the following are some of my interpretations of the _technological singularity_. please forgive my many necessarily vague dictions.
first of all, some seem to believe that current technological growth trends fit a hyperbolic curve and will therefore reach a true mathematical singularity some time in the near future. however, my calculus reference calls the hyperbolic functions "a class of exponential functions," and a cursory examination seems to indicate that hyperbolic functions do not grow to infinity in finite time. what gives?
in fact, a very brief review of the most elementary functions
gives one the impression that almost all functions that reach a
singularity involve division of two distinct forces or what is essentially
the same, a logarithm. examples include rational funtions
(f(x) = -1 / (x - 5)), logarithmic functions (f(x) = -ln(5-x)), and
trignometric functions (f(x) = tan(x)).
thus a speculative leap: at least two interacting forces are
necessary to reach a true mathematical singularity, and no single force
can "grow" to infinity in finite time. that is, faster-than-exponential
growth (x!, e^(x^x), etc.) does not imply singularity per se.
thus a speculative leap: at least two interacting forces are necessary to reach a true mathematical singularity, and no single force can "grow" to infinity in finite time. that is, faster-than-exponential growth (x!, e^(x^x), etc.) does not imply singularity per se.
the above leads me back to vinge's interpretation of the _technological singularity_: that the singularity is a dialectic between accelerating growth of technology on the one hand and static human nature on the other. what the singularity delineates is the ever-shrinking gap between the rate of change that a human being can accomodate and the amount of change that transpires in unit time. it decribes a progression of rapidly shrinking "prediction horizons" at the end of which is a darkness in which the human being is essentially blind -- unable to guess what is to come in the very next moment.
however, in order for the preceding to be true, the force behind technological growth must be independent of the human being (or else it will most likely level off as a bacterial population exhausting its nutrient supply). that is, to obtain two truly interacting forces, the human being must create her nemesis, the self-modifying intelligence.
all of the above suggests that the _technological singularity_ is in some sense a trick of perpective -- technology never really grows infinitely fast, but we won't be able to tell the difference if we grow too slowly or not at all.
ergo, the implications can be summarized as follows: with AI, the singularity is possible; with IA, the singularity is avoidable; and with both, the singularity is uncertain. if this is true, then the race between AI and IA may be the driving conflict on the road to the singularity.