Is a technological singularity likely?

The question makes no mention of time. Given enough time, one of the definitions of the singularity will happen, it is inevitable.

The technological singularity is likely to happen in the middle of the 21st Century.

"Smarter than human" is a vague concept. We don't consider powerful calculating machines to be smarter than us. For the purpose of the Singularity, to get accelerating technological growth, we must mean inventing a an AI that is better at inventing new technologies than we are.

I think we are far away from inventing a machine that can invent its own machines. AI research today focuses on getting machines to accomplish the same tasks of perception and learning that humans (and animals) do. I think it's clear that we'll get much better at machine perception. In my lifetime we may well get a machine that comprehends language the way humans do. But I don't know if anyone's even working on machines that can innovate. That may be a severely hard problem.

Should this perhaps be separated into a few different questions, for the divergent ways people have used the term "singularity" as explained here and here? I was considering adding a quote from a post by PZ Myers where he harshly criticizes the idea of "the singularity", but he is focusing entirely on Kurzweil's idea of predictably accelerating progress, and he says nothing about the likelihood or desirability of a smarter-than-human AI undergoing an intelligence explosion (which appears to be the focus of this question's description).

I can see several paths to a Singularity (I'm working under the intelligence explosion interpretation). If we create an Artificial General Intelligence that is smarter than humans — smart enough that it has significant advantages over humans in skills like programming and engineering — then we get an intelligence explosion pretty much right away. Or if we get to the point where we have enough processing power and brain-scanning precision to perform whole-brain emulation, we could create a million copies of the world's best programmers and have them work on improving their own software, a million copies of the world's best engineers and physicists and have them work on improving their own hardware, or a million copies of the world's best cognitive scientists and computer scientists and have them work on reverse-engineering the ingredients of general intelligence and then implementing it. And so forth. (Personally, if we're going to go that route, I think a million copies of Eliezer Yudkowsky would work best.) Similar things could also happen if powerful Intelligence Amplification techniques are developed, though I think the end goal should remain Friendly AI, with IA/uploading as secondary means to that end.

Anyway, if we can keep ourselves from going extinct for long enough, a Singularity of some kind is just about inevitable, though not as a prophecy of a utopian future; indeed, its inevitability necessitates serious thought and research on how we can make sure we get it right the first time.

Technology is advancing rapidly, and contributing to the increase in its advancement. Unless we destroy ourselves first, this feedback will lead to a singularity.