I recently came to understand the singularity, and now that I do the argument is pretty funny; it basically is the result of a bad mathematical model.

Here's the idea: Suppose you built a computer to design a new computer twice as fast as itself, whose job is the same, and so on for its children, ad infinitum.

The first computer takes 1 day to do its job. Its speed is 1 exaflop.

The second computer takes 1/2 day to do its job. Its speed is 2 exaflops.

The third computer takes 1/4 day to do its job. Its speed is 4 exaflops.

...and so on.

Hence the total time it takes all the (infinite) computers in this series to work is given by the convergent geometric series,

1 + 1/2 + 1/4 + 1/8 + ... = 2 days.

In other words, you design an infinite number of computers in finite time. And in this finite time, you've managed to produce infinitely *fast* computers, since their speeds go with 2^N. So the event referred to as "the singularity" is not called this just out of a love for words that sound like they belong in bad Star Trek dialogue; rather it is *literally* a mathematical singularity of the day-number--to-computer-speed map.

Kind of silly, no?