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Article 4401 of comp.ai.philosophy:
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>From: clarke@acme.ucf.edu (Thomas Clarke)
Newsgroups: comp.ai.philosophy
Subject: Re: Infinite Minds?
Message-ID: <1992Mar11.135759.4941@cs.ucf.edu>
Date: 11 Mar 92 13:57:59 GMT
References: <1992Mar10.165603.11788@neptune.inf.ethz.ch>
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In article <1992Mar10.165603.11788@neptune.inf.ethz.ch> santas@inf.ethz.ch  
(Philip Santas) writes:
| There seems to be no evidence against "digital functioning" of the human 
| nerves. Furthermore, humans have no problem to accept digitized picture
| and sound. 
| If humans do not operate under this model then they must have an 
| "analogical functioning" which would observe all the problems related
| to digital functioning: listening to a CD would have been nothing more
| than listening to Morse code...

Don't every say this to a dyed in the wool audiophile.  You'll get a very
vigorous argument (or flame on rec.audio) about the big mistake made in going
from the analog LP to the digital CD.  The autdiophiles believe something is
missing from the digital CD that is captured in the analog LP.  As a true  
believer in Mr. Nyquist's theorem, I have my doubts about this, but physics and  
mathematics are not complete (never will be, math anyway), so maybe the  
audiophiles are on to something.

At the risk of crossing to the quantum thread, here is a thought experiment  
that shows how things are not as cut and dried as one might like in the  
analog/digital arena.

Consider the two slit experiment, a photon passes through (both of) two slits  
so that an interference pattern appears on the detector screen.  Let the  
photons be in the microwave range so that the slits can be replaced by  
receiving antennae, (perfect) linear amplifiers, and transmitting antennae.   
The interference pattern will be preserved.  

Actually a calculation by Glauber (in Frontiers in Quantum Optics, 1986, eds  
Pike and Sarkar) shows that a uniform pattern with a superimposed interference  
pattern will be observed, the relative strength of the two patterns being  
determined by the rate at which photons arrive, the limit of the occassional  
odd photon producing a more uniform pattern.  The important thing is that even  
when a single photon enters the dual antenna/amplifier/antenna system,  
interference occurs so that quantum language such as "the photon is amplified  
by both amplifiers" is natural.

Now, replace the amplifier with an analog to digital convertor, some digital  
signal processing, and a digital to analog convertor.  This is done all the  
time for microwaves in electronic contermeasure equipment on the B1 bomber and  
the like.  I haven't been clever enough to do a quantum mechanically analysis  
of how the D/A-process-A/D chain works, but intuitively if the D/A has enough  
bits and if the sample rate satisfies the (quantum?) Nyquist theorem, the chain  
should be indistinguishable from an amplifier. The Nyquist rate and limited  
precision of the D/A then conspire to imply that only a finite information rate  
(finite symbols/unit time) is needed to reproduce the physical process. 

More for this group is to replace the D/A-process-A/D chain with a  
transducer/pulse-rate-coded-biological-neural-network/transducer (organism for  
short).  Provided system bandwidths etc are respected, the organism will be in  
a quantum state.  One has to speak of a photon producing activitation of  
neurons in ways that would not occur if the photon were absorbed by a single  
antenna then transduced into the neural network.  A bit of neural tissue has  
thus been put into a quantum state in a way that can be analyzed by something  
like Glauber's methods. Note that the D/A-process-A/D chain has limnited  
precision whereas the pulse rate modulated neural tissue is analog so the  
quantum mechanical analysis of the organism might give different results.

The question is open, the D/A-process-A/D and/or the  
transducer/network/transducer chain may or may not be quantum mechanically  
equivalent to an analog amplifier.  If the answer is no/yes it would be strong  
evidence for the reality of the audiophile's perception of LP/CD differences  
and for what

In (an earlier) article <1992Mar4.142249.9478@husc3.harvard.edu> 
zeleny@coolidge.harvard.edu (Mikhail Zeleny) writes:

|Nonsense.  Why is m, the number of all possible sign-types, a finite
|number?  

Anyone out there have any good ideas to shorten the analysis?


