That is the OP's main point, except turned around. He was measuring progress by results, not by effort expended, and saying that it takes exponential effort to reach linear results.
The singularity doesn't promise certain invention (for example it's possible that there is no and will never be a way to go faster than the speed of light) it only promises exponential growth which will bring the "end of science" into the foreseeable future. So if we found maybe 80% of all physics in the last 200 years, with linear progress we would reach the end of physics in 40 years.