Probably not. At least in practice. I imagine that the internal limitations (i.e. quantum mechanics, finite size) of our universe prevent the existence of any true analog computers, physical computation being limited to finite Turing computability [1]…
Given that everything computable is computable by a Turing machine and thus all computers are equivalent – analog (non-digital) computers are no more (less?) efficient than digital computers*. Nevertheless it’s hard to argue against analog computers having a certain cachet. And despite – or perhaps in spite of the internal limitations of our universe, and always being one for a challenge, I thought it high time I built a computer…
*According to the Strong Church thesis (Vergis et al [2]), analogue (non-digital) computers are no more efficient than digital computers. Informally the thesis states that if some method (i.e. analogue computer) exists to carry out a calculation, then the same calculation can also be carried efficiently (that is in polynomial not exponential time) out by a Turing machine (i.e. digital computer).
[1] Eric Steinhart in The Blackwell Guide to the Philosophy of Computing and Information, p. 184, ed. Luciano Floridi, 2004.
[2] A. Vergis, K. Steiglitz, and B. Dickinson, ‘The Complexity of Analog Computation’, Mathematics & Computers in Simulation, 28 (1986) pp. 91-113.
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