"J. R. Molloy" wrote:
>
> From: <Eugene.Leitl@lrz.uni-muenchen.de>
> > J.R., you can add "analog computer" to your list of useless
> > hypotheses.
>
> Ah, yes... even a difference engine is digital at the atomic level, and for
> the purposes of computation, every number is digital.
For the purposes of (digital) computation, you have to know,
unambiguously, which digit a storage location contains (0 or 1,
if your machine uses bi-state logic), at the instant of time
corresponding to the edge of a clock cycle. At the **atomic**
level, quantum uncertainty blurs such sharp boundaries.
In the realms of digital audio and the digitization of photographs
and video, a little uncertainty around the edges is considered a
Good Thing -- a deliberately-injected low level of random noise,
called dither, turns what would otherwise be obnoxious quantization
distortion into benign white noise (in digitized audio), or turns
an unpleasant jagged edge in a photograph into a less objectionable
blurred edge, and permits information to be encoded **below** the
level of the least significant bit.
When Edelman talks about using digital Turing-type devices
to **simulate** biological brains, he points out that what has
to be added beyond the classic Turing machine to get the
simulation to work realistically is an injector of randomness. Two
of them, actually -- one for the stochasticity of the external world,
and one for the stochasticity of the components of the simulated
brain. It's at the intersection of these two dithered streams
(think of two fire-hoses intersecting at right angles) that
the "magic" happens.
> Is Pi an analog ratio?
It's not a ratio of **integers** at all, which means it
can't be represented **exactly** by any finite string
of digits.
The analog/digital dichotomy, both at the macroscopic level of
actual physical computers (including CD players and DVD players!)
of the present day, and at the hypothesized "quantum foam" level
of reality, is a paradoxical one. The "digital" nature of
any real machine is an idealization, an abstraction -- if you
hook up an oscilloscope to the innards of a computer, you
see things happening at the **analog** level -- square waves
aren't perfectly square; they have finite rise and fall
times, etc. At the quantum level, you have things taking
on "digital", quantized, discrete states, but the closer
you get to something the harder it is to be certain which
of those states it's in, which brings back the "analog"
element in terms of continuous probability distributions.
These are extraordinarily suble issues, which the most brilliant
minds in the world have yet to come to grips with completely.
There's no point in trying to divide this list, or any
other realm of discourse, into tribes of "analogists" and
"digitalists" and then picking sides.
If you want a real rip-roaring battle between two such camps
(which you may get tired of after a time, I warn you ;-> ),
look up the LP vs. CD wars which have raged on the
rec.audio.* newsgroups, if and when Google gets the
Usernet archives back on line.
Jim F.
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:59:44 MDT