Re: Analog vs Digital

RobertMaas_at_YahooGroups.Com
Date: 06/26/04 

Date: Sat, 26 Jun 2004 04:56:40 +0000 (UTC)

> From: john_SPAM@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
these mistakes are very rare, perhaps one mistake per generation, out
of millions of base pairs all correctly anti-replicated except that one
mismatch. High-fidelty analog would be like a linear amplifier that was
very very linear with only slight differences from linear. DNA
anti-copying is nothing at all like a linear amplifier. It's very very
very close to being pure digital with absolute accuracy, and only
slightly teensy bit mistake prone. Nothing analog at all gets even one
generation down the line, like the temperature of the DNA, or the
amplitude of oscillation of a particular side chain, or the distance
from the North pole (except for the fact the creature doesn't miagrate
far), or anything else analog. But the digital data gets passed down
many generations with just those rare errors that accumulate over
millions of generations. A digital system with occasional mistakes is
nothing at all like an analog system.

> if we were watching the process of a "digital" signal being
> laid down in a magnetic medium, fo rexample, we'd see an analog process,
> with fuzzy edges and varying strengths.

No, we wouldn't see anything analog in the overall design. We'd see two
distinct values of data being attempted-written, such that the zero bit
has a range of possible magnetization values, and the one bit has
another range of possible magnetization values, with the design being
such that the two ranges are disjoint and separated by a gap. Due to
noise, sometimes the ranges overlap. The sensing circuit for reading
out the data has a threshold, whereby anything on one side is forced to
logical 0, and anything to the other side is forced to logical 1.
Occasionally the ranges overlap and a particular bit is on the wrong
side of the threshold. The result is a completely wrong bit, a 1 where
there should have been a 0, or vice versa, but never anything
inbetween. Error-correction codes are used to fix these bad bits. Again
the error-correction code is purely digital.

> Atractor points need not be digital. Whatever gave you the idea that
> they have to be? Sure, they can be *described* or *derived* using a
> digital simulator, but we all know that the slightest differences in
> precision can generate quite different outcomes in chaotic math, so a
> physical attractor is not digital as such, just representable by a
> sutiably high precision model.

There's nothing chaotic about D.C. (direct-current, constant-value)
attractors, assuming there's damping of oscillations/orbits around the
attractor. Any value that strays within the capture well of the
attractor, falls toward the attractor, deeper into the well, decays to
the bottom of the well where the attractor is, and remains near the
bottom of the well forever after (so long as the well remains). Thermal
noise can knock it slightly away from the attractor, but the attractor
keeps it from straying too far away. If there are two or more such D.C.
attractors, then the process of an object of arbitrary initial position
falling into one or another well is an analog-to-digital conversion
process, while the process of an object of only specific starting
points each within a capture well of an attractor with not enough noise
to leave the well, is a purely digital process from the view of input
and output.

> "Presence" and "absence" defined according to which threshold? :-)

One molecule, or more, is presence. Zero is absence. Since we're
talking about replicators here, either the replicator has basic
fecundity greater than one, in which case it exponentially grows until
it starts to exhaust its food supply at which point starvation reduces
actual fedundity to exactly one, or it has basic fecundity less than
one, in which case it exponentially decays to zero instances. So if
you're worried about measuring the presence of such a replicator,
either there's a lot of it and you'll see it with any decent measuring
device, especially if you deliberately feed extra food to it to see
whether it grows to consume the food, or there's none of it at all.

Given the two possibilities: zero or much, it's impossible for zero to
change to much, and unlikely for much to change to zero except during a
crisis such as no food for a long time or invasion, we can regard the
digital presence/absence of each different replicator within a bag as a
digital genome. If, due to food pressure, each different replicator
tends to distribute its instances uniformly around the surface of the
bag, we can expect each daughter lipid-bag to have the same genome as
its parent.

Side remark: If there are two different replicators in the same bag,
such that each is limited by the same short-supply nutrient, then the
mixture of the two will be uniformly distributed around the bag, but
whereever one of one type is adjacent to one of the other type,
whichever has better nutrient-grabbing ability will get all the food
that is halfway between the two, so that type of replicator will
reproduce faster, eventually exterminating the other by starvation.
During this process of competition, before the less-fit replicator is
fully exterminated, the proportions of the two replicators will be
approximately the same in each daughter cell whenever a division
happens, but not exactly the same, so all the nth-generation daughters
will finally exterminate the less-fit replicator at roughly the same
time but not exactly the same time. Consequently there would be a
period of time when some nth-generation daughter cells have lost the
less-fit replicant while other cells still have it. If during such a
time period the short-supply nutrient becomes abundant again, the loss
of the less-fit replicant would cease, and the two versions of cells
would continue indefinitely as separate species. How would such a
competition occur in the first place? If that particular nutrient was
in good supply for a very long time, such that the two particular
replicators were never in competition for it, so they could co-exist
peacibly on a single lipid bag. But at some time the nutrient started
becoming short-supply, causing competition between the two replicators.
Another way is if the more-fit replicator was a mutation from the other
(or from an unrelated chemical) which invaded the lipid bag and began
replacing the oldtimer that is less-fit.

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