X-Message-Number: 8652
From: eli+@gs160.sp.cs.cmu.edu
Subject: analog computing retry
Date: Thu, 2 Oct 97 14:40:10 EDT

>From: Thomas Donaldson <>
>Subject: Re: CryoNet #8636 - #8641
>Date: Tue, 30 Sep 1997 21:46:03 -0700 (PDT)

>This means that they are no more physically impossible than a Turing machine
>with a single infinite tape.  Both do suffer from some impracticality, but
>that does not mean that one is less impractical than the other.

I believe that this is incorrect.  Could you address my previous
comment on this point?

To restate briefly: finding arbitrary space is easy.  Finding arbitrary
analog precision is hard.  Given an irreducible noise floor (neurons,
for example, are damned noisy devices), it takes exponential signal size
to implement the linear precision that the model requires.

Can you think of a implementation that's practical even in principle?
As far as I can see, the only way is to use multiple signals to encode
each value, e.g. to work digitally.  You'd take a speed hit operating 
on these arbitrary-precision values, of course, but this should be 
manageable. I don't remember the operations used here, but multiplication
for example is only mildly superlinear: O(n log n log log n).

-- 
     Eli Brandt  |  eli+@cs.cmu.edu  |  http://www.cs.cmu.edu/~eli/

Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=8652