Here is  presentation from a researcher at MIT on a novel way of designing computer processors. It relies on performing approximate, rather than exact, mathematical operations (like the meat-based processor in our heads!). Claimed benefits are a 10,000-fold improvement in speed, while the errors introduced by the approximations are postulated to be insignificant in many applications.

http://web.media.mit.edu/~bates/Summary_files/BatesTalk.pdf

Slide #2 of the presentation offers a fascinating insight: We currently work around the limitations of the processing substrate to implement a precise computation, and it is becoming increasingly difficult:

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THE MOTIVATING PROBLEM:

Computations specified by programmers are implemented as behavior in physical material

• Hardware designer’s job: 

efficiently implement Math (what sw wants) using Physics (what silicon offers)

                              (near) perfect arith                           noisy, approximate                 

                                   uniform mem delay                          delay ~ distance

• Increasingly difficult as decades passed and transistor counts exploded

• Now each instruction (increment, load register, occasionally multiply) invokes >10M transistor operations, even though a single transistor can perform, for instance, an approximate exponentiate or logarithm

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The parallels and contrasts with our own brain are what interested me the most. Perhaps one day the most powerful computers will be running on "corrupted hardware" of sorts.