From: James Rogers (jarogers@cisco.com)
Date: Wed Mar 04 1998 - 15:05:50 MST
At 11:55 AM 3/4/98 -0800, Reilly Jones wrote:
>James Rogers wrote 3/3/98 (and Mr. Kamphuis chimed in on the same point):
><What 50% are digital systems missing? Digital systems have the same
>resolution/perception capability as analog systems within the limits of the
>noise floor (which affects analog systems as well). There is nothing
>analog that can not be represented digitally within the limits of the
>analog system. There are well known methods for reading and storing
>arbitrary precision analog values with digital devices as primitive as a
>1-bit signal converters.>
>
>"Within the limits of the noise floor" is a cute way of pretending that the
>noise floor doesn't count, yet half of reality is hidden away there.
>Analog systems are affected by noise floor, yes, they don't pretend it
>away. "Represented digitally with the limits of the analog system" is
>another cute way of saying that the representation of reality is good
>enough, yet half of reality goes unrepresented. "Reading and storing
>arbitrary precision analog values with digital devices" is another cute way
>of saying that arbitrary precision is good enough for government work. Why
>settle for arbitrary precision, which cannot be precise enough for
>consciousness to work, why not go for all of reality?
You do not understand the ramifications of what I said, and show a lack of
understanding of the terms. To clarify my stance, I will define the terms
for anyone who may be interested.
The noise floor is the limit of resolution of a signal. By definition,
there is no means to resolve a signal at resolutions below the noise floor.
This is a function of the signal and is independent of how the signal is
detected and/or stored, whether by digital or by analog means.
Ideal analog signal detection/storage will always store a signal at the
maximum possible resolution by definition. (Note that real analog systems
behave more like high-resolution digital systems than theoretical ideal
analog systems.)
Digital systems have a resolution limited by design. That is, the higher
the resolution you want to resolve, the more bits you have to dedicate to
resolution. Most digital systems designed today are designed to resolve to
the limits of human resolution capability, which is roughly between 20 and
40-bits depending on the particular part of the body in question.
Here is the catch.
The *only* signal that cannot be accurately resolved by a digital system is
one where there is zero noise. When the noise floor disappears, the number
of bits required to accurately resolve the signal becomes infinite. In this
case you are correct that digital systems cannot resolve the entire signal.
However, like Absolute Zero, zero noise can only be approached but never
reached.
More importantly (and succinctly):
The noise floor of the universe is such that all signals within this
universe can be fully resolved in less than 100 bits, which is well within
the capabilities of current technology. Therefore, there is nothing in this
universe that cannot be represented in a digital system *at least* as well
as in the analog systems that are our brains. And fact is, the noise floor
for our brains is much higher than the universe at large, therefore making
it reasonable to assert that digital AI's will be capable of
detecting/storing information at much higher resolution and precision than
any human due to differences in the noise floors.
NOTE: One factor that I did neglect to mention is dynamic range. While not
an issue for the theoretical "ideal analog system", real analog systems
actually behave exactly like high-precision digital systems in this respect.
-James Rogers
jamesr@best.com
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