Re: time, memory of one and many, zipf's law.

From: Bill Barowy (wbarowy@yahoo.com)
Date: Sun Aug 12 2001 - 18:24:26 PDT


--- Eva Ekeblad <eva.ekeblad@goteborg.utfors.se> wrote:
>
> Oh, is that it? what the assumption is: independent of their OWN prior
> postings? Was I wrong to think each posting event should be independent of
> ALL prior events for Zipf to be applicable?

This requires careful thought. If first we ignore that writing is independent
of reading, then perhaps yes, any one persons posting is somewhat "independent"
of another's. What "independent" means for Mandelbrot, who did the theoretical
derivation of Zipf's empirical observation (Zipf's law), is in terms of *cost"
to produce the event. Mandelbrot considered the cost of writing words in terms
of the cost of the constituting letters -- writing words "cost" something in
time or effort. Writing longer words cost more time/effort than writing shorter
ones. Thought this way, the cost of one person's writing an email is
independent of their writing of another. But this assumption fails, of course.
 In the extreme case, a person has a maximum of 24 hours each day to write
messages, so there is a clear cutoff, and it is built into the counting scheme.
 Furthermore, the time people have available to participate varies from day to
day, and is much less than a full 24 hours. If a person has made one posting
in a day, there is less time available for the next posting -- and this is part
of why perhaps the top writers fail to meet the pattern. And also, time spent
reading other messages reduces the time available for writing a response -- so
if there is a "swarm" of emails that are posted, this also tends to regulate
the amount of responses.

Consciousness of one's prior postings i.e. memory, can also serve as an
additional constraint.

The analysis here does not engage in what makes people post -- whether there is
something that interests and whether someone can make a contribution. A
"swarm" of email messages also has the effect of amplifying the number of
responses, partially because it increases the probablility that a person will
find something of interest. What is involved with time however is one of
constraint, and time here is a constraint on people's productivity. This is
how I presently think the pattern appears. Mandelbrot did not consider these
ecological limits on time, but did involved constraint through the minimization
of cost for each event, and this could be one of the things contributing to the
break among the top xmca writers, from the pattern of zipf's law. He
apparently did extend his analysis to what happens if the cost of producing a
letter ( as in the letters "a", "b"...) was dependent upon the one prior to the
total cost of writing a word. I have to take some time to further research and
examine his work in order to see if it can be adapted to our situation. But it
will be a while, with other things pressing to the top of the list of
priorities. And the topic is entirely one of statistical information theory,
which is new to me, although the mathmatics is looking familiar.

bb

=====
"One of life's quiet excitements is to stand somewhat apart from yourself and watch yourself softly become the author of something beautiful."
[Norman Maclean in "A river runs through it."]

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