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                          The Socio-technological Singularity

   Although acceleration and complexity have made most concrete developments
   impossible to predict, large scale, statistical factors, such as wealth, life
   expectancy, intelligence, productivity, speed of information transmission and
   speed of information processing, increase in a surprisingly regular way. This
   makes it possible to extrapolate their development into the future. Most of these
   growth processes are exponential, characterized by a constant doubling period, or
   a constant increase in percentage per year. This means that the underlying growth
   mechanism is stable, producing a fixed number of new items for a given number of
   existing ones.

   However, some processes grow even more quickly. For example, population growth in
   percentage per year is much larger now than it was a century ago. This is because
   medical progress has augmented the gap between the percentage of births and the
   percentage of deaths per year. If the growth of the world population over the
   past millenia is plotted out, the pattern appears to be hyperbolic rather than
   exponential. Hyperbolic growth is characterized by the fact that the inverse of
   the increasing variable (e.g. 1 divided by the total population) evolves
   according to a straight line that slopes downward. When the line reaches zero,
   this means that the variable (world population in this case) would become equal
   to 1 divided by zero, which means infinity. This is essentially different from an
   exponential growth process, which can never reach infinity in a finite time.

   [Singularity.gif]

   Fig. 1: a hyperbolic growth process, where the growing number becomes infinite in
   the singular point, while its inverse (1 divided by the number) becomes zero.

   If the line describing the inverse of world population until recently is extended
   into the future, we see that it reaches zero around the year 2035. Of course,
   such an extrapolation is not realistic. It is clear that world population can
   never become infinite. In fact, population growth is slowing down at this moment.
   However, that slowdown itself is a revolutionary event, which breaks a trend that
   has persisted over all of human history.

   In mathematics, the point where the value of an otherwise finite and continuous
   function becomes infinite is called a "singularity". Since traditional
   mathematical operations, like differentiation, integration and extrapolation, are
   based on continuity, they cannot be applied to this singular point. If you ask a
   computer to calculate the value of one divided by zero it will respond with an
   error message. A singularity can be defined as the point where mathematical
   modelling breaks down. The inside of a "black hole" is an example of a
   singularity in the geometry of space. No scientific theory can say anything about
   what happens beyond its boundary. We can only postulate that different laws will
   apply inside, but these laws remain forever out of sight. Similarly, the Big
   Bang, the beginning of the universe, is a singularity in time, and no amount of
   extrapolation can describe what happened before this singular event.

   The mathematician and science fiction writer [externallink.GIF] [2]Vernor Vinge
   has [externallink.GIF] [3]proposed that technological innovation is racing
   towards a singularity. Scientific discovery appears as an exponentially growing
   process with a doubling period of about 15 years. However, the doubling period is
   diminishing because of increasingly efficient communication and processing of the
   newly derived knowledge. The rate of growth is itself growing. This makes the
   process super-exponential, and possibly hyperbolic. Vinge would argue that at
   some point in the near future the doubling period would reach zero, which means
   that an infinite amount of knowledge would be generated in a finite time. At that
   point, every extrapolation that we could make based on our present understanding
   would become meaningless. The world will have entered a new stage, where wholly
   different rules apply. Whatever remains of humanity as we know it will have
   changed beyond recognition.

   Some data supporting this conjecture can be found in a chart provided by Peter
   Peeters, in which the time elapsed between a dozen fundamental discoveries and
   their practical application is plotted against the year in which the invention
   was applied. The graph shows a downward sloping line, which reaches zero in the
   year 2000. These are just a few data points, and the implication that inventions
   will be applied virtually instantaneously after 2000 does not yet mean that
   scientific progress will be infinite. Vinge himself would situate the date of the
   singularity between 2010 and 2040. His reasoning is based on the accelerating
   growth of computer-aided intelligence. Rather than considering the IQ of an
   isolated individual, he would look at the team formed by a person and computer.
   According to Vinge, a PhD armed with an advanced workstation should already be
   able to solve all IQ tests ever devised. Since computing power undergoes a rapid
   exponential growth, we will soon reach the stage where the team (or perhaps even
   the computer on its own) would reach superhuman intelligence. Vinge defines this
   as the ability to create even greater intelligence than oneself. That is the
   point at which our understanding, which is based on the experience of our own
   intelligence, must break down.

   A related reasoning was proposed by Jacques Vallée. Extrapolating from the
   phenomenal growth of computer networks and their power to transmit information,
   he noted that at some point all existing information would become available
   instantaneously everywhere. This is the "information singularity".

   These models should not be taken too literally. They are metaphors, proposed to
   stimulate reflection. It does not make much sense to debate whether "the
   Singularity", if such a thing exists, will take place in 2029 or in 2035.
   Depending on the variable you consider most important, and the range over which
   you collect data points, you may find one date in which infinity is reached, or
   another, or none at all. Even if nothing as radical as a "New Age" could be
   predicted, the zero point method is certainly useful to attract the attention to
   possible crisis points, where the dynamics of change itself are altered. Peeters
   has used this method with some success to "predict" historical crises, such as
   the First World War and the 1930 and 1974 economic recessions. (The Second World
   War, strangely enough, did not seem to fit the model...).

   The point to remember, however, is that abstract, non-material variables, such as
   intelligence, information, or innovation, aren't subjected to the same "limits to
   growth" which characterize the exhaustion of finite resources. Such variables
   could conceivably reach values which for all practical purposes may be called
   "infinite". Several parallel trends show a hyperbolic type of acceleration which
   seems to reach its asymptote (the point of infinite speed) somewhere in the first
   half of the 21st century. This does not mean that actual infinity will be
   reached, only that a fundamental transition is likely to take place. This will
   start a wholly new mode of development, governed by laws which we cannot as yet
   guess.

   References:
     * P. Peeters: Can We Avoid a Third World War in 2010?
     * [externallink.GIF] [4]Vernor Vinge on the Singularity
     * [externallink.GIF] [5]The technological singularity
     * Eliezer S. Yudkowsky: [externallink.GIF] [6]Staring into the Singularity
     * [externallink.GIF] [7]Singularity Watch: John Smart's extensive observation
       of accelerating change in technology and society
     * [externallink.GIF] [8]Singularity in the Google Directory
     ____________________________________________________________________________

   [9]Copyright© 2002 Principia Cybernetica - [10]Referencing this page

   Author
   F. [11]Heylighen,

   Date
   Feb 1, 2002 (modified)
   Jan 15, 1997 (created)

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                                    [17]Discussion
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     * [18]Singularity Page moved, Correction by Eliezer Yudkowsky
     * [19]Fast track to Singularity, Comment by Arthur T. Murray
     * [20]The Singularity Necessarily so?, Comment by Don Stockbauer
     * [21]Possible Explanation , Comment by Aaron Wilson

                                  [22]Add comment...

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References

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   2. http://www.ugcs.caltech.edu/~phoenix/vinge.html
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   5. http://www.aleph.se/Trans/Global/Singularity/
   6. http://tezcat.com/~eliezer/singularity.html
   7. http://www.SingularityWatch.com/
   8. http://directory.google.com/Top/Society/Philosophy/Current_Movements/Transhumanism/Singularity/
   9. http://pespmc1.vub.ac.be/COPYR.html
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  13. http://pespmc1.vub.ac.be/MSTT.html
  14. http://pespmc1.vub.ac.be/FUTEVOL.html
  15. http://pespmc1.vub.ac.be/CHINNEG.html
  16. http://pespmc1.vub.ac.be/MEMEEVOL.html
  17. http://pespmc1.vub.ac.be/MAKANNOT.html
  18. http://pespmc1.vub.ac.be/Annotations/SINGULAR.0.html
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  20. http://pespmc1.vub.ac.be/Annotations/SINGULAR.2.html
  21. http://pespmc1.vub.ac.be/Annotations/SINGULAR.3.html
  22. http://pespmc1.vub.ac.be/hypercard.acgi$annotform?

[USEMAP]
http://pespmc1.vub.ac.be/SINGULAR.html#PCP-header
   1. http://pespmc1.vub.ac.be/DEFAULT.html
   2. http://pespmc1.vub.ac.be/HOWWEB.html
   3. http://pcp.lanl.gov/SINGULAR.html
   4. http://pespmc1.vub.ac.be/SINGULAR.html
   5. http://pespmc1.vub.ac.be/SERVER.html
   6. http://pespmc1.vub.ac.be/hypercard.acgi$randomlink?searchstring=.html
   7. http://pespmc1.vub.ac.be/RECENT.html
   8. http://pespmc1.vub.ac.be/TOC.html#SINGULAR
   9. http://pespmc1.vub.ac.be/SEARCH.html