It has been proven that recurrent neural networks with analog weights can solve problems that are insoluble using Turing machines. However, the prevailing view of those involved in computing research is that a) nonTuring computation is unnecessary for intelligence and b) machines with non-Turing abilities cannot be built in practice. Two reasons are commonly cited for this. First, the effects of noise are said to remove any possibility of using an analog system to represent quantities with continuous infinite precision. Second, the (asserted) discrete nature of the Universe, is cited as proof that truly analog systems cannot exist. These are issues of physics that exist well outside the domain of computer science and engineering. Here, we will examine the technical and mathematical bases of these claims, suggest counter arguments, and discuss the deep physical questions that they raise.