I disagree. Turing's original paper where he introduced the Turing machine addressed the question of whether a discrete machine is interchangeable with an analo

I disagree. Turing's original paper where he introduced the Turing machine addressed the question of whether a discrete machine is interchangeable with an analog mind; Turing's argument is that even if the states are continuously variable there comes a point where two states are too close to be distinguished by the mind itself, and therefore it is permissible to say that the number of states IS finite and can be modeled by a discrete state Turing machine. Now put Shannon's information theory in the mix: a channel, even a sloppy one, has a bit rate and an error rate. My intuition is that whatever speed increase you get from allowing sloppy cirfuits will be matched by an increased error rate. If you trade off error rate of a sloppy channel against using fewer bits of precision in a discrete/non error prone channel, you should get the same effective information rate. All of these claims of increasing performance by sacrificing precision are achieving it by ignoring the tradeoff between rate and precision. It would be the same as if I claimed to speed up a lossless compression algorithm by discarding every other byte while measuring data rate as if I were not losing information. My point is any tradeoff you can make by losing information in hardware, you can make the same information tradeoff in software.