**Next message:**Jim Fehlinger: "Re: A belated addition to the Science/Religion thread"**Previous message:**Natasha Vita-More: "Re: UFO Raël and the definition privilege"**In reply to:**J. R. Molloy: ""analog computer" = useless hypothesis?"**Next in thread:**James Rogers: "Re: "analog computer" = useless hypothesis?"**Reply:**James Rogers: "Re: "analog computer" = useless hypothesis?"**Reply:**Ken Clements: "Re: "analog computer" = useless hypothesis?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

"J. R. Molloy" wrote:

*>
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*> From: <Eugene.Leitl@lrz.uni-muenchen.de>
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*> > J.R., you can add "analog computer" to your list of useless
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*> > hypotheses.
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*>
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*> Ah, yes... even a difference engine is digital at the atomic level, and for
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*> the purposes of computation, every number is digital.
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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.

**Next message:**Jim Fehlinger: "Re: A belated addition to the Science/Religion thread"**Previous message:**Natasha Vita-More: "Re: UFO Raël and the definition privilege"**In reply to:**J. R. Molloy: ""analog computer" = useless hypothesis?"**Next in thread:**James Rogers: "Re: "analog computer" = useless hypothesis?"**Reply:**James Rogers: "Re: "analog computer" = useless hypothesis?"**Reply:**Ken Clements: "Re: "analog computer" = useless hypothesis?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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