Re: Simulation: digital vs analogue

A.G.McDowell wrote:
In article <DsMmj.283013$S37.84001@xxxxxxxxxxxxxxxxxxxxxxxxx>, Tim Tyler

``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

Oops - I mean page 149.

What?!?

Both can do universal computation - and so can simulate
any other type of system with an arbitrary degree of
precision.
Quantum computing is being investigated precisely because it cannot be
simulated efficiently with traditional digital computers, so, quoted out
of context, Kurzweil appears to be 180 degrees wrong.

Quantum computing doesn't seem to crop up in the context -
and even that can be simulated on ordinary digital computers,
just rather slowly.

But if his context identifies analog computing with consensus models of
neurones he may be practically correct; very few people believe that
neurones are exploiting quantum computing, and they appear to be suffer
too much from noise and general irreproducibility to make it practical
to use them as building blocks for general purpose digital computing.

He doesn't mention efficiency. He says it's impossible:

``we can't simulate all of the functions of the digital computer
with an analogue one.''

I reckon the most parsimonious explanation is a bad day, and
a lack of proof reading.

While there are theoretical schemes for building reliable digital
computers from unreliable components, in practice the cost is high and
the payoff low. Systems faced with this problem (e.g. satellite
electronics, which face radiation-induced errors) tend to put a lot of
effort into physical hardening to stop the problem at source, leaving
them with fairly simple dual redundancy schemes for the main computer,
backed up with a core of hardwired electronics sufficient to reboot and
reload the computer under orders from the ground if necessary.

IMO, the prevalance of hardware error correction doesn't mean it's a
good engineering solution.

Indeed, I rate it as an engineering roadblock - since self-assembled nano-scale computing crystals *will* have simple non-error correcting units which are vulnerable to noise, cosmic rays, etc - so low-level software engineers will *need* to get to grips with dealing with systems with unreliable components - and at the moment, they are being lulled into thinking that this is a problem for the hardware guys.
--
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