OK, forgive me for going mathematical on the thread, but I think it's a little necessary for what I want to get across...
So in math, a singular point (usually on a function or other mathematical object) is a point at which the item in question is not well-behaved. It can be a point where a differentiable function isn't, a value where an algebraic function is undefined, a solution to a differential equation that isn't unique at a point, a matrix that has no inverse, ... there are lots of versions, but they all orbit around the same idea, "We have no way of dealing with this because there's no way to know exactly what's going on".
Now, if you think of a function of time, the one-way variable, and there
seems to be a singular point ahead - change (slope) is speeding up remarkably, with no signs of moderation and slowing - you may think you're approaching a singular point on the graph (a vertical asymptote of some sort).
The thing is, when you're trapped on the function's graph, there's no way to see ahead to find out what's on the other side of the singularity. Or even how you're going to get past it...
Now, here's the thing - it's pretty well accepted that most change happens exponentially. Computer processing speed, population changes, human behavioral change, adoption of new technologies, learning curves - there are limits, things like saturation points, but most changes have an exponential base.
Exponential change
does happen faster and faster, that's the whole idea behind it - doubling times, half lives and all that. But it's not singular.
Is it sustainable? Maybe. And as you look at it from one side, it sure
seems that it
should have a singularity. A point at which it heads to infinity.
But it doesn't.
Now, things will merge - they already are, look at the progress with mental control of artificial limbs - and again, that change after a merge point will happen exponentially to the point where human augmentation may become quite common. And we've seen incredible growth in the
simulation of intelligence by artificial means. The two of those may even merge in some way. it's the stuff of science fiction, sure, but there's a lot of science fiction that becomes true, often before predictions, because predictions tend to be linear (we're linear thinkers), and the real change tends towards the exponential.
Doesn't mean there's going to be a singularity, though.
But there's another type of singularity that I think may apply, the non-differentiable sort. That is, a point where there's a sudden change in direction. The change that we see happening more and more quickly can all of a sudden do something else - level off, get suddenly steeper (or less steep), or even take a sudden jump. And, when two paths merge, there's often a sudden change - when technology meets art, when a medical advance changes lifespan or quality, and when a sudden flash of insight goes beyond current knowledge. Again, the results are (at best) unpredictable. But it's not the "infinite point" that most people think of or expect when they talk about a singularity.
Well, sorry for the wall-o-text, but I think it's important to remember where these words we use come from. I find that it helps make sense of the ideas behind them. Otherwise,
we're just strawmannin'.