I've roughly calculated when the Singularity will occur. Someone sanity check this.
We'll use this as our definition for the Singularity: The point at which the total CPU capacity of all devices of humankind equals the CPU capacity of all the brains of humankind.
According to an article in Science, written up in Ars Technica, the world's total CPU power in 2007 equaled one second of neuron firings in one human brain.
Moore's law states that we can double the number of transistors on a chip every 18 months. Yes, at some point we will hit the limit; perhaps we'll change to optics, or qbits, but let's run with it.
There are 31,536,000 seconds each year, or a little under 2*2^24.
Based on an 18-month cycle of doublings, that puts us at 34.5 years away from total capacity equalling one brain. Figuring around 8 billion humans by the end of the century, that's a little over another 33 doublings required to equal all brains. Call it about 49.5 years. Population growth may push that out a few more months, but not much; that's on a very, very close order of magnitude (2^33 = 8.6x10^9.)
The Singularity will be in 2095.
I probably won't live that long, but my daughter has a damn good shot at it. AWESOME.
(Thanks to Stross's Accelerando for the inspiration, and Ars Technica science writer John Timmer for providing the data required for this.