A central theme underlying all of the analysis we do here at Trends is the realization that the rate of change is constantly increasing — and it’s been doing so in a measurable way for at least the past 500 years.

The cumulative effect of this accelerating change is unlike the gradual, steady change that mankind is used to seeing. Instead, it unfolds with such powerful momentum that it is unlike anything we’ve ever encountered. Today, we can expect the world to change more in one lifetime than it once did in a millennium.

To comprehend what this means, consider the familiar metaphor of waves lapping against a sea shore. When each wave is the same size and strength as the one before it, as in gradual change, the landscape evolves slowly over time. Soil is eroded and rocks wear down gradually over thousands, or even millions, of years.

But accelerated change is anything but gradual. It is the equivalent of a wave hitting the shore, followed by another wave twice as strong, then another wave four times stronger, until one tsunami after another is pounding the landscape, each more powerful than the one that preceded it. Under accelerated change, the environment is transformed not in millennia, but in minutes.

Similarly, as the intelligence of our computers continues to increase, and the rate of the increase continues to increase, we can expect to see machines that are millions of times faster and more powerful than today’s machines arriving in just a few decades.

Consider that the rate of technological innovation has been speeding up throughout history, and currently it is doubling every 10 years. That rate is eclipsed by the dizzying pace of improvements in IT. By every measure — including speed, capacity, bandwidth, and price-performance — the power of IT is now doubling every 12 months.

What’s more, the advances we will discuss appear ready to unleash a perfect storm of technological progress. The implications of this trend were first recognized in the 1940s by Princeton mathematician John Von Neumann, one of the pioneers of the computer architecture we still use today.

Von Neumann coined the term “singularity” to describe the point beyond which progress is so rapid that for all practical purposes, it is infinite.

In the past 15 years or so, a small but growing...