Re: Analog = digital?

In article <458d4783$0$16155$4fafbaef@xxxxxxxxxxxxxxxxxxx>,
JMF <jfavaro@xxxxxx> wrote:
A friend of mine said he thought he remembered that someone had once proven
that digital computers were theoretically equivalent to analog computers --
that is, that they could compute anything that an analog computer could
compute.

But somebody just said, "No, there is no such proof."

I thought I'd ask here whether anybody knew either way.

The mistake here is in thinking that "analog = digital?" is a unique,
well-defined question, of the type that is amenable to either proof or
disproof.

Depending on how you choose to make the question precise, it may have
a proof or not. Proving that one particular version of the question is
true does not, of course, say anything a priori about other versions of
the question.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.

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