I want to point out that people should be wary of this recent wave of press surrounding "neural" computing. A lot of this involves trying to emulate biophysical properties of neurons we observe in the brain, but it is not clear how these properties affect function or if they are even necessary for the types of computations we are interested in emulating in silicon.
That being said, memristors are a fascinating piece of technology and we need to make progress on all fronts if neurally-inspired computing is to become a reality. This latest development (capturing the nonlinear properties of sodium and potassium channels in a microelectronic device) is quite interesting, as these properties are crucial for reproducing the spiking behavior of real neurons. All I'm saying is take these results with a grain of salt, there is still a lot of work to do!
I think it is fair to say that we just don't know yet. Neuroscience has learned a great deal about the underlying machinery (neurons, synapses, and so forth), but we have no idea how you put that machinery together to generate something like consciousness. This is, for me, what makes the field interesting, because I think these questions are answerable.
As far as the original article, I think anyone who tries to argue that you are not your brain is ignoring over a hundred years of scientific evidence that suggests otherwise.
I disagree with a lot of points made here. First, this is focused exclusively on the biological sciences, and is largely not applicable to other fields (hence the title is misleading). Second, there are a lot of personal anecdotes which don't move the central ideas forward. Finally, there was little in the article that discussed how to think about science, most of it was how to pursue science.
That being said, I agree with the sentiment. Most of what we teach undergraduates is about the knowledge science is produced, rather than about the process of doing science itself.