Magazine: Whole Earth Review
Issue: December 10, 1993
Title: Technological Singularity
Author: Vernor Vinge
Technological Singularity
by Vernor Vinge
Vernor Vinge's vision of a technological "singularity" in humanity's
near future has haunted me since I first read of it in his science-fiction
novel, Marooned in Realtime (1986). I'm persuaded that the acceleration of
technology-acceleration is even now distorting human institutions and
expectations, whether or not we are approaching a metaphorical "event
horizon" beyond which everything becomes unrecognizable.
When I invited Vinge to write something about his current views on the
singularity for the recent issue of Whole Earth Review that I guest-edited,
he replied that he had just presented a paper on the subject for the
VISION-21 Symposium, sponsored by the NASA Lewis Research Center and the
Ohio Aerospace Institute. In due course he revised the piece and sent it
along. I can think of no other technical paper that has so many references
to science-fiction literature, as well it should.
Vinge is a mathematician at San Diego State University, specializing
in distributed computing and computer architecture. One of his short
stories, "True Names" (1981), is often mentioned along with John Brunner's
Shockwave Rider and William Gibson's Neuromancer as an inspiration to the
current generation of online computer pioneers. Vinge's two "Realtime"
novels (combined in Across Realtime -- 1991) have been nominated for Hugo
Awards, science fiction's top prize. His new novel, A Fire Upon the Deep,
won the 1993 Hugo; it's reviewed on p. 95.
--Stewart Brand
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TECHNOLOGICAL SINGULARITY
(c) 1993 by Vernor Vinge
(This article may be reproduced for noncommercial
purposes if it is copied in its entirety,
including this notice.)
A slightly different version of this article was presented at the
VISION-21 Symposium sponsored by NASA Lewis Research Center and the Ohio
Aerospace Institute, March 30-31, 1993. --Vernor Vinge
1. What Is The Singularity?
The acceleration of technological progress has been the central
feature of this century. We are on the edge of change comparable to the
rise of human life on Earth. The precise cause of this change is the
imminent creation by technology of entities with greater-than-human
intelligence. Science may achieve this breakthrough by several means (and
this is another reason for having confidence that the event will occur):
Computers that are "awake" and superhumanly intelligent may be developed.
(To date, there has been much controversy as to whether we can create
human equivalence in a machine. But if the answer is "yes," then there is
little doubt that more intelligent beings can be constructed shortly there-
after.)
Large computer networks and their associated users may "wake up" as super-
humanly intelligent entities.
Computer/human interfaces may become so intimate that users may reasonably
be considered superhumanly intelligent.
Biological science may provide means to improve natural human intellect.
The first three possibilities depend on improvements in computer
hardware. Progress in hardware has followed an amazingly steady curve in
the last few decades. Based on this trend, I believe that the creation of
greater-than-human intelligence will occur during the next thirty years.
(Charles Platt has pointed out that AI enthusiasts have been making claims
like this for thirty years. Just so I'm not guilty of a relative-time
ambiguity, let me be more specific: I'll be surprised if this event occurs
before 2005 or after 2030.)
What are the consequences of this event? When greater-than-human
intelligence drives progress, that progress will be much more rapid. In
fact, there seems no reason why progress itself would not involve the
creation of still more intelligent entities -- on a still-shorter time
scale. The best analogy I see is to the evolutionary past: Animals can
adapt to problems and make inventions, but often no faster than natural
selection can do its work -- the world acts as its own simulator in the
case of natural selection. We humans have the ability to internalize the
world and conduct what-if's in our heads; we can solve many problems
thousands of times faster than natural selection could. Now, by creating
the means to execute those simulations at much higher speeds, we are
entering a regime as radically different from our human past as we humans
are from the lower animals.
This change will be a throwing-away of all the human rules, perhaps in
the blink of an eye -- an exponential runaway beyond any hope of control.
Developments that were thought might only happen in "a million years" (if
ever) will likely happen in the next century.
It's fair to call this event a singularity ("the Singularity" for the
purposes of this piece). It is a point where our old models must be
discarded and a new reality rules, a point that will loom vaster and vaster
over human affairs until the notion becomes a commonplace. Yet when it
finally happens, it may still be a great surprise and a greater unknown.
In the 1950s very few saw it: Stan Ulam 1 paraphrased John von Neumann as
saying:
One conversation centered on the ever-accelerating progress of
technology and changes in the mode of human life, which gives the
appearance of approaching some essential singularity in the history of the
race beyond which human affairs, as we know them, could not continue.
Von Neumann even uses the term singularity, though it appears he is
thinking of normal progress, not the creation of superhuman intellect.
(For me, the superhumanity is the essence of the Singularity. Without that
we would get a glut of technical riches, never properly absorbed.)
The 1960s saw recognition of some of the implications of superhuman
intelligence. I. J. Good wrote:
Let an ultraintelligent machine be defined as a machine that can far
surpass all the intellectual activities of any man however clever. Since
the design of machines is one of these intellectual activities, an
ultraintelligent machine could design even better machines; there would
then unquestionably be an "intelligence explosion," and the intelligence of
man would be left far behind. Thus the first ultraintelligent machine is
the last invention that man need ever make, provided that the machine is
docile enough to tell us how to keep it under control. . . . It is more
probable than not that, within the twentieth century, an ultraintelligent
machine will be built and that it will be the last invention that man need
make.
Good has captured the essence of the runaway, but he does not pursue
its most disturbing consequences. Any intelligent machine of the sort he
describes would not be humankind's "tool" -- any more than humans are the
tools of rabbits, robins, or chimpanzees.
Through the sixties and seventies and eighties, recognition of the
cataclysm spread. Perhaps it was the science-fiction writers who felt the
first concrete impact. After all, the "hard" science-fiction writers are
the ones who try to write specific stories about all that technology may do
for us. More and more, these writers felt an opaque wall across the
future. Once, they could put such fantasies millions of years in the
future. Now they saw that their most diligent extrapolations resulted in
the unknowable . . . soon. Once, galactic empires might have seemed a
Posthuman domain. Now, sadly, even interplanetary ones are.
What about the coming decades, as we slide toward the edge? How will
the approach of the Singularity spread across the human world view? For a
while yet, the general critics of machine sapience will have good press.
After all, until we have hardware as powerful as a human brain it is
probably foolish to think we'll be able to create human-equivalent (or
greater) intelligence. (There is the farfetched possibility that we could
make a human equivalent out of less powerful hardware -- if we were willing
to give up speed, if we were willing to settle for an artificial being that
was literally slow. But it's much more likely that devising the software
will be a tricky process, involving lots of false starts and
experimentation. If so, then the arrival of self-aware machines will not
happen until after the development of hardware that is substantially more
powerful than humans' natural equipment.)
But as time passes, we should see more symptoms. The dilemma felt by
science-fiction writers will be perceived in other creative endeavors. (I
have heard thoughtful comicbook writers worry about how to create
spectacular effects when everything visible can be produced by the
technologically commonplace.) We will see automation replacing higher- and
higher-level jobs. We have tools right now (symbolic math programs,
cad/cam) that release us from most low-level drudgery. Put another way:
the work that is truly productive is the domain of a steadily smaller and
more elite fraction of humanity. In the coming of the Singularity, we will
see the predictions of true technological unemployment finally come true.
Another symptom of progress toward the Singularity: ideas themselves
should spread ever faster, and even the most radical will quickly become
commonplace.
And what of the arrival of the Singularity itself? What can be said
of its actual appearance? Since it involves an intellectual runaway, it
will probably occur faster than any technical revolution seen so far. The
precipitating event will likely be unexpected -- perhaps even by the
researchers involved ("But all our previous models were catatonic! We were
just tweaking some parameters . . ."). If networking is widespread enough
(into ubiquitous embedded systems), it may seem as if our artifacts as a
whole had suddenly awakened.
And what happens a month or two (or a day or two) after that? I have
only analogies to point to: The rise of humankind. We will be in the
Posthuman era. And for all my technological optimism, I think I'd be more
comfortable if I were regarding these transcendental events from one
thousand years' remove . . . instead of twenty.
2. Can the Singularity Be Avoided?
Well, maybe it won't happen at all: sometimes I try to imagine the
symptoms we should expect to see if the Singularity is not to develop.
There are the widely respected arguments of Penrose3 and Searle4 against
the practicality of machine sapience. In August 1992, Thinking Machines
Corporation held a workshop to investigate "How We Will Build a Machine
That Thinks." As you might guess from the workshop's title, the
participants were not especially supportive of the arguments against
machine intelligence. In fact, there was general agreement that minds can
exist on nonbiological substrates and that algorithms are of central
importance to the existence of minds. However, there was much debate about
the raw hardware power present in organic brains. A minority felt that the
largest 1992 computers were within three orders of magnitude of the power
of the human brain. The majority of the participants agreed with Hans
Moravec's estimate5 that we are ten to forty years away from hardware
parity. And yet there was an other minority who conjectured that the
computational competence of single neurons may be far higher than generally
believed. If so, our present computer hardware might be as much as ten
orders of magnitude short of the equipment we carry around in our heads.
If this is true (or for that matter, if the Penrose or Searle critique is
valid), we might never see a Singularity. Instead, in the early '00s we
would find our hardware performance curves beginning to level off --
because of our inability to automate the design work needed to support
further hardware improvements. We'd end up with some very powerful
hardware, but without the ability to push it further. Commercial digital
signal processing might be awesome, giving an analog appearance even to
digital operations, but nothing would ever "wake up" and there would never
be the intellectual runaway that is the essence of the Singularity. It
would likely be seen as a golden age . . . and it would also be an end of
progress. This is very like the future predic ted by Gunther Stent,6 who
explicitly cites the development of transhuman intelligence as a sufficient
condition to break his projections.
But if the technological Singularity can happen, it will. Even if all
the governments of the world were to understand the "threat" and be in
deadly fear of it, progress toward the goal would continue. The
competitive advantage -- economic, military, even artistic -- of every
advance in automation is so compelling that forbidding such things merely
assures that someone else will get them first.
Eric Drexler has provided spectacular insights about how far technical
improvement may go.7 He agrees that superhuman intelligences will be
available in the near future. But Drexler argues that we can confine such
transhuman devices so that their results can be examined and used safely.
I argue that confinement is intrinsically impractical. Imagine
yourself locked in your home with only limited data access to the outside,
to your masters. If those masters thought at a rate -- say -- one million
times slower than you, there is little doubt that over a period of years
(your time) you could come up with a way to escape. I call this "fast
thinking" form of superintelligence "weak superhumanity." Such a "weakly
superhuman" entity would probably burn out in a few weeks of outside time.
"Strong superhumanity" would be more than cranking up the clock speed on a
human-equivalent mind. It's hard to say precisely what "strong
superhumanity" would be like, but the difference appears to be profound.
Imagine running a dog mind at very high speed. Would a thousand years of
doggy living add up to any human insight? Many speculations about
superintelligence seem to be based on the weakly superhuman model. I
believe that our best guesses about the post-Singularity world can be
obtained by thinking on the nat ure of strong superhumanity. I will return
to this point.
Another approach to confinement is to build rules into the mind of the
created superhuman entity. I think that any rules strict enough to be
effective would also produce a device whose ability was clearly inferior to
the unfettered versions (so human competition would favor the development
of the more dangerous models).
If the Singularity can not be prevented or confined, just how bad
could the Posthuman era be? Well . . . pretty bad. The physical
extinction of the human race is one possibility. (Or, as Eric Drexler put
it of nanotechnology: given all that such technology can do, perhaps
governments would simply decide that they no longer need citizens.) Yet
physical extinction may not be the scariest possibility. Think of the
different ways we relate to animals. A Posthuman world would still have
plenty of niches where human-equivalent automation would be desirable:
embedded systems in autonomous devices, self-aware daemons in the lower
functioning of larger sentients. (A strongly superhuman intelligence would
likely be a Society of Mind8 with some very competent components.) Some of
these human equivalents might be used for nothing more than digital signal
processing. Others might be very humanlike, yet with a onesidedness, a
dedication that would put them in a mental hospital in our era. Though
none of these creatures mi ght be flesh-and-blood humans, they might be the
closest things in the new environment to what we call human now.
I have argued above that we cannot prevent the Singularity, that its
coming is an inevitable consequence of humans' natural competitiveness and
the possibilities inherent in technology. And yet: we are the initiators.
Even the largest avalanche is triggered by small things. We have the
freedom to establish initial conditions, to make things happen in ways that
are less inimical than others. Of course (as with starting avalanches), it
may not be clear what the right guiding nudge really is:
3. Other Paths to the Singularity
When people speak of creating superhumanly intelligent beings, they
are usually imagining an AI project. But as I noted at the beginning of
this article, there are other paths to superhumanity. Computer networks
and human-computer interfaces seem more mundane than AI, yet they could
lead to the Singularity. I call this contrasting approach Intelligence
Amplification (IA). IA is proceeding very naturally, in most cases not
even recognized for what it is by its developers. But every time our
ability to access information and to communicate it to others is improved,
in some sense we have achieved an increase over natural intelligence. Even
now, the team of a Ph.D. human and good computer workstation (even an
off-net workstation) could probably max any written intelligence test in
existence.
And it's very likely that IA is a much easier road to the achievement
of superhumanity than pure AI. In humans, the hardest development problems
have already been solved. Building up from within ourselves ought to be
easier than figuring out what we really are and then building machines that
are all of that. And there is at least conjectural precedent for this
approach. Cairns-Smith9 has speculated that biological life may have begun
as an adjunct to still more primitive life based on crystalline growth.
Lynn Margulis (in10 and elsewhere) has made strong arguments that mutualism
is a great driving force in evolution.
Note that I am not proposing that AI research be ignored. AI advances
will often have applications in IA, and vice versa. I am suggesting that
we recognize that in network and interface research there is something as
profound (and potentially wild) as artificial intelligence. With that
insight, we may see projects that are not as directly applicable as
conventional interface and network design work, but which serve to advance
us toward the Singularity along the IA path.
Here are some possible projects that take on special significance,
given the IA point of view:
Human/computer team automation: Take problems that are normally
considered for purely machine solution (like hillclimbing problems), and
design programs and interfaces that take advantage of humans' intuition and
available computer hardware. Considering the bizarreness of
higher-dimensional hillclimbing problems (and the neat algorithms that have
been devised for their solution), some very interesting displays and
control tools could be provided to the human team member.
Human/computer symbiosis in art: Combine the graphic generation
capability of modern machines and the esthetic sensibility of humans. Of
course, an enormous amount of research has gone into designing computer
aids for artists. I'm suggesting that we explicitly aim for a greater
merging of competence, that we explicitly recognize the cooperative
approach that is possible. Karl Sims has done wonderful work in this
direction.11
Human/computer teams at chess tournaments: We already have programs
that can play better than almost all humans. But how much work has been
done on how this power could be used by a human, to get something even
better? If such teams were allowed in at least some chess tournaments, it
could have the positive effect on IA research that allowing computers in
tournaments had for the corresponding niche in AI.
Interfaces that allow computer and network access without requiring
the human to be tied to one spot, sitting in front of a computer. (This
aspect of IA fits so well with known economic advantages that lots of
effort is already being spent on it.)
More symmetrical decision support systems. A popular research/product
area in recent years has been decision support systems. This is a form of
IA, but may be too focused on systems that are oracular. As much as the
program giving the user information, there must be the idea of the user
giving the program guidance.
Local area nets to make human teams more effective than their
component members. This is generally the area of "groupware"; the change
in viewpoint here would be to regard the group activity as a combination
organism.
In one sense, this suggestion's goal might be to invent a "Rules of
Order" for such combination operations. For instance, group focus might be
more easily maintained than in classical meetings. Individual members'
expertise could be isolated from ego issues so that the contribution of
different members is focused on the team project. And of course shared
databases could be used much more conveniently than in conventional
committee operations.
The Internet as a combination human/machine tool. Of all the items on
the list, progress in this is proceeding the fastest. The power and
influence of the Internet are vastly underestimated. The very anarchy of
the worldwide net's development is evidence of its potential. As
connectivity, bandwidth, archive size, and computer speed all increase, we
are seeing something like Lynn Margulis' vision of the biosphere as data
processor recapitulated, but at a million times greater speed and with
millions of humanly intelligent agents (ourselves).
The above examples illustrate research that can be done within the
context of contemporary computer science departments. There are other
paradigms. For example, much of the work in artificial intelligence and
neural nets would benefit from a closer connection with biological life.
Instead of simply trying to model and understand biological life with
computers, research could be directed toward the creation of composite
systems that rely on biological life for guidance, or for the features we
don't understand well enough yet to implement in hardware. A longtime
dream of science fiction has been direct brain-to-computer interfaces. In
fact, concrete work is being done in this area:
Limb prosthetics is a topic of direct commercial applicability.
Nerve-to-silicon transducers can be made. This is an exciting near-term
step toward direct communication.
Direct links into brains seem feasible, if the bit rate is low: given
human learning flexibility, the actual brain neuron targets might not have
to be precisely selected. Even 100 bits per second would be of great use
to stroke victims who would otherwise be confined to menu-driven
interfaces.
Plugging into the optic trunk has the potential for bandwidths of 1
Mbit/second or so. But for this, we need to know the fine-scale
architecture of vision, and we need to place an enormous web of electrodes
with exquisite precision. If we want our high-bandwidth connection to add
to the paths already present in the brain, the problem becomes vastly more
intractable. Just sticking a grid of high-bandwidth receivers into a brain
certainly won't do it. But suppose that the high-bandwidth grid were
present as the brain structure was setting up, as the embryo developed.
That suggests:
Animal embryo experiments. I wouldn't expect any IA success in the
first years of such research, but giving developing brains access to
complex simulated neural structures might, in the long run, produce animals
with additional sense paths and interesting intellectual abilities.
I had hoped that this discussion of IA would yield some clearly safer
approaches to the Singularity (after all, IA allows our participation in a
kind of transcendence). Alas, about all I am sure of is that these
proposals should be considered, that they may give us more options. But as
for safety -- some of the suggestions are a little scary on their face. IA
for individual humans creates a rather sinister elite. We humans have
millions of years of evolutionary baggage that makes us regard competition
in a deadly light. Much of that deadliness may not be necessary in today's
world, one where losers take on the winners' tricks and are coopted into
the winners' enterprises. A creature that was built de novo might possibly
be a much more benign entity than one based on fang and talon.
The problem is not simply that the Singularity represents the passing
of humankind from center stage, but that it contradicts our most deeply
held notions of being. I think a closer look at the notion of strong
superhumanity can show why that is.
4. Strong Superhumanity and the Best We Can Ask For
Suppose we could tailor the Singularity. Suppose we could attain our
most extravagant hopes. What then would we ask for? That humans
themselves would become their own successors, that whatever injustice
occurred would be tempered by our knowledge of our roots. For those who
remained unaltered, the goal would be benign treatment (perhaps even giving
the stay-behinds the appearance of being masters of godlike slaves). It
could be a golden age that also involved progress (leaping Stent's
barrier). Immortality (or at least a lifetime as long as we can make the
universe survive) would be achievable.
But in this brightest and kindest world, the philosophical problems
themselves become intimidating. A mind that stays at the same capacity
cannot live forever; after a few thousand years it would look more like a
repeating tape loop than a person. To live indefinitely long, the mind
itself must grow . . . and when it becomes great enough, and looks back . .
. what fellow-feeling can it have with the soul that it was originally?
The later being would be everything the original was, but vastly more. And
so even for the individual, the Cairns-Smith or Lynn Margulis notion of new
life growing incrementally out of the old must still be valid.
This "problem" about immortality comes up in much more direct ways.
The notion of ego and self-awareness has been the bedrock of the hardheaded
rationalism of the last few centuries. Yet now the notion of
self-awareness is under attack from the artificial intelligence people.
Intelligence Amplification undercuts our concept of ego from another
direction. The post-Singularity world will involve extremely
high-bandwidth networking. A central feature of strongly superhuman
entities will likely be their ability to communicate at variable
bandwidths, including ones far higher than speech or written messages.
What happens when pieces of ego can be copied and merged, when
self-awareness can grow or shrink to fit the nature of the problems under
consideration? These are essential features of strong superhumanity and
the Singularity. Thinking about them, one begins to feel how essentially
strange and different the Posthuman era will be -- no matter how cleverly
and benignly it is brought to be.
From one angle, the vision fits many of our happiest dreams: a time
unending, where we can truly know one another and understand the deepest
mysteries. From another angle, it's a lot like the worst-case scenario I
imagined earlier.
In fact, I think the new era is simply too different to fit into the
classical frame of good and evil. That frame is based on the idea of
isolated, immutable minds connected by tenuous, low-bandwith links. But
the post-Singularity world does fit with the larger tradition of change and
cooperation that started long ago (perhaps even before the rise of
biological life). I think certain notions of ethics would apply in such an
era. Research into IA and high-bandwidth communications should improve
this understanding. I see just the glimmerings of this now; perhaps there
are rules for distinguishing self from others on the basis of bandwidth of
connection. And while mind and self will be vastly more labile than in the
past, much of what we value (knowledge, memory, thought) need never be
lost. I think Freeman Dyson has it right when he says, "God is what mind
becomes when it has passed beyond the scale of our comprehension."12 \xA6
1. Ulam, S., "Tribute to John von Neumann," Bulletin of the American
Mathematical Society, vol. 64. no. 3, May 1958, pp. 1-49.
2. Good, I. J., "Speculations Concerning the First Ultraintelligent
Machine," in Advances in Computers, vol 6, Franz L. Alt and Morris
Rubinoff, eds., 31-88, 1965, Academic Press.
3. Penrose, Roger, The Emperor's New Mind, Oxford University Press,
1989.
4. Searle, John R., "Minds, Brains, and Programs," in The Behavioral
and Brain Sciences, vol. 3, Cambridge University Press, 1980.
5. Moravec, Hans, Mind Children, Harvard University Press, 1988.
6. Stent, Gunther S., The Coming of the Golden Age: A View of the End
of Progress, The Natural History Press, 1969.
7. Drexler, K. Eric, Engines of Creation, Anchor Press/Doubleday,
1986.
8. Minsky, Marvin, Society of Mind, Simon and Schuster, 1985.
9. Cairns-Smith, A. G., Seven Clues to the Origin of Life, Cambridge
University Press, 1985.
10. Margulis, Lynn and Dorian Sagan, Microcosmoss: Four Billion Years
of Evolution From Our Microbial Ancestors, Summit Books, 1986.
11. Sims, Karl, "Interactive Evolution of Dynamical Systems,"
Thinking Machines Corporation, Technical Report Series (published in Toward
a Practice of Autonomous Systems: Proceedings of the First European
Conference on Artificial Life, Paris, MIT Press, December 1991.
12. Dyson, Freeman, Infinite in All Directions, Harper & Row, 1988.
Other Sources
Alfvin, Hannes, writing as Olof Johanneson, The End of Man?, Award
Books, 1969.
Anderson, Poul, "Kings Who Die," If, March 1962, 8-36.
Asimov, Isaac, "Runaround," Astounding Science Fiction, March 1942,
94.
Barrow, John D. and Frank J. Tipler, The Anthropic Cosmological
Principle, Oxford University Press, 1986.
Bear, Greg, "Blood Music," Analog Science Fiction-Science Fact, June,
1983.
Conrad, Michael, et al., "Towards an Artificial Brain," BioSystems,
vol. 23, 175-218, 1989.
Dyson, Freeman, "Physics and Biology in an Open Universe," Review of
Modern Physics, vol. 51, 447-460, 1979.
Herbert, Frank, Dune, Berkeley Books, 1985.
Kovacs, G. T. A., et al., "Regeneration Microelectrode Array for
Peripheral Nerve Recording and Stimulation," IEEE Transactions on
Biomedical Engineering, vol. 39, no. 9, 893-902.
Niven, Larry, "The Ethics of Madness," If, April 1967, 82-108.
Platt, Charles, private communication.
Rasmussen, S. et al., "Computational Connectionism within Neurons: a
Model of Cytoskeletal Automata Subserving Neural Networks," in Emergent
Computation, Stephanie Forrest, ed., 428-449, MIT Press, 1991.
Stapledon, Olaf, The Starmaker, Berkeley Books, 1961.
Swanwick Michael, Vacuum Flowers, serialized in Isaac Asimov's Science
Fiction Magazine, December 1986 - February 1987.
Thearling, Kurt, "How We Will Build a Machine That Thinks," a workshop
at Thinking Machines Corporation, August 24-26, 1992.
Vinge, Vernor, "Bookworm, Run!", Analog, March 1966, 8-40.
Vinge, Vernor, "True Names," Binary Star Number 5, Dell, 1981.
Vinge, Vernor, "First Word," Omni, January 1983, 10.
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