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From: toms@fcs260c2.ncifcrf.gov (Tom Schneider)
Newsgroups: comp.ai,sci.bio,sci.psychology,alt.cyberpunk
Subject: Re: The Bandwidth of the Brain
Summary: please get those units straight
Message-ID: <1998@fcs280s.ncifcrf.gov>
Date: 5 Jan 91 21:45:16 GMT
References: <37034@cup.portal.com> <37353@cup.portal.com> <2753@infinet.UUCP>
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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.

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.

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"}

>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