Essentially, the rate at which technology advances is increasing, but the complexity of the problems that it is intended to resolve remains constant. An example: We can measure the rate of advancement in live-extending technologies as the number-of-months-life-is-extended per year, on average. Each year, let's say, people live one month longer, on average, than they did before. So, singularity would occur when, for each year that passes, technological advancements allow us to extend the life of a person by one year- clinical immortality.
The concept of singularity can be applied to everything from advancements in processor architecture, medicine, transportation, etc.
But I had an interesting thought about its application to historical cycles. History does repeat itself, and we can guage the state of a civilization by comparing it to the same cycles as the occured in preceeding civilizations. These cycles have begun shrinking- "everything changes so fast", as they say- the same things keep happening, but they start happening more and more frequently.
What happens when the rate at which culture cycles through its phases approaches infinity- or better put, when the length of a cycle approaches zero? All different states of culture, co-existing at the same time. That, more so than any other singluarity scenario demonstrates to me the flaw of the logic of singularity.
First, singularity presupposes that the curve we follow is geometric along its entire length- however, there is quite possibly- and quite probably- a plataeu, caused by other disruptions- like for example, the illogic of competing cultural states coexisting simultaneously. What would actually happen is that these different cycles would fragment, form their own distinct cultures, which would then, on a smaller scale, undergo the same cycles that they did in a larger scale.