perplexed in peoria

"Insufficient lighting", huh. Well, that is certainly an improvement over my formulation.


Thanks for the pointer to Oyama - I hadn't heard of her. Googling
and Entrezing her has revealed that she has published very little
in accessible reviewed journals, but there is nonetheless a quite
perceptible "buzz" about her work. So even though I have encountered
frightening warning signs ("Lewontin & Levin", "Evolutionary Psychology"),
I'll try to read her books before writing more on the subject of "telos".

perplexed in peoria

Huh? AFAIK, neither FM nor AM is digital. Nor is there any
thresholding involved. Perhaps you are misled by the fact that
your FM tuner has discrete channels whereas your AM tuning knob
permits fine tuning. That has nothing to do with whether the
signal from the transmitter is analog or digital.

Aha! I think I see the source of the confusion. But clearing it
up will take some work. Please bear with me.

I am thinking of the words analog and digital in an engineering
sense. The words are terms of art referring to two different
strategies for encoding and transmitting information. Teleology
is inevitably involved in the distinction. And, since Nature
(in the sense of natural selection) is also a competent
engineer, we can recognize the use of the same strategies on
her part.

You seem to be seeking to remove all teleology from these
words. You imagine a sender, a receiver, and a purely
passive channel between them carrying a signal. You want to
totally divorce the analysis of the signal from any consideration
of the purposes of the sender or receiver. Therefore, it is
quite natural for you to conclude that analog is the only
"real" kind of signal, and that "digital" is an abstraction.

I must ask you to (temporarily?) set aside your reductionist,
anti-teleological instincts and join me in considering
information from an engineering viewpoint.

The first clarification that must be made is that there are
at least three levels involved in communication. At the
highest level, we have meaning. Meaning can be reduced
to information, which can in turn be reduced to physical
state. We are not interested here in the reduction from
meaning to information. We are interested in the reduction
from information to state. There is still a residue of
teleology involved in this reduction - at the information
level, that is. We WANT the information to be transmitted
without error, though we won't ask why.

Let's begin with "naive information theory". There are
two kinds of information - analog and digital. For digital
information you have a set of discrete points, perhaps
only two of them. The sender provides digital information
by specifying one of those points. The receiver receives
the information by (somehow) learning which point was
specified. For analog information, you have a continuum,
perhaps the real line. The sender provides analog
information by specifying a point on that line. We can
even provide a kind of internal reduction for representing
digital information as analog. Simply choose a threshold
on the real line, and reach an agreement between sender
and receiver that an analog signal higher than the
threshold will be interpreted as a digital 1 and a
signal lower than the threshold will be interpreted as 0.

Naively, it would seem that analog is much better, because
an infinite amount of information can be sent in a single
communication event. Clearly we need a better theory.
This one cannot be successfully reduced to physical state,
at least not by an engineer.

So, we move on to Shannon's information theory. There
are several innovations here.
1. The "active channel".
2. An abstraction of noise is added to the theory. Thus
we have enough of the real world in our theory that we
can successfully complete the reduction to physical state.
3. A metric is imposed on information. You can now
answer the question "How much information is here?"
and get a more reasonable answer than "Infinity".
4. Essentially the same theory works for both analog
and digital information.

Start with the active channel (something I never really
appreciated before today). Remember your picture of
a sender, a receiver, and a passive channel in between.
Shannon worked for AT&T, the American phone monopoly, so
he was aware that channels are never truly passive.
There are various engineered devices sitting between
the sender and receiver, some of which inevitably
weaken and distort the signal (attenuation along wires),
and some of which try to improve the signal (amplifiers).
So, already we have to be able to discuss signal
strength as well as signal content.

For some purposes, it is appropriate to think of those
devices as receivers and senders in their own right.
Thus the channel from the original sender to the ultimate
receiver is broken down into a sequence of senders and
receivers, each separated by passive channels. But,
says Shannon, why not treat the sequence - first channel,
sender/receiver device, second channel - as if it were
a single channel. The only thing is, we now have to
treat our channels as active. And, the whole point
of the theory then becomes: "How can we engineer the
best possible channels?". Notice how this has moved
teleology into the channel. I never really appreciated
this before.

I will pass over noise quickly. Suffice it to say that
some noise is inevitable in any channel, that a metric
of the amount of noise can be defined as the "temperature"
of the channel, that the noise temperature is closely
related to old-fashioned thermodynamic temperature,
and that the theory of noise has a close formal
analogy to the notion of drift due to sampling error
in population genetics.

Metric: For our naive theory's set of discrete points
for digital information, assign a probability to each
point. Define the amount of information present in
a particular signal using a well known formula involving
summations and logarithms that I won't try to reproduce
here. But how do we extend this definition to
analog information? Well, we can't assign probabilities
to infinitely many points on a continuum. But we
can introduce a probability distribution - for example,
the normal (bell shaped) curve. This is called the
a priori distribution. Furthermore, our analog
sender will no longer be asked to specify a single
point in the continuum as his signal. That would
exceed any finite being's capabilities for precision.
Instead, he supplies a second a postiori distribution.
And, as with Shannon's digital formula, there is an
analog formula that involves a ratio between the
a priori and a postiori probabilities.

Now, let us look at the engineering of a good channel.
Analog is easy. Try to eliminate all distortion of
the signal. (Or, at least eliminate unpredictable
distortion. The receiver can compensate for the
predictable kind.) Provide enough amplification to
compensate for the attenuation. And try somehow
to hold the noise temperature as low as possible.
Or amplify the signal first, so that the noise
makes less difference proportionately.

Digital is quite different, especially if you are
reducing digital information to analog before
transmitting it. I suppose you could use the naive
theory's digital-to-analog method, and then try to
transmit the resulting analog information over an
ideal analog channel. But this would be wasteful.
You can do much better - in fact, you can do so
much better that it makes sense in many cases to
convert analog to digital and then back to analog
before sending it, send it through a channel that
introduces deliberate irreversible distortions,
and then go through the reverse analog to digital
to analog conversion at receiver.

Here is how it works (for binary digital information).
Instead of the naive theory's threshold point, we
need to two target points as the analog representation
of 0 and the analog representation of 1. Call these
points the nominal values. Around each of these
nominal values define a region of the continuum that
is called the acceptable range. Between these two
ranges lies another region of the continuum that
can be called the threshold region. The two remaining
regions on the outside can be called the danger zone.
We want to avoid trying to send signals in the danger
zone as they might damage the equipment.

The sender is responsible for supplying a signal
near one or the other of the nominal values. As
with analog, he actually only promises that he
will adhere to an a postiori analog distribution
around the nominal. The channel is responsible
for keeping the signal within the same acceptable
region where it started. It does so by supplying
a "force" driving the signal toward nominal from
either direction. That is, the potential function
for this system should be shaped like a "W". A
signal that starts in one of the two wells of the
"W" will tend to stay there. I hope that this
makes my bowling analogy clear.

Please note that this design of a digital channel
(or if you prefer, an analog channel tailored
for carrying digital information) is fairly
immune to loss of information due to components
that are slightly out-of-spec. One of the wells
of the "W" can be deeper than the other, the
nominal points can be slightly off, the threshold
can be slightly off center. The ball is still
very unlikely to skip from one gutter to the
other.

In any case, that is what I mean when I talk about
analog and digital. It is also what I think most
engineers mean by the terms. The terms are pretty
much useless, it seems to me, if you try to use
them in a world view which rejects engineering and
its teleological baggage as somehow "artificial".
So, I would suggest that you either use the words
in that intended engineering context, or don't use
them at all.

I should point out that the dichotomy of "analog"
versus "digital" does not exhaust the range of
possibilities for engineering solutions to the
problem of transmitting information. Also, I have
completely bypassed consideration of information
as a time series. I should mention, though, that
the transmission of data by the frequency of some
oscillation (used in FM radio, by the way) has
some of the advantages of both analog and digital.
The signal, abstractly, is a point chosen from
the continuum - like analog. But a reasonably
good channel can be constructed that eliminates
all distortion due to noise, subject only to the
restriction that if the noise level is high enough
the signal fails completely. The thing is, to get
very high resolution out of frequency data, you
have to listen for a long time. Is frequency data
analog, or digital, or something else? I would
say analog, but I can't guarantee that my choice
is standard.