Robin Hanson addressed this same thing today, but found faults in Allen's reasoning. I made a comment there too but I don't know if it has posted yet, so I included it below:
The connectomics project between Harvard and MIT is a particular place where a useful approximate link between specific technologies and ability to emulate brains may be calculable in the short term.
FWIW, I am studying in this course this semester and I am working on some research that uses connectomics to provide plausible complexity bounds on some brain operations, for the purpose of arguing against Ian Parberry’s analysis and conclusion that human cognitive resources are prohibitively difficult to emulate without better abstract knowledge of cognitive science.
There is other recent evidence that suggests an algorithmic approach to brain activity will at the very least give us short term access to replicating certain specific human cognitive functionality. I think this is a case where Leo Breiman’s distinction between “the two cultures” of data analysis is pretty apt.
Perhaps you can answer this: does Hanson start from a factually wrong claim about sufficient conditions for brain emulation? Would we need to know the strength of the connections within the brain, as this link claims, and does this pose more difficult problems?
Here's a great article by Paul Allen about why the singularity won't happen anytime soon. Basically a lot of the things we do are just not amenable to awesome looking exponential graphs.