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From: ken@uswat.uswest.com (Kenny Chaffin)
Newsgroups: comp.ai
Subject: Re: The Bandwidth of the Brain
Message-ID: <14225@uswat.UUCP>
Date: 9 Jan 91 21:29:42 GMT
References: <37034@cup.portal.com-> <37353@cup.portal.com> <2753@infinet.UUCP> <1998@fcs280s.ncifcrf.gov>
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In article <1998@fcs280s.ncifcrf.gov-> toms@fcs260c2.ncifcrf.gov (Tom Schneider) writes:
->In article <2753@infinet.UUCP> sena@infinet.UUCP (Fred Sena) writes:
->
->>In article <37353@cup.portal.com> mmm@cup.portal.com (Mark Robert Thorson)
->writes:
->>>Fred Sena says:
->>>> I think that measuring the "bandwidth" of transmission can be a
->>>> misleading indicator of the amount of complexity of the
->>>> transmission sequence, or the complexity of the entities performing
->>
->>>Oh yeah?  Are you telling me you thought of all those associations
->>>instantaneously?  When I hear the word "nuclear", the association
->>>"bomb" pops up near-instantaneously, with "reactor" following a
->>>fraction of a second later.  I'd have to rack my brains for several
->>>seconds before "family" or "Enola Gay" pops up.
->>
->>Yes, you have a point.  I think that most people would have also thought of
->>"bomb" immediately as well (I did).
->
->>  However, I was just trying to emphasize that there are a variety of
->>pre-understandings between people that are immediately reconized *before* the
->>next word follows.  In other words, all of the common understandings that are
->>transmitted along with a word, which would imply much more information
->>transmission than is obvious.  I'm trying to show the limitations of our
->>ability to evaluate information content per unit time, or bandwidth.

	True. This is the "Meaning" of the data that is transmitted. The problem
is that the meaning to me may be different than the meaning to you. In most
cases there is a shared meaning and understanding of common words and those
words are "generally" associated with common concepts and other words--but not
always.
This interpretation of bandwidth is different than the way it is normally 
used (see the following information). Normally bandwidth is defined as the 
capacity  of a communication channel--i.e. how many bits per second can it
carry. In your case the single word is what is being transmitted--that is
used to compute the bandwidth. the meaning, ideas, and concepts are a function
of the receiver, not the communication channel bandwidth. Now if you are 
talking about information processing capability of the brain, that's a 
different question.

->
->Now hold on a second.  You had better get your technical terms straight.
->Bandwidth is a reference to the range in the frequency domain of the signal.
->For example, each radio station is given a particular band width within which
->to work.  The interesting thing people do is to take speech, and sounds in the
->range that people can hear, 0 to 20,000 cycles per second (ie "Hertz") and they
->multiply that signal by a high frequency sine wave.  This effectively shifts
->the signal to high frequency, but the required bandwidth stays the same at
->20 kHz for each station.
->
->Summary:  bandwidth has units of cycles per second (Hz).
->
->Information content per unit time is the rate of information transmission
->(R) or the the channel capacity.  These have units of bits per second.
->A bit is the choice between two equally likely possibilities.  Clearly this
->has different units from the bandwidth.  Indeed Shannon's famous formula:
->
->             P + N
->  C = W log (-----)
->           2   N
->
->has units bits per second, where W is the bandwith in Hz.
->
->If you are going to stick to the strict definitions that have been successfully
->used by communications engineers for 40 years, then the associations that pop
->up when one mentions a word are not an appropriate measure of the information
->content of the word.  Shannon's measure is based entirely on the actual symbols
->or messages sent over the channel and received at the receiver, NOT on how the
->symbols are USED by the receiver.  If you want to reject the original
->definitions, you had better have excellent reasons for doing so.

	True, but Shannon never used the term information. His theory was
called "A Mathematical Theory of Communication" He did unfortunately call the
probability of a particular word or bit being transmitted information and others
have subsequently taken his theory to be an information theory. Unfortunately
they are wrong. Information is much more than the probability of a particular
symbol being transmitted down a communication channel.

->
->An excellent introduction to this topic can be found in:
->
->@book{Pierce1980,
->author = "J. R. Pierce",
->title = "An Introduction to Information Theory:
->Symbols, Signals and Noise",
->edition = "second",
->year = "1980",
->publisher = "Dover Publications, Inc.",
->address = "New York"}

	Yes this is definitely a good book.

->
->>Frederick J. Sena                sena@infinet.UUCP
->>Memotec Datacom, Inc.  N. Andover, MA
->
->  Tom Schneider
->  National Cancer Institute
->  Laboratory of Mathematical Biology
->  Frederick, Maryland  21702-1201
->  toms@ncifcrf.gov