My take on the singularity
You can add two numbers together. Adding bigger numbers results in bigger sums. Adding more numbers results in bigger sums. But when you generalize the process, to multiplication, you now have the ability to succinctly represent huge numbers, much more easily than with addition. Multiplication can be generalized, to exponentiation, and exponentiation can be generalized as well. Even the processing of creating new generalizations can be generalized.
A generalization is like a paradigm shift. In the history of the universe, human language, especially the written word, was a paradigm shift, from unintelligent directed processes evolving complexity, to directed intelligence creating complexity. The next paradigm shift is with directed intelligence creating intelligence, and it’s just as large as the previous one. Much bigger than the printing press. Much bigger than the industrial revolution.
I don’t think any arguments about the “rate of change” really hold water, because a paradigm shift causes a discontinuity in many trends. At best, rate of change arguments can show how specific technologies that will help us understand the nature of intelligence, and eventually to recreate it, are being developed at a rate to where by year X we will have Y resources available to throw at the problem of intelligence.
So, is it possible to create intelligence? Yes. It logically follows from naturalism. Evolution created intelligence, and intelligence is simply a computational process, (as every physical thing is,) so humans can create intelligence using any Turing complete machine, i.e. a sufficiently fast computer. The question of whether we will have the ability to create intelligence within the next twenty or two hundred years requires a lot more argument, but this is the starting point.