Re: Analog = digital?


<tchow@xxxxxxxxxxxxx> wrote in message
news:458d8dd8$0$577$b45e6eb0@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
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.

Well, I think the basic idea behind the question was a bit analogous to when
Dijstra wrote that article about "Goto considered harmful." Dijstra appealed
to the proof somebody had made that all programs could be written without
gotos -- so that he could reassure anybody that you wouldn't be giving up
any computational power by eliminating the goto. In an analogous fashion, my
friend thought he remembered that way back then when the pro-digital folks
were pushing for going completely digital and abandoning analog computers,
they appealed to this proof somebody had supposedly made that digital
computers could compute anything analog computers could -- and that
therefore by going the digital route they wouldn't be giving up
computational possibilities. But as I said, he's begun to wonder whether
that supposed proof exists.

John


.

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