Re: Simulation: digital vs analogue

Paul E. Black wrote:
On Saturday 26 January 2008 15:10, Tim Tyler wrote:

``We should keep in mind as well that you digital computing
can be functionally equivalent to analog computing - that
is we can perform any of the functions of a hybrid
digital-analog network with an all digital computer.
The reverse is not true: we can't simulate all of the
functions of the digital computer with an analogue one.''

- The Singularity is Near, Ray Kurzweil, page 130

What?!?

Both can do universal computation - and so can simulate
any other type of system with an arbitrary degree of
precision.

True analog computation doesn't have an arbitrary degree of
precision.

A slide rule is an analog computer which can multiply two numbers. It is limited to three, maybe four significant
figures. [...]

A digital computer with ten bits is just the same.

The topic is the limits of analog and digital computation -
not the limits of a slide rule.

A CPU with no floating point unit doesn't have
"an arbitrary degree of precision" either. Yet
strangely it can do floating point arithmetic
(to an arbitrary degree of precision) with a
software FP library that uses multiple integers
to represent one FP number.

General Purpose Analog Computers are no different.
--
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