The Speculist

Now perhaps I'm way overanalyzing this "singularity" meme, but given that it supposedly came from mathematical origins, it seems odd to me that the current discussion of singularities, accelating change, etc don't seem to have a logical relationship with their origins.

For example, accelerating change in math doesn't mean a singularity can be reached. For example, the function exp(x) (the usual exponential function) embodies "accelerating change" (though it's logarithm is linear). If that function doesn't explode fast enough for you, then there's exp(exp(x)) or indeed an arbitrary chain, exp(exp(...(exp(x))...)). All of these functions are defined for all x. There's no singularities of any sort (aside from a big "essential singularity" at infinity).

On the other hand, 1/x has a simple pole at x=0 (a relatively dull singularity). And exp(1/x) has an essential singularity at x=0 (the math analogue to the "anything can happen" singularity). A lot of the mathematics of these things lies in x being complex (including "i" a square root of -1), but I sense we're straying off topic with that.

Here's a couple more problems. We all agree that the rate of change is increasing. But is it "accelerating rate of change"? (Eg, x^2 (the cube of x) has an increasing rate of change, but it's rate of change isn't accelerating. Second, what appears to be a singularity to me may not be a singularity to you. For example, in paramagnetic materials (like a bar of iron), you can magnetize the material by subjecting it to a heavy magnetic field yielding neat things like compass needles.

There's no particular requirement for the orientation of the resulting magnetic field. Eg, either end of the compass needle could be pointing north. The actual singularity here occurs as the needle is heated. As the temperature increases, the residual magnetic weakens until it vanishes at some point. This temperature is the "critical point" (a type of singularity) dividing the cooler paramagnetic regime from a regime with no residual magnetic fields.

But there are certain physical attributes that don't depend on the magnetic properties of the material (eg, mass). If all I care about is the mass of the object, then a change in the magnetic properties just isn't a singularity for me.

So logically here's the chain of logic that I'm concerned about. Increasing change doesn't imply accelerating change. Accelerating change doesn't imply existence of singularities. Existence of singularities doesn't imply the existence of a singularity (eg, "the Singularity") for everyone.

That's enough handwringing for now. Back to you, Phil.

Karl

That's good. Give your hands a break. ;-)

We colloquially speak of "The Singularity" as the technological or developmental point beyond which we cannot now (from this vantage point) make meaningful predictions or descriptions. So I was really just suggesting that perhaps it would not be a bad thing for government to be changed beyond recognition.

Kurzweil claims that technological change is not only increasing, it is coming ever faster. John Smart makes the same point. Actually, it's pretty easy to see the acceleration if you look at it from the historical perspective. We were hunter-gatherers for tens of thousands of years before becoming agrarians. We were then pre-industrial for less than 10,000 years. The industrial age started, say, a little more than 200 years ago and yet we have seen more technological change in that period than we had seen in the previous several millenia. The age of information started only a little more than 50 years ago. It would appear that we are moving through major developmental cycles much more quickly than we have in the past.

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