People speak of the coming of a Singularity, in about a quarter of a century's time, at which time technological progress will become effectively infinite. They have nice graphs of our exponential (or even double exponential) rate of progress, and how this is the beginning of the really steep bit.
They forget that on an exponential curve, every point is the beginning of the really steep bit, and there is no singularity.
A mediaeval man may have just as well argued that, in a few years time and with the pace of innovation accelerating, soon the King won't have time for anything but granting new patents, and soon thereafter it'll be the end of humanity as we know it. Yet we have passed that point, and hardly noticed.
A lot of things will happen in the next quarter of a century, sure. We are likely to meet what will effectively be an alien species, for one thing. But nowhere is there any singularity, and calling it that just clouds our thinking.
Update 7.2.2005: A good phrase to use instead might be "intersection point"; it would refer to the point when the level our creations' intelligence intersects with our own (assuming it will).
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