European scientists are building silicon chips containing large scale artificial neural networks (200,000 neurons and 50 million synapses, scalable to a billion neurons and 10 to the 13 synapses). (Thanks to Neal Anderson for the link.)

IBM scientists and working on “cognitive computing”, an attempt to build a new generation of computers inspired by how the brain works.

Finally, Peter Bradley wonders “if [the IBM effort] has any actual impact on the theory of computability, or if this is just going to be a significant increase in the speed of computation“.

I just read the IBM press release linked to above, which is too vague to understand what’s going on. From my limited understanding, I would conjecture the following:

None of this revolutionizes the theory of computability properly so called, that is, the study of computable functions over denumerable domains (e.g., natural numbers). However, it might help develop the branch of computability theory that deals with what can be computed by certain kinds of neural networks, and with what resources. This, in turn, might help develop faster and more efficient computing components for ordinary computers.

This work may even lie outside the boundaries of computability theory, because the networks in question may operate on vehicles that do not quite constitute well-defined denumerable domains. If so, these studies might contribute to understanding the brain and perhaps to building interesting special purpose applications and to develop the relevant mathematical theories (which I would prefer not to call “theory of computation” so as not to confuse with the mathematical theory of computation in the sense above), but it would be unlikely to replace ordinary computing technology (“universal” computers like the ones we use).

Does anyone else know more about these efforts and their implications?

*Related*

No, this will not have any impact on either computability theory, or the present consensus that the physically computable functions are within the Turing computable.

What it will have an impact on is our understanding of the complexity of the computational processes in the brain.

FYI, there are two main branches to the classical theory of computation: computability theory and complexity theory. For some reason, philosophers generally only know about the former, although the philosophical import of the latter is, in my opinion, greater.