In article ,
 William Morse  wrote:

> john_SPAM{at}wilkins.id.au (John Wilkins) wrote in
> news:cbnlsc$2p3m$1{at}darwin.ediacara.org: 
> 
> >  wrote:
> > 
> >> > From: john_SPAM{at}wilkins.id.au (John Wilkins)
> >> > Mistakes also get made that show that this process is not digital
> >> > at all, but merely a high-fidelity analogue process - despite the
> >> > bonding sites, G can mispair with A and C with T.
> >> 
> >> No, it's not analog at all, it's digital, with occasional mistakes.
> >> But 
> > ...
> > 
> > Rather than answer you point for point - there is a fundamental
> > distinction here that I am making that appears not to be getting
> > across. Of course, I may just not be convincing you of this, which is
> > another matter, but allow me to make the positive case.
> > 
> > A digital device is a purely abstract object. Consider the granddaddy
> > of digital devices - a universal Turing machine (UTM). This is a
> > frictionless, energy-less device on an infinite strip of paper, with a
> > read-write head that can move left or right without making a single
> > error, with an infinite amount of ink, etc. It computes any algorithm
> > infinitely, should that algorithm never halt. No thermodynamic
> > considerations apply to it. It never crashes, jams, or runs out of
> > electricity or ink.
> > 
> > Now consider what *we* call digital devices. My laptop can crash due
> > to heat, dust shorting out circuits, a failure of the RAM or magnetic
> > storage media, or because it got rained on. It generates signals by
> > way of a waveform that can fall below the threshold of the logic
> > gates, producing noise. It can run out of electricity. The screen can
> > fail and the printer I attach it to jam and run out of ink. My kids
> > can drop jam on the keyboard, etc...
> > 
> > The difference between what a *logician* would call "digital"
> > (Turing's abstract device) and what an *electrical engineer* would, is
> > that in a Truly Digital Device error is not possible. If the algorithm
> > is an error with respect to a problem, nevertheless the algorithm will
> > go on doing exactly what it is programmed to do for all eternity,
> > should it not halt.
> > 
> > DNA is simply not digital. It is a high-fidelity but still error-prone
> > molecular structure that can carry heredity from cell to cell. But it
> > is, for all that, analogue (unless you are a neo-Pythagorean who wants
> > to claim that all analogue and all digital processes are at base the
> > same thing). DNA is subject to the laws of thermodynamics, while a
> > digital device would not be. At the *very* best we *approximate*
> > digital devices with computers and DNA. No physical device can *ever*
> > be purely digital.
> > 
> > I hope this makes my point clear. If not, then we are left at an
> > impassé.
> > 
> 
> I don't know how you are left with Robert Maas, but you are at an
> impasse with me. An analog device is also a purely abstract object  - at
> some point it becomes lumpy. And thank goodness for that, because
> otherwise I would be typing this reply with  (square root of 26) fingers
> on a keyboard with (102 plus or minus the square root of 2) keys. Pi is
> a wonderful number, but it only expresses the ratio of circumference to
> diameter for an ideal circle....

*
No, it also represents the ratio of log(-1) to sqrt(-1).

earle
*

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