[Hans Blom, 970502]
(Bill Powers (970501.1532 MST))
Would you believe that a resistor, all by itself, _generates_ a
white noise signal?
Not the way you define it. The noise from a resistor is quite
measurable with instruments that have a finite frequency response,
so it can't be white noise. In fact, it is about 1/f noise as far as
I remember.
No, it's not. As I said, "white noise" is a mathematical notion, an
idealization. In resistors, thermal noise -- also called Johnson
noise -- is constant in amplitude upto very high frequencies, where
it starts to decay with 1/f^2. The 1/f noise that you mention is one
of the types of noise that we find in semiconductors, where it seems
to be caused by inhomogeneities of the impurities. Thus, as long as
we limit ourselves to the 0 Hz to 10 GHz region or so, the noise that
resistors generate resembles the mathematical notion of "white noise"
very, very faithfully. Search the www for "noise theory" and you'll
find some answers. And even applications, where amplified resistor
noise is used as an extremely good and fast random number generator.
In fact, it is about 1/f noise as far as I remember.
Going up a level: I find this a confusing statement, by the way. You
combine "in fact" with "as far as I can remember". I cannot make much
sense of that. Except, maybe, that (1) an external observer can know
that your memory (internal model's "prediction") is defective here,
(2) you hesitate whether that might be the case, (3) you do not wish
to take the effort to verify or update your "internal model" because
(4) that costs mental and/or physical energy and (5) it would hardly
serve a goal. But, if so, why make a statement like this at all?
What's useful about a word?
Well, words seem to be a prime form for communication, especially the
type that we conduct here. So let's stick to precise definitions, if
they exist, and not to the "intuitive feel" of words.
Actually, I don't think we should allow mathematicians to try to
speak in verbal languages. They always come up with misleading
terms.
Regrettably, mathematicians were there first :-). They might
interpret your use of the word "misleading" as signifying
misunderstanding of the way _they_ use the word.
And who are you to tell mathematicians which words they are allowed
to utter? 
The prime problem of (verbal) communication is that we all speak a
different language, in that words have different connotatations --
and thus a different meaning -- for different people (for a Test of
this principle try "free association"). It is only when we develop
and adhere to a precise common language that misunderstandings can be
eliminated and results are as reliable as the concepts on which they
are built. Mathematics has done exceedingly well in this respect. As
a result, one mathematician can use another one's results and build
upon them. Such an accumulation of knowledge is not possible if the
terminology is so fuzzy that each new investigator has to restart
from scratch, because there is still doubt about the meaning of even
the most elementary concepts.
We've had quite a few discussions along these lines, and each time
you doubt -- and we have to go back to -- the very basics. That's
hardly productive...
In "reverse engineering" (trying to understand a system that
already exists) it helps to be aware of or discover the design
objectives (the top level goals).
I don't buy your notion that organisms have "design objectives."
I don't say that they _have_ design objectives. I say that it helps
_me_ to think of how _I_ would "design" an organism so that it could
control well in the environment in which it lives. That may not be
true for _you_. Your toolbox may be stocked with different tools.
I'm sorry, you're talking theology and it makes no impression on me.
Nobody designed organisms, as far as I can see. Any design
principles exist only in your imagination.
My theory says that _everything_ I know exists only in my imagination
(internal model). So I couldn't agree with you more. My theory also
says that _you_ are talking your own private theology, based on a
different internal model. So be it. There's no escape. It helps,
however, to be aware that different theologies exist, and that each
may be helpful in its own particular way.
Greetings,
Hans