[iandanforth]

Turing didn't specify how reads and writes happened on the tape. For the argument he was making it was clearer to assume there was no noise in the system.

As for "digital" computers remember they are built out of noisy physical systems. Any bit in the CPU is actually a range of voltages that we squash into the abstract concept of binary.

[gugagore]

I don't think that is really relevant to the discussion. Regardless of how a digital computer is physically implemented, we use it according to specification. We concretize the concept of binary by designing the machine to withstand noise. The thing what we get when we choose the digital abstraction is that this is actually realistic. Digital computers pretty much operate digitally. Corruption happens, but we consider that an error, and we try to design so that a programmer designing all but the most critical of applications, should assume that memory does not get corrupted

We don't squash the range of voltages. The digital component that interprets that voltage does the squashing. And we design it that way purposefully. https://en.wikipedia.org/wiki/Static_discipline

Turing specified that the reads and the writes are done by heads, which touch a single tape position. You can have multiple (finitely many) tapes and heads, without leaving the class of "Turing machine". But nothing like blending symbols from adjacent locations on the tape, or requiring non-local access to the tape.