transistor radios, and is going on now for pocket
calculators and digital wristwatches. It is begining for
microcomputers, as these are incorporated into consumer products such
as stoves, washing machines, televisions and sewing machines, and soon
cars. During such periods the price can plummet by a factor of 100 in
a five year period. Since the range of application for cheap
processors is larger than for radios and calculators, the explosion
will be more pronounced.
The pace of these gains is in no danger of slackening in the
forseeable future. In the next decade the current period may seem to
be merely the flat portion of an exponential rise. On the immediate
horizon are the new semiconductor techniques, I2L, and super fast
D-MOS, CCD for large sensors and fast bulk memory, and magnetic
bubbles for mass storage. The new 16K RAM designs use a folded
(thicker) cell structure to reduce the area required per bit, which
can be interpreted as the first step towards 3 dimensional
integration, which could vastly increase the density of circuitry.
The use of V-MOS, an IC technique that vertically stacks the elements
of a MOS transistor is expanding. In the same direction, electron beam
and X-ray lithography will permit smaller circuit elements.
In the longer run we have ultra fast and efficient Josephson
junction logic, of which small IC's exist in an IBM lab, optical
communication techniques, currently being incorporated into
intermediate distance telephone links, and other things now just
gleams in the eye of some fledgling physicist or engineer.
My favorite fantasies include the "electronics" of
super-dense matter, either made of muonic atoms, where the electrons
are replaced by more massive negative particles or of atoms
constructed of magnetic monopoles which (if they exist) are very
massive and affect each other more strongly than electric charges.
The electronics and chemistry of such matter, where the
"electron" orbitals are extremely close to the nucleus,
would be more energetic, and circuitry built of it should be
astronomically faster and smaller, and probably hotter. Mechanically
it should exhibit higher strength to weight ratios. The critical
superconducting transition field strengths and temperatures would be
higher. For monopoles there is the possibility of combination
magnetic electric circuitry which can contain, among many other
goodies, DC transformers, where an electric current induces a monopole
current at right angles to it, which in turn induces another electric
current. One might also imagine quantum DC transformers, matter
composed of a chainlike mesh of alternating orbiting electric and
magnetic charges.
I interpret these things to mean that the cost of computing
will fall by a factor of 100 during the next 5 years, as a consequence
of the processor explosion, and by the usual factor of 10 in the 5
years after that. As an approximation to what is available today,
note that in large quantities an LSI-11 sells for under $500. This
provides a moderately fast 16 bit processor with 4K of memory.
Another $500 could buy an additional 32K of memory, if we bought in
quantity. The result would be a respectable machine, somewhat less
powerful than the KA-10, for $1000. At the crude level of
approximation employed in the previous section, a million machines of
this type should permit human equivalence. A million dollars would
provide a thousand of them today (a much better buy, in terms of raw
processing power, than a million dollar large processor). In ten
years a million dollars should provide the equivalent of a million
such machines, in the form of a smaller number of faster processors,
putting human equivalence within reach.
We now have the problem of what to do with this roomful of
isolated computers. The next section describes what seems to be the
best known solution to the problem of interconnecting a large number
of processors with maximum generality, at reasonable cost.
References:
McWHORTER, Eugene W.
"The Small Electronic Calculator",
Scientific American, Vol. 234, No. 3,
March 1976, 88-98.
HODGES, David A.,
"Trends in Computer Hardware Technology",
Computer Design, Vol. 15, No. 2,
February 1976, 77-85.
SCRUPSKI, Stephen E., et al.,
"Technology Update",
Electronics, Vol. 48, No. 21, McGraw-Hill,
October 16, 1975, 74-127.
VACROUX, Andre G.
"Microcomputers",
Scientific American, Vol. 232, No. 5,
May 1975, 32-40.
TURN, Rien
"Computers in the 1980's",
Columbia University Press,
Rand Corporation, 1974.
TIEN, P. K.
"Integrated Optics",
Scientific American, Vol. 230, No. 4,
April 1974, 28-35.
HITTINGER, William C.
"Metal-Oxide-Semiconductor Technology",
Scientific American, Vol. 229, No. 2,
August 1973, 48-57.
BOBECK, Andrew H. and Scovil, H. E. D.
"Magnetic Bubbles",
Scientific American, Vol. 224, No. 6,
June 1971, 78-90.
HEATH, F. G.
"Large-Scale Integration in Electronics",
Scientific American, Vol. 222, No. 3,
February 1970, 22-31.
RAJCHMAN, Jan A.
"Integrated Computer Memories",
Scientific American, Vol. 217, No. 1,
July 1967, 18-31.
HITTINGER, William C. and Sparks, Morgan
"Microelectronics",
Scientific American, Vol. 213, No. 5,
November 1965, 56-70.
Section 4: Interconnecting Processors
The highest bandwidth and most flexible way for a number of
computers to interact is by shared memory. Systems of the size
considered here would require a large, but not unreasonable, address
space of 100 billion words (40 bits of address). They would also
demand memories with a thousand to a million ports. Although a
variant of the method below could be used to construct such monsters,
they would cost much more than the processors they served.
Alternatively, we might consider how a mass of the usual kind
of machine, each with a moderate amount of local memory, could
communicate through their bandwidth limited IO busses. Define a
message period as the minimum interval in which a processor may
transmit and receive one message. Assuming that messages are
addressed to particular destination machines, an ideal interconnection
system would allow every processor to issue a message during each
message period, and deliver the highest priority message for each
processor to it, providing notices of success or failure to the
originators. The delay between transmission and reception of a
message would be uniform and short, and the cost of the network would
be reasonable (on the order of the cost of the processors served).
It so happens that this specification can be met. The
following construction is a design due to K.E. Batcher [Batcher],
extended considerably to permit pipelining of messages and higher
speed.
Log^2 sorting net construction:
Batcher's major contribution is a method for constructing nets
that can sort N numbers in (log(N))^2 time, using only Nxlog^2 N
primitive two element sorters. Two nets plus a little additional
circuitry can accomplish the message routing task.
The construction consists of a method for making a merger for
two ordered lists of 2N numbers (call it a 2N-merger) from two
N-mergers and 2N additional primitive elements. A primitive sorting
element is a 1-merger.
An N-merger can thus be constructed from Nxlog2(N) primitive
elements. A sorter is made of a cascade of ever larger mergers,
forming length two ordered lists from individual inputs with
1-mergers, combining these pairwise into length 4 lists with
2-mergers, and so on, until the entire sorted list of N numbers comes
out of a final N/2-merger. The number of primitive elements involved
is Nxlog2(N)x(log2(N)+1)/4.
sorting
__________ elements
A1 ______________| |_________________________
_____| | _____
A2 ______ | ____| 3 |_______________| |_____
| || | | ____________| |_____
A3 ______|_|| |__ M |__|__________ |___|
| | | E | | |
A4 _____ | | ___| R |__|_________ |
|| | ___| G | | || _____
A5 _____||__|| __| E |__|________ ||_| |_____
I || || _| R | | _______||__| |_____ O
A6 ____ || ||| | |__||______ || |___|
N ||| ||| |________| || ||| U
||| ||| || |||
P ||| ||| || ||| _____ T
||| ||| || |||__| |_____
U ||| ||| || _____||___| |_____ P
||| ||| ||| || |___|
T B1_____|||___||| __________ ||| || U
|||____||_| |__||| ||
S ||_____||_| | || || _____ T
B2 ___ |______||_| 3 |___|| ||___| |_____
| || | | | ____|____| |_____
B3 ___|_______|| |__ M |____|| | |___|
| | | E | | |
B4 __ | | ___| R |_____| | _____
||________|_| G | |____| |_____
B5 __|_________| | E |_______________| |_____
|___________| R | |___|
B6 ______________| |_________________________
|________|
FIG 1: An illustration of Batcher's odd-even merger construction,
producing a 6-merger from two 3-mergers and five primitive
elements. The first and last outputs undergo less delay than the
intermediate ones, which is undesirable. The delays can be
equalized by passing the first and last outputs through an extra
primitive element. Batcher provides an alternate construction,
which he calls a "bitonic sorter" which merges, has constant
delay, and uses the same number of elements as the above
construction with the extra element added.
Communication scheme organization:
___________ _________ _____ ____________
1 ->| |-->| |-->| |-->| |-> 1
| | | | | | | |
2 ->| |-->| |-->| |-->| |-> 2
| N | | | | | | | Processor
Processor 3 ->| |-->| |-->| |-->| |-> 3
| Input | | | | | | | Acknowledgement
Outgoing | | | | | | | |
. | Sorter | . | | . | | . | | . Input
Message . | | . | | . | | . | | .
. | (Desti- | . | | . | | . | 2N | . Ports
Ports | nation | | | | | | |
| field) | | 2 | | E | | Input |
| | | N | | x | | |
N ->| |-->| |-->| c |-->| Sorter |-> N
|_________| |__ M | | h | | |
| e | | a | | (Source | ----------------
__| r | | n | | field) |
1 -->| g |-->| g |-->| |-> 1
| e | | e | | |
2 -->| r |-->| r |-->| |-> 2
| | | | | | Processor
Dummy 3 -->| |-->| |-->| |-> 3
| | | | | | Incoming
Message | | | | | |
. | | . | | . | | . Message
Injection . | | . | | . | | .
. | | . | | . | | . Ports
| | | | | |
| | | | | |
N -->| |-->| |-->| |-> N
|_______| |___| |__________|
FIG 2: Block diagram of the multiprocessor interconnection scheme.
The cost per processor, and the delay in the net, grows as the
square of the log of N, the number of processors.
_____________________________________________________________________________
| | | | | |
| Data | Source Address | 0 | Priority | Destination Ad |
|________________________|_________________|___|__________|_________________|
FIG 3: Processor message format. High order bit is on the right.
_____________________________________________________________________________
| | | | | |
| Unused | Position Number | 1 | Infinity | Position Number |
|________________________|_________________|___|__________|_________________|
FIG 4: Dummy message format.
The interconnection scheme is diagrammed in Figs 2, 3 and 4.
Each processor is assigned a number, its "address", as
indicated. In the sorters and the merger the smaller numbers come out
towards the top of the diagram.
Messages are serial bit streams, and consist of a destination
processor address, a priority number (invented by the originating
computer), a one bit "dummy" flag field (set to 0 for actual
messages), the address of the source processor (i.e. a return
address), and the data to be communicated. A low priority number
implies high priority. Zero is the highest priority.
The net is assumed to run at 100% duty cycle, with the
processors emitting successive synchronized waves of messages. Every
processor emits a message every message interval. The following
discussion examines a single message wave.
The first sorting net orders the messages by destination
address, and within a given destination by priority number. Thus the
upper inputs of the merger receive a list of messages, grouped by
destination, with the highest priority message to each processor
heading its group.
The lower inputs of the merger receive N dummy messages,
exactly one for each destination processor. The priority field is the
highest possible (i.e. zero), the dummy flag is 1, the source address
is the same as the destination, and the data portion is unused.
Merging these dummies with the sorted list of real messages
results in a list still grouped by destination, with each group headed
by a dummy, by virtue of its high priority, followed immediately by
the highest priority real message, if any, for the destination.
This list is fed to the exchange network, which examines
adjacent pairs of messages (considering overlapping pairs), and
exchanges the data portions of a pair if the first member happens to
be a dummy to a given address, and the second is a real message to the
same address (i.e. it is the highest priority real message to that
destination).
The sorting network following the exchanger sorts the messages
by the field begining with the dummy flag, which acts as the high
order bit, followed by the source address. Since there were N real
messages, one from each processor, and N dummies, also nominally one
from each processor, and since real messages are sorted ahead of dummy
messages due to the high order bit, (i.e. the dummy flag) being 0, the
second sorter restores the messages into the same order in which they
were introduced.
Each processor has two input ports, one labeled
"acknowledgement", and the other "incoming
message". The acknowledgement input of processor i is connected
to output i of the second sorter. The incoming message input is
connected to output N+i (i.e. the i'th output of the lower half).
In the absence of the exchange network, the i'th processor
would receive its own message back on its acknowledgement input, and
the i'th dummy message on the incoming message input.
Because of the exchanger, however, if the message that
processor i had sent happened to be the highest priority message to
the requested destination, then the data portion of the message on the
acknowledgement input would be that of the dummy it had been swapped
with (signaling success). Also, if any messages had been addressed to
processor i, the data portion of the highest priority one would arrive
on the incoming message port, in place of the dummy message.
Thus a processor receives the highest priority message
addressed to it on its incoming message port, or a dummy if nobody
wanted to talk to it. It receives a dummy on its acknowledgement port
if its message has gotten through, or the message back if it hasn't,
due to the existence of a higher priority message to the same
destination.
Actually the serial nature of the sorter causes the
destination and priority field to be lost in the source address sorter
(it tails after the previous wave of messages). In the case of
messages that fail to get delivered, this means that the originating
processor must remember to whom it sent the message (about four
message times ago in a typical design, due to the latency of the net),
if it wants to try again. This is probably undesirable. Also,
delivered messages contain no indication of who sent them, having had
their source address field exchanged with that of a dummy, unless the
source address is included in the data field.
These shortcomings can be overcome if the exchanger shuffles
the destination address, source address and priority fields in the
manner suggested by Figs 5, 6 and 7. Such shuffling can be
accomplished with an amount of storage at each exchanger position
equal to the number of bits in the destination and priority fields.
Before:
_____________________________________________________________________________
| | | | | |
| Unused | Destination Ad | 1 | Infinity | Destination Ad |
|________________________|_________________|___|__________|_________________|
_____________________________________________________________________________
| | | | | |
| Data | Source Address | 0 | Priority | Destination Ad |
|________________________|_________________|___|__________|_________________|
After:
_____________________________________________________________________________
| | | | | |
| Priority | Source Address | Data | Destination Ad | 1 |
|__________|_________________|________________________|_________________|___|
_____________________________________________________________________________
| | | | | |
| Infinity | Destination Ad | Unused | Source Address | 0 |
|__________|_________________|________________________|_________________|___|
FIG 5: Rearrangements effected by the exchanger in an exchanged pair.
Before:
_____________________________________________________________________________
| | | | | |
| Data | Source Address | 0 | Priority | Destination Ad |
|________________________|_________________|___|__________|_________________|
After:
_____________________________________________________________________________
| | | | | |
| Priority | Destination Ad | Data | Source Address | 0 |
|__________|_________________|________________________|_________________|___|
FIG 6: Rearrangements in an unsuccessful message.
Before:
_____________________________________________________________________________
| | | | | |
| Unused | Destination Ad | 1 | Infinity | Destination Ad |
|________________________|_________________|___|__________|_________________|
After:
_____________________________________________________________________________
| | | | | |
| Infinity | Destination Ad | Unused | Destination Ad | 1 |
|__________|_________________|________________________|_________________|___|
FIG 7: Rearrangements in an isolated dummy message.
Package counts:
If the numbers to be sorted are sent into such a net as serial
bit streams, high order bit first, then a primitive sorting element
has two output wires labelled "smaller" and
"larger", two input wires and a reset and a clock line, and
works as follows:
Just before the first bit time the element is reset. Bits then
stream into the input terminals, and simply stream out of the output
terminals until the first bit position in which the two inputs differ
comes along. At that instant, the input with the 0 is connected to
the "smaller" output, and the one with the 1 is connected to
"larger". This interconnection is latched by the element and
all subsequent bits stream from the inputs to the outputs on the basis
of it, until the next reset.
Such a unit can be built with approximately 20 gates, and
introduces one bit time of delay. Careful design should permit an ECL
version with a 100 or 200 MHz bit rate. These could be packed into 48
(say) pin LSI packages, 8 independent elements per package (the clock
and reset lines are common), 16 per package, configured into 4
2-mergers, 24 per package, arranged into two 4-mergers, and 32 per
package containing a single 8-merger.
Larger mergers can be constructed out of these using an
extension of the bitonic sorter strategies given in [Batcher],
resulting in total package counts (and partial eight merger, four, two
and single element package counts) shown in Fig. 8 (to re-iterate, a
merger size of N refers to one which takes two lists of size N and
produces a list of size 2N).
Merger size Package count
Total Eights Fours Twos Ones
1 1/8 1/8
2 1/4 1/4
4 1/2 1/2
8 1 1
16 4 2 2
32 8 4 4
64 16 8 8
128 32 32
256 96 64 32
512 192 128 64
1,024 384 256 128
2,048 768 768
4,096 2,048 1536 512
8,192 4,096 3072 1024
16,384 8,192 6144 2048
32,768 16,384 16384
65,536 40,960 32768 8192
131,072 81,920 65536 16384
262,144 163,840 131072 32768
524,288 327,680 327680
1,048,576 786,432 655360 131072
FIG 8: Package counts for mergers
These counts can now be used to calculate the number of
packages required to build sorters of various sizes:
Sorter size Package count
Total Eights Fours Twos Ones
2 1/8 1/8
4 1/2 1/4 1/4
8 3/2 1/2 1/2 1/2
16 4 1 1 1 1
32 12 4 2 2 4
64 32 12 4 8 8
128 80 32 16 16 16
256 192 96 32 32 32
512 480 256 64 64 96
1,024 1,152 640 128 192 192
2,048 2,688 1536 384 384 384
4,096 6,144 3840 768 768 768
8,192 14,336 9216 1536 1536 2048
16,384 32,768 21504 3072 4096 4096
32,768 73,728 49152 8192 8192 8192
65,536 163,840 114688 16384 16384 16384
131,072 368,640 262144 32768 32768 40960
262,144 819,200 589824 65536 81920 81920
524,288 1,802,240 1310720 163840 163840 163840
1,048,576 3,932,160 2949120 327680 327680 327680
2,097,152 8,650,752 6553600 655360 655360 786432
FIG 9: Package counts for sorters
An interconnection net for N processors involves an N sorter,
an N merger and a 2N sorter. Thus a 128 processor system would require
304 48 pin sorter packages, 2.3 for each processor. A 1024 processor
needs 4224, roughly four per processor. A size 16,384 system needs 7
for each computer. A million processor would have 12.75 per machine.
It is likely that the biggest versions of this system will
require denser packaging. Remember, though, that a thousand processor
system is sufficient for human equivalence if each machine is big and
fast enough. It will probably not be necessary to build a
megaprocessor in the decade envisioned here.
Speed calculations:
As outlined, a message consists of a destination address, a
priority, a bit, a source address and a data portion. The two
addresses must be at least large enough to uniquely specify each
machine. Considering the case of a thousand and a million machine
system, we note that the address lengths are 10 and 20 bits. Let's
make the priority field the same length, leaving room for considerable
flexibility in priority assignment schemes. The message portion should
be fairly long, to permit messages like memory write requests, which
require both a memory address and the data. Four address lengths,
say. This gives us a message length 7 addresses long, 70 bits in a
1000 processor, 140 bits in a megaprocessor.
The full time taken by a message from start of transmission to
completion of reception, in bit times, is the message length, plus the
depth of the net (in primitive elements), plus an address and a
priority time due to the buffering at the exchanger.
The depth of a 1024 processor net is 110 elements. This
combines with the message and exchanger delays to result in a transit
time of 110+70+20 = 200 bit times. If the bit rate is 100 MHz then
messages are delivered in two microseconds. If the bit rate is 200
MHz, the time is 1 microsecond. The net contains about two full
message waves at any instant, and a message time is 700 nanoseconds
for 100 MHz, or 350 nanoseconds for 200 MHz.
The same calculation for a megaprocessor reveals a depth of
420 and a total transit time of 420+140+40 = 600 bit times. This
corresponds to 6 and 3 microsecond transits for 100 and 200 MHz data
rates. Corresponding message times are 1.4 microseconds and 700
nanoseconds. The net contains slightly more than 3 message waves at a
time.
Possible refinements:
The transit time of the net can be decreased, at the cost of
increasing the message times a little, by running some of the
primitive sorter elements asynchronously, clocking (and introducing
bit time delays) at larger intervals. For instance, an 8-merger might
accept a bit time worth of inputs, which would then trickle through
four stages of primitive sorters built without shift register delays
between them. When everything had settled down, the entire merger
would be clocked, and those elements which had decided to latch at
this bit time would do so. The delay of the unit is one bit time
rather than four, which reduces the 110 or the 420 term in the transit
calculations. The settling time is longer, however, so the bit rate
would be slower. Perhaps a factor of two in transit time can be gained
in this way, at a cost of 1.5 in data rate.
At an increase in gate count, several levels of asynchronous
primitive sorters can be replaced by an equivalent circuit with fewer
gate delays. This might enable a given data rate to be maintained
while the transit time was reduced.
[Van Voorhis] offers some slight reductions in primitive
sorter count, essentially by substituting special case solutions
better than the systematic construction wherever possible in a large
net. Unfortunately these invariably have an uneven amount of delay
along the various paths, making them almost worthless as synchronous
nets. They may be useful as designs for asynchronous subnets.
I have generalizations of Batcher's constructions using
primitive elements that are M sorters (as opposed to 2 sorters).
These allow building a merger which combines M sorted lists of size
NxM into a single sorted MxMxN length list, out of M mergers each
capable of merging M size N lists, and some layers of extra M sorter
primitive elements to combine the output of the mergers (these are
analogous to the single layer of 2-sorters following the mergers in
the odd-even merger of Fig 1. The number of such layers grows
(empirically) roughly as log(M)). Although the number of gates needed
for a given size sorter grows slowly with M, the number packages used
shrinks. This is because each package, being a sorter rather than a
merger, contains more logic. My constructions are complete for M<=8,
and partially complete for general M.
Well, now we have a room full of not only processors, but a
massive switching system as well. Can it be made to pay for its keep?
The next section examines some programming implications and
opportunities.
References:
BATCHER, K.E.
"Sorting Networks and their Applications",
1968 Spring Joint Computer Conference Proceedings
April 1968, 307-314.
VAN VOORHIS, David C.
"An Economical Construction for Sorting Networks",
1974 National Computer Conference Proceedings
April 1974, 921-927.
KNUTH, D.E.
"Sorting and Searching",
The Art of Computer Programming, Vol. 3
Addison-Wesley, 1973.
Section 5: Programming Interconnected Processors
A major feature of the scheme outlined is its flexibility. It
can function as any of the fixed interconnection patterns of the
current lackluster multiprocessors, like Illiac IV, or as a hexagonal
mesh, or a 7 dimensional cubic lattice, should that be desired, or the
tree organization being considered in a Stanford proposal. It can
simulate programmed pipeline machines, such as CDC Star, by using
processors as arithmetic units. What is more, it can do all of these
things simultaneously, since messages within one isolated subset of
the processors have no effect on messages in a disjoint subset. This
permits a very convenient kind of "time" sharing, where
individual users get and return processors as their demands change.
Such mimicry fails to take advantage of the ability to
reconfigure the interconnection totally every message wave. It is easy
to find particular applications, such as tree searching, where the net
could be used effectively by special purpose programs. It is clearly
desirable to have systems which minimize the user effort needed to
implement these algorithms.
As an example of a high level language well suited to the
architecture, consider the following parallel variant of Lisp:
A little Lisp:
Take an existing Lisp and purify it to something closer to its
lambda calculus foundations. Flush RPLACA and RPLACD and even SETQ (a
pseudo SETQ can be introduced later), and discourage PROGs, which are
inherently sequential and do things that could have been stated more
clearly as recursive functions. In this system recursive programs are
also more efficient.
An evaluation is handled as follows. A free processor (one not
currently doing an evaluation) receives a message demanding the value
of Expr with variable bindings given in ALIST. Call this the task
[Expr,ALIST]. If the top level of Expr is F(exprA,exprB,exprC), it
generates the tasks [exprA,ALIST], [exprB,ALIST] and [exprC,ALIST],
and passes them to three other free processors. These evaluate them
and sooner or later return valA (the value of exprA), valB and valC to
the original processor. This processor then refers to the definition
of F, and in particular to the names of the dummy arguments in the
definition. Suppose these were A, B and C. It combines the ALIST it
was given with the (name, value) pairs (A, valA), (B, valB), (C, valC)
to form a new ALIST'. Then it generates the task [bodyF,ALIST'], where
bodyF is the body of the definition of F, which is passed to another
free processor. On receiving the value of this expression, it passes
it back to whoever had given it the original task, and then declares
itself free.
If Expr had happened to be an atom, the processor would simply
have looked it up in ALIST, and returned its value. If F had been a
predefined system function (such as CAR or CONS) the sequence of
actions would have been whatever the machine code for those functions
(of which each processor would have a copy) specified.
The parallelism comes from the fact that the arguments in a
multi-argument function can be evaluated simultaneously. This causes
moderate parallelism when functions are nested, and can cause
explosive parallelism when a function which at some level uses a
multi-argument function, invokes itself recursively (as in a tree
search). Most non-trivial programs stated as recursive functions do
this.
The description above implies that the processor waits for the
results of tasks it has farmed out to other machines. These waits can
be arbitrarily long. Also, the number of tasks spawned can easily
become more than the number of processors. In that case, presumably, a
processor with a task to farm out would have to wait until a machine
becomes free. Keeping a processor idle under these conditions is
clearly undesirable.
If each processor were time shared, pretending to be many
machines, then when the job being run becomes temporarily idle there
may be another to switch to. When a message pertaining to a given
waiting job arrives, the processor deals with it, and if it provides
the information necessary to allow that job to resume, it is resumed.
This scheme makes the number of processors available seem larger,
perhaps enough to make it possible to acquire a processor for a new
task simply by picking a machine at random and asking if it has a free
job slot. This works well if the answer is usually yes, (i.e. if there
reasonably more slots than tasks), and replaces a more complicated
free processor pool method that must be able to deal with many
requests simultaneously.
Alternatively instead of each processor having its own little
pool of running jobs, the whole Lisp system can maintain a communal
pool, which processors refer to as they become free. In this
organization a task that must pause is placed into the pool (freeing
the processor that was running it), to be taken up again by a free
processor when its requirements are met. Moderate processing power is
required to manage the pool.
The list structure is spread out among all the processors in
the system. Pointers consist of a processor number and address within
processor field. A machine evaluating an expression whose top level
function is CONS creates the new cell in its own memory. A CAR or CDR
involves sending a message to the processor which owns the cell
involved, and waiting for a reply (thus a CONS is usually cheaper than
a CAR!).
Since RPLACA and RPLACD are eliminated, circular lists cannot
be created. This permits garbage collection to be mediated by
reference counts. A small fixed reference count field (three bits
wide, say) is part of each cell. A processor doing a CONS sends
messages to the owners of the cells that the new cell will be pointing
to, indicating that their reference count should be incremented. If a
cell getting a message of this type has a reference count that has
already reached maximum (7 in our example), it sends back an indignant
message to the CONS'ing processor saying, effectively, "I'm full,
you can't point to me. But here are my CAR and my CDR, roll your own
and point to that". This not only makes the reference count field
size manageable, but reduces message traffic jams to processors
containing very popular cells. It does make it mandatory to use EQUAL
rather than EQ when comparing lists. When a processor no longer
requires a cell to which it had a pointer it sends a message to the
owner saying so. The reference count of the cell is decreased by one,
and if it reaches zero, it is freed, and similar messages are sent to
the cells pointed to by its CAR and CDR. This garbage collection
process goes on continuously and independently of the main
computations.
How is the A-list of bindings to be handled? The canonical
representation, using a simple list of dotted pairs, is very
inefficient, since it forces a sequential search. A hash table, as in
most current Lisp implementations is also undesirable, partly because
it requires an incompatible data type (a relatively large contiguous
block of memory), but primarily because in this parallel system there
are many different contexts (in different branches of the computation)
active at one time. The entire hash table would need to be duplicated
whenever new bindings are made (i.e. at every level of evaluation),
since the older context is in use in another branch.
A nice alternative is to use essentially an A-list, but to
structure it as a balanced tree, with each node containing a binding,
a left subtree for those variables with names lexicographically (say)
less than it, and a right subtree for those greater. An entry in such
a structure can be found in time proportional to the logarithm of the
number of nodes, and a version of the list with an entry added,
deleted or modified can also be constructed in log time without
affecting the original in any way, by building a new path down to the
element (and sometimes a few side paths, to keep the tree reasonably
balanced), which points to many of the subtrees of the original.
Since this structure can be built of standard list elements, it can be
managed via the normal allocation and garbage collection
mechanisms. Call this structure an A-tree.
In general applications a balanced tree is capable of being
used in this system more effectively than a simple list, because a
parallel process can get to all the nodes in log time, whereas the
last node takes linear time in a linear list. This suggests that
programmers wanting maximum efficiency will be coerced into using them
much more frequently than is now the case. This is similar to the
pressure on present day Lisp programmers to use PROGS rather than
recursive functions, because compiled PROGS run faster.
The [expr,ALIST] task description is conveyed simply as a pair
of pointers, expr to an S expression version of expr, and ALIST to the
head of the balanced A-tree. The result returned in an evaluation is
likewise a pointer.
Since the list structure is only built upon, and never
altered, it is possible to speed up the operation of the system by
having individual processors maintain software managed caches of
frequently referred to cells that reside in remote machines. This cuts
down on the message traffic, and generally speeds things up.
A little Algol:
Although recursive functions provide an excellent way of
exploiting a very parallel architecture, there are other ways. An
algorithmic (iterative) language can be made to serve, if a few
features are present.
Existing Algol unfortunately has few of these. Consider the
following pair of statements excerpted from an imaginary program:
A := 3 ;
B := 4 ;
These say that first A is set to 3, then B is assigned the value 4.
There is an implied sequentialness. Presumably the programmer knew
that the order of the assignments was unimportant, and that they could
be done simultaneously. The syntax of the language provided no way for
him to indicate this.
A simple construct which permits information of this type to
be conveyed is the "parallel semicolon", which we will
indicate by a vertical bar "|". Statements seperated by
parallel semicolons may be executed simultaneously. The following is
an example of its use:
A := 3 |
B := 4 |
C := 6 ;
D := A+B+C ;
The first three statements may be executed together, the fourth must
wait for their completion. It is implied that compound statements,
bracketed by BEGIN END pairs can be similarly separated by parallel as
well as sequential semicolons.
If compound statements are permitted to return as a value the
value of their last component statement, then the structure
T := BEGIN
INTEGER A,B,C ;
A := expressionA |
B := expressionB |
C := expressionC ;
expression involving A, B and C
END;
is equivalent to a lambda expression construct in Lisp. A, B and C are
the dummy arguments, evaluated in parallel, and the fourth expression,
which must wait for A, B and C, is the body of the lambda. The
constructs involved can be used in many other ways, unlike a real
lambda expression.
If the Algol also has recursion, then it is possible to obtain
massive parallelism in the same way it was achieved in Lisp, namely by
writing functions which recurse deeply, and invoke themselves a few
times in parallel at each level.
A minor form of parallelism already automatically available
resides in arithmetic expressions. Different subexpressions of larger
formulas can be evaluated simultaneously, and then combined. This is
analogous to the evaluation of Lisp expressions.
More massive concurrency can be obtained if the data types of
Algol are expanded to include a complete set of array operators and
genuine dynamic allocation of arrays. It is this type of data and
operator set that makes APL an extremely powerful language in spite of
an execrable control structure.
The idea is that operators such as addition and multiplication
work not only on simple variables representing single numbers, but on
whole multi-dimensional arrays. Since arrays are more complex objects
a much larger range of operators is required. Included are such
things as array restructuring, subscript permutation (generalized
transpose), element shuffling, subarray extraction, generalized cross
and dot products, etc.. In general an operator combines one or more
arrays and produces a value which is a new array, often of a different
size and shape.
Compounding of such operators substitutes for a large amount
of explicit loop control, and results in substantially more compact
source code. On conventional computers such code also runs much faster
because most the run time is spent in carefully hand coded
implementations of the basic operators, which do a great deal at each
invokation if the arrays are large. Typical equivalent Algol programs
execute second rate compiler produced code almost exclusively. An
operator set of this kind provides the same capabilities as a
hypothetical parallel FOR loop construct, with greater
clarity. Conditionals can be handled by first selecting out subarrays
according to the condition, and then applying the appropriate
operations.
It is desirable in our system for large arrays to be spread
out among many machines, so that array operations can be carried out
in parallel where possible. An often occurring process is the
application of an arithmetic or other operator to one or more arrays
of a given size, producing a result of the same size. This could be
made maximally efficient if corresponding elements of the arrays
resided in the same processor. Assigning a processor to an array
element by means of a hash function of both the array dimensions and
the indices of the element will cause arrays of different size to be
stored in different places, but will put corresponding elements of
arrays of the same size in the same place.
Now comes the question of how a gaggle of processors managing
a given array gets word that an operation concerning the array is to
be executed. The initiator of the operation is the single processor
running the code requesting it. The fastest way to propagate such
information is to initiate a "chain letter". The
originating processor can consider the array as two equal (or almost
equal) pieces, and send a message to a member of each piece. Each
recipient then divides the piece of which it is a member into two, and
sends a message to a representative of each of those smaller subsets,
etc. When the subset size becomes one, the operation is performed.
It may be more efficient to store larger pieces of arrays in
individual processors. This adds a slight serial component to the run
times, but saves message handling time.
How are programs communicated from processor to processor, as
the number of executing instruction streams grows? It would be an
extravagant waste of memory to duplicate the entire source program in
every processor (besides, it might not fit). A software caching
scheme is called for. When a processor initiates a subtask, it obtains
a free processor and passes to it a moderate amount of the code needed
for the task. When the new processor runs out, it sends a message
back to the first machine for more. This machine trys to obtain it
from its own cache, and if it too is out, sends a message further up
in the hierarchy, to the machine which had initiated the task which it
is running, and so on until the requested code is obtained. At top
level the entire runnable program is assumed to be available from some
sort of file, maintained by the combined storage of a number of
processors.
A little operating systems:
Assume that most input/output devices are connected to
individual processors, and that, to maximize the bandwidth, each of
these processors has only one, or a most a very small number, of
devices associated with it. Included among these are communications
lines to user terminals, so that each console talks directly to a
dedicated processor with sorting net access to the entire system.
If we expect to support more than one user on such a system,
it will be necessary to have some type of protection scheme, to
prevent one user's processes from accidentally interfering with
another's.
If each processor contains a monitor, then message sending can
handled by system calls. The monitor can then check for validity,
testing if the requested destination is within the set of processors
assigned to the user. This monitor, which every machine assigned to a
user must run, can be flexible enough to time share the machine it
runs on, to provide multiple simulated processors.
Controlling the state of the individual machines' monitors is
the task of a global system monitor, operated by several machines,
which maintains a pool of free processors, and parcels them out on
request, and which also handles file system requests (bulk storage
would be connected to a handful of the processors), and allocation of
other devices.
Processes belonging to a single user will be initiated by a
particular master machine, probably the one connected to his console.
This master can create a tree of subprocesses, possibly
intercommunicating, running on different machines. It should be
possible, for example, to have one subset configured as an array
processor for efficient implementation of low level vision operations,
while another is running an Algol/APL for the less structured analytic
geometry needed to interpret the image, and yet a third is operating a
Lisp system doing abstract reasoning about the scene. Many existing
systems permit this kind of organization, but they are hampered by
having an absurdly small amount of computing power.
How is a system of this kind initialized, and how does one
abort an out of control process taking place in part of it without
affecting the rest? A possibility is to have an "executive"
class of messages (perhaps signalled by a particular bit in the data
portion), which user jobs are not permitted to emit. Reception of
such messages might cause resetting of the processor, loading of
memory locations within it, and starting execution at a requested
locations. A single externally controllable machine can be used to
get things going, fairly quickly if emits a self replicating
"chain letter".
Now consider reliability. The system can obviously tolerate
any reasonable number of inoperable processors, by simply declaring
them unavailable for use. Failures in the communication net are much
more serious, and under most situations will require the system to
stop operating normally. It is possible to write diagnostic programs
which can track down defective comparator elements or broken data
wires. If something should happen to the clock signals to a given
level it would be necessary to wheel out an oscilloscope. If
reliability were a critical issue it would be possible to include a
duplicate net, to run things the while other was being debugged.
Disclaimer:
The software outlines are obviously only partly baked. This is
mostly due to the limited amount of thought and work that has gone
into them. On the other hand, it is my belief that even well thought
out designs at this point will look naive in the light of experience
with a working version of such a machine. Many of the fundamental
decisions depend on things difficult to estimate, including the number
of processors, communication speed compared with processor speed,
memory size, and most importantly the kinds, sizes and mix of
operations that people will tend to run (these will surely differ from
what is being done now, the limitations being so different).
This is not to say that more thought isn't called for. The
nature of the memory protection, interrupt scheme, word size,
instruction set, I/O structure, etc. of the individual machines
should be tailored to permit convenient implementation of the
individual processor operating systems, and typical message types.
What these are can best be determined by trying to write some
monitors, interpreters, compilers and array crunchers.
Simulation of the system on a conventional machine is next to
useless. Since the total amount of memory envisaged is larger than
conventional machines carry, and since a simulation will have to jump
around from simulated core image to simulated core image, in order to
keep a realistic message synchrony, there would be an enormous amount
of disk accessing. The slowness of this, combined with the inherent
speed difference, would allow only the most trivial (and therefore
unrepresentative) things to be tried, and not many of these.
Construction of a moderate size version is a better use of
manpower. Undoubtedly there will be mistakes made in the first (or
first few) models, which will become apparent after a bit of
experience.
The flexibility offered should make this design much more
attractive to a large class of programmers than current essentially
special purpose architectures such as ILLIAC IV. Making it out of
existing processors with proven machine languages will help too. I,
for one, can hardly wait to start programming even a flawed version of
a machine that can process and generate real time television with
programs written in Algol, and simultaneously jump over tall game and
proof trees in a single bound.
Bombast:
The enormous shortage of ability to compute is distorting our
work, creating problems where there are none, making others impossibly
difficult, and generally causing effort to be misdirected. Shouldn't
this view be more widespread, if it is as obvious as I claim?
In the early days of AI the thought that existing machines
might be much too small was widespread, but there was hope that clever
mathematics and advancing computer technology could soon make up the
difference. Since then computers have improved by a factor of ten
every five years, but, in spite of reasonably diligent work by a
reasonable number of people, the results have been embarrassingly
sparse. The realization that available compute power might still be
vastly inadequate has since been swept under the rug, due to wishful
thinking and a feeling that there was nothing to be done about it
anyway and that voicing such an opinion could cause AI to be
considered impractical, resulting in reduced funding.
There is also an element of scientific snobbery. Many of the
most influential names in the field seem to feel that AI should be
like the theoretical side of physics, the essential problem being to
find the laws of universe relating to intelligence. Once these are
known, the thinking goes, construction of efficient intelligent
machines will be trivial. Suggestions that the problems are
essentially engineering ones of scale and complexity, and can be
solved by incremental improvements and occasional insights into
sub-problems, are treated with disdain.
This attitude is a variant of the philosophical notion that
all truth can be arrived at by pure thought, and is unfounded and
harmful. One wonders what state space travel would be in if the
Goddards and von Brauns had spent their time trying to find the
universal laws of rocket construction before trying to build space
ships. AI needs a stronger experimental base. Like other branches of
endeavor (notably physics, aeronautics and meteorology), we should
realize our desperate need for more computing, and do things about it.
c
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