If you think about technology, and where it may be taking us, it’s impossible to ignore the idea of the Singularity. But if you’re going to talk about it at all, it’s best to start off by **defining just what it is you mean**. Different people are using the term for a few different concepts these days. (Though at least the memetic mutation isn’t nearly so scattered as the ridiculous array of meanings and outright hot air clustered around “Web 2.0″.)

### The Original Singularity: Mathematicians, Represent!

The original concept was the mathematical singularity: A point at which a given mathematical function’s output is not defined. For example, the asymptotic point in the graph of y = 1/x (the classic hyperbolic curve); when x = 0, y is completely undefined — a literal “divide by zero” error.

This gave rise to the gravitational singularity: A point in space-time where the manifold’s curvature (and hence the gravitational field, and the density of any objects) is either unmeasurable or infinite.

Vernor Vinge’s seminal paper, The Coming Technological Singularity, maintains this idea of “change that becomes too fast to measure”, of graph-lines going asymptotic. Vinge writes: When greater-than-human intelligence drives progress, that progress will be much more rapid. In fact, there seems no reason why progress itself would not involve the creation of still more intelligent entities — on a still-shorter time scale…. Developments that before were thought might only happen in “a million years” (if ever) will likely happen in the next century. (In [Blood Music], Greg Bear paints a picture of the major changes happening in a matter of hours.)

Marc Stiegler’s 1989 short story “The Gentle Seduction” also uses the term in a rate-of-change sense, with one character introducing the idea as “a time in the future. It’ll occur when the rate of change of technology is very great — so great that the effort to keep up with the change will overwhelm us.”

### Variations Abound

But others are using the term in slightly different ways. Wikipedia’s article on the technological singularity describes it as an event where the rate of change is so great that “the future after the singularity becomes qualitatively different and harder to predict.” This isn’t quite the same idea. Instead of saying that **the Singularity itself** will be too difficult to comprehend, it’s saying that **the time after the Singularity** will be too different for us to understand. It’s something like the distinction between a singularity and an event horizon (a boundary beyond which we cannot see). Yes, one causes the other, but they’re not the same thing.

**Originally published at Coyote Tracks. You can comment here or there.**