People don't often ask me what I mean by 'the singularity' when I mention it; instead, they get this confused expression and say nothing. After I've clarified that I'm not talking about a black hole or about the theoretical start-point of the universe-as-we-know-it, they usually continue to look confused.
Words may well be the most powerful drug known to humankind, but they don't always make things easy. Try communicating with someone with whom you share no common language, or with someone in a profession which makes heavy use of area-specific jargon (computer programmers, for example), and you'll see exactly what I mean. Words are only useful when the meaning is shared between the people attempting to use those words and meanings to facilitate communication.
'Singularity' is a great word. It draws the mind to images of stars and galactic vistas, handily coloured for artistic appreciation by NASA's tireless scientists. It implies a beginning, and one of vast significance, equivalent to the birth of the universe itself. It allows us the warm and fuzzy subconscious certainty that we are all in this game together, that the spheres are aligning and some new utopian age will be here any second now. But it doesn't actually mean anything in the context in which we're using it. We might just as well call the singularity "the pyramid". We'd get the same blank looks form those not in the know.
What we should call it, what we mean when we refer to it, is a paradigm shift.

I know the official line: the singularity is the point in time at which strong AI comes into being. When artificial (man-made) intelligences emerge which are capable of self-improvement, which necessitates that they engage in self-improvement until they become weakly godlike beings superior to us humans in understanding, intellect, knowledge, and information processing power.
My usual description, and one which I believe to more correctly capture the idea of the singularity, is that it is the point in time at which the rate of technological change - visualised as an exponential curve of change vs time - is so large that unaugmented human beings are incapable of predicting further changes or consequences. That is, when the exponential curve approaches vertical.

But either one of those definitions, if followed through, boils down to paradigm shift. Not purely within the hard sciences, as in the original sense of the term, but applied to all of human culture and society. A change in basic assumptions, a crisis brought on by new information - factual anomalies which refute the existing 'truth' and require a new truth, a new mode of thought and action to be created and implemented.
The singularity is not unique, though the term may lead one to assume that it is, or should be. Paradigm shifts have occurred within society many times, as a result of technology or social innovation. Like puberty for a mammal, paradigm shift is a time of change and sudden growth for a species. Species such as our own have the dubious pleasure of entering the tumult of puberty and adolescence more than once, of learning to adjust to the changes we are undergoing.
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